Datasets:

yananchen

/

aqua_shots_128

like 0

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? options: A)1267 B)1201 C)1200 D)1209 E)1216 SOLUTION:P --- 10 ---- 600 P --- 5 ----- 300 3P --- 5 ----- 900 ------ => 1200 Answer: C #### C QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:if a person cover 3/5 part of his journey by train,7/20 part of his journey by bus and rest 6.5 km. by walk.what is total distance of his journey? options: A)65 km B)100 km C)120 km D)130 km E)75 km SOLUTION:let total distance be=x km.then, 3x/5+7x/20+6.5=x;12x+7x+130=20x;x=130 hence total distance=130 km. answer D #### D QUESTION:By selling an article for $180, a person gains $30. What is the gain %? options: A)25% B)30% C)50% D)20% E)10% SOLUTION:S.P. = $180 Gain = $30 C.P. = 180-30 = 150 Gain% = 30/150 * 100 = 20% Answer is D #### D QUESTION:The forth proportional to 2,4,6 is? options: A)8 B)12 C)15 D)18 E)22 SOLUTION:Let the fourth proportional to 2,4,6 be x then 2:4::6:x 2x = 4*6 x = 12 Answer is B #### B QUESTION:In a class, there are 21 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ? options: A)8 B)14 C)18 D)24 E)26 SOLUTION:Explanation: Let the number of boys be x. Then, (3/4)x = 21 or x = 21 x(4/3) = 28. If total number of students is y, then (2/3) y = 28 or y = 28 x (3/2) = 42. Therefore Number of girls in the class = (42 - 28) = 14. Answer: B #### B QUESTION:At a certain restaurant, 30 percent of the servers reported their tips, while 40 percent of the servers who were tipped didn't report their tips. What percent of the servers were tipped? options: A)30% B)60% C)50% D)70% E)80% SOLUTION:Statement: 30% of Servers (S) Reported their Tips (RT). Of the servers who were tipped (T) 40% didn't report their tips (notRT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RT/S = 30% notRT/T = 40% => 100% - 40% => RT/T = 60% T/S = (30)/(60)% = 50% Answer: C #### C QUESTION:In how many ways letters of the word LEADER be arranged? options: A)5 B)78 C)69 D)58 E)120 SOLUTION:LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways E #### E QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:Tough and Tricky questions: Coordinate Geometry. Line L contains the points (2,3) and (p,c). If c = 2, which of the following could be the equation of line m, which is perpendicular to line L? options: A) 2x + y = px + 7 B) 2x + y = –px C) x + 2y = px + 7 D) y – 7 = x ÷ (p – 2) E) 2x + y = 7 – px SOLUTION:So we need m=p-2, so we should get y=mx+b form in answer choices (A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need (B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong (C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong (D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong (E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong A #### A QUESTION:The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ? options: A) 10^9 B) 10^8 C) 10^2 D) 10^6 E) 10^5 SOLUTION:P = 2*3*5*7 ~ 10^ 2 Answer : C #### C QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get? options: A)40% B)45% C)57% D)58% E)60% SOLUTION:tot no of votes = (1136+7636+11628) = 20400 req = > (11628/20400 * 100) = > 57% ANSWER C #### C QUESTION:A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box? options: A)5 m B)6 m C)4 m D)7 m E)8 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 * 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was? options: A)15002 B)15001 C)15000 D)15007 E)15009 SOLUTION:Principal = (100 * 5400) / (12 * 3) = Rs. 15000.Answer:C #### C QUESTION:Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly? options: A)Rs.1261 B)Rs.1440 C)Rs.1185 D)Rs.1346 E)Rs.1446 SOLUTION:A = 8000(21/20)3 = 9261 = 8000 --------- 1261 ANSWER:A #### A QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let the sequence have N terms starting 18*K --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence. The sum of the sequence is ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2). So the average is 153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*). On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**). By *), **) we have K=2, N=14. Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms R which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C. #### C QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed options: A)5040 B)1254 C)4510 D)1203 E)4510 SOLUTION:'LOGARITHMS' contains 10 different letters Required number of words = Number of arrangements of 100 letters taking 4 at a time = 10P4 = 10 * 9 * 8 * 7 = 5040 Ans: A #### A QUESTION:A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $335,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment? options: A)$1,395 B)$1,733 C)$3,466 D)$13,333 E)$20,796 SOLUTION:0.04x + 0.09y = 335000 [1] 0.04x = 0.80 * 335000 = 268000 [2] 268000 + 0.09y = 320000 --> 0.09y = 67000 [3] 268000 / 12 = 22333.3333 [4] 67000 / 12 = 5583.333 [5] Adding [4,5] we get: 27916 [6] Dividing [6] / 2 to get an average we get 1.395,ANS A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)246 m B)240 m C)257 m D)577 m E)567 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey? options: A)67.0 km /hr B)67.2 km /hr C)69.0 km /hr D)69.2 km /hr E)None SOLUTION:Solution Required average speed =(2xy / x+y)km/hr = 2 x 84 x 56 /(84 + 56) = (2 x 84 x 85 /140) = 67.2 km/hr. Answer B #### B QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:In a recent election, James received 5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election? options: A)901 B)989 C)990 D)991 E)1,001 SOLUTION:James = (5/100)*2000 = 100 Votes to win = (50/100)*Total Votes +1 = (50/100)*2000 +1 = 1001 Remaining Voted needed to win election = 1001 - 100 = 901 Answer: option A #### A QUESTION:When N is divided by T, the quotient is S and the remainder is M. Which of the following expressions is equal to N? options: A)ST B)S + V C)ST + M D)T(S+V) E)T(S – V) SOLUTION:Using the rule dividend = Quotient * divisor + remainder =>ST + M C is correct #### C QUESTION:A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? options: A)109 ways B)908 ways C)128 ways D)108 ways E)104 ways SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways. Answer:D #### D QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 6*8.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:Share Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John? options: A)900 B)1000 C)1254 D)1795 E)1400 SOLUTION:Amount received by sanjay. 4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount So, the Amount received by sanjay is 1400. E #### E QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(6900*6)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:If x percent of 400 is 20 percent of 700, then x = options: A)200 B)350 C)700 D)400 E)1,400 SOLUTION:x/100(400) = 2/10(700) x = 400. Option D. #### D QUESTION:(A% of 5B + B% of A) is equal to ? options: A)A% of B B)B% of A C)6% of AB D)AB% of 3 E)None SOLUTION:Answer A% of 5B + B% of A =5AB/100 + AB/100 = 6AB/100 = 6% of AB Correct Option: C #### C QUESTION:A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-38 E)36-37 SOLUTION:5%(35.5) = 1.775 8%(35.5) = 2.84 total amount could have been 35.5+1.775 and 35.5+2.84 => could have been between 37.275 and 38.34 => approximately between 37 and 38 Answer is B.D #### D QUESTION:(+15) + (-11) - (+5) - (-7) options: A)8 B)2 C)6 D)5 E)3 SOLUTION:= 15-11-57 22-16, [adding all integers with plus (+) sign together and with minus (-) sign respectively together = +6 or simply 6. correct answer (C) #### C QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these SOLUTION:Solution Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr. Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables w are there in the warehouse? options: A)6 B)8 C)10 D)15 E)30 SOLUTION:Total number of ways to choose 2 chairs from 5 w= 5C2=10 Total number of combination=150 That means we need get 15 combinations from the selection of tables.... Screening through the answers.... 6C2=15..... 15*10=150 Answer is 6... A #### A QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002? options: A)62% B)69.45% C)70% D)71% E)72% SOLUTION:Required percentage = [ (288 + 98 + 3.00 + 23.4 + 83) x 100 ] % (420 + 142 + 3.96 + 49.4 + 98) = [ 495.4 x 100 ] % 713.36 ~= 69.45%. B) #### B QUESTION:By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)228 B)480 C)267 D)288 E)276 SOLUTION:SP = 800 Profit = 25% CP = (SP)*[100/(100+P)] = 800 * [100/125] = 640 Loss = 25% = 25% of 640 = Rs.160 SP = CP - Loss = 640 - 160 = Rs.480 Answer: B #### B QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:Two brothers took the GMAT exam, the higher score is M and the lower one is N. If the difference between the two scores is equal to their average, what is the value of N/M ? options: A)3 B)2 C)1/2 D)1/3 E)There isn't enough data to answer the question. SOLUTION:M - N = (M + N)/2 Solving for N/M = 1/3 D #### D QUESTION:If each side of the square is increased by 25% find the percentage change in its area? options: A)89.45% B)56.25% C)89.98% D)54.48% E)45.0% SOLUTION:let each side of the square be a. then area =a^2 new side=125a/100=5a/4 new area=(5a/4)^2=25a^2/16 increase in area=(25a^2/16-a^2)=9a^2/16 increased %=(9a^2/16*1/a^2*100)=56.25% Answer is(B) #### B QUESTION:A set consist of 2k-1 element. What is the number of subsets of this set which contain at most k-1 elements? options: A)2^(2k-2) B)2^(2k) - 2 C)2^(2k) -1 D)2^(2k) E)2^(2k-1) SOLUTION:I used k=3, so then we have 5!/2!3! + 5!/4!1! + 5!/0!5! 10 + 5 + 1 = 16 So our target is 16 Now replace in answer choices A gives us 2^4 = 16 Hence A is the correct option Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes Avoid 2 since you will get 1 arrangement (k-1) and may be risky since 1 is a number with certain unique properties #### A QUESTION:If (a-3)(b-2) =0, which of the following must be true ? I. a=3 and b=2 II. if a is not = 3, then b=2 III. if a=3, then b is not=2 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:(a-3)(b-2)=0 So either a=3 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true. The answer is B. #### B QUESTION:Three friends X, Y, Z rented a auto for Rs.520. A used it for 6 hours, B used it for 9 hours and C used it for 11 hours. What is the hire charges paid by Y: options: A)Rs 140 B)Rs 160 C)Rs 180 D)Rs 200 E)None SOLUTION:X : Y : Z = 7 : 8 : 11. Hire charges paid by Y = Rs(520×9/26) = Rs.180. Answer C #### C QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)3630 B)3637 C)3630 D)3631 E)3635 SOLUTION:6300:4200:10500 3:2:5 3/10 * 12100 = 3630 Answer: A #### A QUESTION:A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? options: A)158 m B)150 m C)110 m D)130 m E)157 m SOLUTION:Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 => y = x/15 (x + 100)/25 = x/15 => x = 150 m. Answer: B #### B QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)7 B)4 C)6 D)9 E)3 SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer: B #### B QUESTION:total dinning bill of 3 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared . options: A)21.84 B)50.96 C)53.84 D)24.84 E)50.26 SOLUTION:dinner bill of 3 person = 139 + 10% tip so, 10% of 139 = (139*10)/100 = 13.9 So, the actual total amount = 139+13.9 = $ 152.9 so per head bill = 152.9/3 = $ 50.96 ANSWER:B #### B QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers? options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 8 is 8!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!6!. # of arrangements when 3 boys do not sit together would be: 8!-3!6!. Answer: B). #### B QUESTION:The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? options: A)c is not changed. B)c is halved. C)c is doubled. D)c is multiplied by 4. E)c is multiplied by 16. SOLUTION:a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. E c is multiplied by 16. #### E QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.9 - 19 x 15) kg = 13 kg. Correct Option: D #### D QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,700 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Price in 96 = 22000 Price decrease each year = 2.5/100*22000 = 550 Price in 97 = 22000 - 550 Price in 98 = 22000 - 2*550 Price in 99 = 22000 - 3*550 Price in 00 = 22000 - 4*550 Price in 01 = 22000 - 5*550 Price in 02 = 22000 - 6*550 = 18700 Investment in the car = 1000 Net price of the car in 02 = 18700 + 1000 = $19700 Correct Option: B #### B QUESTION:If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 40 men in 3 days? options: A)65mtr. B)52mtr C)70mtr. D)112mtr. E)17mtr. SOLUTION:20 men is 6 days can build 112 metres 25 men in 3 days can build = 112*(40/20)x(3/6) = 112 meters Answer: D. #### D QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 20:50:80. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)520 B)640 C)700 D)750 E)800 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 20:50:80 Initial soap:alcohol = 20/50 =20:50 after doubled soap:alcohol =2* 20/50 = 40:50 Initial soap:water = 20/80=20:80 after halved soap:water: 1/2 * 20/80 = 10/80 = 10:80 After soap: alcohol:water --> 40:50:320-->4:5:32 given alcohol 100 cubic centimeter. ratio is 80:100:640(4:5:32) For 100 cubic centimeter of Alcohol --- 640cubic cm water is required. Answer-B #### B QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)3 B)3.3 C)3.5 D)3.6 E)None SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4. Answer: Option D #### D QUESTION:A tank is filled in SIX hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank? options: A)56 hours B)28 hours C)55 hours D)66 hours E)21 hours SOLUTION:1/A + 1/B + 1/C = 1/6 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/6 => (1 + 2 + 4)/2B = 1/6 => 2B/7 = 6 => B = 21 hours. Answer: E #### E QUESTION:John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease? options: A)90% B)30% C)40% D)70% E)80% SOLUTION:The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)*100 = (0.9)*100 = 90%. A #### A QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430 ? options: A)s. 832 B)s. 830 C)s. 822 D)s. 812 E)s. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2430 = 20 (2430/60) = Rs. 810. Answer: E #### E QUESTION:At what rate percent per annum will a sum of money double in 8 years. options: A)12.5% B)13.5% C)11.5% D)14.5% E)21.5% SOLUTION:Let principal = P, Then, S.I.=P and Time=8 years Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum. Answer: A #### A QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:How many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately followed by an even number? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:A is followed by B means : A comes first,B comes next A preceded by B means : B comes first, A comes next The sets which satisfy the condition is: 5 3 8 1 3 8 7 3 4 ANSWER:C #### C QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:Let J – John’s weight S – Susan’s weight M – Mark’s weight A – Sam’s weight L – Lynn’s weight J = 2S S = 0.6A M = 0.5L L = 1.9J Let us convert these weights to one variable S = J/2 A = S/0.6 = J/1.2 = 5J/6 L = 1.9J M = 0.5 * 1.9J = 0.95J So Susan has the least weight. Answer - B #### B QUESTION:If the area of a circle is 81pi square feet, find its circumference. options: A)48 B)38 C)51 D)92 E)18 SOLUTION:The area is given by pi pi × r × r = 81 pi r × r = 81 ; hence r = 81 feet The circumference is given by 2 × pi × r = 2 × pi × 9 = 18 pi feet correct answer is E) 18 #### E QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:Twenty four men can do a work in 32 days. How many men are required to complete the work in 12 days? options: A)32 B)10 C)64 D)40 E)60 SOLUTION:C 64 We have M1 D1 = M2 D2 So, 24 * 32 = M2 * 12 => M2 = 64. Answer is C #### C QUESTION:A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time? options: A)75 m. B)80 m. C)150 m. D)100 m. E)None of the above SOLUTION:ratio of speeds of a and b is 2:1 b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b the time taken for a to cover 50m is 50/1=50m so the total time taken by a and b to reach =2*50=100m ANSWER:D #### D QUESTION:If the product of the integers r, s, t and u is 770, and if 1 < r< s< t< u, what is the value of r+ u? options: A)10 B)13 C)16 D)18 E)21 SOLUTION:770 = 2 * 5 * 7 * 11 So r= 2, s= 5, t= 7, u= 11 r+ u= 2 + 11 = 13 Answer - B #### B QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)2200 miles. B)2300 miles. C)1900 miles. D)2500 miles. E)2100 miles. SOLUTION:E 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 #### E QUESTION:A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 3 percent and 6 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate? options: A) 3/8 B) 21/25 C) 1/2 D) 3/5 E) 3/4 SOLUTION:x * 3/100 * 1 + (20000 - x) * 8/100 * 1 = 1440 3x - 8x = 144000 - 160000 => -5x = -16000 => x = 32000 So 16800/20000 = 21/25 Answer - B #### B QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=8 and y=6, then x^2-y^2=28 and 28 is divisible only by 4 from the options, thus it must be correct. Answer: B. #### B QUESTION:The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ? options: A)12 B)14 C)15 D)16 E)20 SOLUTION:HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D #### D QUESTION:The wages earned by Robin is 44% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin? options: A)23% B)18.75% C)30% D)30.55% E)100% SOLUTION:Explanatory Answer Let the wages earned by Erica be $100 Then, wages earned by Robin and Charles will be $144 and $160 respectively. Charles earns $44 more than Robin who earns $144. Therefore, Charles' wage is 44/144*100 = 30.55%. The correct choice is (D) #### D QUESTION:A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box? options: A)6 m B)9 m C)10 m D)7 m E)11 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:Depreciation applicable to an equipment is 20%.The value of the equipment 3 years from now will be less by options: A)48.8% B)47.8% C)46.8% D)49.8% E)45.8% SOLUTION:Value after 3 years will be 0.8^3 = 0.512 times the present value. so it will be less by 48.8%. ANSWER:A #### A QUESTION:Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? options: A)635.50 B)635.53 C)635.57 D)635.52 E)635.51 SOLUTION:4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 Answer: A #### A QUESTION:The sector of a circle has radius of 24 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)104.6 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 24) + 2(24) = 56.6 + 48 = 104.6 cm Answer:C #### C QUESTION:A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent? options: A)27% B)20% C)80% D)30% E)25% SOLUTION:900 ---- 225 100 ---- ? => 25% Answer: E #### E QUESTION:A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job? options: A)77 days B)21 days C)88 days D)55 days E)44 days SOLUTION:WC = 1:2 2x + x = 1/14 => x = 1/42 2x = 1/21 => 21 days Answer: B #### B QUESTION:Sid obtained 76, 65, 82, 67 and 80 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)A)87 B)B)99 C)C)68 D)D)82 E)E)74 SOLUTION:Average = (76 + 65 + 82 + 67 + 80)/5 = 370/5 = 74. Answer:E #### E QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700 P1’s income = Rs 5*700 = Rs.3500 ANSWER:D #### D QUESTION:Simplify: 256 x 256 - 144 x 144 options: A)761200 B)44800 C)761800 D)761500 E)None of them SOLUTION:(256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800 Answer is B #### B QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)2/215 B)3/155 C)1/216 D)2/213 E)3/212 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:A store sells four different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:4C2=6. The answer is B. #### B QUESTION:The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to: options: A)0.04 B)0.004 C)0.4 D)0.0004 E)None of them SOLUTION:Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is A #### A QUESTION:If x is an even integer and y = 5x + 1, which of the following CANNOT be a divisor of y? options: A)11 B)31 C)21 D)41 E)30 SOLUTION:x takes even values as 2,4,6,8., y=5x+1 x is an even term so 5x must be an even term when it adds with 1 so it must be a odd integer 30 didn't follows this condition ans is E #### E QUESTION:There are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? . options: A)75 Kg B)80 Kg C)85 Kg. D)90 Kg E)92 Kg SOLUTION:New average weight= 110+60/2= 85 kgs Since avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85 C is the answer #### C QUESTION:A boy has thirteen trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)186 ways B)177 ways C)188 ways D)195 ways E)189 ways SOLUTION:The boy can select one trouser in thirteen ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 13 * 15 = 195 ways. Answer:D #### D QUESTION:A rectangular courtyard 3.78 metres long and 2.25 metres wide is to be paved exactly with square title, all of the same size. What is the largest size of the tile which could be used for the purpose ? options: A)11 cms B)21 cms C)42 cms D)None of these E)46 cms SOLUTION:Solution Largest size of the tile = H.C.F. of 378 cm an= 21 cm = 525 cm. Answer B #### B QUESTION:9 people decided to split the restaurant bill evenly. If the bill was $514.16 dollars, how much money did they 1 cent is the smallest unit? options: A)$514.16 B)$514.17 C)$514.18 D)$514.19 E)$514.20 SOLUTION:This is equivalent to finding the first number that is divisible by 9 that occurs after 51416. In order to divide the sum in 9 parts, the amount must be divisible by 9 Divisibility rule of 9: The sum of the digits must be divisible by 9 Sum of digits of 51416 = 17 and 18 is divisible by 9. Hence, we need to add 1 to this number for it to be divisible by 9 Correct Option: B #### B QUESTION:In how many ways can 6 boys and 3 girls be arranged at a table if 3 girls are never together? options: A)47520 B)45620 C)47888 D)42156 E)43210 SOLUTION:Total ways of arranging 10 person in a circle = 9! = 51840 ways If we consider three women as one, then we have 6+1=7 persons. Arranging these seven persons in circle will take = 6! = 720 ways And three women can arrange themselves in 3! ways Total ways in which three women sit together in circle = 6!*3! = 4320 ways Total ways in which three women doesn’t sit together in circle = 9! - 6!*3! = 51840 - 4320 = 47520 ways A #### A QUESTION:A merchant marks his goods up by 50% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)21% B)25% C)69% D)35% E)19% SOLUTION:Let the price be 100. The price becomes 150 after a 50% markup. Now a discount of 10% on 150. Profit=135-100 35% answer D #### D QUESTION:Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:2 + 3 + 5 + 7 + 11= 28 ( sum is even) Least number = 2 A #### A QUESTION:575.104 x 15.98 ÷ 9.001 + 21.25 = ? options: A)983.578 B)1043.65 C)1033.65 D)656.112 E)456.512 SOLUTION:Explanation: ? = 575.104 x 15.98 ÷ 9.001 + 21.25 ≈ (575.104 x 16/9) + 21.25 ≈ 1022.40 + 21.25 ≈ 1043.65 Answer: Option B #### B QUESTION:Three walls have wallpaper covering a combined area of 280 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 36 square meters. What is the area that is covered with three layers of wallpaper? options: A)5 Square Meters B)32 Square Meters C)42 Square Meters D)83.3 Square Meters E)120 Square Meters SOLUTION:280 - 180 = 100 sq m of the wallpaper overlaps (in either two layers or three layers) If 36 sq m has two layers, 100 - 36 = 64 sq m of the wallpaper overlaps in three layers. 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m. Answer (B). #### B QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result? options: A)132 B)127 C)125 D)152 E)112 SOLUTION:C 125 96 passes out of 125 give an average of 76.8% #### C QUESTION:Which of the following is a prime number ? options: A)33 B)81 C)97 D)93 E)none SOLUTION:Clearly, 97 is a prime number #### C QUESTION:What is the perimeter of a square field whose diagonal is 8√2? options: A)82 m B)32 m C)27 m D)26 m E)76 m SOLUTION:4a = 32 m Answer: B #### B QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ? options: A)2015 B)2088 C)270 D)1881 E)1781 SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4 .............. f(2014) = 2015 Ans: A #### A QUESTION:Shaun is starting a new diet plan that offers him the choice of fruit or yogurt for breakfast, 6 different entrees for lunch, and 9 different entrees for dinner. If Shaun chooses an Italian entree for lunch, he always chooses an Italian entree for dinner. If Shaun chooses a Chinese entree for lunch, he never chooses a Chinese entree for dinner. If there are 2 Italian entrees and 2 Chinese entrees among the lunch choices, and 3 Italian entrees and 3 Chinese entrees among the dinner choices, from how many different daily menus can Shaun choose? options: A)24 B)36 C)72 D)90 E)108 SOLUTION:Let the Breakfast set be {F , Y} Lunch be {I ,I , C,C , L1,L2} Dinner be {I,I,I , C,C,C, D1,D2,D3} There are only 2 restrictions, Italian Lunch has to go with Italian Dinner and Chinese Lunch cannot go with Chinese dinner. So the set of Breakfast, Lunch and Dinner will {Any BF, Italian Lunch, Italian Dinner } = 2 * 2 * 2 {Any BF, Chinese Lunch, Not Chinese Dinner} = 2 * 2 * 6 {Any BF, Not Italian or Chinese Lunch, Any Dinner} = 2 * 2 * 9 Adding all these gives 72. Answer is C #### C QUESTION:The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)8:9 B)B)3:5 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 6x and 8x years respectively. Then, 8x - 6x = 4 => x =2 Required ratio = (6x + 4) : (7x + 4) 16 : 18 = 8:9 ANSWER:A #### A QUESTION:If the sum of a set of 5 different positive prime numbers is 94, what is the difference between largest and smallest prime numbers between them? options: A)53 B)51 C)47 D)41 E)31 SOLUTION:All prime numbers apart from 2 are odd. Even + Even = Even Odd + Even = Odd Odd + Odd = Even We are given 5 different prime numbers, whose sum is 94 i.e even If we include 2, we will have 4 odd prime numbers and one even. This sum would be odd If we exclude 2, we will have 5 odd numbers. This sum would be even Hence 2 is included. The possible 5 no. are = 11+7+2+43+31 = 94 the difference between largest and smallest prime numbers between them = 43 - 2 = 41 Ans - D #### D QUESTION:Two trains 200m and 160m long run at the speed of 68kmph and 40kmph in opposite directions in parallel tracks. The time which they take to cross each other is? options: A)5.6sec B)8.9sec C)10.8sec D)12 sec E)15sec SOLUTION:Relative speed = 68+40 = 108kmph * 5/18 = 30 m/s Distance covered in crossing each other = 200+160 = 360m Required time = 360*1/30 = 12 sec Answer is D #### D QUESTION:What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9? options: A)397 B)401 C)403 D)405 E)399 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=405. Answer: D. #### D QUESTION:If the price of a certain bond on May 1st was 1/2 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? options: A)50% B)75% C)120% D)133 1/3% E)160% SOLUTION:The price on June 1st = 12 (assume); The price on May 1st = 1/2*12 = 6; The price on July 1st = 6*1.5 = 9. The average price of the bond on May 1st and July 1st = (6+9)/2 = 7.5. The price of the bond on June 1st (12) is 8/5 times (160%) the average price of the bond on May 1st and July 1st. Answer: E. #### E QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre. options: A)$8250 B)$8350 C)$8650 D)$8450 E)$8500 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $400 Hence, total cost =5.5×3.75×400= $8250 A #### A QUESTION:9, 16, 18, 25, 36,49 options: A)9 B)16 C)18 D)25 E)36 SOLUTION:Each of the numbers except 18, is perfect square. Answer: Option C #### C QUESTION:Aishwarya’s mom was 28 years of age at the time of her birth, while her mom was 20 years old when her 2 years younger sister was born. The variance between the parents ages is : options: A)10 years B)11 years C)15 years D)9 years E)4 years SOLUTION:A 6 years Mom’s age when Aishwarya’s sister was born = 20 years. Dad’s age when Aishwarya’s sister was born = (28 + 2) years = 30 years. Needed Variance = (30 – 20) years = 10 years. Answer is A #### A QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B QUESTION:A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 70,000, A receives : options: A)14700 B)24703 C)29400 D)33777 E)34778 SOLUTION:Explanation: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=> x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. A's share = Rs. (70000 * 21/50 ) = Rs. 29,400. Answer: C) #### C QUESTION:What is the speed required for a car to cover a distance of 600 km in 5 hours? options: A)160 kmh B)140 kmh C)150 kmh D)130 kmh E)120 kmh SOLUTION:Speed= Distance / Time Speed = 600 / 5 = 140 Answer: B #### B QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 63 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)40 E)55 SOLUTION:I didn't understand How did we get 100? Total = 75 books. 65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned. Now, there are 63 books, thus 76-63=12 books are NOT returned. {loaned out}*0.30=7 --> {loaned out}=40. Answer: D. #### D QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:A bag contains 8 red and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? options: A)4/7 B)2/3 C)8/11 D)1/4 E)5/7 SOLUTION:Total number of balls = 8+3 = 11 number of white balls = 8 Probability = 8/11 = 8/11 Answer is C #### C QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:If 3<x<6<y<7, then what is the greatest possible positive integer difference of x and y? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:3 < x < 6 < y < 7; 3 < x y < 7 3 + y < x + 7 y - x < 4. Positive integer difference is 3(for example y = 6.5 and x = 3.5) Answer:A. #### A QUESTION:P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left? options: A)8/15 B)7/15 C)6/15 D)5/15 E)4/15 SOLUTION:Amount of work P can do in 1 day = 1/15 Amount of work Q can do in 1 day = 1/20 Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15 Fraction of work left = 1 – 7/15= 8/15 Answer is A. #### A QUESTION:If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is: options: A)Rs. 182 B)Rs. 190 C)Rs. 196 D)Rs. 204 E)Rs. 210 SOLUTION:Explanation: Given ratio =1/2:2/3:3/4=6:8:9 1st part = Rs. 782*6/23=Rs. 204 Answer is D #### D QUESTION:The speed at which a man can row a boat in still water is 18 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)16 seconds B)15.4 seconds C)26 seconds D)12 seconds E)18 seconds SOLUTION:Speed of the boat downstream = 18 + 3 = 21 kmph = 21 * 5/18 = 35/9 m/s Hence time taken to cover 60 m = 60*9/35 = 15.4 seconds. Answer: B #### B QUESTION:A train running at 1/3 of its own speed reached a place in 9 hours. How much time could be saved if the train would have run at its own speed? options: A)8hrs B)10hrs C)12hrs D)15hrs E)6hrs SOLUTION:time taken if run its own speed = 1/3*9 =3 hrs Time saved = 9 - 3 = 6 hrs Answer : E #### E QUESTION:Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.? options: A)8 kmph B)11 kmph C)12 kmph D)14 kmph E)16 kmph SOLUTION:Explanation: Let the distance travelled by x km. Then, x/10-x/15=2 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr =60/10 hrs= 6 hrs. So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60/5kmph= 12 kmph ANSWER IS C #### C QUESTION:Find the smallest number which should be multiplied with 13225 to make it a perfect square. options: A)25 B)5 C)1 D)23 E)6 SOLUTION:13225 = 5*5*23*23 Required smallest number = 1 1 is the smallest number which should be multiplied with 13225 to make it a perfect square. ANSWER:C #### C QUESTION:If A : B = 4 : 9 and B : C = 5 : 9 then A : B : C is : options: A)20 : 35 : 63 B)35 : 36 : 63 C)30 : 35 : 65 D)20 :45: 81 E)None of these SOLUTION:Expl : A : B = 4 : 9 B : C = 5 :9 = 5*9/5 : 9 *9/5 = 9 : 81/5 A : B : C = 4 : 9 : 81/5 = 20 : 45 : 81 Answer: D #### D <<<Examples ends QUESTION:The speed at which a man can row a boat in still water is 18 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)16 seconds B)15.4 seconds C)26 seconds D)12 seconds E)18 seconds SOLUTION:Speed of the boat downstream = 18 + 3 = 21 kmph = 21 * 5/18 = 35/9 m/s Hence time taken to cover 60 m = 60*9/35 = 15.4 seconds. Answer: B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ??? options: A)a,b B)a,c C)b,c D)a,d E)b,d SOLUTION:a. 3i+2j and c. 2i-3j are orthogonal pair. as the dot product of two vectors is zero;so they are orthogonal. ANSWER:B #### B QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 * 11 * 7 = 154 ANSWER:B #### B QUESTION:What is the difference between local value & face value of 9 in the numeral 65793? options: A)8453 B)8956 C)8991 D)9890 E)10000 SOLUTION:(Local value of 9) - (Face value of 9) = (9000 - 9) = 8991 C #### C QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)109% B)160% C)100% D)600% E)108% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy? options: A)4 B)10 C)7 D)8 E)12 SOLUTION:Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence X + Y = 20 If X is the number of cards at $0.25, then the X cards cost 0.25 X If Y is the number of cards at $0.15, then the Y cards cost 0.15 Y The total cost of the X cards and the the Y cards is known to be $4.2 and also given by 0.25 X + 0.15 Y = 4.2 We now need to solve the system of equations X + Y = 20 0.25 X + 0.15 Y = 4.2 The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve 0.25 X + 0.15 (20 - X) = 4.2 X(0.25 - 0.15) + 3 = 4.2 0.1 X = 1.2 X = 12 and Y = 20 - 12 = 8 correct answer D #### D QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)28 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (14000 × 7) + 6000 ( x – 7) ‹=› 2000x = 56000 ‹=› x = 28. Answer D #### D QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? options: A)25% B)33 1/3% C)50% D)66 2/3% E)75% SOLUTION:General formula for percent increase or decrease, (percent change): percent=Change/Original∗100 So, the time between maintenance checks increased by 25−20/20∗100=25 Answer: A. #### A QUESTION:The area of a triangle is with base 5.5m and height 6m? options: A)11 m2 B)16.5 m2 C)18.5 m2 D)19.5 m2 E)12 m2 SOLUTION:1/2 * 5.5* 6 = 16.5 m2 Answer: B #### B QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? options: A)5729 B)5760 C)2889 D)3600 E)2799 SOLUTION:1/x - 1/6 = -1/8 x = 24 hrs 24 * 60 * 2.5 = 3600.Answer: D #### D QUESTION:Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many T applicants majored in political science and had a GPA higher than 3.0? options: A)5 B)10 C)15 D)25 E)35 SOLUTION:Total applicants = 40 Political science = 15 and Non political science = 40 - 15 = 25 GPA > 3.0 = 20 and GPA <= 3.0 = 20 10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0 GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5 Answer: A #### A QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)276 m B)279 m C)240 m D)207 m E)285 m SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 39 = 15 x + 300 = 585 x =285m. Answer: E #### E QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 110/100 × 110/100 = 12100 C #### C QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D QUESTION:The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is? options: A)288 B)267 C)200 D)4096 E)2771 SOLUTION:Principal = [4913 / (1 + 25/(4 * 100))3] = 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096. Answer: D #### D QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was? options: A)160000 B)228788 C)266891 D)267689 E)127791 SOLUTION:X * (105/100) * (105/100) * (105/100) = 185220 X = 185220/1.157625 X = 160000 Answer:A #### A QUESTION:How many quarters are equal to 4 dollars? options: A)16 B)8 C)12 D)9 E)7 SOLUTION:4*4 = 16 quarters Answer : A #### A QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 7 years older than B, the present age of B is options: A)35 B)37 C)39 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 7) years. (x+7+10)=2(x—10) hence x=37. Present age of B = 37 years Answer: Option B #### B QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/7) B)Rs. 2(1/9) C)Rs. 3(2/11) D)Rs. 2(2/13) E)Rs. 2(2/7) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B #### B QUESTION:A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is: options: A)35.55 km/hr B)36 km/hr C)71 km/hr D)71.11 km/hr E)70 km/hr SOLUTION:Total time taken =((160/64)+(160/80))hrs=9/2hrs. Average speed =(320 x2/9)km/hr= 71.11 km/hr. ANSWER D #### D QUESTION:In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ? options: A)8% B)5% C)7% D)12% E)19% SOLUTION:A 8% of student hate all four subjects. #### A QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? options: A)700 B)666 C)600 D)400 E)800 SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C #### C QUESTION:The reflex angle between the hands of a clock at 10.25 is: options: A)180º B)192 1/2 º C)195º D)197 1/2 º E)197 º SOLUTION:Angle traced by hour hand in 125/12 hrs ={(360/12)x(125/2)}º = 312 1/2 º . Angle traced by minute hand in 25 min =(360/60)x 25 º= 150º. Reflex angle = 360º -(312 1/2- 150º )= 360º - 162 1/2º= 197 1/2º . Answer: D #### D QUESTION:If a randomly selected non-negative single digit integer is added to {2, 3, 4, 9}. What is the probability that the median of the set will increase but the range still remains the same? options: A)0.2 B)0.3 C)0.4 D)0.5 E)0.6 SOLUTION:We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes. Hence, the total number of outcomes is 10. We need to find the probability that the median of the set will increase but the range still remains the same. The median of the set is (3 + 4)/2 = 3.5, thus the number selected must be 4 or greater. For the range to remain the same, the number must be between 2 and 9 inclusive. To satisfy both conditions, the number selected must be 4, 5, 6, 7, 8, or 9. The probability is 6/10 = 0.6 The answer is E. #### E QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is options: A)51:52 B)52:54 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (104% of x) / (108% of x) =104/108 =52/54 = 52:54. Answer: B #### B QUESTION:In a two digit number, the digit in the units place is two times the digit in ten's place and sum of the digits is equal to 6. What is the number? options: A)24 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=2x Therefore x + 2x = 6 ‹=›3x = 6 ‹=›x= 2. So, ten's digit = 2, unit's digit = 4. Hence, the required number is 24. Answer A #### A QUESTION:In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday? options: A)Thursday B)Friday C)Saturday D)Sunday E)Monday SOLUTION:Day of week after 64 days after Arman's birthday = 7*9 + 1 Saturday as the period will have 9 weeks and 1 days . The 1 days in the end will be Friday . Answer B #### B QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 145° each? options: A)96 cm B)108 cm C)120 cm D)132 cm E)154.28 cm SOLUTION:Sum of all interior angles is given by: 180(n-2) = n is number of sides 180(n-2) = 145*n from here n = 10.28 So perimeter becomes 15*10.28= 154.28 Answer: E #### E QUESTION:A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)3/5 C)3/8 D)4/9 E)7/10 SOLUTION:The total possible choices are 10C3 = 120 The ways to choose 3 apples: 5C3 = 10 The ways to choose 2 apples: 5C2 * 5C1 = 50 P(at least 2 apples) = 60/120 = 1/2 The answer is A. #### A QUESTION:January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008? options: A)Monday B)Tuesday C)Wednesday D)Friday E)Sunday SOLUTION:The year 2007 is an ordinary year. So, it has 1 odd day. day of the year 2007 was Monday day of the year 2008 will be 1 day beyond Monday Hence, It will be Tuesday. answer : B #### B QUESTION:In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner? options: A)$9 x 10^4 B)$9.90 x 10^6 C)$1.00 x 10^7 D)$1.05 x 10^7 E)$9.90 x 10^7 SOLUTION:The max product of any two balls can be 9 * 10 = 9900 = 9 * 10 If we multiply it by $1000 the max amount will be 9 * 10^4. A #### A QUESTION:Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? options: A)5 B)3 C)4 D)6 E)1 SOLUTION:Rate of one machine = 1 job / (20*4) days let X = number of machines needed to complete the job in 10 days 1/(4*20) * 10 * X = 1 job X = 8 8-4= 4 ANSWER: C #### C QUESTION:If (x + 1)^2 = 144, which of the following could be the value of 2x? options: A)–26 B)–13 C)–10 D)12 E)-21 SOLUTION:You can also get to the answer by backsolving using answer choices Starting with choice B = -13 (x + 1)^2 = 144 (-13 + 1)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -13 will result in 144 in the equation so x must be -11, Then 2x = 2 * -13 = -26 Answer: A #### A QUESTION:A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper? options: A)140 B)388 C)238 D)119 E)112 SOLUTION:when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 14*10 = 140 sq cmV Answer: A #### A QUESTION:Four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. In 18 minutes, how many times do they toll together ? options: A)43 B)44 C)45 D)46 E)47 SOLUTION:LCM of 2, 4, 6, 8 is 24. So, after each 24 seconds, they would toll together. Hence, in 18 minutes, they would toll 18*60 seconds / 24 seconds = 45 times But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second). So, total tolls together = 45+1 = 46 Answer C #### C QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)None of these SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111.. Answer : Option C #### C QUESTION:Which of the following is not a prime number ? options: A)502 B)503 C)509 D)521 E)523 SOLUTION:Clearly, 502 is not a prime number. Answer : A #### A QUESTION:Carol spends 1/4 of her savings on a stereo and 1/2 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? options: A)1/4 B)2/7 C)5/12 D)3/8 E)7/12 SOLUTION:Total Savings = S Amount spent on stereo = (1/4)S Amount spent on television = (1-1/2)(1/4)S = (1/2)*(1/4)*S = (1/8)S (Stereo + TV)/Total Savings = S(1/4 + 1/8)/S = 3/8 Answer: D #### D QUESTION:In a box of 8 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)2/10 B)3/11 C)4/13 D)5/14 E)6/17 SOLUTION:P(neither pen is defective) = 5/8*4/7 = 5/14 The answer is D. #### D QUESTION:Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in? options: A)15 hours B)12 hours C)76 hours D)16 hours E)81 hours SOLUTION:The part of the tank filled by three pipes in one hour = 1/8 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12. The tank can be filled in 12 hours. Answer: B #### B QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)7 1/2 years B)20 years C)15 years D)38 years E)30 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years ANSWER:B #### B QUESTION:The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday? options: A)1,159 B)1,333 C)1,860 D)2,160 E)2,272 SOLUTION:The question states that all these 4,999 locations were measured twice, once on each day. It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W. Therefore, we can write two equations: For each of the first and second day count of locations, T + W = 4999 But, for the second day count, W = 1.20 T i.e. for Second day count, T + 1.20T = 4999 i.e. 2.20 T = 4999 i.e. T = 2272 E #### E QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/4. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)5. B)7. C)9. D)10. E)17. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10 Lets take LCM of three balls 4,5 and 10 =20. The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS. Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls. IMO option C is correct. #### C QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.9 sec C)3.5 sec D)7.5 sec E)5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 200/40 = 5 sec. Answer: E #### E QUESTION:What is 30% of 210? options: A)61 B)63 C)65 D)67 E)69 SOLUTION:X/210 = 30/100 100X = 210X30 X =(210X30)/100 X =6300/100 = 63 ANSWER = B = 63 #### B QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10 SOLUTION:(p-2)(p-4) = q p = 3 for this to be true, so 1/10 Ans :B #### B QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer is C. #### C QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage? options: A)80% B)50% C)75% D)40% E)53% SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 175 (35 * 5) Profit percentage = (175 - 100)/100 * 100 = 75% Answer: C #### C QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum? options: A)8 B)2 C)9 D)4 E)6 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96 15000[(1 + R/100)2 - 1 - 2R/100] = 96 15000[(100 + R)2 - 10000 - 200R]/10000 = 96 R2 = (96 * 2)/3 = 64 => R = 8 Rate = 8% Answer: Option A #### A QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have? options: A)10 B)16 C)8 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1080 180n - 360 = 1080 180n = 1440 n = 1440/180 = 8 ANSWER:C #### C QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence. options: A)21 B)20 C)40 D)42 E)19 SOLUTION:n for cyclic hand shake and n-1 for linear handshake. so here no of hand shake is 20. ANSWER:B #### B QUESTION:4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there. options: A)6! x 7P4 B)6! x 9P4 C)6! x 5P4 D)6! x 3P4 E)6! x 2P4 SOLUTION:Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways. So total ways are 6! x 7P4 Answer:A #### A QUESTION:16.02 × 0.1 = ? options: A)0.1602 B)0.001602 C)1.6021 D)0.01602 E)None of these SOLUTION:16.02 × 0.1 = 1.602 The answer is C. #### C QUESTION:If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:The H.C.F of two numbers is 8. Which of the following can never be their L.C.M? options: A)55 B)44 C)66 D)60 E)12 SOLUTION:H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60. Answer:D #### D QUESTION:There are 12 cans in the refrigerator. 8 of them are red and 4 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)460 B)490 C)493 D)455 E)424 SOLUTION:Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator = total ways to pick 4 can out of 12 - ways to pick 4 red out of 8 red - ways to pick 4 blue out of 4 blue 12C4−8C4−4C4=495−70−1=424 ANSWER:E #### E QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 30 percent decrease in y would result in which of the following changes in z? options: A)decrease of 7.5% B)decrease of 26.5% C)increase of 16.5% D)increase of 24.5% E)increase of 32.5% SOLUTION:After the changes, z = 1.5x*(0.7y)^2 = (1.5*0.49)xy^2 = 0.735*z The answer is B. #### B QUESTION:A cube of side one meter length is cut into small cubes of side 5 cm each. How many such small cubes can be obtained? options: A)2878 B)8000 C)1000 D)2997 E)2701 SOLUTION:Along one edge, the number of small cubes that can be cut = 100/5 = 20 Along each edge 5 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 20 * 20 * 20 = 8000 Answer: B #### B QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)16 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 324/3 = 108 sq m l b = 108 i.e., l * l/3 = 108 l2 = 324 => l = 18. Answer:C #### C QUESTION:How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length? options: A)18.9 sec B)88.9 sec C)22.9 sec D)30.00 sec E)72.0 sec SOLUTION:D = 110 + 390 = 500 m S = 60 * 5/18 = 50/3 T = 500 * 3/50 = 30 sec Answer: D #### D QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is options: A)2970 B)297 C)2997 D)300 E)30 SOLUTION:(1/10)*3000 - (1/10)%*3000 = 300 - (1/1000)*3000 = 300 - 3 = 297 The answer is B. #### B QUESTION:Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and fiveteen copper coins, how many different sums from 1¢ to 160¢ can he make with a combination of his coins? options: A)80 B)85 C)81 D)160 E)157 SOLUTION:The total sum is 5*2 + 15*5 = 85¢. If you can make each sum from 1 to 85 (1¢, 2¢, 3¢, ..., 85¢), then the answer would be 85 (maximum possible). Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 84¢ and 82¢ (since total sum is 85¢ we cannot remove 1¢ or 3¢ to get 84¢ or 82¢). So, out of 85 sums 4 are for sure not possible, so the answer must be 85 - 4 = 81 sums or less. Only A fits. Answer: C. #### C QUESTION:A customer pays 50 dollars for a coffee maker after a discount of 20 dollars What is the original price of the coffe maker? options: A)70 B)80 C)90 D)50 E)60 SOLUTION:Solution Let x be the original price. x - 20 = 50 x - 20 + 20 = 50 + 20 x + 0 = 70 x = 70 Answer A #### A QUESTION:Walking across campus, a student interviewed a group of students. 35% of the students took a finance class last semester, 45% took a marketing class last semester, and 50% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? options: A)40% B)30% C)25% D)15% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 35 + 45 - {both} + 50 {both} = 30%. The answer is B. #### B QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? options: A)4% B)8% C)4.2% D)4.8% E)5% SOLUTION:Let's say there is a TOTAL of100students at this college. 60 percent of the total number of students are freshmen. # of freshmen = 60% of 100 =60 40 percent of the fresh-men are enrolled in the school of liberal arts... Number of liberal arts freshmen = 40% of 60 =24 ...and, of these, 20 percent are psychology majors... Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8 What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? 4.8/100= 4.8% Answer:D #### D QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0 SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant). In options B , if you put x = -5, you get -ve value for y co-ordinate. Answer must be (B) #### B QUESTION:Convert the 11/36 m/s into kilometers per hour? options: A)2.9 kmph B)1.1 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:11/36 m/s = 11/36 * 18/5 = 11/10 = 1.1 kmph. Answer: B #### B QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20 SOLUTION:5p3 =5 x4= 20 Option 'E' #### E QUESTION:A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)80 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B #### B QUESTION:A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. options: A)15/7 B)4/17 C)7/18 D)19/6 E)7/15 SOLUTION:Let S be the sample space Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45 Let E=event of getting both balls of same colour Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4) =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21 P(E)=n(E)/n(S)=21/45=7/15 Option E #### E QUESTION:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of options: A)18% B)20% C)25% D)23% E)Cannot be determined SOLUTION:Answer: C. #### C QUESTION:In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water? options: A)3:1 B)3:5 C)7:8 D)7:9 E)9:11 SOLUTION:First mixture: milk and water in the ratio of 3x:4x. Second mixture: milk and water in the ratio 5y:2y. We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3. Answer: A. #### A QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,500 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Important point to notice- 2.5% decrease from the original price 2.5% of 22,000= 550 Total reduction in 6 years= 550*6= 3300 Final price= 22,000 +1500 - 3300= 20,200 C is the answer #### C QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)7 B)9 C)8 D)4 E)5 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 8 Answer:C #### C QUESTION:Solve for x if (log2)(1-x/2)=x-2. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(log2)(1-x/2)=x-2 or,log2-(x/2)log2=x-2 or,2log2-xlog2=2x-4 or,log4+4=2x+xlog2 or,4.60=2.3x i.e.x=2. ANSWER:B #### B QUESTION:A polling company reports that there is a 50% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z? options: A)11 B)10 C)6 D)4 E)5 SOLUTION:50% - Candidate Elected 100%-60% = 40% - Candidate doesnotsigh Bill X 50% - Candidate randomly chooses between two bills. These are multiplicative: 50% x 40% x 50% 0.5 x 0.4 x 0.5 = 0.10 = 10% Answer (B) #### B QUESTION:A certain telescope increases the visual range at a particular location from 70 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ? options: A) 30% B) 33 1/2% C) 40% D) 60% E) 114.28% SOLUTION:Original visual range = 70 km New visual range = 150 km Percent increase in the visual range by using the telescope = (150-70)/70 * 100% = 8/7 * 100% = 114.28 % Answer E #### E QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)1/2 D)5/6 E)2/3 SOLUTION:The product to be even either one or both must be even, so: P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3; Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1. Answer: E. #### E QUESTION:Which of the following is equal to 1(4/5)%? options: A)0.012/100 B)0.12/100 C)1.2/100 D)1.8/100 E)12/10 SOLUTION:This notation may be confusing for some, since it looks like we're multiplying 1 and 4/5 How about adding a space:Which of the following is equal to (1 4/5)% (1 4/5)% = 1.8% = 1.8/100 Answer: D #### D QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)200 B)300 C)500 D)600 E)700 SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: Option C #### C QUESTION:50% of a number is 10 less than 3/5th of that number. What is the number? options: A)100 B)50 C)150 D)200 E)75 SOLUTION:Let the number be x Then, 3x/5 - (50% of x) = 10 3x/5-50x/100 = 10 x = 100 Answer is A #### A QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 878 in 4 years. The sum is: options: A)500 B)698 C)626 D)910 E)None SOLUTION:Sol. S.I. for 1 year = Rs. (878 - 815) = Rs. 63. S.I. for 3 years = Rs. (63 * 3) = Rs. 189. ∴ Principal = Rs. (815 - 189) = Rs. 626 Answer C #### C QUESTION:At what rate percent on simple interest will Rs.750 amount to Rs.900 in 4 years? options: A)6% B)2% C)4% D)5% E)3% SOLUTION:150 = (750*4*R)/100 R = 5% Answer: D #### D QUESTION:The avg. age of a group of 28 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is? options: A)22 years B)23 years C)24 years D)25 years E)28 years SOLUTION:Total age of 28 students=28*20=560 If total age of 4 students=x Then, (560+x)/(28+4) =(20+1), x=112 So average age of new students=112/4= 28 years ANSWER:E #### E QUESTION:The average age of 29 students in a group is 15 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years? options: A)31 B)36 C)29 D)53 E)57 SOLUTION:age of the teacher=(29*16-29*15) =29 years. ANSWER:C #### C QUESTION:You need to climb 10 stairs. At each support, you can walk one stair or you can jump two stairs. In what number alternative ways you'll climb ten stairs? options: A)99 B)79 C)55 D)89 E)66 SOLUTION:D #### D QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -. options: A)7/18 B)7/19 C)7/11 D)7/12 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ways. 7/15 Answer: E #### E QUESTION:If n = 30! + 27, then n is divisible by which of the following? I. 25 II. 27 III. 29 options: A)None B)I only C)II only D)I and II E)II and III SOLUTION:27 divides 30! so 27 also divides 30! + 27. 25 and 29 divide 30! so they do not divide 30! + 27. The answer is C. #### C QUESTION:The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? options: A)18 2/18% B)18 2/11% C)18 2/91% D)18 9/11% E)12 2/11% SOLUTION:13 CP = 11 SP 11 --- 2 CP 100 --- ? =>18 2/11% Answer: B #### B QUESTION:On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is? options: A)22 B)99 C)27 D)11 E)37 SOLUTION:Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30. S.I for one year = Rs. 330. S.I. on Rs. 330 for 1 year = Rs. 36.30 Rate = (100 * 36.30)/(330 * 1) = 11%.Answer: D #### D QUESTION:If x and y are integers such that (x+1)^2 is less than or equal to 16 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy? options: A) -16 B) -10 C) 0 D) 14 E) 16 SOLUTION:(x+1)^2 <= 16 x <= 3 x >= -5 (y-1)^2< 64 y < 9 y > -7 Max possible value of xy is -5 × -6 = 30 minimum possible value of xy is -5 × 8 = -40 -40 + 30 = -10 Answer : B #### B QUESTION:The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Also note here the relevance of 'K must be less than 400'. 21K is 180n (a multiple of 180). 180n = 2^2 * 3^2 * 5 * n = 3*7*K n must have a 7 at least. K must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60. So K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 60*7 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 60*2 or 60*3*2 or 60*5 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has. Answer (C) #### C QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 7 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them? options: A)22 km B)40 km C)65 km D)18 km E)16 km SOLUTION:Distance = Relative Speed * Time = (7 + 3) * 4 = 40 km [ They are travelling in the opposite direction, relative speed = sum of the speeds]. Answer: B #### B QUESTION:Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)50 B)88 C)77 D)66 E)55 SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 46 - 36 = 10 km/hr. = 10 * 5/18 = 25/9 m/sec. 2x/36 = 25/9 => x = 50. Answer: A #### A QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12 SOLUTION:6a/100 = 12 a = 200 12b/100 = 6 b = 50 c = b/a = 50 / 200 = 1/4 The answer is C. #### C QUESTION:A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480? options: A)170Rs B)108Rs C)100Rs D)160Rs E)103Rs SOLUTION:3x 4x 5x 6 9 4 18x + 36x + 20x = 1480 74x = 1480 => x = 20 5x =100Rs. Answer:C #### C QUESTION:The wages earned by Robin is 44% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin? options: A)23% B)18.75% C)30% D)30.55% E)100% SOLUTION:Explanatory Answer Let the wages earned by Erica be $100 Then, wages earned by Robin and Charles will be $144 and $160 respectively. Charles earns $44 more than Robin who earns $144. Therefore, Charles' wage is 44/144*100 = 30.55%. The correct choice is (D) #### D QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)15.125% D)27.78% E)none SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land. What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options. The correct answer is (D). #### D QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded? options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV SOLUTION:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Z Y X W V U T S R Q P O N M L K J I H G F E D C B A So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN. so this way CAMEL becomes OVNZX ANSWER:C #### C QUESTION:A no. when divided by 35leaves a remainder 20, what is the remainder if the same no.be divided by 15? options: A)2 B)4 C)7 D)8 E)9 SOLUTION:Explanation: 35 + 25 = 60/15 = 4 (Remainder) B #### B QUESTION:6x + 2y = -4 4x + y = 1 In the system of equations above, what is the value of x? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:6x + 2y = -4 can be written as 3x + y = -2 Let's subtract the second equation from this equation. -x = -3 x = 3 The answer is C. #### C QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8840 and in 3 years to Rs.9261? options: A)8054 B)8877 C)2877 D)2678 E)1011 SOLUTION:8840 ---- 421 100 ---- ? => 4.76% x *104.76/100 * 104.76/100 = 8840 x*1.0975=8840 x=8840/1.0975 => 8054.54 Answer: A #### A QUESTION:If x=kc and y=kt,then 2y+x =? options: A)k(t-c) B)k(c-t) C)c(k-t) D)k(2t+c) E)k(1-t) SOLUTION:Just put in the given values of y and x 2y +x =2 kt +kc Now take k common 2y + x = k(2t +c) You get (D) as your answer. #### D QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)720 D)32 E)120 SOLUTION:Has to be C. Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle hence (7-1)! = 6!= 720 #### C QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove? options: A)$240 B)$260 C)$280 D)$300 E)$320 SOLUTION:J+K=700 so K=700-J 2J=K+80 2J=(700-J)+80 3J=780 J=260 The answer is B. #### B QUESTION:A man sells two articles for Rs.3600 each and he gains 40% on the first and loses 40% on the next. Find his total gain or loss? options: A)16% loss B)400 C)4000 D)324 E)8% LOSS SOLUTION:(40*40)/100 = 16%loss ANSWER:A #### A QUESTION:Adding 30% of x to x is equivalent to multiplying x by which of the following? options: A)12.5 B)1.05 C)1.15 D)1.3 E)1.25 SOLUTION:130x/100= 1.3*x ANSWER:D #### D QUESTION:Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If they are 85 km apart both 3 and 6 hours after start, then find the distance between the two stations. options: A)255km B)210km C)220km D)180km E)200km SOLUTION:In first 3 hours T1 travels R km and T2 travels S km. After 6 hours they traveled R+S+85+ 85 2(R+S ) = R+S +170 R+S = 170 Hence distance between XY is R+S+ 85 = 170 +85 =255 Answer : A #### A QUESTION:What is the number of integers from 1 to 100 (inclusive) that are divisible by neither 5 nor by 6? options: A)35 B)47 C)58 D)26 E)34 SOLUTION:In 100 consecutive numbers, number of multiples of 5 = 100/5 = 20 (Ignore decimals) In 100 consecutive numbers, number of multiples of 6 = 100/6 = 16 Number of multiples of 5*6 i.e. 30 = 100/30 = 3 Number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - (29 + 16 - 3) {Using the concept of sets here) = 58 Answer is C #### C QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)5.14 SOLUTION:Time taken by First tank Fill 1/2 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank =12 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours Answer: option E #### E QUESTION:If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers? I. x II. x + y III. y/x options: A)I only B)II only C)III only D)I and II E)I ,II and III SOLUTION:Ans: from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D). #### D QUESTION:Given positive even integer y, which of the following CAN be evenly divisible by y? options: A)y + 1 B)2y - 2 C)2y + 1 D)3y - 1 E)y + 1⁄2 SOLUTION:This can be easily solved by substituting values: Assume y to be 2 A. y + 1: 3 is not evenly divisible by 2 B. 2y - 2: 2 is evenly divisible by 2 C. 2y + 1: 5 is not evenly divisible by 2 D. 3y − 1: 5 is not evenly divisible by 2 E. y + 1⁄2: 5/2 is not evenly divisible by 2 Option B #### B QUESTION:From given equation find the value of x: 2x² + 9x − 5 options: A)−5 B)-4 C)-3 D)3 E)4 SOLUTION:That quadratic is factored as follows: 2x² + 9x − 5 = (2x − 1)(x + 5). Lesson 17. Now, it is easy to see that the second factor will be 0 when x = −5. As for the value of x that will make 2x − 1 = 0, we must solve that little equation. (Lesson 9.) We have: 2x = 1 x = 1 2 The solutions are: x = 1/2 or −5 A #### A QUESTION:At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? options: A)5% B)3 1/2% C)4% D)5 1/2 % E)6% SOLUTION:150 = (750*5*R)/100 R = 4% Answer :C #### C QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/3*60/55 = 40 min D #### D QUESTION:Karthikeyan arranged a party to celebrate his birth day.20 of his close friends were invited. One friend left before the cake was cut due to an urgent phone call.The big cake was drawing the attention of the party visitors. This cake is to be divided among friends and of course Karthikeyan will get his share. A man eats 3 pieces, a woman eats two pieces and a child eats half a piece of cake. Including Karthikeyan count the number of men,women and children in the party. There are 20 pieces of cake in all. options: A)6 women, 2 men and 12 children B)7 women, 1 men and 12 children C)5 women, 1 men and 14 children D)4 women, 2 men and 14 children E)None of these SOLUTION:Let the number of men be m, number of women be w and number of children be c Total number of pieces = Pieces ate by men + Pieces ate by women + Pieces ate by children There are 20 total pieces. Also a man eats 3 pieces, a woman eats 2 and children half. Therefore above equation becomes. 20 = 3m + 2w + 1/2c In the above equation, you have to substitute the values given in options to find which one satisfies the equation. Option c with m = 1, c = 14 and w = 5 perfectly satisfies the equation as follows 20 = 3(1) + 2(5) + (1/2)(14) 20 = 20 i,e our equation is satisfied perfectly by option c ANSWER:C #### C QUESTION:A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos? options: A)2 films and 6 photos B)5 films and 6 photos C)5 films and 14 photos D)6 films and 4 photos E)6 films and 28 photos SOLUTION:1st photo = 0.50 Subsequent = 0.50*0.6=0.3 Price of 1 full film=0.50+0.3*35=11 Price of 2 full film = 11*2=22 24-22=2 2=0.5+0.3x x=5 24--->2 full films and 1+5=6 photos Answer: A #### A QUESTION:If x and y are integers, what is the least positive number of 24x+9y? options: A)1 B)3 C)4 D)6 E)9 SOLUTION:24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1. 8(-1) + 3(3) = 1 Then 3(8x+3y) can have a minimum positive value of 3. The answer is B. #### B QUESTION:In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13. If the shop carries 352 dogs and bunnies total in stock, how many dogs are there? options: A)42 B)66 C)98 D)112 E)154 SOLUTION:Let us assume the number of dogs, cats and bunnies to be 3x, 7x and 13x Total dogs and bunnies = 16x. And we are given that 16x = 352. Hence x = 22. Dogs = 3x = 3*22 = 66 (Option B) #### B <<<Examples ends QUESTION:A searchlight on top of the watchtower makes 4 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds? options: A)5/6 B)4/5 C)3/4 D)2/3 E)1/2 SOLUTION:The searchlight completes one revolution every 15 seconds. The probability that the man's area will be lit up is 5/15=1/3. The probability that he will stay in the dark is 1-1/3=2/3 The answer is D. #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is? options: A)38 B)27 C)75 D)28 E)21 SOLUTION:Explanation: The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75. Answer: C #### C QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? options: A)3 B)5 C)4 D)2 E)6 SOLUTION:A rate = 1/8 B rate = 1/24 (A+B) rate = (1/8)+(1/24) = 1/6 A & B finish the work in 6days correct option is E #### E QUESTION:If 2994 ÷ 14.5 = 171, then 29.94 ÷ 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.2 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ] = 171/10 = 17.1 Answer is A. #### A QUESTION:A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 5 hour to row to a place and come back, how far is the place? options: A)24km B)30km C)48km D)12km E)15km SOLUTION:Speed of down stream = 10+2 = 12kmph speed of upstream = 10-2 = 8kmph Let the required distance be xkm x/12 + x/8 = 5 2x+3x = 120 x = 24 km Answer is A #### A QUESTION:During a certain two-week period, 75 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 2/3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period? options: A)5 A B)10 A C)15 A D)18 A E)25 A SOLUTION:Movies: 75 % comedies. 25 % remaining genre. Now in this 25 %, there are only 2 categories. Action movies and Drama Movies. If Action = x; Drama movies = 2x/3. Total 5x/3. 5x/3 = 25; x = 15 Action movies: 15 % Drama movies: 10 % we can say that out of 100 z,: comedies: 75 z action: 15 z drama: 10 z Now action movies were A This means: A = 15 z. z = A/ 15 Comedies: 75 z = 75 * (A/15) 5 A A is the answer. #### A QUESTION:curie bakes 5 cookies for 5 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:curie made 5*5 cookies = 25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends. 9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same. The nearest multiple of 2 is 8. 9-8=1 A is the correct answer #### A QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)58 km/hr SOLUTION:Speed of the train relative to man = 125/10 m/sec = 25/2 m/sec. 2 = 25/2 x 18/5 km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 x = 50 km/hr. Option B #### B QUESTION:A candidate got 35% of the votes and lost to the rival by 1350 votes. How many votes were cast? options: A)4000 B)4500 C)5000 D)5500 E)6000 SOLUTION:35%-----------L 65%-----------W ------------------ 30% = 1350 10% = 450 100% of the votes = 4500 Answer: B #### B QUESTION:Which of the following can be expressed as a terminating decimal? options: A)1/25 + 1/35 B)1/225 + 1/1,250 C)1/11,000 + 1/13,000 D)1/75 + 1/35 E)1/125 + 1/8 SOLUTION:In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first. A. 1/25 + 1/35 = 12/175 = 12/25*1/7 1/7 does is not a terminating decimal. E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000 This is a terminating decimal and our answer. Correct Option: E #### E QUESTION:In a box, there are 4 green, 5 black and 7 red pencils. One pen is picked up randomly. What is the probability that it is neither black nor red? options: A)2/5 B)1/5 C)1/2 D)1/3 E)1/4 SOLUTION:Explanation : Neither black nor red means the pencils drawn is green. Total number of outcomes = (4+5+7) = 16. Number of Favourable outcomes = 4 = Number of green pencils. Hence, Probability of the event = 4/16 = 1/4. Answer : E #### E QUESTION:The greatest number of four digits which is divisible by 12, 20, 36 and 60 is: options: A)9000 B)9900 C)9500 D)9800 E)9700 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 12, 20, 36 and 60 is 180. On dividing 9999 by 180, the remainder is 99. Required number (9999 - 99) = 9900. Answer: Option B #### B QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer: B #### B QUESTION:On a certain day, Tim invested $600 at 10 percent annual interest, compounded annually, and Lana invested 800 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$44 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 600(1.10)^2 = 600(1.21) = 726 and Lana would have 800(1.05)^2 = 800(1.1025) = 882 Thus, Tim earned 126 dollars, while Lana earned 82 dollars The difference is $44 and the answer is C. #### C QUESTION:Rohit spent 30 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Rohit have left over? options: A)29% B)35% C)46% D)47% E)52% SOLUTION:SayRohit's earning last month was $100. Rohit spent 30 percent of his earning last month on rent --> $30 on rent; 20 percent less than what he spent on rent to purchase a new dishwasher --> $30*0.8=$24 on the dishwasher. Left over amount 100 - (30 + 24) = $46 Answer: C #### C QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 13 km/hr downstream and 10 km/hr upstream. options: A)3 kmph B)9 kmph C)4 kmph D)8 kmph E)6 kmph SOLUTION:Speed in still water = (13 + 5)1/2 kmph = 9 kmph. answer :B #### B QUESTION:If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor S of 2x and 3y? options: A)1 B)S=Cannot be determined C)S=2 D)5 E)6 SOLUTION:My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2. and hence answer B #### B QUESTION:A scuba diver descends at a rate of 30 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 2400feet below the sea level..how long will he take to reach the ship? options: A)70 minutes B)72 minutes C)80 minutes D)76 minutes E)77 minutes SOLUTION:Time taken to reach = 2400/30= 80 minutes ANSWER:C #### C QUESTION:If n is an integer greater than 8, which of the following must be divisible by 3? options: A)1. n (n+1) (n-4) B)2. n (n+2) (n-1) C)3. n (n+3) (n-5) D)4. n (n+4) (n-2) E)5. n (n+5) (n-6) SOLUTION:We need to find out the number which is divisible by three, In every 3 consecutive integers, there must contain 1 multiple of 3. So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three 1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1) 2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1) 3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n) 4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1) 5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2) from the above onlyoption Ais product of consecutive three numbers. C #### C QUESTION:A company has 2 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director? options: A)500 B)720 C)4500 D)20 E)55 SOLUTION:atleast one means exactly one and more than one. different committees with 5 people can be chosen having at least 1 director is (2c1*5c4) + (2c2*5c3) = 20; Hence D. #### D QUESTION:Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam? options: A) 1/4 B) 12/47 C) 1/3 D) 5/12 E) 20/47 SOLUTION:Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs. adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work R>( 60/47 *12)/60 =12/47 Answer B #### B QUESTION:A tank is filled in 10 hours by three pipes A, B and C. Pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? options: A)70 hours B)30 hours C)35 hours D)50 hours E)40 hours SOLUTION:Efficiency of pipes A,B,C =1:2:4 Therefore, in 10 hours, part of the tank filled by A =17 Therefore, pipe A alone requires 10×7=70 hours to fill the tank. Answer: Option A #### A QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6? options: A)300 B)992 C)772 D)552 E)280 SOLUTION:1/3:1/3:1/6 = 2:2:1 1/5*1400 = 280 560-280 = 280 Answer: E #### E QUESTION:A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$333.33 C)$100.25 D)$277.78 E)$377.00 SOLUTION:Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 ) $25000 is 60% of total amount. So total amount = 25000 * 100/60 Remaining amount is 40% of total amount. 40% of total amount = 25000 * (100/60) * (40/100) = 50000/3 This amount has to be divided by 50( remaining people are 50 ) So per head amount is 50000/3 / 50 = 32000/180 = 333.33; ANSWER:B #### B QUESTION:Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is the probability that none of the objects occupy the place corresponding to its number? options: A)17/24 B)3/8 C)1/2 D)5/8 E)5/3 SOLUTION:Explanation : Let a particular number (say) number 2 occupies position 1. Then all possible arrangement are given as: =>(2,1,3,4), (2,1,4,3), (2,3,4,1), (2,4,1,4), (2,4,1,3), (2,4,3,1). Out of these six, three (2,1,3,4), (2,3,1,4), (2,4,3,1) are not acceptable because numbers 3 and 4 occupy the correct positions. Hence, the required probability = 3/6 = 1/2. Answer : C #### C QUESTION:Sandy had $231 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? options: A)$270 B)$290 C)$310 D)$330 E)$350 SOLUTION:Let the money Sandy took for shopping be x. 0.7x = 231 x = 330 The answer is D. #### D QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:Mr. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck options: A)$145 B)$250 C)$300 D)$175 E)$150 SOLUTION:Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A) #### A QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 10 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)80 C)100 D)125 E)21 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 4.4 , so radius is 2.2 New area = 4.84π Increase in area is 0.84π % increase in area = 0.84/4*100 So, % increase is 21% Answer will be (E) #### E QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss? options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents SOLUTION:50 % profit on $ 1 = $ 50/100 × 1 = $ 0.50× 1 = $ 0.50 Similarly, 40 % loss on $ 1 = $ 40/100 × 1 = $ 0.40× 1 = $ 0.40 Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40 So profit by amount $0.40. Answer is E. #### E QUESTION:If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due? options: A)8 months B)11 months C)10 months D)9 months E)12 months SOLUTION:Explanation : F = Rs. 498 TD = Rs. 18 PW = F - TD = 498 - 18 = Rs. 480 R = 5% TD = (PW × TR)/100 ⇒ 18 = (480 × T × 5)/100 ⇒ 18 = 24 × T ⇒ T = 18/24 = 3/4 years = (12×3)/4 months = 9 months Answer : Option D #### D QUESTION:In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ? options: A)13/40 B)13/80 C)2/13 D)Data inadequate E)None SOLUTION:Answer Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp. ∴ 2/13 of total number of students took part in the camp. Correct Option: C #### C QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)18 B)20 C)24 D)30 E)40 SOLUTION:Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30 Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20 Answer:B #### B QUESTION:If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 200 units? options: A)50 hours B)40 hours C)25 hours D)12 hours E)8 hours SOLUTION:Here, we're told that 5 machines can produce 20 units in 10 hours.... That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units. 20 units/5 machines = 4 units are made by each machine every 10 hours Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to... 10 hours/4 units = 2.5 hours per unit when 1 machine is working. The prompt asks us how long would it take 20 machines to produce 200 units. If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 200 units is '10 times' 20, we need '10 times' more TIME. (2.5 hours)(10 times) = 25 hours Final Answer: [Reveal]Spoiler: C #### C QUESTION:In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students? options: A)80% B)20% C)40% D)50% E)None of these SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84 Number of students failed = 140 - 84 = 56. Required percentage = 28/56 * 100 = 50%. ANSWER:D #### D QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/800*1/600=1/4,800. Answer: B. #### B QUESTION:1+ 1+ 1+ 2 × 1^2 + 2 × 1^1+ 2 × 1^4 + 2 × 1^5 + 2 × 1^6 + 2 × 1^7 = options: A) 1^7 B) 1^8 C) 1^14 D) 1^28 E) 3^30 SOLUTION:We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*1^7 we would have: sum=9*(2*1^7)=2*1^9=~1^10, so the actual sum is less than 1^10 and more than 1^7 (option A) as the last term is already more than that. So the answer is clearly B. Answer: B. #### B QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3? options: A)9 B)10 C)11 D)12 E)14 SOLUTION:A number will be divisible by 3 if sum of all the digits of the number is divisible by 3 Here the Possible sum of the two distinct digits can be 3, 6, 9 and 12 only in order to satisfy the given condition If sum of Digits = 3, No. = 12, 21 --- 2 Cases If sum of Digits = 6, No. = 15, 24, 42, 51 --- 4 Cases If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases If sum of Digits = 12, No. = 57, 75 --- 2 Cases Total Cases = 2+4+6+2 = 14 cases Answer: option E #### E QUESTION:In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia? options: A)c/e B)e/c C)e/(c-e) D)c/(c-e) E)1- (e/c) SOLUTION:We're given a couple of facts to work with: 1) There were a total of c earthquakes 2) Of those earthquakes, e of them occurred in Asia We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia. Let's TEST VALUES c = 5 total earthquakes e = 2 occurred in Asia Thus, there were 3 earthquakes that DID NOT occur in Asia.... The answer to the question is 2:3 We just need to plug in the values for c and e and find the match... Answer A: c/e = 5/2 NOT a match Answer B: e/c = 2/5 NOT a match Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match C #### C QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] Q=z-x = x+9-x= 9 Ans:D #### D QUESTION:If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5 of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students. options: A)200 B)210 C)220 D)230 E)240 SOLUTION:210 ANSWER:B #### B QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)Rs.81.60 B)Rs.160 C)Rs.172 D)Rs.727 E)Rs.728 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer:A #### A QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is options: A)11 B)15 C)6 D)8 E)76 SOLUTION:Explanation: Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A) 11 #### A QUESTION:A football field is 9600 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards? options: A)450 B)600 C)700 D)2400 E)3200 SOLUTION:Answer C) 9600 yards need 1200 lbs 1 Yard will need 1200/9600 = 1/8 lbs 3600 Yards will need 1/8* 5600 Yards = 700lbs #### C QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:8 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)66 B)52 C)58 D)55 E)56 SOLUTION:Though 2*(8C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used. The first guy has to play 2 matches with the rest of 7, so he'll play 14 matches. Similarly, second guy has to play with the rest of 6 as his 2 games with the first guy are already played. So he plays 12 matches. This continues like this and the total matches are 14+12+10...+2 14+12+...+2 = 2(7+6+...+1) = 2((7*8)/2) = 7*8 =56. ANSWER:E #### E QUESTION:There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is: options: A)9 B)13 C)15 D)12 E)19 SOLUTION:Explanation: abc/bcd=385/1001=>a/d=5/13 So d = 13 Option B #### B QUESTION:If “*” is called “+”, “/” is called “*”, “-” is called “/”, “+” is called “-”. 240*80 / 60 + 40 / 10 = ? options: A)-2305 B)-2407 C)2509 D)-2101 E)None of these SOLUTION:Explanation: Given : 240*80 / 60 + 40 / 10 = ? Substituting the coded symbols for mathematical operations, we get, 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = -2407 ANSWER : B #### B QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)140 C)200 D)150 E)250 SOLUTION:624/6 = 104 kmph ANSWER A #### A QUESTION:10, 20, 12, 24, 16, 32, ? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:E 24 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7? options: A)397 B)401 C)403 D)405 E)364 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=364. Answer: E. #### E QUESTION:The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class? options: A)1:2 B)3:4 C)3:5 D)2:3 E)None of these SOLUTION:let x = number of girls y = number of boys sum of girls ages / x = 15.4 sum of boys ages / y = 16.4 The sum of the girls' ages is 15.4x, and boys' sum is 16.4y (sum of girls ages + sum of boys ages) / (x+y)= 15.8 (15.4x + 16.4y) / (x+y) = 15.8 15.4x + 16.4y = 15.8(x+y) 15.4x + 16.4y = 15.8x + 15.8y 0.6y = 0.4x 0.6y/x = 0.4 y/x = 0.4/0.6 y/x = 2/3 which is the ratio of boys to girls ANSWER:D #### D QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 40*9/40 = 9 seconds. Answer: C #### C QUESTION:If x is an integer, then x(x – 1)(x – k) must be evenly divisible by six when k is any of the following values EXCEPT options: A)-4 B)-2 C)-1 D)2 E)5 SOLUTION:We have the product of 3 integers: (x-1)x(x-k). Note that the product of 3 integers is divisible by 6 if at least one multiple is divisible by 6. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 6 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 6. Next, if k=2 then we'll have (x-1)x(x-2)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 6. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 6. Answer: D. #### D QUESTION:AB +BA ___ 101 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)10 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. only 10 fits in.. C #### C QUESTION:In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ? options: A)27 B)26 C)25 D)24 E)20 SOLUTION:Explanation: n(A)=(60/100∗96)=288/5 n(B)=(30/100∗96)=144/5 n(A∩B)=(15100∗96)=72/5 People who have either or both lunch n(A∪B)=288/5+144/5−72/5 =360/5=72 So People who do no have either lunch were = 96 -72 = 24 ANSWER IS D #### D QUESTION:Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.870? options: A)Rs.700 B)Rs.780 C)Rs.750 D)Rs.1000 E)None of these SOLUTION:Explanation: 870 = P [1 + (5*16/5)/100] P= 750 Answer: Option C #### C QUESTION:At what rate p.a a sum of Rs. 2400 will become Rs. 3600/- in 5 years. options: A)10% B)15% C)20% D)12% E)23% SOLUTION:Explanation: principal P = 2400/- Rate of interest R = ? Time T = 5 years Accumulated Amount A = Rs.10400/- A = P + I A = P + PTR/100 A = P(1+ TR/100) 2400[ 1 + (5 x R)/100] = 3600 2[(20 + R)/20] = 3 20 + R = 30 R = 10% Answer: Option A #### A QUESTION:(+15) + (-11) - (+5) - (-7) options: A)8 B)2 C)6 D)5 E)3 SOLUTION:= 15-11-57 22-16, [adding all integers with plus (+) sign together and with minus (-) sign respectively together = +6 or simply 6. correct answer (C) #### C QUESTION:From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn options: A)4/13 B)1/52 C)1/4 D)1/5 E)None of above SOLUTION:Explanation: Total number of cases = 52 Total face cards = 16 [favourable cases] So probability = 16/52 = 4/13 Answer: A #### A QUESTION:A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road? options: A)576 metres B)589 metres C)600 metres D)700 metres E)None SOLUTION:Solution Let the length of the outer edges be x metres. Then, length of the inner edge = ( x - 6)m. ∴ x2 - (x-6)2 = 1764 ‹=› x2-(x2-12x+36)= 1764 ‹=›12x = 1800 ‹=›x = 150. ∴ Required perimeter = (4x)m ‹=› (4 x 150)m = 600m. Answer C #### C QUESTION:As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found? options: A)14 B)18 C)15 D)10 E)20 SOLUTION:E 20 If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14. #### A QUESTION:A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 60% above the original cost per share of stock, then interns of m for how many dollars was each share sold? options: A)a) 2m/300 B)b) m/300 C)c) 5m/900 D)d) m/300 + 50 E)e) 350/m SOLUTION:Let Cost of 300 shares be $ 3000 So, Cost of 1 shares be $ 10 =>m/300 Selling price per share = (100+60)/100 * m/300 Or, Selling price per share = 5/3 * m/300 => 5m/900 Hence answer will be (C) #### C QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 13*0 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:A right circular cylinder has a height of 25 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? options: A)500(π – 3) B)500(π – 2.5) C)500(π – 2) D)500(π – 1) E)625(π – 1.5) SOLUTION:[quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? The square base has sides of sqrt(50) due to the 45-45-90 triangle 25*25*pi - 15*sqrt(50)^2 =625(π – 1.5) E. 500(π – 1.5) #### E QUESTION:A train covers a distance of 12 km in 10 min. If it takes 8 sec to pass a telegraph post, then the length of the train is? options: A)100 B)110 C)160 D)130 E)140 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 8 = 160 m. Answer: Option C #### C QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)6 months B)8 months C)10 months D)7 months E)12 months SOLUTION:Explanation: 7 * 8 : 9 * x = 8:9 => x= 7 ANSWER IS D #### D QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3). If 3y = –30, then y = options: A) –15 B) –6 C) -3 D) 6 E) 15 SOLUTION:(3+2)(y-3)=-30.. x-3=-6.. x=-3 C #### C QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60 total S=84 outcomes D #### D QUESTION:The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes. options: A)$0.94 B)$0.96 C)$0.99 D)$1.00 E)$1.20 SOLUTION:Assume the manager bought 100 tomatoes. Cost Price = 80 Given: 10% are damaged --> Available tomatoes to sell = 90 90 * x - 80 = 0.12 * 80 90x - 80 = 9.6 90x = 89.6 x = 89.6/90 = 0.995 x is slightly under 0.9955 = 0.99 Answer: C #### C QUESTION:A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting? options: A)200 B)250 C)350 D)800 E)830 SOLUTION:science books sold = 2x × 0.2 = 0.4x science books unsold = 2x – 0.4x = 1.6x art books sold = 5x × 0.2 = x art books unsold = 5x – x = 4x total books unsold = 1.6x + 4x = 5.6x 5.6x = 2240 x = 400 2x science = 800 D #### D QUESTION:Denise is trying to open a safe whose combination she does not know. IF the safe has 3000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one correct combination. options: A)1 B)159/160 C)157/160 D)0.875 E)0.975 SOLUTION:If Denise does not pick the correct combination in first 75 try, then the correct combination is one of remaining 2925. So Probability = 2925/3000 = 0.975. answer is E #### E QUESTION:What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for two years? options: A)29893 B)27773 C)29989 D)28800 E)23400 SOLUTION:Simple interest = (18000 * 2 * 15)/100 = Rs. 5400 Amount = P + I = 18000 + 5400 = Rs. 23400 Answer: E #### E QUESTION:A invested some money in 10% stock at 96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of : options: A)Rs.80 B)Rs.115.20 C)Rs.120 D)Rs.125.40 E)None of these SOLUTION:Explanation: For an income of Rs. 10, investment = Rs. 96. For an income of Rs. 12, investment = (96/10x12) =115.20 Answer: B #### B QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0. What is the difference between the two greatest possible values of x? Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. options: A)124 B)241 C)394 D)421 E)842 SOLUTION:Ratio of a:b:c= 2:4:1 Two possible greatest single digit values for b are 8 and 4 if b is 8, then x= 482 if b is 4, then x= 241 difference= 482-241= 241 B is the answer #### B QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? options: A)176 m B)198 m C)197 m D)150 m E)168 m SOLUTION:Let the length of the train be x meters and its speed be y m/sec. They, x / y = 15 => y = x/15 x + 100 / 25 = x / 15 x = 150 m. Answer:D #### D QUESTION:What is the minimum number of square marbles required to tile a floor of length 3 metres 39cm and width 2 metres 26 cm? options: A)176 B)187 C)540 D)748 E)6 SOLUTION:The marbles used to tile the floor are square marbles. Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble. As we have to use whole number of marbles, the side of the square should a factor of both 3 m 39 cm and 2m 26. And it should be the highest factor of 3 m 39 cm and 2m 26. 3 m 39 cm = 339 cm and 2 m 26 cm = 226 cm. The HCF of 339 and 226 = 113. Hence, the side of the square is 113. The number of such square marbles required, =339×226/113×113 =6 marbles Option(E) #### E QUESTION:In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time. options: A)10 hours B)12 hours C)14 hours D)16 hours E)None of these SOLUTION:Explanation : speed of the boat = 6 km/hr Speed downstream = (6+2) = 8 km/hr Speed upstream = (6-2) = 4 km/hr Distance travelled downstream = Distance travelled upstream = 32 km Total time taken = Time taken downstream + Time taken upstream = (32/8) + (32/4) = (32/8) + (64/8) = (96/8) = 12 hr. Answer : Option B #### B QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 * 58 = Rs. 2784. Answer:A #### A QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest? options: A)Rs. 560 B)Rs. 560.75 C)Rs. 551.25 D)Rs. 550 E)Rs. 560 SOLUTION:Explanation: Present worth of Rs. x due T years hence is given by Present Worth (PW) = x/(1+R/100)T Let x be the annual payment Then, present worth of x due 1 year hence + present worth of x due 2 year hence = 1025 x(1 + 5/100)1 + x(1 + 5/100)2 = 1025 x/(21/20) + x/(21/20)2 = 1025 20x/21 + 400x/441 = 1025 820x/441 = 1025 x = (1025 × 441)/820 = (205 × 441)/164 = Rs. 551.25 Answer: Option C #### C QUESTION:If n is a positive integer, which of the following is a possible value of |36 - 5n|? options: A)7 B)14 C)12 D)15 E)20 SOLUTION:When 36>5n, then |36- 5n| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1 When 36<=5n, then |36- 5n| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits. Answer: B #### B QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 130*4=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:What is the smallest integer k for which 64^k > 4^16? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:64^k > 4^16 4^(3k) > 4^16 3k > 16 k = 6 The answer is C. #### C QUESTION:how many prime no. are there from 0 to 50? options: A)14 B)15 C)16 D)17 E)19 SOLUTION:we calculate it manually.we know the definition of prime no.prime no. should only have two distinct​ natural no. divisor 1 and itself. note:1 is not a prime no. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 total no.=15 answer B #### B QUESTION:A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.5 per sq m? options: A)6500 B)2779 C)2779 D)3900 E)2781 SOLUTION:Area = (l + b – d) d (80 + 60 – 10)10 => 1300 m2 1300 * 5 = Rs.6500 Answer:A #### A QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? options: A)165 B)161 C)162 D)163 E)164 SOLUTION:To minimize one quantity maximize other. 164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165. Answer: A. #### A QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:The least number, which when divided by 12, 31, 20 and 54 leaves in each case a remainder of 8 is: options: A)448 B)488 C)16748 D)548 E)560 SOLUTION:Required number = (L.C.M. of 12, 31, 20, 54) + 8 = 16740+ 8 = 16748. answer :C #### C QUESTION:The product of two numbers is 220 and the sum of their squares is 289. The sum of the number is? options: A)A)23 B)B)25 C)C)27 D)D)31 E)E)35 SOLUTION:Let the numbers be x and y. Then, xy = 220 and x2 + y2 = 289. (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 220) = 729 x + y = 27. Option C #### C QUESTION:A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum? options: A)7000 B)7029 C)7290 D)7010 E)7102 SOLUTION:Let the sum be Rs. x. (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840 => 12x/100 = 840 => x = 7000. Answer:A #### A QUESTION:Three times the first of three consecutive odd integers is 5 more than twice the third. The third integer is: options: A)9 B)11 C)13 D)15 E)17 SOLUTION:Let the three integers be x, x + 2 and x+ 4. Then, 3x = 2(x + 4) + 5 x = 12 Third integer = x + 4 = 17. ANSWER:E #### E QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these SOLUTION:Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.150 15x + 5x = Rs.150 X = 150/20 = 7.50 :. Cost of 1 pen = 5x = 5 x 7.50 = 37.50 :. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450 Answer: Option D #### D QUESTION:From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 13 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ? options: A)38 B)39 C)40 D)41 E)42 SOLUTION:Soln:- 13x=45 --> 87/77*x=45 --> x=45*77/87=677/17=~40. Answer: C. #### C QUESTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 4y) is odd II. xy^2 is an even negative integer III. (y^2 - x) is an odd negative integer options: A)(3X-4Y) IS ODD TRUE B)II only C)I and II D)I and III E)II and III SOLUTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 4y) is odd 3x - is always negative and odd 2y - can be 0, when y=0, or always even integer (positivie or negative) odd integer +/- even integer = always odd I statement is always true II. xy^2 is an even negative integer y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true III. (y^2 - x) is an odd negative integer y can be 0 => -x will be positive => III statement is not true basing on above, only I statement will always be true answer is A #### A QUESTION:If x and y are integers and x + y = 7, which of the following must be true? options: A)x and y are consecutive integers. B)Both x and y are less than 5. C)If x > 0, then y < 0. D)Both x and y are even. E)If x < 0, then y > 0. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option E is right could you explain #### E QUESTION:A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)18 seconds C)40 seconds D)19 seconds E)44 seconds SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 410+140 = 550 meter Time = Distance/speed = 550 * (2/25) = 44 seconds Answer: E #### E QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in? options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days SOLUTION:B = 1/4 – 1/20 =0.2 days ANSWER:E #### E QUESTION:A, B and C enter into a partnership. They invest Rs. 70,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years? options: A)21 : 32 : 4 B)21 : 26 : 4 C)21: 12 : 1 D)21: 16 : 28 E)none SOLUTION:Sol. A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) =252 : 192 : 336 = 21: 16 : 28 Answer D #### D QUESTION:A circle graph shows how the budget of a certain company was spent: 60 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation? options: A)18° B)36° C)54° D)72° E)90° SOLUTION:The percent of the budget for transportation is 100 - (60+9+5+4+2)= 20% 100% of the circle is 360 degrees. Then (20%/100%)*360 = 72 degrees The answer is D. #### D QUESTION:A man invests Rs. 4,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? options: A)Rs. 1200 B)Rs. 1300 C)Rs. 1500 D)Rs. 2000 E)None of these SOLUTION:Explanation : Interest on Rs.4000 at 5% per annum = ( 4000 × 5 × 1) / 100 = Rs. 200 Let his additional investment at 8% = x Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25. To earn 6% per annum for the total, interest = (4000 + x) × 6 × 1/100. => 200 + 2x/25 = (4000 + x) × 6 × 1/100. => 20000 + 8x = (4000 + x) × 6. => 20000 + 8x = 24000 + 6x. => 2x=4000. => x=2000. Answer : D #### D QUESTION:A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ? options: A)115 B)117 C)116 D)114 E)112 SOLUTION:Explanation: Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117. Answer IS B #### B QUESTION:How many numbers from 10 to 1000 are exactly divisible by 9? options: A)100 B)10 C)11 D)12 E)14 SOLUTION:10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100 Answer : A #### A QUESTION:A certain number X when divided by 253 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81? options: A)17 B)27 C)27 D)47 E)57 SOLUTION:Least possible value of the number is 253 + 98 = 351 Further it is given the number must be divisible by 81 . 351/81 = Gives remainder as 27 So, 27 must be subtracted from the number , answer is (C) #### C QUESTION:Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive? options: A)20% B)17% C)4.0% D)3.3% E)2.8% SOLUTION:20/6 =3.33 Answer : D #### D QUESTION:There are 14 songs in that 5 Rock songs, 6 western songs & 3 Hindi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song & 1 western song? options: A)15624 B)16478 C)17953 D)19655 E)28958 SOLUTION:15624 A #### A QUESTION:There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division? options: A)22 B)35 C)37 D)20 E)75 SOLUTION:D 20 29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30 = 20. #### D QUESTION:8, 24, 12, 36, 18, 54, (....) options: A)72 B)68 C)108 D)27 E)86 SOLUTION:8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 Answer is D. #### D QUESTION:The length of a rectangle is reduced by 10%. By what % would the width have to be increased to maintain the original area? options: A)10% B)11.1% C)25% D)30% E)35% SOLUTION:Sol. Required change = (10*100)/(100-10)=11.1% B #### B QUESTION:If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? options: A)100 B)10 C)0.01 D)0.0001 E)0.0001 SOLUTION:Given that 100 microns = 1 decimeter =10,000 angstroms So, 1 micron = 10,000/100 =100 Answer : A #### A QUESTION:A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? options: A)8 B)12 C)15 D)21 E)27 SOLUTION:As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain: A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15 B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12 A+B=15+12=27 Answer: E. #### E QUESTION:On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have four times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences? options: A)6 B)7 C)8 D)10 E)12 SOLUTION:If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does: (w + 4) = 4(p - 4) If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded: p + 5 = w - 5 Solving gives p = 10 and w = 20. Answer: D. #### D QUESTION:For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 1*3*5*7*9*...*99 g(97) = 1*3*5*7*9*...*97 g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98 hence:A. #### A QUESTION:A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 8000. options: A)Rs. 2500 B)Rs. 8500 C)Rs. 7200 D)Rs. 8000 E)None of these SOLUTION:Explanation: A = 2B and B = 5C => A : B = 2 :1and B : C = 5 : 1 => A : B : C = 10 : 5 : 1 Ratio of capitals of A, B and C = 10 : 5 : 1 B's share = Rs.[(5/16) × 8000] = Rs. 2500 Answer: Option A #### A QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? options: A)6 hrs 21 min B)6 hrs 91 min C)6 hrs 01 min D)6 hrs 23 min E)3 hrs 21 min SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs. Number of stoppages = 600/75 - 1 = 7 Total time of stoppages = 3 * 7 = 21 min Hence, total time taken = 6 hrs 21 min. Answer:A #### A QUESTION:A man can do a piece of work in 6 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? options: A)7 days B)6 days C)5 days D)4 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/3−1/6)=(6−3)/18=1/6 So son will do whole work in 6 days Answer: B #### B QUESTION:If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true? I. c is even II. ab is even III. ab > 0 options: A)I only B)II only C)I and II D)I and III E)I, II, and III SOLUTION:Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above. II only.letter B #### B QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:Employee A work from 01:00 to 08:45 (24 hour clock) on each of the five days this week. Next week, he is scheduled to work the same total hours, but will work a compressed 4 day work schedule. If he starts work at 01:00 next week, what time will he finish each day? options: A)09:04 B)10:41 C)10:45 D)11:56 E)16:19 SOLUTION:working hours between 01:00 - 08:45 for 5 days are 7:45*5 (5 days) = 38:45 same total hours are to be scheduled for 4 days, so 38:45/4 = 10:41 ANSWER:B #### B QUESTION:John throws a coin until a series of six consecutive heads or three consecutive tails appears. What is the probability that the game will end after the seventh throw? options: A)1/64 B)2/16 C)3/16 D)7/16 E)9/16 SOLUTION:Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are H-T-T-T-T-T ----> P = (1/2)^7= 1/128 T-H-H-H-H-H ----> P = (1/2)^7= 1/128 Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability. 1/128 + 1/128 = 2/128 = 1/64 Answer(A). #### A QUESTION:Remainder of (6^17+17^6)/7= ? options: A)2 B)1 C)0 D)3 E)4 SOLUTION:6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7 17^6/7 = (2*7+3)^6/7 = 3^6/7 = 27^2/7 =(4*7-1)^2/7 =(-1)^2/7 = 1/7 so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0 ANSWER:C #### C QUESTION:In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together? options: A)120 B)360 C)1440 D)13440 E)4320 SOLUTION:The word 'SOFTWARE' contains 8 different letters. when the vowels OAE are always together, they can be supposed to form one letter. Thus, we have to arrange the letters SFTWR (OAE) Now, 5 letters can be arranged in 6!=720 ways. The vowels (OAE) can be arranged among themselves in 3!=6 ways. Required number of ways =(720*6)=4320. Answer is E #### E <<<Examples ends QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT options: A)38 B)41 C)30 D)31 E)29 SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results? options: A)30 B)25 C)48 D)50 E)None SOLUTION:Answer Sum of 85 result = sum of 20 result + sum of 65 result. = 20 x 65 + 65 x 20 = 2600 Correct Option: A #### A QUESTION:A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 80 km downstream? options: A)2 hours B)3 hours C)4 hours D)5 hours E)None SOLUTION:Solution Speed Downstream = (13 + 4) km/hr = 17 km/hr. Time taken to travel 80 km downstream =(80 / 17)hrs = 4 hrs 42 minutes. Answer E #### E QUESTION:Calculate the largest 3 digit number which is exactly divisible by 89? options: A)911 B)969 C)979 D)977 E)971 SOLUTION:Largest 4 digit number is 999 After doing 999 ÷ 89 we get remainder 20 Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 C #### C QUESTION:Anitha had 80 currency notes in all, some of which are of Rs 95 denomination and the remaining of Rs 45 denomination. The total amount of all these currency notes was Rs. 4000. How much amount (in Rs) did she have in the denomination of Rs 45? options: A)3500 B)72 C)2000 D)3000 E)4000 SOLUTION:Let the number of 45-rupee notes = x Then, the number of 95-rupee notes = (80 – x) 45x + 95(80 – x) = 4000 or x + 2(80 – x) = 95 or x = 72. ANSWER:B #### B QUESTION:Zoey won the lottery and got $7,348,340. she wants to split it among herself and 5 friends evenly. how much money must she add if she wants to split it evenly? options: A)$3 B)$2 C)$9 D)$1 E)$4 SOLUTION:Zoey and her 5 friends is 6 people in all. $7,348,340 must be divisible by 6 if she wants to split it evenly. The money is divisible by 6 if it's divisible by 2 and 3. 7+3+4+8+3+4+0=29. 2 and 3 cant go into 29. Adding 1 dollar makes it 30. 2 and 3 can go into 30 so 6 can also. The answer is D. #### D QUESTION:If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ? options: A)11. B)13. C)17. D)10. E)7. SOLUTION:If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd) If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option which implies y is odd, Now M(odd)+Y(odd)=Even 10 is the only option that is even=D #### D QUESTION:x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median W of x, y, and z? I. 9 II. 10 III. 11 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:Average gives us an idea that 3 nos. are close to 10. so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations. Let us see options. If 9 has to be median W. 1st term has to less than 9 or equal to 9. (also maintain z-x = 3) 9 9 12 --> satisfies all conditions so 9 can be a median value. If 11 has to be a median 3rd term has to be 11 or more than 11. (also maintain z-x = 3) 8 11 11 -->satisfies all conditions so 9 can be a median value. Now for 10 to be median. z+ x = 20 and z-x = 3, we wont have integer values of z. 10 cannot be a median E is the answer. #### E QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers? options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89 SOLUTION:(5x-25):(7x-25) = 35:59 x = 12 => 60,84 Answer:D #### D QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 – 4xy (x- y)2 = 625 – 576 => (x – y) = 7 ANSWER: A #### A QUESTION:A and B can do a piece of work in 11 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? options: A)15.5 days B)19.5 days C)17.5 days D)9.2 days E)18.5 days SOLUTION:C = 1/5 – 1/11 = 6/55 => 9.2 days ANSWER:D #### D QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 24 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)4 D)6 E)8 SOLUTION:C 24 As stated 4=24 => 24=4 Answer is C #### C QUESTION:Find the value of x. (47% of 1442 - 36% of 1412) + 66 = x? options: A)1 B)2 C)3 D)6 E)5 SOLUTION:D) 6 #### D QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number? options: A)40 B)50 C)65 D)70 E)90 SOLUTION:Let the original # be x then 1.25x−0.7x=22 --> x=40 Answer: A. #### A QUESTION:If x = 4 and y = −2, what is the value of (x − 2y)^y? options: A)−100 B)0.015 C)0.25 D)4 E)8 SOLUTION:Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE by inversing and squaring 0.015 Answer: B #### B QUESTION:√7 percent of 7√7 = options: A)0.55 B)0.96 C)0.1 D)0.45 E)0.6 SOLUTION:The other solutions are great, but here's one more approach. First, we scan the answer choices to see that they are quite spread apart. This means we can also use someAPPROXIMATION All test-takers must memorize the following approximations: √2 ≈ 1.4 √3 ≈ 1.7 √5 ≈ 2.2 √6 ≈ 2.4 √7 ≈ 2.6 So, √7 percent of 7√7 ≈ 2.6 percent of (7)(2.6) ≈ (2.6/100)(18.2) ≈ 47.32/100 ≈ 0.47 Check the answer choices to see that D is the only answer that's close. Answer: D #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent? options: A)28% B)25% C)55% D)17.6% E)55% SOLUTION:850 --- 150 100 --- ? => 17.6% Answer: D #### D QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:If p is the product of the integers from 1 to 38, inclusive, what is the greatest integer k for which 3^k is a factor of p? options: A)13 B)15 C)17 D)19 E)21 SOLUTION:38! has 3, 6, 9,....30, 33, 36 as factors, which are 12 multiples of 3. We need to add 5 more to these 12 because of 9, 18, 27, and 36. The greatest integer of k is 17. The answer is C. #### C QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 215 m long? options: A)40 B)46 C)88 D)77 E)21 SOLUTION:: Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 215 = 575 m Required time = 575 * 2/25 = 46 sec Answer:B #### B QUESTION:The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there? options: A)62 B)66 C)70 D)74 E)78 SOLUTION:There are 12 integers from -5 to 6 inclusive. 12C2 = 66. The answer is B. #### B QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)Rs.18000 B)Rs.15000 C)Rs.17000 D)Rs.14000 E)NONE SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 ANSWER:D #### D QUESTION:It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish? options: A)20 B)22 C)24 D)26 E)28 SOLUTION:The bacteria doubles each day, so after 29 days, the dish was half full. After 28 days, the dish was one quarter full. After 27 days, the dish was one eighth full. After 26 days, the dish was one sixteenth full. After 25 days, the dish was 1/32 full. After 24 days, the dish was 1/64 full. The answer is C. #### C QUESTION:Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number? options: A)6 B)9 C)11 D)12 E)15 SOLUTION:Explanation: 3x/5 – x/5 = 6 => x =15 1 + 5 = 6 A) #### A QUESTION:Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving. options: A)180% B)124% C)160% D)154% E)140% SOLUTION:Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24% correct answer - B #### B QUESTION:Rahul take a loan of sum Rs.550.This is to be repaid in two equal annual installments. If the rate of interest be 20% compounded annually,then find the value of each installment? options: A)360 B)420 C)230 D)540 E)610 SOLUTION:Let the value of each installment be Rs.x [x/(1+(20/100))]+[x/(1+(20/100))2]=550 (100x/120)+(10000x/14400)=550 (5x/6)+(25x/36)=550 x=360 Option A #### A QUESTION:Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together? options: A)6 B)7 C)7.5 D)8 E)9 SOLUTION:Each day, Molly can do 1/15 of the task. Each day, Sandy can do 1/10 of the task. Each day, they can do 1/15 + 1/10 = 1/6 of the task. The task will be completed in 6 days. The answer is A. #### A QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence. options: A)19 B)20 C)21 D)22 E)23 SOLUTION:in case of cycle no of handshakes = no of persons hence ans = 20 ANSWER:B #### B QUESTION:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $20 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year? options: A) $752 B) $755 C) $765 D) $773 E) $775 SOLUTION:= (750*6+ 770 *20)/26 = 765 Answer is C. Posted from my mobile device #### C QUESTION:Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky's salary more than Ashu's? options: A)96% B)51.1% C)90% D)52.1% E)None of these SOLUTION:Solution: Let Ashu's salary = 100; Ashu's salary after rise = 125. Then Vicky's salary = 175. Vicky's salary after rise of 40% = 245. [As 10% of Vicky's salary is 17.5 then 40% = 17.5*4 = 70] . Difference between Vicky's salary and Ashu's salary = 245-125 = 120; . % more Vicky's salary than Ashu's = 120*100/125 = 96%. Answer: Option A #### A QUESTION:Given two fair dice, what is the probability E that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. E=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:A man buys Rs. 60 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is: options: A)s. 12 B)s. 15 C)s. 18 D)s. 21 E)s. 45 SOLUTION:Dividend on Rs. 60 = Rs. 9/100 x 60 =Rs. 5.4 . Rs. 12 is an income on Rs. 100. Rs. 5.4 is an income on Rs.100/12 x 5.4 = Rs. 45. Answer: Option E #### E QUESTION:What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21? options: A)2327 B)2757 C)3147 D)3587 E)3997 SOLUTION:When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150 The answer is C. #### C QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible? options: A)30 B)42 C)120 D)360 E)720 SOLUTION:5 people ,7 seats, only 2 can drive if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways since any one can drive total ways = 24 *2= 48 ways 4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways 48*15=720 ANSWER:E #### E QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8 SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 5(5/11) min. ANSWER:D #### D QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:If 8 men or 12 women can do a piece of work in 40 days, in how many days can the same work be done by 6 men and 11 women? options: A)10 days B)11 days C)13 days D)15 days E)24 days SOLUTION:8men = 12women (i.e 2men = 3women) 12women 1 day work= 1/40 soln: 6men(9women)+ 11women=20women=? 1 women 1 day work =12*40= 1/480 so, 20 women work= 20/480=1/24 ans: 24 days ANSWER:E #### E QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is: options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62 SOLUTION:(3x-9):(5x-9) = 3:2 x = 1 => 3x = 3 Answer:A #### A QUESTION:Two men are going along a track rail in the opposite direction. One goods train crossed the first person in 20 sec. After 10 min the train crossed the other person who is coming in opposite direction in 18 sec .After the train has passed, when the two persons will meet? options: A)95 minutes B)90 minutes C)88 minutes D)95 minutes E)None of these SOLUTION:Explanation : Let us consider that speed of train , first man and second man are respectively t, f and s. According to first given condition goods train crossed the first person moving in same direction in 20 sec. So length of the will be 20(t-f) Similarly train crossed the second man in 18 sec. So length of the train will be 18(t+s) on comparing these two equations, we get 20(t-f) = 18(t+s) => 2t = 20f + 18s => t = 10f + 9s Now it is given that After 10 min the train crossed the other person who is coming in opposite direction. So,If we consider this way of train as L then the next equation will be L = 600t (here 600 is used for 10 minutes) Finally as asked in the question the time required to meet the two man after the train has passed will be given by Time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes} => = (600t-600f) / (f+s) => = [600(10f+9s)-600f] / (f+s) => = 600(10f+9s-f) / (f+s) = 600 * 9(f+s) / (f+s) => =600*9 seconds => = 600*9/60min => = 90 minutes Hence (B) is the correct answer. Answer : B #### B QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)15 kmph B)10 kmph C)12 kmph D)12.5 kmph E)None of these SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. ANSWER:D #### D QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? options: A)4 B)5 C)6 D)9 E)7 SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even. 1) 2(6 times) 2) 2(3 times) + 3(2 times) 3) 2(2 times) + 3 + 5 4) 2 + 3 + 7 5) 2 + 5 + 5 6) 3(4 times) 7) 5 + 7 Answer: E #### E QUESTION:If B and C are digits and 8BC is a 3-digit number that is divisible by 5, which of the following is a possible product of B and C? options: A)1 B)2 C)5 D)7 E)14 SOLUTION:Try with the options - A. If BC = 1 , both B and C must be 1 B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3 C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3 D. If BC = 6 , then we can have the following possibilities i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3 ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3 E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 5 Thus answer is (D) #### D QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:What inequality represents the condition 1<x<13? options: A)|x|<3 B)|x+5|<4 C)|x-7|<6 D)|-5+x|<4 E)|3+x|<5 SOLUTION:1<x<13 represents segment with length: 13-1 = 12 center: (13+1)/2 = 7 For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer C) #### C QUESTION:If KING is coded as 17 and MASS is coded as 29 Then DON is coded as options: A)12 B)16 C)18 D)None E)cannot be determined SOLUTION:Explanation : KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17 MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29 DON = 4+14+15=33 i.e(3*3)+(3*3)=18 Hence (C) is correct Answer : C #### C QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)*(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)*(r+4)/(y+r+6) D)(y+3)/(y+r+7)*(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:In a stack of cards, 11 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 5/6 . What is the number of cards in the stack? options: A)10 B)11 C)12 D)15 E)18 SOLUTION:This question can be solved by TESTing THE ANSWERS. Answer C: 12 total cards With 12 total cards, and 11 blue cards, the probability of pulling two blue cards is... (11/12)(10/11) = 110/132 ~= 5/6 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: C #### C QUESTION:How many even multiples of 55 are there between 549 and 1101? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:550 = 10*55 1100 = 20*55 The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Given: positive integer n is a perfect square and a perfect cube --> n is of a form of n=x6 for some positive integer x --> 0<x^6<10^3 --> 0<x^2<10 --> x can be 1, 2 or 3 hence nn can be 1^6, 2^6 or 3^6. Answer: B. #### B QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:The area of square ABCD above is 18. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9/4∗π B)18−9/2∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =18- pi*18/4 =18- pi*9/2 ANSWER:B #### B QUESTION:A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen? options: A)Rs.6.40 B)Rs.10 C)Rs.9.6 D)Rs.10.2 E)None of the above SOLUTION:4 dozens of bananas cost is rs12 then 4*12=48 6 dozens of bananas cost is rs8 then 6*8=48 48+48/4+6=96/10=9.6 ANSWER:C #### C QUESTION:A rectangular box of volume x has width, depth and height in the ratio of 5:1:2 (in that order). What is the width as a function of x? options: A)(4x/12)^(1/2) B)(10x/4)^(1/2) C)(5x)^(1/2) D)(2x/5)^(1/2) E)(4x/3)^(1/2) SOLUTION:We are given width = 5, depth = 1, height = 2 Then Volume x = Width x Depth x Height = 5*1*2 = 10 i.e. x = 10 i.e. The correct option should result in 5 (the width) on substituting the value of x=10 Checking options with x=10 A) (4x/12)^(1/2) = (4*10/12)^(1/2) = (40/12)^(1/2) INCORRECT ANSWER B) (10x/4)^(1/2) = (10*10/4)^(1/2) = 25^(1/2) = 5 CORRECT ANSWER C) (5x)^(1/2) = (5*10)^(1/2) = 50^(1/2) INCORRECT ANSWER D) (2x/5)^(1/2) = (2*10/5)^(1/2) = 4^(1/2) = 2 INCORRECT ANSWER E) (4x/3)^(1/2) = (4*10/3)^(1/2) = 40/3^(1/2) INCORRECT ANSWER Answer: Option B #### B QUESTION:A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work? options: A)30 days B)20 days C)25 days D)35 days E)45 days SOLUTION:Work done by A in 10 days = 10/80 = 1/8 Remaining work = (1 - (1/8)) = 7/8 Now, work will be done by B in 42 days. Whole work will be done by B in (42 x 8/7) = 48 days Therefore, A’s one day’s work = 1/80 B’s one day’s work = 1/48 (A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30 Hence, both will finish the work in 30 days. ANSWER:A #### A QUESTION:Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in options: A)7.5 hr B)8 hr C)8.5 hr D)10 hr E)None of these SOLUTION:Solution: Work done by all the tanks working together in 1 hour. 1/10+1/12−1/20=2/15 Hence, tank will be filled in 15/2=7.5 hour Option(A) #### A QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:If p/q = 5/4 , then 2p+q= ? options: A)12 B)14 C)13 D)15 E)16 SOLUTION:let p=5, q=4 then 2*5+4=14 so 2p+q=14. ANSWER:B #### B QUESTION:Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed? options: A)1050 B)25200 C)32400 D)5800 E)6800 SOLUTION:Number of ways of selecting (4 consonants out of 6) and (2 vowels out of 3) = 6C4 * 3C2 = 6C2 * 3C1 = 6*5 *3 2*1 = 15*3= 45 Number of groups, each having 4 consonants and 2 vowels= 45. Each group consists of 6 letters. Number of ways of arranging 6 letters among themselves = 6! = (6*5*4*3*2*1)= 720 Therefore, Required number of words= 45*720= 32400 ANSWER:C #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A? options: A)1000 B)1500 C)2000 D)3000 E)4000 SOLUTION:Let monthly income of A = a monthly income of B = b monthly income of C = c a + b = 2 × 5050 .... (Equation 1) b + c = 2 × 6250 .... (Equation 2) a + c = 2 × 5200 .... (Equation 3) (Equation 1) + (Equation 3) - (Equation 2) => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250) => 2a = 2(5050 + 5200 - 6250) => a = 4000 i.e., Monthly income of A = 4000 Answer is E. #### E QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 878 in 4 years. The sum is: options: A)500 B)698 C)626 D)910 E)None SOLUTION:Sol. S.I. for 1 year = Rs. (878 - 815) = Rs. 63. S.I. for 3 years = Rs. (63 * 3) = Rs. 189. ∴ Principal = Rs. (815 - 189) = Rs. 626 Answer C #### C QUESTION:What is the minimum number of square marbles required to tile a floor of length 3 metres 39cm and width 2 metres 26 cm? options: A)176 B)187 C)540 D)748 E)6 SOLUTION:The marbles used to tile the floor are square marbles. Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble. As we have to use whole number of marbles, the side of the square should a factor of both 3 m 39 cm and 2m 26. And it should be the highest factor of 3 m 39 cm and 2m 26. 3 m 39 cm = 339 cm and 2 m 26 cm = 226 cm. The HCF of 339 and 226 = 113. Hence, the side of the square is 113. The number of such square marbles required, =339×226/113×113 =6 marbles Option(E) #### E QUESTION:A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k? options: A)3/4 B)1 C)4/3 D)2 E)7/2 SOLUTION:This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k. {{k + 4}/4} = k k + 4 = 4k 4 = 3k k = 4/3 Answer = C #### C QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:The equation of line q is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line q? options: A)48 B)50 C)60 D)75 E)100 SOLUTION:This can be solve in two steps and without any complex calculation. Given : equation of line q as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.5*100*75=0.5*125* x => x=60; SO answer is 60=C #### C QUESTION:Marge has C candies, where C is an integer such that 20 <C< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children? options: A) 0 B) 1 C) 2 D) 3 E) 4 SOLUTION:If Marge divides the candies equally among 5 children, she will have 2 candies remaining. This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47 If she divides the candies among 6 children, she will have 1 candy remaining. this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49 ONLY 37 is common, so candies are 37 in number.. if 37 is divided in 7 kids, remainder C= 2 C #### C QUESTION:A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is : options: A)16000 B)18000 C)20000 D)30000 E)None of these SOLUTION:Explanation: Number of bricks =Courtyard area /1 brick area =(1800×1200 /12×6)=30000 Option D #### D QUESTION:If n is the product of three consecutive integers, and n is divisible by 6, which of the following is not necessarily a divisor of n ? options: A)242 B)4 C)6.8 D)5 E)0. SOLUTION:IF ONE NO. IS 6 THEN OTHER CONSEQUTIVE NO. ARE 4*5*6 =120 , 5*6*7=210 , 6*7*8 =336 NO NUMBER WILL NO BE DIVISOR OF N E #### E QUESTION:A train 225 m long passes a man, running at 10km/hr in the same direction in which the train is going, in10 seconds. The speed of the train is: options: A)81 B)90 C)91 D)85 E)96 SOLUTION:Speed of the train relative to man =225/10 m/sec =45/2m/sec. =45/2x18/5km/hr = 81 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 10 = 81 =91km/hr. Answer:C #### C QUESTION:Which of the following must be true? 1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1 2) Every prime number greater than 5 can be written as 4n+1 or 4n-1 3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number. options: A)1,2,3 B)2,3 C)1,2 D)only 1 E)only 2 SOLUTION:Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible. 3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1. C #### C QUESTION:A train 120 m long running at 60 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)213 B)298 C)350 D)726 E)267 SOLUTION:D = 60 * 5/18 = 20 = 333 – 120 = 213 Answer: A #### A QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer is C. #### C QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5 SOLUTION:36 * 5/18 = 12.5 20:25 => 4:5 Answer: E #### E QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/3*60/55 = 40 min D #### D QUESTION:Select the non termination decimal among the following. options: A)5/3 B)3/4 C)4/5 D)7/8 E)9/10 SOLUTION:A. Non terminating decimal means that 5/3 = 1.66666 and so on. #### A QUESTION:The purchase price of an article is $48. In order to include 30% of cost for overhead and to provide $12 of net profit, the markup should be options: A)15% B)25% C)35% D)40% E)55% SOLUTION:Cost price of article = 48$ % of overhead cost = 30 Net profit = 12 $ We need to calculate % markup Net profit as % of cost price = (12/48)*100 = 25% Total markup should be = 25 + 30 = 55% Answer E #### E QUESTION:How many digits are in (8×10^10)(10×10^5)? options: A)17 B)25 C)26 D)27 E)28 SOLUTION:The question simplfies to (8×10^10)(10^6) => 8*10^16 => Will contain 16 zeros +1 digit 8 =>17 Ans A #### A QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)15 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15 Option B #### B QUESTION:In a certain neighborhood, there are half as many beige houses as white houses, and 3 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses? options: A)4:1 B)3:5 C)2:3 D)1:3 E)1:4 SOLUTION:The ratio of beige:white:brown = 3:6:2 The answer is C. #### C QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60 total S=84 outcomes D #### D QUESTION:A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km. options: A)24 kmph B)22 kmph C)21 kmph D)28 kmph E)29 kmph SOLUTION:A 24 kmph Total time taken = x/40 + 2x/20 hours = 5x/40 = x/8 hours Average speed = 3x/(x/8) = 24 kmph #### A QUESTION:How many digits are in (12×10^14)(10×10^15)? options: A)24 B)25 C)26 D)27 E)32 SOLUTION:The question simplfies to (12×10^14)(10^16) => 12*10^30 => Will contain 30 zeros +2 digit 12 =>32 Ans E #### E QUESTION:Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children? options: A)60 B)180 C)240 D)360 E)720 SOLUTION:If we wanted, we could make this one extremely difficult, counting out all kinds of possibilities in several different cases. Instead, we are going to make this ridiculously easy. First of all, with absolutely no restrictions, how many ways can the six children be arranged on the six chairs? That’s a permutation of the 6 items —- 6P6 = 6! = 720. That’s the total number of arrangements with no restrictions. Of course, those 720 arrangements have all kinds of symmetry to them. In particular, in all of those arrangements overall, it’s just as likely for E to be to the left of F as it is for E to be to the right of F. Therefore, exactly half must have E to the right of F, and exactly half must have E to the left of F. Therefore, exactly (1/2)*720 = 360 of the arrangements have E to the left of F. Answer = D. #### D QUESTION:If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers? I. x II. x + y III. y/x options: A)I only B)II only C)III only D)I and II E)I ,II and III SOLUTION:Ans: from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D). #### D QUESTION:If the product of two numbers is 17820 and their H.C.F. is 12, find their L.C.M. options: A)2574 B)2500 C)1485 D)1574 E)None of these SOLUTION:Explanation: HCF * LCM = 17820, because we know Product of two numbers = Product of HCF and LCM LCM = 17820/12 = 1485 Option C #### C QUESTION:Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube? options: A)236 B)256 C)216 D)246 E)206 SOLUTION:Volume of the new cube = [ 5(power)3 + 4(power)3 + 3(power)3 ] Cm(power)3 = 125 + 64 + 27 = 216 Cm(power)3 => a(power)3 = 216 Cm(power)3 Answer is C. #### C QUESTION:There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)Rs. 30 B)Rs. 34 C)Rs. 42 D)Rs. 48 E)Rs. 50 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1 or, 35x + 42 = 42x – 42 or, x = 12 Thus the original expenditure of the mess = 35 x 12 = Rs. 42 C #### C QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes options: A)18kms B)16kms C)50kms D)30kms E)40kms SOLUTION:total eastward distance= 25kmph*1/4hr=6.25 km total westward distance= 40kmph*1/4hr=10 km total distn betn them= 6.25+10=16.25km ans 16km ANSWER:B #### B QUESTION:The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer? options: A)5 B)3 C)4 D)2 E)1 SOLUTION:Let the second integer be x and the fourth be a. Then [3x + x + (x+2) + a]/4 = 9 => 5x + 2 + a = 36 => 5x + a = 34 => a = 34 - 5x From the above equation we can see that a is minimum when x is maximum, provided both are positive The maximum value that x can take in the above equation while still keeping a positive is x=6 This gives us a= 34 - 30 = 4 Therefore the minimum value that the fourth integer can have is 4. Answer:C #### C QUESTION:A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse. options: A)2200 B)1800 C)1200 D)1000 E)1500 SOLUTION:Let the C.P of the horse be Rs. X, Then, C.P of the carriage = Rs.(3000- x). 20% of x - 10% of ( 3000-x ) =2% of 3000 = 60, x/5 - ( 3000-x )/10 = 60, 3x - 3000 = 600, 3x =3600, x = 1200. Hence, C.P of the horse = Rs. 1200 ANSWER:C #### C QUESTION:Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely? options: A)15 sec B)19 sec C)12 sec D)10 sec E)11 sec SOLUTION:Explanation: D = 250 m + 250 m = 500 m RS = 80 + 40 = 120 * 5/18 = 100/3 T = 500 * 3/100 = 15 sec Answer: Option A #### A QUESTION:Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days. options: A)11 B)12 C)13 D)15 E)16 SOLUTION:Work done by Kamal in 1 day = 1/20 Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16 => Suresh can complete the work in 16 days Answer is E. #### E QUESTION:Rahul went to a shop and bought things worth Rs. 45, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)A)19.7 B)B)19.9 C)C)20.9 D)D)21.9 E)E)39.7 SOLUTION:Total cost of the items he purchased = Rs.45 Given that out of this Rs.45, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (45−30/100−x)6/100 = 30/100 ⇒ 6(45 −0.3 −x) = 30 ⇒ (45 − 0.3 − x) = 5 ⇒ x = 45 − 0.3 − 5 = 39.7 E) #### E QUESTION:In how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together? options: A)6!/2! B)3!*3! C)4!/2! D)4! *(3!/2!) E)3!*3!/2 SOLUTION:In the word ABROAD , there are 3 vowels - 2 A's and O Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together = (4! * 3! )/2! We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! . The entire vowel group is considered as a single group . Answer D #### D QUESTION:A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 845 in the same period of 2 years, What must be the rate of interest? options: A)5% p.a. B)7.5% p.a. C)10% p.a. D)12.5% p.a. E)None of these SOLUTION:Explanation: Given: 800 = (P * R * 2) / 100 S.I. For 1 year = Rs. 400 Thus, (840 – 800) = S.I. on Rs. 400 for 1 year 40 = (400 * R * 1) / 100 R = 10% p.a. ANSWER C #### C QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = p*r*t/100 = 1000000*4*3/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? options: A)2.04% B)6.12% C)8% D)8.25% E)10% SOLUTION:Per quarter, interest = 2% So for a year, interest = 8% Due to quarter cumulation, effective yield (YTM) would be slight higher than 8% Answer = 8.25% =ANSWER:D #### D QUESTION:The sum of three consecutive integers is 102. Find the lowest of the three? options: A)18 B)67 C)98 D)33 E)26 SOLUTION:Three consecutive numbers can be taken as (P - 1), P, (P + 1). So, (P - 1) + P + (P + 1) = 102 3P = 102 => P = 34. The lowest of the three = (P - 1) = 34 - 1 = 33. Answer: D #### D QUESTION:D is the set of all the multiples of 3 between 20 and 100. E is the set of all the factors of 700. Set D and Set E have how many numbers in common? options: A)None of these B)1 C)3 D)5 E)12 SOLUTION:D is a set of multiples of 3. 700 is NOT a multiple of 3, hence none of its factors is a multiple of 3. Therefore, those two sets won't have any overlap. Answer: A. #### A QUESTION:Two employees X and Y are paid a total of Rs. 800 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.200.63 B)s.250.63 C)s.290.63 D)s.300.63 E)s.363.63 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 800 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 800 ⇒ y[12/10 + 1] = 800 ⇒ 22y/10 = 800 ⇒ 22y = 8000 ⇒ y = 8000/22 =Rs.363.63 E) #### E QUESTION:In 24 minutes, the hour hand of a clock moves through an angle of: options: A)60° B)24° C)12° D)5° E)None SOLUTION:12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚ Answer: C #### C QUESTION:Three people (1 couple and 1 single) are seated at random in a row of 4 chairs. What is the probability that the couple does not sit together? options: A)3/7 B)1/2 C)2/5 D)3/4 E)5/12 SOLUTION:The total number of arrangements of 3 people is 4*3*2 = 24 Let's think of the couple as a single unit. The number of arrangements when the couple sits together is 3*2*2 = 12. Note that we multiply by 2 because the couple can switch places with each other. The number of ways the couple won't sit together is 24 - 12 = 12 P(couple won't sit together) = 12/24 = 1/2 The answer is B. #### B QUESTION:The value of (4.7×13.26 + 4.7×9.43+4.7×77.31) is options: A)0.47 B)47 C)470 D)4700 E)None SOLUTION:Solution Given expression = 4.7×(13.26+9.43+77.31) = 4.7 ×100 = 470. Answer C #### C QUESTION:From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond? options: A)238/5525 B)176/5534 C)253/5523 D)234/5525 E)1/5525 SOLUTION:Solution Let S be the sample space. Then, n(S) = 52C3 = 22100 Let E = event of getting 1 face card. n(E) = number of ways of choosing 1 face card out of 26 =13C1 * 13C2= 13*72 = 936 P(E) = n(E) / n(S) = 936 / 22100 = 234/5525 = 234/5525. Answer D #### D QUESTION:A manufacturer of a certain type of screw rejects any screw whose length is less than 2.44 + 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable? options: A)|k + 0.03| > 2.5 B)|k — 0.03| <= 2.5 C)|k — 2.5| > 0.03 D)|k — 2.5| >= 0.06 E)|k — 2.5| <= 0.03 SOLUTION:So, let's go through this step by step: rejects any screw whose length is less than 2.44 + 0.03 centimeters or greater than 2.5 + 0.03 centimeters. In other words, any screw that is less than: 2.44 + 0.03 =2.47 or greater than 2.50 + 0.03 =2.53 will be rejected. If k represents the length of a screw In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So: 2.47 ≤ K ≤ 2.53 You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths. Let's look at (E): |k — 2.5| <= 0.03 For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53 For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47 2.47 ≤ k ≤ 2.53 (E) #### E QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)200 B)220 C)240 D)250 E)260 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: Option C #### C QUESTION:In a tree, 3/7 of the birds are parrots while the rest are toucans. If 2/3 of the parrots are female and 7/10 of the toucans are female, what fraction of the birds in the tree are male? options: A)3/7 B)11/35 C)16/35 D)31/70 E)37/70 SOLUTION:Let x be the number of birds in the tree. The fraction of birds that are male parrots is (1/3)(3/7)=1/7. The fraction of birds that are male toucans is (3/10)(4/7)=6/35. The total fraction of male birds is 1/7 + 6/35 = 11/35. The answer is B. #### B QUESTION:In a certain store, the profit is 350% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)72.2% B)70% C)100% D)250% E)120% SOLUTION:Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 450 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420 Profit = 450 - 125 = Rs. 325 Required percentage = 295/420 * 100 = 72.2% ANSWER:A #### A QUESTION:12 times a number gives 156. The number is options: A)11 B)12 C)13 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 12×N=156⇒N=13 Correct Option: C #### C QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer: A #### A QUESTION:A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water? options: A)22 B)37 C)32 D)27 E)18 SOLUTION:US = 25 DS = 39 M = (39 + 25)/2 = 32 Answer:C #### C QUESTION:A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 B)67 C)108 D)26 E)27 SOLUTION:Length = Speed * time Speed = L/T S = 600/20 S = 30 M/Sec Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 108 Kmph Answer:C #### C QUESTION:JERRY has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If JERRY needs to pay exactly $128, what is the least number of bills he will need to use? options: A)16 B)35 C)46 D)577 E)576 SOLUTION:128 is the total sum of money. as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils 128-120 = 8 so now we need to get 8 from either 5 dollar bills or 1 dollar bills 8 - 5 (use only 1 5 dollar bill) = 3 so we can get 3 from using 3 $1 bills. Hence 16 ( 12+1+3 ) ANSWER IS A #### A QUESTION:Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other? options: A)300 kms from A B)280 kms from A C)305 kms from A D)295 kms from A E)265 kms from A SOLUTION:DETAILED SOLUTION Bus A Travels 200km @ 40kmph the next 200km @ 50kmph and the final 200km @ 60kmph So, Bus A will be at a distance of 200km from city M after 5 hours, and at a distance of 400km after 9 hours, and reach N after 12 hours and 20 mins Bus B Travels at an overall average speed of 50kmph, so will take 12 hours for the entire trip. So, Bus B will travel 160 kms in the first 4 hours 200 kms in the next 4 hours and 240 in the final 4 hours So, both buses cross each other when they are in their middle legs. After 5 hours, bus A will be at a position 200kms from city M. At the same time, bus B will be at a distance 210kms from city N (4 * 40 + 50). The distance between them will be 190kms (600 - 200 - 210). Relative speed = Sum of the the two speeds = 50 + 50 = 100 kmph. Time taken = 190/100 = 1.9 hours. = 1 hour and 54 minutes. So, the two buses will meet after 6 hours and 54 minutes. Bus B will have travelled 210 + 95 = 305 kms. So, the two buses will meet at a point that is 305 kms from City N and 295 kms from city A. CORRECT ANSWER D #### D QUESTION:A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number? options: A)297 B)187 C)278 D)200 E)267 SOLUTION:25 + 25 = 50 25% ------ 50 100% ----- ? => 200 Answer:D #### D QUESTION:On a test consisting of 30 questions. No. of wrong answers is 50% less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers? options: A)1 : 3 B)2 : 3 C)2 : 1 D)3 : 1 E)4 : 5 SOLUTION:Sol. Let the number of wrong answer - x and number of right answer = 30-x x = 50/100 of (30-x) x = 10 Required ratio = 20 : 10 = 2 : 1 C #### C QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y? options: A)6 B)3 C)4 D)5 E)7 SOLUTION:lets start from z, as per the question stem z + 5 + 7 = 16 -->> z= 4 similarly, y + 4 + 5 = 7 --> y = -2 similarly,, x + -2 + 4 = 5 --> x = 3 hence , x-y = 3+2 = 5 ANSWER:D #### D QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1200, what is the reduced price for kg? options: A)s.40 B)s.46 C)s.49 D)s.41 E)s.60 SOLUTION:1200*(25/100) = 300 ---- 5 ? ---- 1 => Rs.60 Answer: E #### E QUESTION:A train crosses a platform in 15 sec, same train crosses another platform of length 250 m in 20 sec. If the speed of the train is 15 m/sec then find the length of the platform? options: A)277m B)180m C)165m D)278m E)175m SOLUTION:Length of the train be ‘X’ (X + 250)/20 = 15 X = 50m Let the length of the platform be y (y + 50)/15 = (50 + 250)/20 4y + 200 = 900 X = 1750m Answer: E #### E QUESTION:Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $10 more than 1/4 of the fine and Peter paid $10 less than 1/3 of the fine, leaving pay $25 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay? options: A)$120 B)$125 C)$130 D)$135 E)$140 SOLUTION:Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F. F = [(1/4)F + 10] + [(1/3)F – 10] + [(1/2)F – 25] F = (1/4)F + (1/3)F + (1/2)F – 25 Multiply all terms by 12 to clear the fractions. 12F = 3F + 4F + 6F – 300 12F = 13 F – 300 –F = – 300 F = 300 Well, if the fine cost $300, then Sam paid the part not covered by Joe or Peter. Half the fine is $150, and Sam paid $25 less than this: $125 Answer = B #### B QUESTION:A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in options: A)18 sec B)12 sec C)15 sec D)20 sec E)13.5 sec SOLUTION:Length of train = 12 × 15 = 180 m. Then, speed of train = 180⁄18 = 10 m/s Now, length of train = 9 × 15 = 135m ∴ Required time = 135⁄10 = 13.5 sec. Answer E #### E QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it? options: A)18 days B)20 days C)24 days D)30 days E)32 days SOLUTION:2c = ¼ + 1/6 – 1/3 = 1/12 c = 1/24 => 24 days ANSWER:C #### C QUESTION:If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is: options: A)53.33 B)54.68 C)55 D)56 E)None of these SOLUTION:Explanation: Required average = (55 × 50 + 60 × 55 + 45 × 60/55 + 60 + 45) = (2750 + 3300 + 2700/160) = 8750/160 = 54.68 Answer: B #### B <<<Examples ends QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40 Answer:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction? options: A)5hours B)10hours C)8hours D)10hours E)12hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 20 =10 hours Answer is B #### B QUESTION:John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him? options: A)10 B)67 C)32 D)44 E)55 SOLUTION:75-20=55. Answer is E #### E QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 1 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)2/5. C)6/11. D)5/9. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 6 = x*15 x = 6/15=2/5 Answer: B #### B QUESTION:Find the unit's digit in the product 2467 153 * 34172? options: A)1 B)3 C)2 D)5 E)7 SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172 Now 7 4 gives unit digit 1 7 152 gives unit digit 1 7 153 gives 1*7=7.Also 172 gives 1 Hence unit's digit in the product =7*1=7. Option A #### A QUESTION:There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)108 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand. #### C QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b? options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given. SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2. Answer: A. #### A QUESTION:Tickets numbered 1 to 10 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 2? options: A)1/3 B)2/5 C)1/2 D)2/3 E)1/4 SOLUTION:Here, S = {1,2,3,......,9,10} E= event getting a multiple of 3 = {2,4,6,8,10} probability = 5/10 = 1/2 correct option is C #### C QUESTION:Of the families in City X in 1956, 25 percent owned a personal computer. The number of families in City X owning a computer in 1960 was 15 percent greater than it was in 1956, and the total number of families in City X was 5 percent greater in 1956 than it was in 1960. what percent of the families in City X owned a personal computer in 1960? options: A)50% B)51.22% C)5.26% D)7.20% E)27.38% SOLUTION:Say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 Number of families owning computer in 1960 = 25 * 115/100 = 28.75 Number of families in 1960 = 105 The percentage = 28.75/105 * 100 = 27.38%. Option: E #### E QUESTION:40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:Let x be the amount of liquid Q to be added. (3/8)*40 + x = (6/11)*(40+x) 1320 + 88x = 1920 + 48x 40x = 600 x = 15 The answer is E. #### E QUESTION:The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult? options: A)$111 B)$52.5 C)$210 D)$58.5 E)$6 SOLUTION:Explanatory Answer Step 1: Assign variables and frame equations Let the basic fare for the child be $X. Basic one-way air fare of a child costs half the regular fare for an adult Therefore, the basic fare for an adult = 2(basic one-way airfare for a child) = $2X. Reservation charge is the same on the child's ticket as on the adult's ticket. Let the reservation charge per ticket be $Y Hence, an adult ticket will cost (Basic fare + Reservation charges) = 2X + Y = $216 ..... (1) And ticket for an adult and a child will cost (2X + Y) + (X + Y) = 3X + 2Y = $327 .... (2) Step 2: Solve the equations and determine basic fare for an adult Multiply equation (1) by 2: 4X + 2Y = 432 .... (3) Subtract equation (2) from equation (3): (4X + 2Y = 432) - (3X + 2Y = 327) ∴ X = $105. The basic fare of an adult ticket = 2X = 2*105 = $210 Answer C #### C QUESTION:In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class? options: A)12 Years B)12.6 Years C)13.6 Years D)14 Years E)14.5 Years SOLUTION:Total age of 50 students (30X 13+20 X 12) = 630 Average = 630/50 = 12.6 Years \ B #### B QUESTION:Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is options: A)4 : 5 B)1 : 2 C)6 : 7 D)5 : 6 E)None SOLUTION:Solution Let us name the brothers as A and B. = (A'S speed) : (B's speed) =√b : √a = √25 : √36 = 5 : 6 Answer D #### D QUESTION:Of the 4 distinguishable wires that lead into an apartment, 2 are for cable television service, and 4 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Given: Total number of wires = 5 Number of cable wires = 2 Number of telephone wires = 3 To find: Number of combination which has at least one cable wires Solution: No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2 Since it is a combination of wires, the arrangement is not important Approach 1: Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire) Selection 1 Number of ways of selecting one cable wire = 2C1 = 2 Number of ways of selecting 2 telephone wires = 3C2 = 3 Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics) Selection 2 Number of ways of selecting one cable wire = 2C2 = 1 Number of ways of selecting 2 telephone wires = 3C1 = 3 Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics) Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire Approach 2 Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires) Total number of ways of selecting 3 wires out of 5 = 5C2 = 10 Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1 Selection X - Selection Y = 6 Answer is Option A #### A QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number? options: A)9 B)11 C)17 D)13 E)15 SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7. Given (x + 1) + (x + 7) = 28 => 2x + 8 = 28 => x = 10 The third number = x + 3 = 10 + 3 = 13. Answer: D #### D QUESTION:In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:Let the number of buffaloes be x and the number of ducks be y. Then 4x+2y=2(x+y)+24 =>x=12 ANSWER D 12 #### D QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 3*20000/5=12000 ANSWER:E #### E QUESTION:A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work? options: A)4 days B)2 days C)6 days D)8 days E)9 days SOLUTION:C 6 days 4/10 + 9/x = 1 => x = 15 1/10 + 1/15 = 1/6 => 6 days #### C QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination. options: A)15 B)21 C)17 D)19 E)21 SOLUTION:Total Money = Rs. 10350. Let 50 rupees note was X. Then 500 rupees note = 36 - X Now, 50*X + 500 * (36 - X) = 10350 50X + 18000 - 500X = 10350 - 450X = - 7650 X = 17. No. of 50 rupees note = 17. Answer: Option C #### C QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)Rs.4082.67 B)Rs.4082.49 C)Rs.4082.48 D)Rs.4082.40 E)Rs.4082.13 SOLUTION:Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs.4082.40 Answer: D #### D QUESTION:What is the value of √36% ? options: A)10% B)20% C)30% D)60% E)40% SOLUTION:Explanation: br>√16% =√36/√100 =6/10 =60/100=60% correct answer is D)60% #### D QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:Which of the following is not divisible by 6? options: A)10032 B)21192 C)47816 D)91232 E)72031 SOLUTION:Divisibility rule of 6: Number must be divisible by both 2 and 3 Option A: 10032, Divisible by 2. Hence divisible by 6 Option B: 21192, Divisible by 2 & 3. Hence divisible by 6 Option C: 47816, Divisible by 2. Hence divisible by 6 Option D: 91232, Divisible by 2. Hence divisible by 6 Option E: 72031, Not divisible by 2 or 3. Hence 72031 is not divisible by 6 #### E QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)227 B)350 C)881 D)277 E)271 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer: B #### B QUESTION:((-1.9)(0.6) – (2.6)(1.2))/2.0 = ? options: A)-0.71 B)1.0 C)1.07 D)1.71 E)-2.13 SOLUTION:Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option. -2.13 Answer E #### E QUESTION:If x/y = 5 and (4a - x)/(b - y) = 5, then the value of a/b is? options: A) –3 B) -2 C) 1 D) 5/4 E) 3 SOLUTION:x = 5y 4a - 5y = 5(b - y) 4a - 5y = 5b - 5y 4a = 5b a/b = 5/4 Answer: D #### D QUESTION:A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is? options: A)1 B)22 1/7 C)2 D)22 1/2 E)3 SOLUTION:100 --- 10 DS = 10 ? ---- 1 200 ---- 30 US = 8 ? ----- 1 S = (10 - 8)/2 = 1 kmph. Answer:A #### A QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1500 B)2000 C)3000 D)3500 E)2500 SOLUTION:Profit as x since 5% and 95% of x will be divided b/w A and B ration 3:2 =>profit 95x/100 * 3/5 given that A's share is Rs 855 => 95x/100 * 3/5 = 855 hence x = 1500 ANSWER A #### A QUESTION:One of the following numbers can be marked out as the odd one out. can you find which one? 1) 680986879 2) 716089780 3) 820670987 4) 932967879 options: A)The odd number is 680986879 B)The odd number is 820670987 C)The odd number is 716089780 D)The odd number is 932967879 E)None SOLUTION:Correct Answer : B if you add up the first three digits of all the numbers, it adds up to 14 except for second option 820670987 #### B QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 27 cm * 16 cm. What is the perimeter of the square? options: A)140 B)240 C)340 D)144 E)122 SOLUTION:Area of the square = s * s = 3(27 * 16) => s = 9 * 4 = 36 cm Perimeter of the square = 4 * 36 = 144 cm. Answer: D #### D QUESTION:A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7}. If no digit may be repeated and each password must be at least 6 digits long, how many passwords are possible? options: A)6! + 7! B)2 x 7! C)6! x 7! D)13! E)14! SOLUTION:If we choose the 7 different digits then they can be arranged in 7! ways. The number of possible 6-digit passwords is 7*6*5*4*3*2 = 7! The total number of passwords is 7! + 7! = 2*7! The answer is B. #### B QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages. options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12 SOLUTION:Explanation: Let the present ages of A and B be 'a' and 'b' respectively. 3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1) a-b = 5 -------(2) Solving (1) and (2) we get b=8 Substituting b = 8 in second equation, we get a= 13. Answer : C => 2a = 32 => a = 16. Answer: C #### C QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these SOLUTION:Explanation: Let their ages be x and (x + 24) years. 5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11. Their present ages are 35 years and 11 years Option D #### D QUESTION:What is the leastvalue of x. So that 23x57 is divisible by 3? options: A)3 B)4 C)1 D)5 E)6 SOLUTION:The sum of the digits of the number is divisible by 3, then the number is divisible by3. 2 + 3 + x + 5 + 7 = 17 + x Least value of x may be 1 Therefore 17 + 1 = 18 is divisible by 3. C #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 18 km/hr. What is the length of the platform? options: A)80 B)240 C)288 D)277 E)221 SOLUTION:Speed = 18 * 5/18 = 5 m/sec. Length of the train =5 * 20 = 100 m. Let the length of the platform be x m . Then, (x + 100)/36 = 5 => x = 80 m. Answer: A #### A QUESTION:Janet has to pay back her bank loan over 10 months following the below sequence. $50, $55, $65, $80, $85, $95, $110, $115, $125, ? How much will she pay back on the tenth month? options: A)$155 B)$140 C)$135 D)$125 E)$130 SOLUTION:The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 10th Month is $140 Ans B #### B QUESTION:Pipe A can fill a tank in 2 hr, pipe B in 4hr and pipe C in 8hr. If all the pipes are open in how many hours will tank be filled? options: A)1hr 27min B)2hr 19min C)3hr 14min D)3hr E)5hr 45min SOLUTION:Part filled by (A+B+C) in 1hour = 1/2 + 1/4 + 1/8 = 7/8 All the 3 pipes together will fill the tank in 1hour 27min Answer is A #### A QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square? options: A)600 cm B)800 cm C)400 cm D)1000 cm E)None of these SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. ANSWER:B #### B QUESTION:We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $390. How many math books did we buy? options: A)57 B)60 C)63 D)66 E)69 SOLUTION:M + H = 90 H = 90 - M 4M + 5H = 390 4M + 5*(90 - M) = 390 M = 60 The answer is B. #### B QUESTION:A survey was sent to 90 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey? options: A)2% B)6% C)14% D)28% E)63% SOLUTION:case 1: (7/90)=x/100 x=8% case 2: (9/63)=y/100 y=14% So percent increase is =(y-x)=(14-8)%=6% Answer is B #### B QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)72 B)27 C)40 D)28 E)20 SOLUTION:800*(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer:C #### C QUESTION:The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? options: A)165 B)161 C)162 D)163 E)164 SOLUTION:To minimize one quantity maximize other. 164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165. Answer: A. #### A QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test. You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it? options: A)48% B)55% C)60% D)71% E)80% SOLUTION:C 60% In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability. In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already. Therefore, P(Second/First) = P (First and Second)/ P (First) = 0.25/0.42 =0.60 =60 % #### C QUESTION:A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6500? options: A)Rs. 5870 B)Rs. 5991 C)Rs. 8870 D)Rs. 6850 E)None of these SOLUTION:Explanation: Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130 Therefore, required sale = Rs. [(6500 * 6) – 30,130] = Rs. (39000 – 30,130) = Rs. 8870 ANSWER C #### C QUESTION:In the class of 50 students, 30 speak Tamil and 30 speak Telugu. What is the lowest possible number of students who speak both the languages? options: A)A)8 B)B)10 C)C)20 D)D)30 E)E)32 SOLUTION:let the student who speaks tamil-x let the student who speaks telugu-y as (xuy)-(xny)=total 30+30-(xny)=50 =10 B) #### B QUESTION:What percent is 2 gm of 1 kg? options: A)0.5 % B)0.2% C)1.5% D)2% E)3% SOLUTION:1 kg = 1000 gm 2/1000 × 100 = 200/1000 =1/5 = 0.2 % B) #### B QUESTION:A day-trader plans to invest a total of $23,300 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment? options: A)$2,800 B)$3,000 C)$3,700 D)$3,800 E)$3,900 SOLUTION:We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice). Total of 14 minimized investments = (14)(1400) = $???600 The 15th investment + $???600 = $23,300 So, the HUNDREDS DIGITS of the 15th investment must be 7 Answer: C #### C QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:Robert ate 7 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel? options: A)A)4 B)B)7 C)C)9 D)D)5 E)E)2 SOLUTION:7-5=2. Answer is E #### E QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick? options: A)5 B)8 C)24 D)15 E)20 SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min Nick's rate - 10 laps per hour --> 10/60 laps/min lets set equations: 20/60*t=4 (since Maria had to run 4 laps before Nick would start) 10/60*t=0 (Hick has just started and hasn't run any lap yet) (20/60-10/60)*t=4-0 (since Nick was chasing Maria) t=24 min needed Maria to run 4 laps Answer : C #### C QUESTION:If the LCM and HCF of 8 and another number is 24 and 4 respectively. Find the other number ? options: A)11 B)12 C)14 D)15 E)16 SOLUTION:HCF x LCM = Product of Numbers 4 x 24 = 8 x the other number other number = (4 x 24) / 8 other number = 12 ANSWER : B #### B QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A QUESTION:What percent is 4 gm of 1 kg? options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 % SOLUTION:1 kg = 1000 gm 4/1000 × 100 = 400/1000 =2/5 = 0.4 % B) #### B QUESTION:Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour? options: A)The average speed is 1/5 miles per hour. B)The average speed is 1/3 miles per hour. C)The average speed is 2/5 miles per hour. D)The average speed is 2/3 miles per hour. E)The average speed is 3/5 miles per hour. SOLUTION:We know the average speed and must find the fraction of time taken at a particular speed. t1/t2 = (A2 – Aavg)/(Aavg – A1) t1/t2 = (60 – 50)/(50 – 30) = 1/2 So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3. ANSWER (B) #### B QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -. options: A)7/18 B)7/19 C)7/11 D)7/12 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ways. 7/15 Answer: E #### E QUESTION:In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ? options: A)12 B)27 C)26 D)11 E)22 SOLUTION:Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11. Answer: D #### D QUESTION:A will states that the estate would be divided among six sons with the remainder donated to charity. One stipulation in the will is that no one among the sons can receive an amount within 12% of another's amount. If one of the beneficiaries received $30,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the six sons? options: A)$4096 B)$14043 C)$7892 D)$17736 E)$15336 SOLUTION:1st - 30,000. 2nd - 0.88*30,000 = 26,400 3rd - 0.88*26,400 = 23,232 4th - 0.88*23,232 = 20,444.16 5th - 0.88*20,444.16 = ~17,990.86 6th - 0.88*17,990.86 = ~15,831.96 Range = 30,000 - 15,831 = 14,168 Answer: B. #### B QUESTION:If n is a natural number, then 6n^2 + 6n is always divisible by? options: A)6 only B)6 and 12 C)12 only D)18 only E)20 only SOLUTION:6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Answer is B #### B QUESTION:In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is? options: A)14 years 8 months B)15 years C)13 years 8 months D)17 years 10 months E)17 years SOLUTION:Total decrease = (20 x 2) months = 3 years 4 months Age of the new boy = 17 years - 3 years 4 months. = 13 years 8 months. ANSWER:C #### C QUESTION:A water tank is three-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely? options: A)6 min B)8 min C)7 min D)9 min E)1 min SOLUTION:The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15 Since the rate is negative, the tank will be emptied. A full tank would take 15 minutes to empty. Since the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes The answer is D. #### D QUESTION:A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain? options: A)12.5% B)16.7% C)22.5% D)27.5% E)33.3% SOLUTION:Let x be the original number of each color so there are a total of 5x candies. Kaz eats all of the green candies and half of the orange ones. There are 0 green candies and 0.5x orange candies remaining. He eats half of the remaining pieces of each color. There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies. He eats red and yellow candies in equal proportions. orange+blue+red+yellow = 0.75x + red + yellow = 1.2x red + yellow = 0.45x red = 0.225x, since red = yellow. The answer is C. #### C QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)18 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :D #### D QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? options: A)3 B)4 C)5 D)8 E)2 SOLUTION:M = 4 S = 2 US = 4 - 2 = 2 D = 6 T = 6/2 = 3 Answer: A #### A QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns? options: A)A)10 B)B)12 C)C)24 D)D)60 E)E)100 SOLUTION:Using anagram method: 4_3_2_1 R_R_B_B so.. 4!/Number of repeated letters (2!)(2!) = 6 ANS:D #### D QUESTION:Find 60/42*4 options: A)14.7653 B)0.5897 C)3.6974 D)0.3571 E)1.2587 SOLUTION:Answer=60/42*4 =60/168=0.3571 Option D is correct #### D QUESTION:If “GREEN” is given number code as 49, what is the difference between the number codes of “VIOLET” and “PINK” ? options: A)55 B)45 C)33 D)60 E)40 SOLUTION:Explanation: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26 GREEN = 7 + 18 + 5 + 5 + 14 = 49 Thus we get, VIOLET = 22 +9 +15+12 + 5 + 20 = 83 PINK = 16 + 9 + 14 + 11 = 50 Thus, difference is 83 – 50 = 33. ANSWER C #### C QUESTION:4 shepherds were watching over the flocks and they were commenting on how many sheep they each had. If ram had 3 more sheep than he would have one less than rahul. wheras akar has the same number as the other 3 shepherds put togeher. If john had 3 less sheep he would have exactly trile the number of ram. If they were evenly distributed if they would each have 11 seep how many sheep did ram have? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:akar has=ram+rahul+john after evenly distribution each has 11. so, total no. is 44 so, akar has=22 & ram+rahul+john=22 also ram=rahul-4 & john-3=3*ram solving these we get the sol. ANSWER:B #### B QUESTION:The contents of a certain box consist of 24 carrots and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be carrrots? options: A) 24 B) 26 C) 30 D) 46 E) 50 SOLUTION:carrrots = (carrrots + kiwi + x)*0.3 24 = (30 + 24 + x)*0.3 x = 26. Answer: B. #### B QUESTION:When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number? options: A)228 B)103 C)286 D)122 E)102 SOLUTION:Explanation: Let the number be x x2 - 732 = 5280 x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609 = 10000 + 2(100)(3) + 32 = (100 + 3)2 x = 100 + 3 = 103. Answer: B #### B QUESTION:If the Average (mean ) of 9 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A)8x B)4x C)5x/3 D)3x/2 E)3x/5 SOLUTION:Let the 5 numbers be 1,2,3,4,5,..9 (since no restrictions are given). There mean is 4 (x). Now the sum of greatest three would be 7+8+9=24 so the answer has to be 8x....that is option A #### A QUESTION:In the coordinate plane, points (x, 1) and (12, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y = options: A) 4.5 B) 7 C) 8 D) 11 E) 12 SOLUTION:Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x. Thus: (x, 1)=(2, 1) and (12, y) = (12,6) --> x+y=2+6=8. Answer: C. #### C QUESTION:Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 1600 then loss of Pyarelal? options: A)600 B)700 C)840 D)940 E)1440 SOLUTION:Let the capital of Pyarelal be x, then capital of Ashok=x/9 So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x Hence out of the total loss of 1600, loss of Pyarelal= 1600*9x/10x=1440 ANSWER:E #### E QUESTION:Alex is shuffling a pack of cards (54 cards in total) and after some time, he takes out a joker card. Now, he splits the remaining cards into two piles. Can you find out the probability where one of the piles has a sequence of card from A to K in order? options: A)5/6227020800 B)4/6227020800 C)3/6227020800 D)1/6227020800 E)2/6227020800 SOLUTION:Solution: 1/6227020800 This can be solved through a simple mathematical equation. N cards have n! permutations. Therefore, the probability of obtaining a specific one by chance is 1/n! Now, in this particular case, n = 13 Therefore, the required probability is 1/6227020800 Answer D #### D QUESTION:The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is: options: A)400 B)500 C)600 D)800 E)1000 SOLUTION:Let the sum be $. P. (P(1+10/100)^2-P)=525 P((11/10)^2-1)=2500 SUM = 2500 So SI = 500 ANSWER B #### B QUESTION:A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A? options: A)388 B)277 C)266 D)280 E)191 SOLUTION:80* 7: x* 3 = 1:1 1/2 560: 3x = 2: 3 x = 280 Answer: D #### D QUESTION:By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)20% B)30% C)40% D)50% E)60% SOLUTION:(SP of 33m)-(CP of 33m)=Gain=SP of 11m SP of 22m = CP of 33m Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33. Gain%=[(11/22)*100]%=50% ANSWER D #### D QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it? options: A)12 days B)18 days C)15 days D)21 days E)22 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/10 work in 1 day B alone can do (1/6 -1/10) =1/15 work in 1 day => complete work can be done in 15 days by B Answer: Option C #### C QUESTION:The perimeters of two squares are 80 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares? options: A)76 cm B)24 cm C)88 cm D)55 cm E)73.2 cm SOLUTION:We know perimeter of square = 4(side) So Side of first square = 80/4 = 20 cm Side of second square = 32/4 = 8 cm Area of third Square = 20*20 - 8*8 = 336 cm So side of third square = 18.3 [because area of square = side*side] Perimeter = 4*Side = 4*18.3 = 73.2 cm Answer:E #### E QUESTION:The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.) options: A) 1 B) 4 C) 7 D) 11 E) 10 SOLUTION:We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 3 ingredients... 3 ingredient blends: ABC ABD ACD BCD Total blends = 4 B #### B QUESTION:If cost of sugar increases by 12%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? options: A)7.5 B)9.2 C)10.7 D)15.3 E)18.6 SOLUTION:100 112 ----- 112 ----- 12 100 ------ ? => 10.7% Answer:C #### C QUESTION:If x is a sum of all even integers on the interval 13...55 and y is their number, what is the GCD (x, y)? options: A) 1 B) 21 C) 26 D) 52 E) 1014 SOLUTION:x = 14 + 16 + ... + 54 = (largest + smallest)/2 *(# of terms) = (14 + 54)/2*21= 34*21. GCD of 21 and 34*21 is 21 Answer: B. #### B QUESTION:What is the units digit of 32! + 50! + 2! + 4!? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:For all N greater than 4, the units digit of N! is 0. The sum of the four units digits is 0 + 0 + 2 + 4 = 6 The units digit is 6. The answer is D. #### D QUESTION:3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day? options: A)33 B)77 C)26 D)12 E)99 SOLUTION:Let the required number of working hours per day be x. More pumps, Less working hours per day (Indirect Proportion) Less days, More working hours per day (Indirect Proportion) Pumps 4 : 3 :: 8 : x Days 1 : 2 4 x 1 x x = 3 x 2 x 8 x = (3 x 2 x 8) (4) x = 12. Answer:D #### D QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 4. What is the ratio of their heights? options: A)A)2:5 B)B)2:7 C)C)2:2 D)D)2:1 E)E)4:3 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(4)2h2 => h1/h2 = 4/3 i.e. h1 : h2 = 4 : 3 Answer: E #### E QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball? options: A)12 cm B)16 cm C)18 cm D)20 cm E)none of the these SOLUTION:similar triangle properties.. 2/r+6 = 6/r-6 giving r = 12. Answer: A #### A QUESTION:y w v t r p n Next letter in the series options: A)L B)M C)N D)O E)P SOLUTION:y--w(y-2) v--t(v-2) r--p(r-2) n--l(n-2) so ans is l ANSWER:A #### A QUESTION:Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 192, what is the area of the side face of the box? options: A)13 B)16 C)18 D)29 E)32 SOLUTION:Lets suppose length= l, breadth= b, depth= d Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l) top face area= w*d side face area= w*d = 1.5 d*l (w=1.5l) Volume = l*w*d= 192 l*1.5l*2l= 192 l=4 Side face area= l*d= l*2l= 4*2*4 =32 E is the answer #### E QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 15 years? options: A)2:6 B)3:5 C)1:4 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×9/100) /(P×R×15/100)]=9PR/15PR=9/15=3:5 Answer B #### B QUESTION:Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds? options: A)22 B)24 C)99 D)27 E)17 SOLUTION:Explanation: Less Cogs more turns and less time less turns Number of turns required=80 × × = 24 times Answer: B) 24 #### B QUESTION:What simple interest will produce Rs.84000 as in 4 years at 3 1/2 percent? options: A)11500 B)12660 C)15220 D)11760 E)16520 SOLUTION:(84000*4*7/2)/100 = i i = 11760 Answer: D #### D QUESTION:While working alone at their respective constant rates, server J uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files? options: A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr SOLUTION:Server J processes 480/4 files per hour = 120 per hour Server Y processes 180/8 files per hour = 60 per hour Total files processed per hour when J and Y work together = 120+60 per hour = 180 files per hour 480/180 = 2 2/3 hours=C #### C QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)5 sec D)12.5 sec E)12 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. ANSWER:A #### A QUESTION:If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king? options: A)6/13 B)7/10 C)4/11 D)7/13 E)5/26 SOLUTION:There are 26 black cards and 2 red kings. P(black card or king) = 28/52 = 7/13 The answer is D. #### D QUESTION:What is the smallest number which when increased by 3 is divisible by 27, 35, 25, & 21 ? options: A)4722 B)4725 C)4728 D)4731 E)4733 SOLUTION:Here smallest number means LCM Hence LCM of 27,35,25,21 = 3^3 x 5^2 x 7 = 4725 Therefore required number is 4725 - 3 =4722 Ans - A #### A QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage? options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3% SOLUTION:Explanation: Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 33 pens = Rs. 33 Profit% = 33/99 * 100 = 33 1/3% Answer: A #### A QUESTION:In how many K ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6*6*6*6= 1296 ------(1) Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2) therefore required value K= (1)-(2)= 1296-360=936.D #### D QUESTION:If f(a)=5b, what is the value of (f(a)-f(6b)) ? options: A)32b B)25b C)6a-6b D)3a+2b E)52a SOLUTION:f(a)=5b f(6b) = 30b (f(6b)-f(a)) = 30b-5b = 25b Answer is B #### B QUESTION:A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it? options: A)76 hrs B)99 hrs C)55 hrs D)90 hrs E)11 hrs SOLUTION:1/9 - 1/x = 1/10 => 90 hrs Answer: D #### D QUESTION:Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rest of the car, then the share of each of the remaining persons increased by ? options: A)1/9 B)1/8 C)1/7 D)7/8 E)8/7 SOLUTION:When there are eight people, the share of each person is 1/8th the total cost ANSWER:B #### B QUESTION:Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 253 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle? options: A)903 B)2209 C)2878 D)1210 E)1560 SOLUTION:As expected, this question boils down to 2 equation, Consider total number of Balls in Triangle = T and number of balls in last row = x. 1+2+3+...+x = T x(x+1)/2 = T ----(a) As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+253) (x-8)^2 = T+253 -----(b) Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk. We can see that option A fits this criteria in eq (b). Add - 903+253 = 1156 = 34^2 = (x-8)^2 Hence, x = 42. Cross check by putting in eq (a) = x(x+1)/2 = T = > 42*43/2=903 Hence, answer is A. #### A QUESTION:Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week? options: A)$0.00 B)$133.00 C)$250.05 D)$66.74 E)$10000.00 SOLUTION:Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be n/4, n/8, n/16, n/32 So, answer will be D #### D QUESTION:If x and y are non-zero integers, and 36x^4 – 4y^4 = 6x^2 + 2y^2, which of the following could be the value of x2 in terms of y? options: A)2y^2+1/6 B)2y^2+1/8 C)2y^2+1 D)2y^2 E)2y SOLUTION:36x^4 – 4y^4 = 6x^2 + 2y^2 (6x^2 + 2y^2) (6x^2 - 2y^2) = 6x^2 + 2y^2 6x^2 - 2y^2 = 1 6x^2 = 2y^2+1 x^2 = 2y^2+1/6 Answer : A #### A QUESTION:In a friendship gang Angel has 3 gang, in how many ways can he invite one or more of the gang to his house? options: A)58 B)5 C)12 D)9 E)7 SOLUTION:Angel can select one or more than one of his 8 gang. => Required number of ways = 2^3 – 1= 7. E #### E QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z? options: A)50% B)40% C)37.5% D)331⁄3% E)25% SOLUTION:Work with fraction of brand Z in the tank. 1st step: brand Z is 1 2nd step: brand Z is 1/2 3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4 4th step: brand Z is (1/2)*(3/4) Q= 3/8 = 37.5% Answer (C) #### C QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 * 72 = 48 Answer: B #### B QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)100 C)110 D)130 E)140 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C QUESTION:Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point? options: A)20sec B)15sec C)30sec D)24sec E)1min SOLUTION:They meet every 360/7+8 = 24sec Answer is D #### D QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10200 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv) Subtracting (ii) from (iv), we get, P = 4050. P's monthly income = Rs.4050. Answer: A #### A QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)81 km/hr B)88 km/hr C)62 km/hr D)46 km/hr E)56 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y - 4.5)(10/36) ---(1) x/8.5 = (y - 5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y - 4.5)/ (y - 5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5 × 5.4 0.1y = 8.5 × 5.4 - 8.4 × 4.5 => .1y = 45.9 - 37.8 = 8.1 => y = 81 km/hr ANSWER:A #### A QUESTION:8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged? options: A)A.1296 B)B.1850 C)C.2880 D)D.3546 E)E.4200 SOLUTION:Glue milk and water bottlestogether: {AB}, {CD}. 6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways. Therefore the final answer is 6!*2!*2!=2,880. Answer: C. #### C QUESTION:Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)300 B)368 C)375 D)337 E)639 SOLUTION:A+B+C = 1200 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1200 => 300 Answer:A #### A QUESTION:If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)Rs. 750 B)Rs. 800 C)Rs. 850 D)Rs. 900 E)None of these SOLUTION:Explanation: Let the cost of Production = Rs. P Then, as per question, =>(125/100∗115/100∗110/100∗P)=1265 =>253/160P=1265 =>P=800 Option B #### B QUESTION:How many bricks, each measuring 125 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm? options: A)1280 B)2400 C)5500 D)7400 E)3400 SOLUTION:Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (125 x 11.25 x 6) = 1280 ANSWER:A #### A QUESTION:P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}? options: A){6, 12} B){6, 15} C){21,28} D){9, 15} E){15, 24} SOLUTION:p/q= d=p/q+7 d= .75 q d= .6(q+7) we get d = 21 and q = 28. Answer = C. #### C QUESTION:A car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+336*6=448c =>c=336*6/112=18 Answer B. #### B QUESTION:If A : B = 4 : 9 and B : C = 5 : 9 then A : B : C is : options: A)20 : 35 : 63 B)35 : 36 : 63 C)30 : 35 : 65 D)20 :45: 81 E)None of these SOLUTION:Expl : A : B = 4 : 9 B : C = 5 :9 = 5*9/5 : 9 *9/5 = 9 : 81/5 A : B : C = 4 : 9 : 81/5 = 20 : 45 : 81 Answer: D #### D QUESTION:If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. ab < 1 III. a/b < 2 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:MANHATTAN GMATOFFICIAL SOLUTION: You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term: 1 > 1 - ab > 0 0 > -a b > -1 Subtract 1 from all three terms. 0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs. Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true. Therefore, the correct answer is (D). #### D QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:A man saves 10% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 5%, he is only able to save Rs. 400 per month. What is his monthly salary? options: A)Rs.6500 B)Rs.7500 C)Rs.7200 D)Rs.7273 E)Rs.6300 SOLUTION:Income = Rs. 100 Expenditure = Rs. 90 Savings = Rs. 10 Present Expenditure 90+90*(5/100) = Rs.94.5 Present Savings = 100 – 94.5 =Rs. 5.50 If savings is Rs. 5.50, salary = Rs. 100 If savings is Rs.400, salary = 100/5.5*400 = 7273 Answer : D #### D <<<Examples ends QUESTION:Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? options: A)635.50 B)635.53 C)635.57 D)635.52 E)635.51 SOLUTION:4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 Answer: A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:The length of a rectangle is halved, while its breadth is tripled. What is the % change in area? options: A)30% B)40% C)50% D)60% E)65% SOLUTION:Let original length = x and original breadth = y. Original area = xy. New length = x . 2 New breadth = 3y. New area = x x 3y = 3 xy. 2 2 Increase % = 1 xy x 1 x 100 % = 50%. 2 xy C #### C QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle? options: A)16 B)25 C)33 D)46 E)58 SOLUTION:The perimeter of a circle is 2*pi*r. The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r The perimeter is pi*9 + 2*9 which is about 46. The answer is D. #### D QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:10, 20, 12, 24, 16, 32, ? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:E 24 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is: options: A)15 B)18 C)19 D)22 E)23 SOLUTION:explanation: 60-6= 54 ,190-10= 180 Highest number that divides 54 and 180 is HCF of numbers HCF of 54 nad 180= 18 Answer:B #### B QUESTION:A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 1170, what will be B's share of the earnings? options: A)$390 B)$520 C)$1080 D)$1170 E)$630 SOLUTION:Explanatory Answer A, B and C will share the amount of $1170 in the ratio of the amounts of work done by them. As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day. Similarly, B will complete 1/8th and C will complete 1/12th of the work. So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12 Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values. We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2. i.e., the ratio in which A : B : C will share $1170 will be 4 : 3 : 2. Hence, B's share will be 3*1170/9 = 390. correct choice is (A) #### A QUESTION:A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 5 hours. During that time, the faster car traveled 2/3 of the distance XY. How long would it take the slower car to travel the distance XY? options: A)6 hours B)8 hours C)10 hours D)12 hours E)15 hours SOLUTION:If one car travelled 2/3, then the other car must have travelled only 1/3, as they are meeting after 5 hours in a certain point. So: (1/3)XY= 4*y --> It took the car 5 hours to travel 1/3 of the distance at a constant speed y. So if we solve this last equation: XY= 3*5*y= 15*y --> It will take this car 15 hours in total to reach its final destination. Answer: E #### E QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)22:21 C)21:32 D)31:21 E)32:28 SOLUTION:Here capital is not the same. Suresh invest 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =( 20000*6 + 15000*6) Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ration = (30000*4 : 50000*4) Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4) = (20*6 + 15*6) : (30*4 + 50*4) = (20*3 + 15*3) : (30*2 : 50*2) = 105:160 = 21:32 Answer is C #### C QUESTION:A and B invests Rs.3000 and Rs.6500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)8:8 B)9:8 C)9:6 D)9:5 E)9:13 SOLUTION:(3*6 + 6*6): (6.5*12) 54:78 => 9:13 Answer: E #### E QUESTION:The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be social teachers? options: A)2/3 B)1/12 C)2/9 D)1/2 E)1/24 SOLUTION:Probability of first member an English teacher = 3/9 Probability of second member an English teacher = 2/8 Probability of both being english teacher = 3/9 x 2/8 =1/12 (B) #### B QUESTION:A train 160m long is running at 30kmph. In how much time will it pass a platform 120m long? options: A)15.89 seconds B)24.36 seconds C)15.96 seconds D)14.93 seconds E)22.23 seconds SOLUTION:Distance travelled = 160 + 120m = 280m Speed = 30 * 5/8 = 75/4m Time = 280 * 4/75 = 14.93 Seconds Answer : D. #### D QUESTION:If the sides of a triangle are 26 cm, 24 cm and 20 cm, what is its area? options: A)120 B)772 C)288 D)266 E)240 SOLUTION:The triangle with sides 26 cm, 24 cm and 20 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 20 = 240 cm2 Answer: E #### E QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:A can do a piece of work 20 days. B can do work in 35 days. In how many days they will complete the work together? options: A)15 days B)16.32 days C)12.72 days D)17 days E)18 days SOLUTION:LCM = 140, Ratio= 20:35=4:7 No of days= 140/(4+7) = 90/5 = 12.72 days ANSWER:C #### C QUESTION:1397 x 1397 = ? options: A)1961609 B)1851609 C)1951619 D)1951609 E)1851619 SOLUTION:1397 x 1397 = (1397)^2 = (1400 - 3)^2 = (1400)^2 + (3)^2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer is D. #### D QUESTION:45 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine? options: A)80 litres B)90 litres C)120 litres D)170 litres E)None of these SOLUTION:Explanatory Answer To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*45 = 60 litres. However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity. i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too. Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*60 = 90 litres. Answer B #### B QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T? options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150 SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1. The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15. Hence, the probability that at least one light bulb fails is 1-0.94^15. Answer: A. Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A QUESTION:Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? options: A)54 B)59 C)63 D)71 E)62 SOLUTION:Total = 70 Thrower = 46 Rest = 70 - 46 = 24 Left Handed = 24/3 = 8 Right handed = 16 If all Thrower are right handed then total right handed is 46 + 16 = 62 so E. 62 is the right answer #### E QUESTION:For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution? options: A)12 B)9 C)3 D)7.5 E)2.5 SOLUTION:we have 2 equations 1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36 2. kx + 12y = 30 substract 1-2, we get (9-K)x = 6 i.e. x = 6/(9-k) then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B #### B QUESTION:Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is options: A)4 : 5 B)1 : 2 C)6 : 7 D)5 : 6 E)None SOLUTION:Solution Let us name the brothers as A and B. = (A'S speed) : (B's speed) =√b : √a = √25 : √36 = 5 : 6 Answer D #### D QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes? options: A)2 B)4 C)6 D)500 E)0 SOLUTION:2 men.....there are no other!!!! #### A QUESTION:If 2994 ÷ 14.5 = 179, then 29.94 ÷ 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.9 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 179 in the place of 2994/14.5 ] = 179/10 = 17.9 Answer is E. #### E QUESTION:Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age? options: A)56 years B)72 years C)56 years D)66 years E)76 years SOLUTION:Let the age before 10 years =x. Then, 115x/100=x+10 ⇒115x=100x+1000 ⇒x=1000/15=66 Present age =x+10=66+10=76 ANSWER:E #### E QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:A man can row upstream at 22 kmph and downstream at 42 kmph, and then find the speed of the man in still water? options: A)29 B)92 C)30 D)32 E)23 SOLUTION:US = 22 DS = 42 M = (42 + 22)/2 = 32 Answer:D #### D QUESTION:A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 70% total profit if he has already sold one of the four cars at Rs. 1.2 lakh? options: A)1.8 lakh B)1.3 lakh C)1.9 lakh D)8.1 lakh E)6.1 lakh SOLUTION:Explanation: Total cost of 4 cars = 1+2 = 3 lakh Total SP of 4 cars = 3 x 1.7 = 5.1 lakh SP of 1 car = 1.2 lakh SP of rest 3 cars = 5.1 - 1.2 = 3.9 lakh Average SP of all the 3 cars = 1.3 lakh Answer: B) #### B QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 6*6 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems? options: A)676 B)833 C)1023 D)839 E)1035 SOLUTION:Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted. Hence, the required number of ways = 45 - 1. = 210 - 1 = 1024 - 1 = 1023 Answer:C #### C QUESTION:If r is a positive integer and r^2 is divisible by 12, then the largest positive integer that must divide r ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since r is an integer so r cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making r^2 as a multiple of 12)) r^2 is divisible by 12 (12 = 2*2*3), So, r should have at least one 2 and one 3 so that r^2 has a 2^2 and two 3 So, r will have a 2 and a 3. Or r will be a multiple of 6 So, largest possible integer than should divide r^3 is 6^3 So, Answer will be D #### D QUESTION:Three friends A, Band C started a business by investing a sum of money in the ratio of 5 : 7 : 6. After 6 months C withdraws half of his capital. If the sum invested by ‘A’ is 40,000, out of a total annual profit of 33,000, C’s share will be options: A)9,000 B)12,000 C)11,000 D)10,000 E)None of these SOLUTION:Sum invested by A, B and C is 5 × 12 : 7 × 12 : 6 × 6 + 3 × 6 or, 60 : 84 : 54 or, 10 : 14 : 9 \Share of C = 9⁄33 × 33,000 = 9,000 Answer A #### A QUESTION:Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3? options: A)2/5 B)2/7 C)33/83 D)51/250 E)100/249 SOLUTION:SOLUTION The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250. Answer: D #### D QUESTION:Becky, Merry and John want to share a chocolate bar evenly. What part of the bar will each of them take? What part of the bar will Becky and Merry have together? options: A)1/3 B)2/3 C)2/4 D)None of these E)Cannot be determined SOLUTION:Solution The children need to divide the bar into three pieces. So everyone will take 1/3 of the chocolate bar. Two girls together will have two pieces, hence, mathematically speaking, they will have 2/3 of the bar Answer B #### B QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5 options: A)134 B)136 C)140 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 72 kmph? options: A)22 sec B)77 sec C)25 sec D)18 sec E)12.5 sec SOLUTION:D = 100 + 150 = 250 S = 72 * 5/18 = 20 mps T = 250/20 = 12.5 sec Answer:E #### E QUESTION:A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings? options: A)16 B)56 C)112 D)28 E)38 SOLUTION:In 8 different toppings, selecting 2 diff toppings = 8c2 formula is n!/(n-c)! n = total number of toppings C = number chosen in a grouping. n=8 and c=2 so we get 8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1) = 8*7 =56 ANSWER:B #### B QUESTION:In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have? options: A)180 B)45 C)60 D)90 E)135 SOLUTION:We can start with the known quantity and then go on to find the others. Shiny igneous ricks are 40. These are (2/3) of total igneous rocks. (2/3)*Total igneous rocks = 40 Total igneous rocks = 40 * (3/2) = 60 Total sedimentary rocks = 2*Total igneous rocks = 2*60 = 120 Total number of rocks = 60 + 120 = 180 Answer (A) #### A QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed? options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5! SOLUTION:Explanation: Total number of letters = 5 Using these letters the number of 5 letters words formed is 5!. Answer: Option E #### E QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students Q in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:If equation |x/2| + |y/2| = 2 encloses a certain region on the coordinate plane, what is the area of this region? options: A)20 B)32 C)100 D)200 E)400 SOLUTION:The equation can be reduced to intercept form as |x/4| + |y/4| = 1, so these are lines in four quadrants with x and y intercept as 14, so it is a rhombus with diagonals of 8 each and hence area = 1/2*d1*d2 = 1/2*8*8 = 32. Answer B. #### B QUESTION:What approximate value should come in plce of question mark (?) in the following equations ? 728.038 x 54.978 - 72.016 x 85.250 = ? options: A)31400 B)32700 C)33900 D)34400 E)32400 SOLUTION:Explanation : ? = 728 x 55 - 72 x 85.25 = 40040 - 6138 = 339900 Answer : Option C #### C QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)11x/y B)10x/y C)x/11y D)11/xy E)xy/11 SOLUTION:Answer is B. The rate of running hards: 10 minutes per y hards. Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y #### B QUESTION:The present age of a father is 3 years more than three times the age of his son. Five years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father. options: A)33 B)38 C)27 D)40 E)48 SOLUTION:if the present age be x years. father's will be (3x+3)years.. so, (3x+3+5)=2(x+3)+10 or, x=8 so the fathers present age =(3x+3)=(3*8+3)years =27 years.. ANSWER : OPTION C #### C QUESTION:Today is Sunday. The day after 59 days will be options: A)Monday B)Wednesday C)Saturday D)Sunday E)None of these SOLUTION:Explanation : 59 days = 8 weeks 3 days = 3 odd days Hence if today is Sunday, After 59 days, it will be = (Sunday + 3 odd days) = Wednesday. Answer : Option B #### B QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B? options: A)128228 B)12800 C)12819 D)12818 E)12812 SOLUTION:16*8: x*4 = 5:2 x = 12.8 => Rs.12800 Answer: B #### B QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,500 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Important point to notice- 2.5% decrease from the original price 2.5% of 22,000= 550 Total reduction in 6 years= 550*6= 3300 Final price= 22,000 +1500 - 3300= 20,200 C is the answer #### C QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work? options: A)6 days B)2 days C)4 4/5 days D)3 days E)9 days SOLUTION:Work done by A in 2 days = 2/10 = 1/5 Remaining work = 4/5 Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6 Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days. Answer: C #### C QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 4. What is the ratio of their heights? options: A)A)2:5 B)B)2:7 C)C)2:2 D)D)2:1 E)E)4:3 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(4)2h2 => h1/h2 = 4/3 i.e. h1 : h2 = 4 : 3 Answer: E #### E QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:In a kilometer race, A beats B by 16 meters or 10 seconds. What time does A take to complete the race? options: A)167 sec B)190 sec C)176 sec D)716 sec E)615 sec SOLUTION:Time taken by B run 1000 meters = (1000 * 10)/16 = 625 sec. Time taken by A = 625 - 10 = 615 sec. Answer:E #### E QUESTION:During a trip, joe traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francine's average speed for the entire trip? options: A)(180-x)/2 B)(x+60)/4 C)(300-x)/5 D)600/(115-x) E)12000/x+300 SOLUTION:total distance =100 ;total time = T t1 = x/30 t2 = 100-x /40 T =t1+t2 = x/30 + 100-x/40 = (40x + 3000- 30x)/1200 = (10x+3000)/1200 = x+300/120 av speed = 100*120/x+300 = 12000/x+300 E #### E QUESTION:If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+w + 11w × 6pw--1=B #### B QUESTION:If x/y =4/3, then (x-y)/x? options: A)-1/2 B)-1/4 C)1/3 D)1/2 E)1/4 SOLUTION:we have this law of fraction: a/b=c/d= (a-c)/(b-d) x/y=4/3 ---> x/4=y/3= (x-y)/(4-3)=(x-y)/(1) ---> (x-y)/x= 1/4 Answer: E #### E QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture? options: A)294 B)235 C)350 D)288 E)580 SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:The present worth of Rs.676 due in 2 years at 4% per annum compound interest is options: A)Rs.150.50 B)Rs.154.75 C)Rs.156.25 D)Rs.625 E)None SOLUTION:Solution Present Worth = Rs.[676/(1+4/100)²] = Rs.(676x25/26x25/26) = Rs.625 Answer D #### D QUESTION:Four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. In 18 minutes, how many times do they toll together ? options: A)43 B)44 C)45 D)46 E)47 SOLUTION:LCM of 2, 4, 6, 8 is 24. So, after each 24 seconds, they would toll together. Hence, in 18 minutes, they would toll 18*60 seconds / 24 seconds = 45 times But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second). So, total tolls together = 45+1 = 46 Answer C #### C QUESTION:The simple form of the ratio 4/5:8/9 is? options: A)5:8 B)4:9 C)5:9 D)5:3 E)9:10 SOLUTION:4/5 : 8/9 = 9:10 Answer: E #### E QUESTION:There are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? options: A)980 B)1150 C)1360 D)1540 E)1720 SOLUTION:The number of ways to choose two teams is 17C2 = 17*16/2 = 136 The total number of games in the season is 10*136 = 1360. The answer is C. #### C QUESTION:Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rest of the car, then the share of each of the remaining persons increased by ? options: A)1/9 B)1/8 C)1/7 D)7/8 E)8/7 SOLUTION:When there are eight people, the share of each person is 1/8th the total cost ANSWER:B #### B QUESTION:The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 8, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median? I. 3 II. 7 III. 12 options: A)I only B)II only C)III only D)I and III only E)I, II, and III SOLUTION:C for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8 #### C QUESTION:If n is a positive integer, which of the following is a possible value of |36 - 5n|? options: A)7 B)14 C)12 D)15 E)20 SOLUTION:When 36>5n, then |36- 5n| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1 When 36<=5n, then |36- 5n| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits. Answer: B #### B QUESTION:Two trains each 170m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 55km/h while the other travels at 50km/h. how long will it take for them to pass each other completely. options: A)15 sec B)11.6 sec C)31.6 sec D)12.6 sec E)23 sec SOLUTION:Explanation: D = 170 m + 170 m = 340 m RS = 55 + 50 = 105 * 5/18 = 146/5 T = 340 * 5/146 = 11.6 sec Answer: Option B #### B QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce options: A)100 B)65 C)25 D)11 E)18 SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. So if machine X produces 100 widgets, then machine Y produces 120 widgets. Ratio of 120/100 = 6/5. This is their speed of work (Y:X). i.e. speed of their work (X:Y) = 5/6 Now, time is inversely proportional to speed. Hence the ratio of the time spent (X:Y)= 6/5 Let us assume that they spend 6x and 5x hours. Given that 6x-5x = 10 So, x = 10. Hence 6x = 6*10 = 60 hours. Hence X takes 120 hours to produce 1080 widgets. So, in 1 hour, it can produce (1 * 1080)/60 = 18 Hence option (E). #### E QUESTION:The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 80%? I will see what is the quickest way to solve it then I will provide the explanation options: A)6 B)7 C)9 D)10 E)11 SOLUTION:The following approach might be the easiest one and less error prone. We need on-time departure rate to be higher than 8/10, so it should be at least 9/11, which means that 9 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 9-3=6 subsequent flights need to depart on-time. Answer: A #### A QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1600. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)70.00% B)86.98% C)76.99% D)45% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1600 = Rs. 17600 and SP = Rs. 31150 Profit(%) = (31150 - 17600)/17600* 100 = 76.99% ANSWER:C #### C QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:A furniture manufacturer has two machines, but only one can be used at a time. Machine W is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine W can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? options: A)14 B)13 C)11 D)9 E)7 SOLUTION:'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days. To finish a work Machine W say you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D #### D QUESTION:Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+34 3x + 6 = x + 34 2x = 28 \inline \therefore x = 14 \inline \therefore Middle number = x + 2 = 14+2 = 16 D #### D QUESTION:The ratio 15:25 expressed as percent equals to options: A)70 % B)60 % C)30 % D)75 % E)None of above SOLUTION:Explanation: Actually it means 15 is what percent of 25, which can be calculated as, (15/25)*100 = 15 * 4 = 60 Answer: Option B #### B QUESTION:The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ? options: A)6 years B)7 years C)8 years D)9 years E)None SOLUTION:Answer Let the age of youngest child be y. so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12 ⇒ 4y + 24= 48 ∴ y = 6 years Correct Option: A #### A QUESTION:Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? options: A)10liters B)15liters C)20liters D)18liters E)22liters SOLUTION:Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters Let x liters of pure milk be added. Then, 0.5/(10+x) = 2/100 2x = 30 x=15 liters Answer is B #### B QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is: options: A)51:52 B)52:53 C)51:53 D)52:55 E)53:54 SOLUTION:Explanation: Let C.P. of the article be Rs. x. Then, required ratio = 104% of x / 106% of x = 104/106 = 52/53 = 52:53 ANSWER IS B #### B QUESTION:How much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)40 sec B)50 sec C)60 sec D)70 sec E)80 sec SOLUTION:The distance to be covered = Sum of their lengths = 400 + 300 = 700 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 700/10 = 70 sec. ANSWER:D #### D QUESTION:If a is an odd integer and b is an even integer which of the following must be an integer : options: A)a/b B)ab C)2a+b D)2(a+b) E)option B C and D SOLUTION:a= odd = e.g 3 b=even = e.g 6 A. odd/even for example 3/6 = 0.5 no even no odd B. odd * even = 3 * 6 = 18 even C. 2*odd + even = even + even even D. 2(even + odd) = 2(odd) even Hence E it is. #### E QUESTION:If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x? options: A)-1 B)2 C)1 D)-2 E)0 SOLUTION:If we solve the question, we get x=-2. Option: D #### D QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec. What is the length of the platform? options: A)389 m B)350 m C)187.5 m D)299 m E)219.5 m SOLUTION:Speed = 300/24 = 25/2 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 25/2 => x = 187.5 m. Answer:C #### C QUESTION:The area of a square is 625 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 20 cm less than the side of the square. options: A)5 : 12 B)5 : 13 C)2:9 D)1:15 E)1:5 SOLUTION:Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm. a2 = 625 a = 25 L = 3a and b = a - 20 b : l = a - 20 : 3a = 5 : 75 = 1:15 Answer: D #### D QUESTION:Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0 options: A)If x>y B)If x>=y C)If x<y D)If x<=y E)x=y or relationship cannot be established SOLUTION:Solution:- Solving we get X= -2/3 or -2 Y= 3/4 or 4 C) #### C QUESTION:What distance will be covered by a bus moving at 72 kmph in 30 seconds? options: A)287 B)600 C)289 D)276 E)207 SOLUTION:72 kmph = 72 * 5/18 = 20 mps D = Speed * time = 20 * 30 = 600 m. Answer:B #### B QUESTION:Find the fourth proportional to 2.8 , 3.4 and 5.2? options: A)5.98 B)6.14 C)6.29 D)6.31 E)5.64 SOLUTION:Formula = fourth proportion =(b x c)/a a=2.8 , b=3.4 and c=5.2 (3.4 x 5.2)/2.8=6.31 D #### D QUESTION:Two clocks are set at 3 0'clock in the morning. If one clock gains 10 minutes per hour and when it shows 6:30 in the morning what does the correct clock show? options: A)5:30 B)5:25 C)7:00 D)6:15 E)6:00 SOLUTION:The faster clock gains 10 minutes per hour. The two clocks at at 3:00 at 3 0'clock in the morning At 4 0'clock - The correct clock is at 4:00 The faster clock is at 4:10 (1 hour + gains 10 minutes) At 5 0'clock - The correct clock is at 5:00 The faster clock is at 5:20 (2 hours + gains 20 minutes) In three hours the faster clock gains 3*10=30 minutes When the faster clock is at 6:30 the correct clock is at 6:00 in the morning. Answer is E #### E QUESTION:There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. options: A)300 B)T=400 C)T=500 D)600 E)None of these SOLUTION:{Managers} = {Female Managers} + {Male Managers}; We are told that the total number of managers in the company is 2/5 of all the employees , thus {Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively. Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200; Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500. Answer: C. #### C QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet? options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location. In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same. Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle. Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate. The correct answer is (E). #### E QUESTION:What annual payment will discharge a debt of Rs. 1030 due in 2 years at the rate of 5% compound interest? options: A)553.94 B)551.25 C)534.33 D)543.33 E)646.33 SOLUTION:Explanation: Let each installment be Rs. x. Then, x/(1 + 5/100) + x/(1 + 5/100)2 = 1030 820x + 1030 * 441 x = 553.94 So, value of each installment = Rs. 553.94 Answer: Option A #### A QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper? options: A)30 B)40 C)42 D)44 E)46 SOLUTION:here two cases are possible. case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3 case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2 thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30 ANS:A #### A QUESTION:Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If they are 85 km apart both 3 and 6 hours after start, then find the distance between the two stations. options: A)255km B)210km C)220km D)180km E)200km SOLUTION:In first 3 hours T1 travels R km and T2 travels S km. After 6 hours they traveled R+S+85+ 85 2(R+S ) = R+S +170 R+S = 170 Hence distance between XY is R+S+ 85 = 170 +85 =255 Answer : A #### A QUESTION:Two trains are moving in the same direction at 126 kmph and 54 kmph. The faster train crosses a man in the slower train in 14 seconds. Find the length of the faster train? options: A)280 B)290 C)300 D)310 E)320 SOLUTION:Relative speed = (126 - 54) * 5/18 = 4 * 5 = 20 mps. Distance covered in 27 sec = 14 * 20 = 280 m. The length of the faster train = 280 m. Answer:A #### A QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was options: A)960 B)980 C)900 D)970 E)1000 SOLUTION:Explanation: Let original Cost price is x Its Selling price = (105/100) * x = 21x/20 New Cost price = (95/100) * x = 19x/20 New Selling price = (110/100 )* (19x/20 )= 209x/200 [(21x/20) - (209x/200)] = 1 => x = 1000 Answer: E) Rs 1000 #### E QUESTION:If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q options: A)1 B)3 C)5 D)7 E)9 SOLUTION:3/7 = 0.428571... (a repeating pattern one digit long) B #### B QUESTION:A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)227 B)400 C)230 D)288 E)271 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 42 = 50/3 3(x + 300) = 2100 è x = 400m. Answer: B #### B QUESTION:How much 60% of 50 is greater than 40% of 30? options: A)18 B)28 C)26 D)27 E)23 SOLUTION:(60/100) * 50 – (40/100) * 30 30 - 12 = 18 Answer:A #### A QUESTION:Which of the following is an integer? I. 9! / 6! II. 9! / 8! III. 9! / 7!5! options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:9!/6! = 9*8*7 which is an integer. 9!/8! = 9 which is an integer. 9!/7!5! = 9*8 / 5*4*3*2 = 3/5 which is not an integer. The answer is D. #### D QUESTION:An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is: options: A)2/91 B)1/22 C)3/22 D)2/77 E)None of these SOLUTION:Explanation : Let S be the sample space. Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455 Let E = event of getting all the 3 questions from simple mathematics section. n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10 P(E) = n(E)/n(S) = 10/455 = 2/91 . Answer : A #### A QUESTION:Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds? options: A)186 B)130 C)180 D)181 E)120 SOLUTION:LCM of 9, 12, 15 and 18 is 180 LCM=180 ANSWER:C #### C QUESTION:A man buys s cycle for $100 and sells it at a loss of 10%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 90% of the $100 = 90/100 * 100 = $90 Answer is E #### E QUESTION:The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago? options: A)1: 3 B)2: 3 C)3:3 D)4: 3 E)5: 4 SOLUTION:3x-25/2x-25 = 4/3 Therefore x=-25 Age cannot be negative. Answer: D #### D QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 3 : 3? options: A)16 B)48 C)277 D)92 E)11 SOLUTION:Let the distances between city A to B and B to C be 3x km and 3x km respectively. Total time taken to cover from A to C = (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph. Answer:B #### B QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/6. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)25. B)24. C)23. D)20. E)16. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 6,5 and 10 Lets take LCM of three balls 6,5 and 10 = 30. The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS. Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls. IMO option E is correct. #### E QUESTION:A, B and C rents a pasture for Rs.638. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay? options: A)270 B)198 C)676 D)156 E)122 SOLUTION:12*8 :16*9 = 18*6 8: 12: 9 9/29 * 638= 198 Answer: B #### B QUESTION:At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock options: A)47 B)76 C)28 D)66 E)99 SOLUTION:Explanation: For ticking 6 times, there are 5 intervals. Each interval has time duration of 45/5 = 9 secs At 12 o'clock, there are 11 intervals, So total time for 11 intervals = 11 × 9 = 99 secs. Answer: E #### E QUESTION:Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number. options: A)42 B)48 C)72 D)67 E)54 SOLUTION:Sol: Let the third number be x. Then second number = 3x. First number=3x/2. Therefore x+3x+(3x/2)=(44*3) or x=24 So largest number= 2nd number=3x=72 ANSWER :C #### C QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:A can do a work in 15 days and B in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is options: A)8/17 B)7/15 C)3/15 D)5/12 E)1/4 SOLUTION:Person ( A ) ( B ) ( A+B ) Time - ( 15 ) ( 20 ) (-) Rate - ( 20 ) ( 15 ) ( 35 ) Work -(300) (300) (300) therefore A+B requires (300/35) days to complete entire work For 1st 5 days they work 35 * 5 = 175 Remaining work is 300 - 175 = 125 Remaining fraction of work is = 125/300 = 5/12 Answer D #### D QUESTION:Albert borrowed a total of $ 6000 from john and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)571 B)581 C)441 D)445 E)631 SOLUTION:Let x be the amount borrowed form john. So amount borrowed form Charlie = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 3*7/100*2100 = 441. C #### C QUESTION:Two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)28 B)266 C)990 D)20 E)22 SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 160 + 280 = 440 m. The time required = d/s = 440/20 = 22 sec. Answer: E #### E QUESTION:In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.0 sec B)2.8 sec C)7.5 sec D)2.3 sec E)1.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 80/40 = 2.0 sec. Answer:A #### A QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent? options: A)28% B)25% C)55% D)17.6% E)55% SOLUTION:850 --- 150 100 --- ? => 17.6% Answer: D #### D QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score? options: A)662 B)678 C)652 D)642 E)721 SOLUTION:8 * 86 = 688 – 10 = 678 ANSWER:B #### B QUESTION:Three faces of a fair die are Yellow, two faces red and two blue.The die is tossed three times. The probability that the colours, yellow, red and blue appear in the first, second and third tosses respectively is options: A)1/36 B)1/18 C)1/32 D)1/37 E)None of these SOLUTION:Probability of getting yellow color = P(Y) = 3/6 = 1/2 Probability of getting red color = P(R) = 2/6 = 1/3 Probability of getting blue color = P(B) = 2/6=1/3 So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/2 x 1/3 x 1/3 = 1/18 ANSWER:B #### B QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze? options: A)1298 B)1228 C)1210 D)1782 E)1762 SOLUTION:π (232 – 122) = 1210 Answer:C #### C QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required? options: A)34 B)40 C)68 D)88 E)26 SOLUTION:We have: l = 20 ft and lb = 60 sq. ft. So, b = 3 ft. Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft. ANSWER:E #### E QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7 SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144. Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520. P = favorable/total = 2520/144 = 35/2. Answer: B. #### B QUESTION:Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time W will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did? options: A)2 minute and 12 seconds. B)two minutes. C)44 seconds. D)20 seconds. E)12 seconds. SOLUTION:Tom is running alone for 20 seconds. So he will cover a distance of 20*2.5 = 50 m in 20 seconds=W Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side D is the answer #### D QUESTION:A no. when divided by 35leaves a remainder 20, what is the remainder if the same no.be divided by 15? options: A)2 B)4 C)7 D)8 E)9 SOLUTION:Explanation: 35 + 25 = 60/15 = 4 (Remainder) B #### B QUESTION:Preeti covers a distance in 40 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 50%. options: A)60 km/h B)70 km/h C)117.64 km/h D)100 km/h E)125.25 km/h SOLUTION:Given Speed = 60 Kmph. It means Preeti covered 60 km in 60 min (1 hour). So, in 40 min he will cover 40 km. 50% time reduced = 40 - 50% of 40 = 20 min. Thus, Preeti needs to cover 40 km in 20 min (0.34 hour). Speed * Time = Distance. Speed * 0.34 = 40 Speed = 117.64 kmph. ANSWER : OPTION C #### C QUESTION:If cost of sugar increases by 25%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? options: A)20 B)40 C)15 D)16 E)12 SOLUTION:100 125 ----- 125 ----- 25 100 ------ ? => 20% ANSWER A #### A QUESTION:How many bricks, each measuring 125 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm? options: A)1280 B)2400 C)5500 D)7400 E)3400 SOLUTION:Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (125 x 11.25 x 6) = 1280 ANSWER:A #### A QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer: A #### A QUESTION:A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers? options: A)700; 1100 B)1072; 528 C)1000; 800 D)1200; 800 E)None of the above SOLUTION:The method given above is the one given in the book. However the method I used was (1*x*5)/100 + (1600-x)*6/100 = 1600*5.67/100 Simplifying we get x= 528 B #### B QUESTION:For a lottery, three numbers are drawn, each from 1 to 40. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning? options: A)01 B)025 C)115 D)125 E)5 SOLUTION:(1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38))((1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38)) ((1/8)−(9/78))((1/8)−(9/78)) (0.125−approx.0.1111)(0.125−approx.0.1111) Approximately 0.010.01 ANSWER :A #### A QUESTION:Which expression is the greatest? options: A)3252/3257 B)3456/3461 C)3591/3596 D)3346/3351 E)3453/3458 SOLUTION:Let 3252/3257 be the original fraction. Notice that it is a positive Proper fraction. Hence adding the same constant to both the numerator and the denominator will increase the fraction as the fraction will move closer to one. Hence we just have to pick the number that adds the greatest value to both the numerator and the denominator. Options can be re-written as (x-5)x => 1-(5/x) A) 1- (5/3257) B) 1- (5/3461) C) 1- (5/3596) D) 1- (5/3351) E) 1- (5/3458) ANSWER:C #### C <<<Examples ends QUESTION:Find the missing in the series: 70, 54, 45, 41,___ options: A)22 B)287 C)2679 D)2767 E)2771 SOLUTION:Answer:B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits? options: A)X-Y B)Y-X +100 C)100X-Y D)X+Y-100 E)100-XY SOLUTION:Using the simple formula 100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values. Hence Answer D #### D QUESTION:If f(x) = (x^2 - 1)/(x), what is f(1/x) in terms of f(x)? options: A)-1*f(x) B)f(x) C)1/f(x) D)-1/f(x) E)2*f(x) SOLUTION:f(1/x) = ((1/x)2 - 1) / ((1/x)) = ((1/x^2) - 1) / (1/x) = ((1-x^2)/(x^2)) / (1/x = (1-x^2)/(x^2) = - ( (x^4) -1) / (x) = -1* f(x) Answer is A. #### A QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)20 B)15 C)25 D)18 E)12 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 6 = 26 => x = 5 Deepak's age = 3x = 15 years. ANSWER B #### B QUESTION:Tanks P and B are each in the shape of a right circular cylinder. The interior of tank P has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank P is what percent of the capacity of tank B? options: A)75% B)80% C)100% D)120% E)125% SOLUTION:B. For P, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi P/B = 160pi/200pi = 0.8 #### B QUESTION:A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is options: A)400 kg B)560 kg C)600 kg D)640 kg E)None SOLUTION:Solution ratio of 1st and 2nd parts = 4 : 6 = 2 : 3. Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg. Answer C #### C QUESTION:A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work? options: A)10 B)12 C)22 D)28 E)20 SOLUTION:A can do the work in 60/4 i.e., 15 days. A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12 So A and B together can do the work in 12 days. Answer: B #### B QUESTION:The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02 is: 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04 options: A)0.0125 B)0.125 C)0.25 D)0.5 E)None of these SOLUTION:Explanation: Given expression = (0.1)3 + (0.02)3=1= 0.125 23 [(0.1)3 + (0.02)3] =8 Answer- B #### B QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow? options: A)4/8 B)9/2 C)7/6 D)9 E)2/21 SOLUTION:Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³Câ‚‚/¹⁵Câ‚‚ = (3 * 2)/(15 * 14) = 1/35 Probability that both are yellow = ²Câ‚‚/¹⁵Câ‚‚ = (2 * 1)/(15 * 14) = 1/105 Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵Câ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35 Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 * 35) = 2/21 Answer: E #### E QUESTION:The 40 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees? options: A)4 B)6 C)8 D)9 E)10 SOLUTION:The formula is Total = A+B+C - sum of exactly two + 2*all three + neither 21+18+19-x-2*5=40 solving for x you get 8 Answer C #### C QUESTION:The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size? options: A)6 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Side of smallest cube = L.C.M of 5,10,20 = 20cm Volume of the cube = (20 x 20 x 20)cm3 = 8000 cm3 Volume of the block= (5 x 10 x 20) cm3 = 1000 cm3 Number of blocks = (8000/1000) = 8 Answer: B #### B QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l * l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: options: A)279 B)283 C)308 D)318 E)342 SOLUTION:Other number = (11 x 7700)/275 = 308. Answer: Option C #### C QUESTION:A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ? options: A)Rs.8600 B)Rs.8620 C)Rs.8820 D)Rs. 8840 E)Rs. 8940 SOLUTION:Amount = 8000 *1+(5/100)2 = 8000 *21/20 * 21/20 = Rs.8820 ANSWER:C #### C QUESTION:When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 42 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile? options: A)5 minutes, 17.6 seconds B)5 minutes, 21.8 seconds C)5 minutes, 43.56 seconds D)5 minutes, 44.44 seconds E)6 minutes, 10.4 seconds SOLUTION:One approach: The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 42 seconds. The only number is 6 minutes, 10.4 seconds. Another approach: 11/25 close to 30 second when added to the 5 minutes, 44 seconds, it means it passes 6 minute. Answer: E #### E QUESTION:2 pipes can separately fill a tank in 20hrs and 30hrs respectively. Both the pipes are opened tofill the tank, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank? options: A)12 hrs B)14 hrs C)16 hrs D)18 hrs E)20 hrs SOLUTION:1/20 + 1/30 = 1/12 1 + 1/3 = 4/3 1 --- 12 4/3 --- ? 4/3 * 12 = 16 hrs C #### C QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days? options: A)87 B)18 C)42 D)16 E)10 SOLUTION:Binders Books Days 35 1400 21 x 1600 20 x/35 = (1600/1400) * (21/20) => x = 42 Answer:C #### C QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? options: A)10 B)88 C)267 D)28 E)21 SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:Pencils, Pens and Exercise books in a shop are in the ratio of 14: 4 : 3. If there are 140 pencils, the number of exercise books in the shop is: options: A)30 B)27 C)35 D)33 E)37 SOLUTION:Explanation : Let Pencils = 14x, Pens = 4x & Exercise books = 3x. Now, 14x = 140 hence x = 10 Number of exercise books = 3x = 30 Answer : A #### A QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet? options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am SOLUTION:meet x hrs after 8 a.m. (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330 ==>60x+75(x-1) = 330 x=3. So,they meet at (8+3). i.e 11a.m. ANSWER A #### A QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)299 B)267 C)269 D)400 E)276 SOLUTION:2*12 : 3*12 : 4*24 1: 3: 4 1/8 * 3200 = 400 Answer: D #### D QUESTION:The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television? options: A)106.75 B)213.5 C)427 D)729 E)1,156 SOLUTION:Diagonal of a square =√2*side of square => side =Diagonal/(√2) Area of square =s*s =(diagonal^2)/2 Difference of both tv's =(34^2-27^2)/2 =427 ANSWER:C #### C QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 4x+ 4y > 4z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 4x+ 4y > 4z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B #### B QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:If x = 3 and y = 2, what is the value of 5(x-y)^2 - xy ? options: A)-8 B)-7 C)-1 D)-2 E)-5 SOLUTION:x = 3 and y = 2 x-y = 3 - 2 = 1 x*y = 3 * 2 = 6 Now we apply it in the equation 5(x-y)^2 - xy =5 (1)^2-6 ==>5*1 -6 = 5-6 =-1 Answer : C #### C QUESTION:The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z? options: A)35 B)33 C)28 D)21 E)15 SOLUTION:The smallest possible product is 33 which is 3*11. All other products are too big. The answer is B. #### B QUESTION:Walking at 8KMPH From Point E to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point E to Railway station? options: A)A)9KM B)B)6.66KM C)C)7.25KM D)D)12.40KM E)E)13KM SOLUTION:Since time differences given are in minutes so let's convert speed in Km per minute 8 kmph = 8/60 km per minute = (2/15) km per minute 10 kmph = 10/60 km per minute = (1/6) km per minute Let, Time of train to depart from station = t minutes Distance between Point E and Railway Station = Speed*Time = (2/15)*(t+5) Distance between Point E and Railway Station = Speed*Time = (1/6)*(t-5) i.e. (2/15)*(t+5) = (1/6)*(t-5) i.e. 12t+60 = 15t - 75 i.e. 3t = 135 i.e. t = 45 minutes i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km Answer: Option B #### B QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)247 m B)256 m C)245 m D)527 m E)725 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C #### C QUESTION:A mixture of 150 liters of wine and water contains 15% water. How much more water should be added so that water becomes 25% of the new mixture? options: A)10 B)30 C)20 D)15 E)17 SOLUTION:Number of liters of water in150 liters of the mixture = 15% of 150 = 15/100 * 150 = 22.5 liters. P liters of water added to the mixture to make water 25% of the new mixture. Total amount of water becomes (22.5 + P) and total volume of mixture is (150 + P). (22.5 + P) = 25/100 * (150 + P) 90+4P = 150+P P = 20 liters. Answer: C #### C QUESTION:in base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 1*72+3*7+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7? options: A)11101 B)11110 C)10111 D)11011 E)11010 SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0) 3+4 + 1 carry from above step= 1 and 1 carry to next digit 2+5 + 1 carry to next digit= 1 and 1 carry 1+6= 11 so ans=11110 ANSWER:B #### B QUESTION:If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? options: A)10,573 B)11,908 C)12,322 D)13,924 E)14,537 SOLUTION:The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9. The answer is D. #### D QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)69 E)71 SOLUTION:1/2 * d (12 + 8) = 690 d = 69 Answer: D #### D QUESTION:If w<0, which of the following must be true? options: A)–100 < w < 100 B)w ≤ –1 C)w ≤ 1 D)w^2 ≥ 1/4 E)–100 < w < 0 SOLUTION:w is a negative number. A. –100 < w < 100w can be a negative number less than -100 B. w ≤ –1w can be a fraction, in which case it would be greater than -1 C. w ≤ 1must be true since 1 is positive and w is negative D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5 E. –100 < w < 0w can be a negative number less than -100=C #### C QUESTION:One computer can upload 100 megabytes worth of data in 4 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 20 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data? options: A) 6 B) 2.5 C) 9 D) 11 E) 13 SOLUTION:Since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4*5=20 seconds it can upload 5*100=500 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-500=800 megabytes worth of data. The second computer can upload 100 megabytes of data in 2.5 seconds. Answer: B. #### B QUESTION:A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively. options: A)200, 360,162 B)200, 460,160 C)200, 360,160 D)200, 360,138 E)200, 360,129 SOLUTION:Explanation: let ratio be x. Hence no. of coins be 5x ,9x , 4x respectively Now given total amount = Rs.206 => (.50)(5x) + (.25)(9x) + (.10)(4x) = 206 we get x = 40 => No. of 50p coins = 200 => No. of 25p coins = 360 => No. of 10p coins = 160 Answer: C) #### C QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:The sale price sarees listed for Rs.528 after successive discount is 20% and 10% is? options: A)288 B)277 C)380 D)290 E)262 SOLUTION:528*(80/100)*(90/100) = 380 Answer: C #### C QUESTION:[1/(1.2.3)] + [1/(2.3.4)] + [1/(3.4.5)] + [1/(4.5.6)] is equal to options: A)7 / 30 B)11 / 30 C)13 / 30 D)17 / 30 E)None SOLUTION:Answer Given Exp. = [(4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3)] / [(2 x 3 x 4 x 5 x 6)] = 168 / (24 x 30) = 7 / 30 Correct Option: A #### A QUESTION:If 20% of a number = 1000, then 120% of that number will be? options: A)20 B)120 C)360 D)6000 E)820 SOLUTION:Let the number x. Then, 20% of x = 1000 x = (1000 * 100)/20 = 5000 120% of x = (120/100 * 5000) = 6000. ANSWER:D #### D QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 10 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)80 C)100 D)125 E)21 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 4.4 , so radius is 2.2 New area = 4.84π Increase in area is 0.84π % increase in area = 0.84/4*100 So, % increase is 21% Answer will be (E) #### E QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4 Total factors = (4+1)*(4+1) = 6*4 = 24 Answer C. #### C QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 8x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400. Hence, (R - p) = (2400 - 900) = 1500 Answer : B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)22 B)287 C)48 D)277 E)21 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: C #### C QUESTION:An investor receives a total combined return of 7% on his two different investments. On his $40,000 investment he receives a return of 6%. What is the return on his $20,000 investment? options: A)7.25% B)7.5% C)8% D)8.5% E)9% SOLUTION:0.06 * 40000 + 20000x = 0.07(60000) solving for x give x = 9% option E #### E QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.2 km long? options: A)2 mins 14 sec B)2 mins 34 sec C)162 sec D)244 sec E)2 mins 44 sec SOLUTION:D = 25 * 60 + 1200 = 2700 m T = 2700/60 * 18/5 = 162 sec ANSWER:C #### C QUESTION:A 270m long train running at the speed of 120kmph crosses another train running in opposite direction at the speed of 80kmph in 9 second. What is the length of the other train? options: A)150m B)230m C)290m D)310m E)420m SOLUTION:Relative speed = 120+80 = 200*5/18 = 500/9 m/s Let the length of the other train be x meters x+270/9 = 500/9 x = 230m Answer is B #### B QUESTION:What is the sum of the numbers between 1 and 20, inclusive? options: A)310 B)200 C)215 D)285 E)210 SOLUTION:Sol. 1+2+3...17+18+19+20 answer. E #### E QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:On a map the distance between two mountains is 310 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain? options: A)14.83 B)14.81 C)14.91 D)14.82 E)14.12 SOLUTION:Explanation: Since 310 inch = 136 km So 1 inch = 136/310 km So 34 inch = (136 × 34)/ 310 = 14.91 km Answer: C #### C QUESTION:walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is. options: A)7 B)8 ½ C)7 ½ D)7 ¾ E)9 ½ SOLUTION:Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T = 5/2 T=15/2 = 7 ½ Answer is C. #### C QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:If A got 80 marks and B got 60 marks, then what percent of A's mark is B's mark? options: A)60% B)80% C)65% D)75% E)None of these SOLUTION:A's marks = 80 ; B's marks = 60. Let x% of A = B => x/100 * 80 = 60 => x = (60 * 100)/80 = 75 B's marks is 75% of A's marks. ANSWER:D #### D QUESTION:A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14% while buying and by 20% while selling. What is his percentage profit? options: A)10.22% B)20.22% C)21.22% D)42.5% E)Can't be calculated SOLUTION:The owner buys 100 kg but actually gets 114kg; The owner sells 100 kg but actually gives 80kg; Profit: (114-80)/80*100=~42.5% Answer: D. #### D QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856 SOLUTION:(900*3*3)/100 = 81 920 + 81 = 1001 ANSWER:B #### B QUESTION:Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select? options: A)54 B)72 C)96 D)144 E)432 SOLUTION:Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement.2 candles from 4 candles: 4C2: 6 8 flowers from 9 flowers: 9C8 : 9 So total grouping 9*6= 54. Answer is A. #### A QUESTION:Excluding stoppages,the speed of the bus is 54kmph and including stoppages,it is 27kmph. For how many minutes does the bus stop per hr options: A)12 min B)11 min C)13 min D)20 min E)30 min SOLUTION:Due to stoppages,it covers 27km less. time taken to cover 27 km is [27/54 *60] min = 30min Answer is E. #### E QUESTION:The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? options: A)58 B)70 C)63 D)65 E)72 SOLUTION:1/2bh=1/2(2a+1)(2a+6) Now 4a-2=2a+6 2a=8 . a=4 Therefore, A(0,0); B(0,14); C(9,14) 1/2*9*14=63 Answer: C #### C QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 66. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 55 C)(c) 82 D)(d) 83 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (66-6)/6+1=11 such multiples. So, final number of sets is 11*5=55 Answer : B #### B QUESTION:Karthikeyan arranged a party to celebrate his birth day.20 of his close friends were invited. One friend left before the cake was cut due to an urgent phone call.The big cake was drawing the attention of the party visitors. This cake is to be divided among friends and of course Karthikeyan will get his share. A man eats 3 pieces, a woman eats two pieces and a child eats half a piece of cake. Including Karthikeyan count the number of men,women and children in the party. There are 20 pieces of cake in all. options: A)6 women, 2 men and 12 children B)7 women, 1 men and 12 children C)5 women, 1 men and 14 children D)4 women, 2 men and 14 children E)None of these SOLUTION:Let the number of men be m, number of women be w and number of children be c Total number of pieces = Pieces ate by men + Pieces ate by women + Pieces ate by children There are 20 total pieces. Also a man eats 3 pieces, a woman eats 2 and children half. Therefore above equation becomes. 20 = 3m + 2w + 1/2c In the above equation, you have to substitute the values given in options to find which one satisfies the equation. Option c with m = 1, c = 14 and w = 5 perfectly satisfies the equation as follows 20 = 3(1) + 2(5) + (1/2)(14) 20 = 20 i,e our equation is satisfied perfectly by option c ANSWER:C #### C QUESTION:In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000 SOLUTION:total vote = N vote cast by independent voters = 0.4 N vote cast by registered voters = 0.6 N vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N Answer choice E #### E QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 26,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,22,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 26,000 = Rs. 1,22,000 ANSWER:C #### C QUESTION:The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 8, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median? I. 3 II. 7 III. 12 options: A)I only B)II only C)III only D)I and III only E)I, II, and III SOLUTION:C for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8 #### C QUESTION:A train 360 m long passed a pole in 30 sec. How long will it take to pass a platform 780 m long? options: A)76 sec B)89 sec C)87 sec D)95 sec E)16 sec SOLUTION:Speed = 360/30 = 12 m/sec. Required time = (360 + 780)/12 = 95 sec. Answer:D #### D QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 7 C) 5 D) 9 E) 12 SOLUTION:If x=6 and y=4, then x^2-y^2=20and 20 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:The total of the ages of Amar, Akbar and Anthony is 40 years. What was the total of their ages two years ago ? options: A)71 B)44 C)36 D)16 E)18 SOLUTION:Explanation: Required sum = (40 - 3 x 2) years = (40 - 6) years = 36 years. Answer: C #### C QUESTION:A train is 360 meter long is running at a speed of 50 km/hour. In what time will it pass a bridge of 140 meter length. options: A)26 seconds B)36 seconds C)46 seconds D)56 seconds E)None of these SOLUTION:Explanation: Speed = 50 Km/hr = 50*(5/18) m/sec = 125/9 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed =500/125/9 = 36 seconds Answer: B #### B QUESTION:A and B form a study group and divide a 75 question study guide. If A answer 7 questions per hour, while B answer 5 every hour, what fraction of the study guide is incomplete after 4 hours? options: A)48/75 B)20/75 C)27/75 D)28/75 E)16/75 SOLUTION:Number of questions A can answer per hour: 7 Number of questions B can answer per hour: 5 Number of questions A and B can answer per hour: 7+5=12 Number of questions A and B can answer in 4 hours: 4x12=48 Fraction of the study guide that is incomplete = 1-48/75=27/75 Answer is C #### C QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:A man buys s cycle for $100 and sells it at a loss of 10%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 90% of the $100 = 90/100 * 100 = $90 Answer is E #### E QUESTION:There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need to remove so that only 96% of the apples are green? options: A)40 B)8 C)15 D)25 E)50 SOLUTION:98−x/100−x=96100 Or, 9800−100x=9600−96x Or, 200=4x Or, x=50 ANSWER:E #### E QUESTION:Half of 2 percent written as decimal is options: A)5 B)0.01 C)0.05 D)0.005 E)None of these SOLUTION:Explanation: It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01 Answer: Option B #### B QUESTION:A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)6 ½ sec B)6 ½ sec C)9 ½ sec D)8 sec E)7 ½ sec SOLUTION:D 8 sec D = 160 S = 72 * 5/18 = 20 mps T = 160/20 = 8 sec #### D QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:If |x + 132| = 32 what is the sum of all the values of x. options: A)-264 B)200 C)-64 D)0 E)-328 SOLUTION:There will be two cases x+132 = 32 and x+132 = -32 Solve for x => x=32-132=> x=-100 or x= -32 - 132 => x= -164 The sum of both values will be -164 + -100 = -264 Answer is A #### A QUESTION:David is able to sell a hand-carved statue for $1150 which was a 15% profit over his cost. How much did the statue originally cost him? options: A)$496.30 B)$512.40 C)$1000 D)$574.90 E)$588.20 SOLUTION:Cost price = 1150/115*100 = 1000 Answer : C #### C QUESTION:Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 3.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn? options: A)1/3 B)1/30 C)1/42 D)2 E)30 SOLUTION:Pete covered 3.5*60=210 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/210=1/42. Answer: C. #### C QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? options: A)17% B)18% C)30% D)17% E)12% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 123.50 Let the marked price be Rs. x. Then, 95/100 x = 123.50 x = 12350/95 = Rs. 130 Now, S.P. = Rs. 130, C.P. = Rs. 100 Profit % = 30%. Answer: C #### C QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually. options: A)812 B)712 C)412 D)512 E)612 SOLUTION:Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112. therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612. Answer is E. #### E QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x*4x=900 x^2= 225 x= 15 Length= 4*15= 60 difference= 60-15= 45 E is the answer #### E QUESTION:The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there? options: A)24 B)30 C)36 D)42 E)48 SOLUTION:Let the number of pens be 5x and the number of pencils be 6x. 6x - 5x = 5 x = 5 The number of pencils is 30. The answer is B. #### B QUESTION:There are 7 couples. If they will sit 14 chairs in a row such that each couple sits side by side, how many possible cases are there? options: A)120 B)240 C)1,200 D)2,460 E)654120 SOLUTION:Tie the couples. Then we have 5 persons that have to be arranged in 4 places. 4! ways. Now the couples can change position with each other. 2! ways. 7! * (2!)^7=5040 *128 = 645120 Answer is E. #### E QUESTION:Pandiyan buys an old scooter for Rs. 6000 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is : options: A)20% B)12% C)9.09% D)5% E)None of these SOLUTION:Explanation : Solution: C.P. =Rs. (6000+600) =Rs. 6600; S.P. = Rs. 7200. Gain% = 7200-6600/6600*100 = 9.09% Answer : C #### C QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)420 E)663 SOLUTION:1h ----- 3 ? ------ 60 12 h RS = 16 + 19 = 35 T = 12 D = 35 * 12 =420 Answer: D #### D QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed? options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5! SOLUTION:Explanation: Total number of letters = 5 Using these letters the number of 5 letters words formed is 5!. Answer: Option E #### E QUESTION:An seller earns an income of Re 3 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 15th day of business, he earns an income of: options: A)19 B)22 C)25 D)20 E)36 SOLUTION:2nd day he earns = 3(2 – 3) 3rd day he earns = 3(3 – 3) On 15th day he earns 3(15 -3) = 36 rupees ANSWER:E #### E QUESTION:Little Praveen had $50.50. He spent $12.25 on sweets and gave same money to his two friends and the amount left with him is $31.25. Find how much he spent to two of his friends? options: A)$ 16.65 B)$ 18.65 C)$ 19.25 D)$ 16.55 E)$ 17.65 SOLUTION:Praveen spent and gave to his two friends a total of 12.25 + 2x= $4.65, x is the amount spent to one friend. Money left 50.50 -2x = $31.85. Then 2x=$18.65. correct answer is B) $ 18.65 #### B QUESTION:A person crosses a 1800 m long street in 12 minutes. What is his speed in km per hour? options: A)4.1 B)4.5 C)4.8 D)5.4 E)9 SOLUTION:Speed = 1800/(12x60) m/sec = 2.5 m/sec. Converting m/sec to km/hr =2.5 x(18/5) km/hr = 9 km/hr. ANSWER :E #### E QUESTION:If k is an integer and 121 < k^2 < 225, then k can have at most how many values? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:given k is an integer 121 < k^2 < 225 11 < | k| < 15 K=-12,-13,-14,12,13,14 ANSWER:D #### D QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 10000 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×5400 / 12×3) => Rs. 15,000. Answer : C #### C QUESTION:Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? options: A)60% B)50% C)25% D)20% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 25 + 55 - {both} + 40 {both} = 20%. Answer: D. #### D QUESTION:Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs. 28000, find the earning of Nandan. options: A)Rs.7000 B)Rs.5000 C)Rs.6000 D)Rs.Rs.4000 E)Rs.6500 SOLUTION:3:1 2:1 ------ 6:1 7 ----- Rs.28000 1 ----- ? => Rs.28,000/7=Rs. 4000 Answer: D #### D QUESTION:Insert the missing number ..., 4, 8, 16, 32, 64, 128, 256 options: A)6 B)5 C)2 D)3 E)8 SOLUTION:series is 2* Previous Number. ANSWER:C #### C QUESTION:A train 200 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)15 sec E)18 sec SOLUTION:Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec Time taken by the train to cross the man = Time taken by It to cover 200 m at 50/3 m / sec = 200 *3/ 50 sec = 12sec Answer : C #### C QUESTION:A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ? options: A)7.5km/hr B)3.5km/hr C)9km/hr D)4km/hr E)5km/hr SOLUTION:given upstream(u) =5km/hr down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C) #### C QUESTION:Walking across campus, a student interviewed a group of students. 35% of the students took a finance class last semester, 45% took a marketing class last semester, and 50% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? options: A)40% B)30% C)25% D)15% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 35 + 45 - {both} + 50 {both} = 30%. The answer is B. #### B QUESTION:Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride? options: A)28 B)30 C)32 D)34 E)36 SOLUTION:The cost of Annie's ride was 2.5+5+(0.25*14) = $11 Let x be the distance of Mike's ride. The cost of Mike's ride is 2.5+(0.25*x) = 11 0.25*x = 8.5 x = 34 miles The answer is D. #### D QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:A ladies hostel had provision of food for 300 women for 45 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is: options: A)38.89 B)39.18 C)38.78 D)38.0 E)38.18 SOLUTION:Explanation : After 10 days : 300 women had food for 35 days. Suppose 275 women had food for x days. Now, Less women, More days (Indirect Proportion) 275 : 300 :: 35 : x => 275 x x = 300 x 35 => x = 300 x 35 / 275 => x = 38.18 Answer : E #### E QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age 4 years back was: options: A)12 years. B)14 years. C)17 years. D)20 years. E)19 years. SOLUTION:Let the son's present age be x years. Then, (48 - x) = x 2x = 48. x = 24 Son's age 4 years back (24- 4) = 20 years. ANSWER :D #### D QUESTION:A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i options: A)8 km / hr B)9 km / hr C)10 km / hr D)12.5 km / hr E)None SOLUTION:Sol. Man's rate in still in water = (12- 2) km / hr = 10km / hr. Man's rate against the current = (10 - 2) km / hr = 8 km / hr. Answer A #### A QUESTION:A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is? options: A)178 m B)240 m C)120 m D)168 m E)178 m SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 12 = 240 m. Answer: B #### B QUESTION:At a certain organisation, the number of male members went up by 15% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000? options: A)1:2 B)1:3 C)2:3 D)3:2 E)2:1 SOLUTION:men increase by 15% ==> 1.15M = males in 2001 women decrease by 6% ==> 0.94F = women in 2001 total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001 Obviously (males in 2001) + (females in 2001) = total number of employees in 2001 1.15M + 0.94F = 1.012*(M + F) 1.15M + 0.94F = 1.012M + 1.012F 1.15M - 1.012M = 1.012F - 0.94F 0.138M = 0.072F M/F = (0.072)/(0.138) = 72/138 = 1/2 Answer =(A) #### A QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)22 B)54 C)99 D)77 E)12 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 900 * 3/50 = 54 sec. Answer: B #### B QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases Answer: option C #### C QUESTION:If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area? options: A)26% B)21% C)15% D)18% E)12% SOLUTION:a =1/2 x b x h or 1/2 x 2a x a(for simplification) New h = 220a / 100 = 22a / 10 New b =(110a x 100) ==11a/10 New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100) increased area== (121a²/100) - a² Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21% answer :B #### B QUESTION:Can you find the smallest non fractional number such that If the number gets divided by 9 , we get the remainder of 1; If the number gets divided by 10 , we get the remainder of 2 If the number gets divided by 11 , we get the remainder of 3; If the number gets divided by 12 , we get the remainder of 4. options: A)1450 B)1300 C)1205 D)2501 E)1978 SOLUTION:E.option E As we know LCM of the numbers 9 10 11 & 12 is 1980. So if i divide 1980 by any of the four number , it gives remainder as 0. Now to get reminder as desired, is should be 2 short of 1978. (3-1,4-2,5-3,6-4 ) Ans:option E #### E QUESTION:if log 2 = 0.30103, the number of digits in 2128 is options: A)22 B)39 C)88 D)28 E)11 SOLUTION:Explanation: log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4 ie, its characteristic = 38 Hence, number of digits in 2128 = 38+1 = 39 Answer: Option B #### B QUESTION:Sum of the local value and the face value of 4 in the numeral 153489216 is options: A)40004 B)4004 C)4000004 D)400004 E)44 SOLUTION:(Local value of 4) + (Face value of 4) = (400000 + 4) = 400004 D #### D QUESTION:A sum of Rs.4000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)2888 B)3120 C)2877 D)2600 E)1277 SOLUTION:Let A be the amount received at the end of the three years. A = 4000[1 + 10/100][1 + 20/100][1 + 25/100] A = (4000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.6600 So the interest = 6600 - 4000 = Rs.2600 Answer: D #### D QUESTION:A sealed envelope contains a card with a single digit written on it. Three of the following statements are true and one is false. I. The digit is 1. II. The digit is not 2. III. The digit is not 9. IV. The digit is 8. Which one of the following must necessarily be correct? options: A)III B)I C)IV D)II E)NONE SOLUTION:Three of the given statements are true. So both II and III are correct, and the given number is one of 1 or 8. So option A is correct. Answer:A #### A QUESTION:A train is 360 meter long is running at a speed of 75 km/hour. In what time will it pass a bridge of 140 meter length? options: A)87 B)69 C)40 D)72 E)24 SOLUTION:Speed = 75 Km/hr = 75*(5/18) m/sec = 125/6 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 * (6/125) = 24 seconds Answer: E #### E QUESTION:JERRY has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If JERRY needs to pay exactly $128, what is the least number of bills he will need to use? options: A)16 B)35 C)46 D)577 E)576 SOLUTION:128 is the total sum of money. as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils 128-120 = 8 so now we need to get 8 from either 5 dollar bills or 1 dollar bills 8 - 5 (use only 1 5 dollar bill) = 3 so we can get 3 from using 3 $1 bills. Hence 16 ( 12+1+3 ) ANSWER IS A #### A QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:There are 12 cans in the refrigerator. 8 of them are red and 4 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)460 B)490 C)493 D)455 E)424 SOLUTION:Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator = total ways to pick 4 can out of 12 - ways to pick 4 red out of 8 red - ways to pick 4 blue out of 4 blue 12C4−8C4−4C4=495−70−1=424 ANSWER:E #### E QUESTION:In a bag containing only blue, red and green marbles, all but 15 are blue, all but 13 are red and all but 12 are green. How many are red? options: A)13 B)7 C)25 D)20 E)10 SOLUTION:All but blue means number of marbles except blue..hence, let x be the red marble,y be the green marble,z be the blue marble... x+y=15 y+z=13 x+z=12 solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7 ANSWER:B #### B QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is: options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (30 x 3) = 90 …. (i) A + B = (25 x 2) = 50 …. (ii) B + C = (28 x 2) = 56 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 106 …. (iv) Subtracting (i) from (iv), we get : B = 16. B’s weight = 16 kg. Answer E #### E QUESTION:If w persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job? options: A)z B)x C)x/y D)z/x E)y/z SOLUTION:the Q doesn't seem to be having the any correct answer as a choice.. since we are looking for days, lets keep days in end and work out a solution.. w person can do z jobs in y days.. so w person can do 1 job in y/z days.. and 1 person can do 1 job in y^2/z days.. so y person can complete 1 job in y^2/zy=y/z.. so the answer should be y/z=E #### E QUESTION:A sum of Rs.1420 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls options: A)8B, 5G B)5B, 8G C)4B, 9G D)9B, 4G E)6B, 7G SOLUTION:120B+100G=1420-----i B+G=13-------ii from i 100B+20B+100G=1420 100(B+G)+20B=1420 100(13)+20B=1420 By simplifing we get B=6;G=7 ANSWER:E #### E QUESTION:If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)? options: A)-f(x) B)f(x) C)2*f(x) D)1/f(x) E)2/f(x) SOLUTION:If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x) answer A #### A QUESTION:Calculate the percentage increase in the area of a square if each of its sides is increased by 15%? options: A)32.25% B)39.25% C)36.25% D)35.25% E)31.25% SOLUTION:Assume original length = 100m by 50m original area = 100*50= 5000 15% increase on each side l = 100 + 15 = 115 w = 50 + 7.5 = 57.5 new area = 115*57.5= 6612.5 increase in area = 6612.5 - 5000 = 1612.5 %increase =21% Answer A #### A QUESTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? options: A)2443200 B)3643200 C)5443200 D)1443200 E)2163200 SOLUTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? A. 24 B. 36 C. 72 D. 144 E. 216 Choosing the digit for p - 9 ways; Choosing the digit for q - 8 ways; Choosing the digit for r - 7ways; Choosing the digit for s - 6ways; Choosing the digit for t - 5ways; # of permutations of 3 digits in ppqrst - 6!/2! Total: 9*8*7*6*5*6!/2!=5443200. Answer: C. #### C QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)3600 C)8900 D)9000 E)5000 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 ANSWER A #### A QUESTION:√(36)^2 options: A)6 B)14 C)36 D)21 E)None of these SOLUTION:explanation √(36)^2 =? or, ? = 36 Answer C #### C QUESTION:Average of first five multiples of 2 is options: A)9 B)6 C)13 D)15 E)16 SOLUTION:Explanation: Average=2(1+2+3+4+5)5=6 Answer: Option B #### B <<<Examples ends QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even now subtract X + (X+2) - (X+4) doing this leaves us with X -2 what even number can we substitute in X to yield an answer choice B works 2 (plug in 4 for X) #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A was born when B was 1 year and 3 months old. C was born when A was 2 years 1 month old. What is the age of B when C is 4 years and 6 months old? options: A)4 yr 10 month B)6 yr 10 month C)7 yr 11 month D)7 yr 10 month E)8 yr 10 month SOLUTION:When C is 4yr 6 month i.e. 54 months old A is 79 month old.. B is 15 month older than A When A is 79 months old then, B is 94 months old i.e. 7yr 10 month ANSWER:D #### D QUESTION:In 24 minutes, the hour hand of a clock moves through an angle of: options: A)60° B)24° C)12° D)5° E)None SOLUTION:12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚ Answer: C #### C QUESTION:The dimensions of a field are 10 m by 10 m. A pit 5 m long, 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ? options: A)2m B)2.5m C)1.5m D)1.25m E)1m SOLUTION:The volume of the earth removed is 5*5*3 = 75 m^3. The remaining area of the field is 10*10 - 5*5 = 75 m^2. 75 m^3 of the earth evenly spread over the area of 75 m^2 will rise the height by (height) = (volume)/(area) = 75/75 = 1 m. Answer: E #### E QUESTION:If x is a positive integer, which of the following must be odd? options: A)x+1 B)x^2+x C)x^2+x+7 D)x^2−1 E)3x^2−3 SOLUTION:A. X+1 = can be odd or even. Since O + O =E or E + O = O B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD] C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 7 = ODD Hence C. #### C QUESTION:How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? options: A)5040 B)40 C)400 D)5000 E)6000 SOLUTION:LOGARITHM => 10 diff letters req no of words = No of arrangements of 10 letters taking 4 at a time => 10P4 = (10*9*8*7) ==> 5040 ANSWER A #### A QUESTION:In an encryption code 'PLAYS' is written as '{:SUD' when encoded and 'SLEEP' is written as 'D:RR{' when encoded. How is ''SLAPPY" written in that encryption code? options: A)D:S{{U B)SLAPPY C){RUDD: D){:SUU{ E)U{{S:D SOLUTION:D = S : = L S = A P = { P = { Y = U Correct Answer: A #### A QUESTION:A group of 11 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase? options: A) E/(12 - n) B) (12 - n)/E C) E/[12(12-n)] D) nE / [11(11-n)] E) (12-n)E/(12n) SOLUTION:total cost =E no of people willing to participate initially =11 initial cost for each =E/11 when n people decided not to participate Cost for each =E/11-n D #### D QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded? options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV SOLUTION:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Z Y X W V U T S R Q P O N M L K J I H G F E D C B A So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN. so this way CAMEL becomes OVNZX ANSWER:C #### C QUESTION:Pavan travelled for 15 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value options: A)31 B)32 C)46 D)47 E)48 SOLUTION:- a + b + ((-a)(b)/100) = -25+75+(-25*75)/100 = -25+75-19 =31 ANSWER:A #### A QUESTION:At a game of billiards,A can give B 15 points in 60 and A can give C 20 points in 60.How many points can B give C in a game of 90 ? options: A)30 points B)20 points C)10 points D)12 points E)None of these SOLUTION:Solution A : B = 60 : 45 and A : C = 60 : 40. ∴ B/C =( B/A x A/C) = (45/60 x 60/40) = 45/40 =90/80= 90 : 80 ∴ B can give C 10 points in a game of 90. Answer C #### C QUESTION:Express 50 mps in kmph? options: A)172 B)160 C)150 D)180 E)120 SOLUTION:25 * 18/5 = 180 kmph Answer:D #### D QUESTION:By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? options: A)9 B)4 C)8 D)7 E)65 SOLUTION:80% --- 12 120% --- ? 80/120 * 12 = 8 Answer: A #### A QUESTION:Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own? options: A)6 B)7 C)8 D)12 E)14 SOLUTION:Lets suppose Anne and Bruce take A and B hrs working separately So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours) After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 3 hours) Solving these 2 equations we can find B as 12 ANSWER:D #### D QUESTION:What is x if x + 5y = 24 and y = 2? options: A)1 B)3 C)5 D)7 E)14 SOLUTION:Substitute y by 2 in x + 5y = 24 x + 5(2) = 24 x + 10 = 24 If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence x = 14 correct answer E #### E QUESTION:The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 32 ? options: A)440 B)512 C)550 D)620 E)750 SOLUTION:Large numbers are made in two ways: Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place. 31*2 = 62 (large prime number) 2^6 = 64 (many small prime numbers) To get a sum as large as 32 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers. You are left with 620 which is 31*2*2*5 (sum greater than 32) Answer D #### D QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)18, 24, 32 E)None of these SOLUTION:Explanation: Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 20x = 80 x = 4. Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively. Answer: B #### B QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. options: A)32 B)15 C)18 D)20 E)25 SOLUTION:Relative speed = (420/18)m/s = (420/18)*(18/5) = 84 kmph speed of goods train = 84-64 = 20 kmph Answer is D #### D QUESTION:Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window? options: A)a 100 B)b 112 C)c 90 D)d 120 E)e 30 SOLUTION:D David's position is fixed. Now we need to arrange all others around David. There are 5x4x3x2x1= 120 ways to arrange five people. #### D QUESTION:George can do 3/5 of work in 9days.He then calls in pauls and they completed the work in 4days.How long paul would take long to complete the work? options: A)32 B)28 C)35 D)30 E)22 SOLUTION:George work is (5/3)*9 =15; 1 day work of george is 1/15 ; remaining is 2/5th; paul & george work is 5/2*4=10 ; their 1 day work is 1/10; and only paul work is (1/10)-(1/15)=30 ANSWER:D #### D QUESTION:A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? options: A)480 B)487 C)720 D)729 E)268 SOLUTION:1/x - 1/20 = -1/24 x = 120 120 * 6 = 720 Answer:C #### C QUESTION:A person travels first 100km at 40km/hr and the next 100km at 60km/hr. The average speed for the first 200km of the tour is? options: A)36km/hr B)50km/hr C)48km/hr D)60km/hr E)55km/hr SOLUTION:Total time taken = 100/40 + 100/60 = 25/6 hrs Average speed = 200*6/25 = 48km/hr Answer is C #### C QUESTION:Find compound interest on $ 8000 at 15% per annum for 2 years 4 months, compounded annually. options: A)3109 B)3209 C)3108 D)3107 E)3100 SOLUTION:Time = 2 years 4 months = 2(4/12) years = 2(1/3) years. Amount = $ [8000 X (1+­(15/100))2 X (1+((1/3)*15)/100)] =$ [8000 * (23/20) * (23/20) * (21/20)] = $ 11109. . :. C.I. = Rs. (11109 - 8000) = $ 3109. Answer A. #### A QUESTION:How many pieces of 0.85 metres can be cut from a rod 42.5 metres long? options: A)30 B)40 C)50 D)60 E)70 SOLUTION:Number of pieces = 42.5/0.85 = 42.50/0.85 = 4250/85 = 50. ANSWER:C #### C QUESTION:A certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? options: A)42 B)70 C)140 D)135 E)315 SOLUTION:1 of 3 will be chosen for the math 2 of 10 will be chosen for the computer None of the 3 chosen people can be in more than one departments. We can choose any of the 3 candidates for the math dep., which gives as 3 selections. We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /2!*8!= (9*10) / 2 = 90 / 2 = 45. We are multiplying our individual selections: 3*45 = 135 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans D #### D QUESTION:Jill works as a waitress at the local diner where she earns an hourly wage of $7.00 per hour and a standard tip rate of 5% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week? options: A)280 B)300 C)320 D)432 E)400 SOLUTION:Jill earns 7 dollars/hour and the hourly tip is (1/20)*40. Jill thus earns 7*12+12*2 per day(or 7(12)+2(12)=9(12)=108). Jill has worked for 4 days -> 108*4=432. This matches answer choice D. #### D QUESTION:Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car options: A)960 km B)950 m C)906 km D)906 m E)950 m SOLUTION:60(x + 1) = 64x X = 15 60 * 16 = 960 km ANSWER A #### A QUESTION:Gary had an average score of 70 on his first four quizzes. He had an average score of 75 on his first five quizzes. What score did he receive on his fifth quiz? options: A)90 B)95 C)65 D)42 E)43 SOLUTION:The sum of Gary's first 4 scores is 4 · 70 and the sum of his first 5 scores is 5 · 75, so he received 5 · 75 − 4 · 70 on his 5th quiz. You can do the arithmetic or note that the answer ends in a 5 and eliminate answer C because it is lower than the average. The correct answer is B. #### B QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit? options: A)28000 B)30000 C)32000 D)34000 E)None of these SOLUTION:Explanation : Suppose B's investment = x. Then A's investment= 3x Suppose Bs period of investment = y, then A's period of investment = 2y A : B = 3x * 2y : xy = 6 : 1 Total profit * 1/7 = 4000 => Total profit = 4000*7 = 28000. Answer : Option A #### A QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5 SOLUTION:36 * 5/18 = 12.5 20:25 => 4:5 Answer: E #### E QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? options: A)3/2 B)5/3 C)1+1/3 D)1 1/2 E)1 1/3 SOLUTION:N is such that when multiplied by 0.75 gives 1" is written mathematically as N * 0.75 = 1 Solve for N N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3 correct answer C #### C QUESTION:When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? options: A)17% increase B)44% decrease C)60% increase D)66% increase E)66% decrease SOLUTION:if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater. ANSWER:A #### A QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)? options: A)2 B)4 C)7 D)9 E)10 SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3. Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9. The answer is D. #### D QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)228 B)200 C)279 D)480 E)221 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480.Answer:D #### D QUESTION:A manufacturer of a certain product can expect that between 0.4 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units? options: A) Between $15,000 and $25,000 B) Between $30,000 and $50,000 C) Between $200,000 and $250,000 D) Between $150,000 and $250,000 E) Between $300,000 and $500,000 SOLUTION:Number of defective units is between = .4 % of 20000 and .5% of 20000 = 80 and 100 Retail Price per unit = 2500 $ Expected price of refund is between = 2500 x 80 and 2500 x 100 =2,00,000 and 2,50,000 dollars Answer C #### C QUESTION:If |x| = 4x - 1, then x = ? options: A)3 B)1/2 C)1 and 1/2 D)-1/2 E)-1 SOLUTION:Answer: A Approach: Substituted option A i.e x=1. Inequality satisfied. #### A QUESTION:A can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares? options: A)600,400 B)500,500 C)300,700 D)800,1200 E)550,1450 SOLUTION:Ratio of their works A:B = 6:4 Ratio of their wages A:B = 2:3 A's share = (2/5)2000 = 800 B's share = (3/5)2000 = 1200 correct option is D #### D QUESTION:A bike covers a certain distance at the speed of 68km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)85 km/h B)85.34 km/h C)87.67 km/h D)90.66 km/h E)90.64 km/h SOLUTION:Ans.(D) Sol. Total distance = 68 × 8 = 544 km Now speed = 544/6 = 90.66 km/h #### D QUESTION:If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is: A 6, B 12, C 24, D 36, E 48 n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B #### B QUESTION:A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 B)30/21 C)30/11 D)30/7 E)30/8 SOLUTION:Speed downstream = 10 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 60/16 = 30/8 hours. Answer:E #### E QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)214 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 64x X = 3.57 60 * 3.57 = 214 km ANSWER:B #### B QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:How many different values of positive integer x, for which |x+7|<x, are there? options: A)0 B)2 C)3 D)8 E)16 SOLUTION:Answer A I opted to put the random value option. i used 0 , 7 , -7 and the the extreme of 30 and -30.. i was able to solve it in 1:09 B #### B QUESTION:One of the longest sides of the triangle is 20 m,the other side is 10 m.Area of the triangle is 80m^2.What is the another side of the triangle? options: A)2sqrt(61) B)2sqrt(62) C)2sqrt(63) D)2sqrt(64) E)2sqrt(65) SOLUTION:base of triangle is 20 and area is 80 therefore height=2*80/20=8. now one side of triangle is of 10. so we can get the point were the base is divided by applying Pythagoras therm so division pt =sqrt(10^2-8^2)=sqrt(36)=6 threfore other half is 14. now second side=sqrt(14^2+8^2)=sqrt(260)=2sqrt(65) ANSWER:E #### E QUESTION:If x/y =4/3, then (x-y)/x? options: A)-1/2 B)-1/4 C)1/3 D)1/2 E)1/4 SOLUTION:we have this law of fraction: a/b=c/d= (a-c)/(b-d) x/y=4/3 ---> x/4=y/3= (x-y)/(4-3)=(x-y)/(1) ---> (x-y)/x= 1/4 Answer: E #### E QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4? options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1 SOLUTION:Solving for y/x gives, 1/17 (C) #### C QUESTION:Which one the following fractions has the biggest value? options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711 SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D QUESTION:A man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses? options: A)5 minutes B)6 minutes C)8 minutes D)9 minutes E)10 minutes SOLUTION:Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus. Let the speed of cyclist be c. Every 18 minutes a bus overtakes cyclist: \frac{d}{b-c}=18, d=18b-18c; Every 6 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=6, d=6b+6c; d=18b-18c=6b+6c, --> b=2c, --> d=18b-9b=9b. Interval=\frac{d}{b}=\frac{9b}{b}=9 Answer: D (9 minutes). #### D QUESTION:The true discount on a bill of Rs.4320 is Rs.720.The banker's discount is options: A)862 B)864 C)866 D)868 E)None of these SOLUTION:Solution P.W = Rs.(4320 - 720) = Rs. 3600 S.I on Rs. 4320 =Rs.(720/3600 x 4320) = Rs. 864. Answer B #### B QUESTION:What is the perimeter of a square field whose diagonal is 8√2? options: A)82 m B)32 m C)27 m D)26 m E)76 m SOLUTION:4a = 32 m Answer: B #### B QUESTION:What is the HCF of 2/3, 5/9 and 6/5 options: A)1/45 B)2/45 C)4/15 D)8/45 E)9/45 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 5, 6)/(LCM of 3, 9, 5) = 1/45 Answer: Option A #### A QUESTION:What percent of a day is 15 hours? options: A)37×1/2% B)16×1/2% C)18×2/3% D)22×1/2% E)None SOLUTION:Solution Required percentage = (15/24×100)% = (75 / 2)%. = 37×1/2%. Answer A #### A QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION:Can you deduce the pattern and find the next number in the series? 3, 24,81, 192, __? options: A)276 B)277 C)278 D)279 E)375 SOLUTION:Solution: 375 Explanation: 3 = 1^1^1 + 1^1^1 + 1^1^1 24 = 2^2^2 + 2^2^2 + 2^2^2 81 = 3^3^3 + 3^3^3 + 3^3^3 192 = 4^4^4 + 4^4^4 + 4^4^4 Thus the next number will be 375 =5^5^5 + 5^5^5 + 5^5^5 Answer E #### E QUESTION:In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.300 and C's share is Rs.130, what is B's capital? options: A)19878 B)12798 C)6166 D)11750 E)22073 SOLUTION:300 + 130 = 430 800 - 430 = 370 300 ---- 5000 370 ---- ? => 6166 Answer: C #### C QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? options: A)12 B)15 C)16 D)18 E)14 SOLUTION:Draw a Venn Diagram yourself ! B + C - BC = Number of students that play either Basketball or Cricket 10 +8 - 4 = 14 E) #### E QUESTION:If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years? options: A)(1+k/100)^n B)(1+k)^n C)(1+kn/100) D)(1+k/100)^4n E)(1+kn) SOLUTION:Amount after 7n years will be = x ( 1 + k/100)^4n Amount after 3n years will be = x ( 1 + k/100)^3n So, required ratio will be - { x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n Hence answer will be a. (1+k/100)^4n D #### D QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 --> 2x = 20 --> x = 10. --> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. Answer : C. #### C QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 30*16=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:The average marks of a class of 30 students is 50 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)56.25 B)52.9 C)52.1 D)52.3 E)42.5 SOLUTION:Sum of the marks for the class of 30 students = 30 * 50 = 1500 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 80 students = 1500 + 3000 = 4500 Average marks of all the students = 4500/80 = 56.25 Answer:A #### A QUESTION:In measuring the sides of a rectangle, one side is taken 14% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)8.3% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000. Now, the area obtained with wrong measurements would be 114*95=10,830, which is 8.3% greater than the actual area. Answer: C. #### C QUESTION:What is the unit’s digit of 7^5 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:7^1=7 7^2=49 7^3=343 7^4=1(last digit) 7^5=7(last digit) and the cycle repeats after every 4 powers Therefore, last digit of 7^5=7 Answer D #### D QUESTION:The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area? options: A)298 B)148 C)289 D)987 E)282 SOLUTION:2(4*5 + 5*6 + 4*6) = 148 Answer:B #### B QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:In a division, divident is 725, divisior is 36 and quotient is 20. Find the remainder. options: A)A)4 B)B)3 C)C)2 D)D)5 E)E)6 SOLUTION:Explanation: 725 = 36 x 20 + r 725 = 720 + r r = 725 - 720 = 5 Answer: Option D #### D QUESTION:Three walls have wallpaper covering a combined area of 280 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 36 square meters. What is the area that is covered with three layers of wallpaper? options: A)5 Square Meters B)32 Square Meters C)42 Square Meters D)83.3 Square Meters E)120 Square Meters SOLUTION:280 - 180 = 100 sq m of the wallpaper overlaps (in either two layers or three layers) If 36 sq m has two layers, 100 - 36 = 64 sq m of the wallpaper overlaps in three layers. 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m. Answer (B). #### B QUESTION:Insert the missing number ..., 4, 8, 16, 32, 64, 128, 256 options: A)6 B)5 C)2 D)3 E)8 SOLUTION:series is 2* Previous Number. ANSWER:C #### C QUESTION:John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend? options: A)$2,125 B)$1,320 C)$2,000 D)$1,580 E)$2,000.75 SOLUTION:Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125. #### A QUESTION:What is the number which when multiplied by 13 is increased by 180? options: A)13 B)15 C)23 D)35 E)45 SOLUTION:13 × 15 = 195 Answer: B #### B QUESTION:In a certain village, 200 litres of water are required per household per month. At this rate, if there are 5 households in the village, how long (in months) will 2000 litres of water last? options: A)9 B)5 C)6 D)2 E)4 SOLUTION:I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p: In a certain village,m 200 litres of water are required per household per month. At this rate, if there aren 5 households in the village, how long (in months) willp2000litres of water last? Water required is 200*5=1000 (m*n) Water available is 2000 (p) It will last 2 months (p/m*n) Ans : D #### D QUESTION:If 60 percent of the members of a certain organization are women and 6/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization. options: A)II B)III C)I, II D)I E)II, III SOLUTION:6/10 (60%) of the members are women and 6/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 6/10*80 = 48 women; 80 - 48= 32 men; 6/8*32 = 24 married men; 32 - 24 = 8 unmarried men. So, option I,II is true. Answer: C #### C QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:60*5:36*6:75*3 100: 72: 75 72/247 * 7410 = 2160 Answer: A #### A QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale? options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these SOLUTION:Let the original price be x and sale be of y units. Then, the revenue collected initially = x × y Now, new price = 0.8x, new sale = 1.8y Then, new revenue collected = 1.44xy % increase in revenue = 0.44xy/xy×100 = 44% increase Answer A #### A QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 13260, how much money did he borrow? options: A)13000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 13260 18x + 45x + 39x = (13260* 100) 102x = 1326000 => x = 13000. Answer:A #### A QUESTION:The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is? options: A)5 kmph B)1 kmph C)6 kmph D)2 kmph E)3 kmph SOLUTION:The current of a stream = 1 The speed of the motor boat in still water= x Speed downstream = x + 1 Speed upstream = x - 1 since distance = speed × time, we have 35/(x + 1) + 35/(x - 1) = 12 kmph=6 kmph Answer : Option C #### C QUESTION:The ratio of the prices of three articles X, Y and Z is 8 : 5 : 3. If the prices of X , Y and Z are increased by 25%, 20% and 33 1/3% respectively, then what would be the ratio of the new prices of X, Y and Z? options: A)5 : 3 : 1 B)5 : 3 : 2 C)10 : 7 : 4 D)10 : 8 : 5 E)None of these SOLUTION:Let the prices of X, Y and Z be 8k, 5k and 3k respectively. After increase Price of X = 8k * 125/100 = 10k Price of Y = 5k * 120/100 = 6k Price of Z = 3k * (133 1/3)/100 = 4k Required ratio = 10k : 6k : 4k = 5 : 3 : 2. ANSWER:B #### B QUESTION:A school has received 30% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 60% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$250 C)$100 D)$350 E)$875 SOLUTION:Let us suppose there are 100 people. 60% of them donated $30000 ( 500 * 60 ) $30000 is 30% of total amount. So total amount = 30000 * 100/60 Remaining amount is 70% of total amount. 70% of total amount = 30000 * (100/60) * (70/100) = 35000 This amount has to be divided by 40 ( remaining people are 40 ) So per head amount is 35000/40 = $875; ANSWER:E #### E QUESTION:A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water? options: A)2 kmph B)8 kmph C)16 kmph D)4 kmph E)6 kmph SOLUTION:30 --- 3 DS = 10 ? ---- 1 18 ---- 3 US = 6 ? ---- 1 M = ? M = (10 + 6)/2 = 8 ANSWER:B #### B QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/12 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 2*x Hence, a1+a2+..+a20+n = 22x So, the fraction asked = 2x/22x = 1/12 B #### B QUESTION:A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone? options: A)4 2/3 B)7 C)9 D)24 E)21 SOLUTION:A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 6 days @ rate=1/x per day Expression: Days*Rate=Work 5*1/7+6*1/x=1 5x+42=7x 2x=42 x=21 days. Ans:E #### E QUESTION:A room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles. What will be the least number of square tiles required to cover the floor? options: A)176 B)124 C)224 D)186 E)190 SOLUTION:LENGTH = 5 M 44 CM = 544 CM BREADTH = 3 M 74 CM = 374 CM AREA = 544 * 374 HCF = 34 AREA OF SQUARE = 34 * 34 CM2 NO OF TILES REQ = 544* 374/34*34 = 16 * 11 =176 ANSWER A #### A QUESTION:Zoey won the lottery and got $7,348,340. she wants to split it among herself and 5 friends evenly. how much money must she add if she wants to split it evenly? options: A)$3 B)$2 C)$9 D)$1 E)$4 SOLUTION:Zoey and her 5 friends is 6 people in all. $7,348,340 must be divisible by 6 if she wants to split it evenly. The money is divisible by 6 if it's divisible by 2 and 3. 7+3+4+8+3+4+0=29. 2 and 3 cant go into 29. Adding 1 dollar makes it 30. 2 and 3 can go into 30 so 6 can also. The answer is D. #### D QUESTION:Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)16.80 × 4.50 + 4.4 B)1600 ÷ 40 + 16 × 2 C)5.5 × 8.4 + 34.6 D)1620 ÷ 20 – 1 E)1856.95 – 1680.65 – 96.3 SOLUTION:Others equal 80 whereas (c) equals 80.8. Answer C #### C QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 3a = b = 3c, and a > 0. What is the difference between the two greatest possible values of x? Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. options: A)131 B)292 C)394 D)424 E)969 SOLUTION:Ratio of a:b:c= 1:3:1 Two possible greatest single digit values for b are 9 and 6 if b is 9, then x= 393 if b is 6, then x= 262 difference= 393-262= 131 A is the answer #### A QUESTION:Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756 options: A)16 B)33 C)105 D)424 E)2124 SOLUTION:2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16. 3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34 4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105 5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424 6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125 3th term should 34 instead of 33. B #### B QUESTION:There is a 70% chance that Flora will visit Ghana this year, while there is a 70% chance that she will visit France this year. What is the probability that Flora will visit either Ghana or France this year, but NOT both? options: A)34% B)36% C)38% D)40% E)42% SOLUTION:P(Ghana but not France)=0.7*0.3=0.21 P(France but not Ghana)=0.7*0.3=0.21 P(Ghana or France but not both)=0.21+0.21=0.42 The answer is E. #### E QUESTION:9886 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)2337 E)None of these SOLUTION:Answer x = 13200 - 9886 = 3314 Option: E #### E QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples? options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24 SOLUTION:The cost of one apple=20/12=1.67 The cost of twenty apples= 1.67x20= $ 33.33 Answer: B #### B QUESTION:The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places options: A)34 B)35 C)56 D)67 E)23.57 SOLUTION:Let the side of the square be a cm. Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm i.e. 4a = 60 A = 15 Diameter of the semicircle = 15 cm Circimference of the semicircle = 1/2(∏)(15) = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places Answer: Option E #### E QUESTION:3 men and 10 boys finish a job in 9 days, 7 men and 7 boys finish it in 8 days. 9 men and 9 boys shall finish it in how many days? options: A)18 B)09 C)07 D)19 E)12 SOLUTION:3 M + 10 B ----- 09 days 7 M + 7 B ------- 8 days 9 M + 9 B -------? 21 M + 70 B = 63 M +63 B 7 B= 42 M => 6 M = 1 B =>1 B =6 M 3 M + 60 M = 63 M ---- 9 days 9 M + 54 M = 63 M -----? => 9 days Answer: B #### B QUESTION:A policeman spotted a criminal from a distance of 200 metres. When the policeman starts the chase, the criminal also starts running. If the criminal was running at 10 km/hr and the policeman was chasing at the speed of 12 km/hr, find the distance the criminal will run before he is catched by the policeman ? options: A)1.5 km B)700 m C)900 m D)1 km E)None of these SOLUTION:Explanation : Solution: Relative speed = (12 - 10) = 2 km/hr. Time taken by policeman to cover 200 m = (200/1000 * 1/2) hr = 1/10 hr. In 1/10 hrs, the criminal covers a distance of (10*1/10) km = 1 km. Answer : D #### D QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is? options: A)Rs.24028 B)Rs.24000 C)Rs.24003 D)Rs.24029 E)Rs.24029 SOLUTION:Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs.24000 Answer: B #### B QUESTION:In the xy-coordinate system, what is the slope of the line that goes through point (2, 4) and is equidistant from the two points P = (9, 3) and Q = (5, 9)? options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:First, get the middle coordinate between (9,3) and (5,9). x = 9 + (5-9)/2 = 7 y = 3 + (9-3)/2 = 6 Second, get the slope of (7,6) and (2,4). m = 6-4 / 7-2 = 2/5 = 0.4 Answer: D #### D QUESTION:The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 422 C)Rs. 419 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2560 TD = Rs. 360 PW = F - TD = 2560 - 360 = Rs. 2200 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2200 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2160 for unexpired time =360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C #### C QUESTION:Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Ram's tour programme is options: A)28 Days B)24 Days C)22 Days D)20 Days E)None of these SOLUTION:Solution: Let Ram under takes a tour of x days. Then, expenses for each day = 360/x 360/x+4=360/x−3 x=20x=20 and −24−24 Hence, x= 20 days. Option(D) #### D QUESTION:23,8,34,81,33,... options: A)24 B)25 C)26 D)27 E)28 SOLUTION:23 : 2^3=8 34 : 3^4=81 33 : 3^3=27 ANSWER:D #### D QUESTION:Marts income is 50 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income options: A)124% B)b) 120 % C)c) 96 % D)d) 90 % E)e) 64 % SOLUTION:M = (150/100)T T = (60/100)J => M = (90/100)J Answer D. #### D QUESTION:If (a-3)(b-2) =0, which of the following must be true ? I. a=3 and b=2 II. if a is not = 3, then b=2 III. if a=3, then b is not=2 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:(a-3)(b-2)=0 So either a=3 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true. The answer is B. #### B QUESTION:Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately. options: A)12 , 18 B)8 , 10 C)18 , 20 D)20 , 25 E)None of these SOLUTION:Explanation : Let speed of ram and shakil be x and y resp. Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute. 2000/x - 1800/y= -60 2000/x= 1800/y -60---------------------(1) Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters 1000/x = (2000- 360y)/y------------------(2) Solve equation 1 and 2 to obtain x and y Answer is x = 8 minutes, y = 10 minutes Hence (B) is the corret answer. Answer : B #### B QUESTION:A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14% while buying and by 20% while selling. What is his percentage profit? options: A)10.22% B)20.22% C)21.22% D)42.5% E)Can't be calculated SOLUTION:The owner buys 100 kg but actually gets 114kg; The owner sells 100 kg but actually gives 80kg; Profit: (114-80)/80*100=~42.5% Answer: D. #### D QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies? options: A)220 B)250 C)320 D)420 E)560 SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7. We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers. Hence , answer is D. #### D QUESTION:Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 32 percent ryegrass, what percent of the weight of this mixture is X ? options: A) 10% B) 33.33 % C) 46.66% D) 50% E) 66.66 % SOLUTION:---------------->Ryegrass X--------------> 40% Y--------------> 25% M(mixture)---->32% 0.4X + (M-X)0.25 = 0.32M 0.15X = 0.07M X = 0.4666M X = 46.66% of M C #### C QUESTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ? options: A) None B) Two C) Four D) Five E) Seven SOLUTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain? R=2,4,6,8,10,12... S=4,16,36,64... Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets. Solution: Five Answer: D #### D QUESTION:Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is: options: A)173 m B)200 m C)273 m D)300 m E)None of these SOLUTION:xplanation: Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, <ACB = 30º and <ADB = 45º. AB/AC=tan30 Answer: C #### C QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible? options: A)270 B)252 C)272 D)292 E)285 SOLUTION:number of astronauts with previous experience = 7 Remaining =9 we need to pick exactly one from the first group and 2 from the second group (7C1)*(9C2) =7*36= 252 Answer : B #### B QUESTION:The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size? options: A)6 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Side of smallest cube = L.C.M of 5,10,20 = 20cm Volume of the cube = (20 x 20 x 20)cm3 = 8000 cm3 Volume of the block= (5 x 10 x 20) cm3 = 1000 cm3 Number of blocks = (8000/1000) = 8 Answer: B #### B QUESTION:What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x options: A)35678 B)73205 C)75653 D)86554 E)87565 SOLUTION:(B) 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205 #### B QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2007 B)2008 C)2002 D)2000 E)2001 SOLUTION:(10*10)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer: D #### D QUESTION:In a mixture of 60 liters, the ratio of milk and water is 4:1. What amount of water must be added to make the ratio of milk and water as 1:4? options: A)60 liters B)42 liters C)68 liters D)65 liters E)62 liters SOLUTION:4:1 --- 60 1:4 2:8 --------------- 5 5 ----------- 60 5 ----------- ? => 60 liters ANSWER:A #### A QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)1687 B)1478 C)1480 D)14000 E)1500 SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 Answer: D #### D QUESTION:If x and y are different integers and x^2 = xy, which of the following must be true ? I. y = 0 II. x = 0 III. x = y options: A)I only B)II only C)III only D)I and III only E)II, and III SOLUTION:Answer choice A is correct. The question gives you x^2=xy you can simplify that as x^2-xy=0 x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer. Answer E #### E QUESTION:A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)224 E)E)302 SOLUTION:If x is the original number of employees, then after 13% reduction in employees number is .87x but we are given .87x = 181 x = 208 So the original number of employees is 208 Correct Answer - B #### B QUESTION:A wildlife preserve is being planned for 6,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population? options: A) 340 B) 330 C) 670 D) 310 E) 300 SOLUTION:Number of rhinos = 6000 Watering area = 10,000 acres Number of rhino to increase by 10 percent ,then number of rhino = 6600 Grazing area for a rhino = 100 Total grazing area for 6600 rhinos= 6600 * 100 = 6,60,000 Total area required for the wildlife preserve = 6,60,000 + 10,000 = 6,70,000 = 670 * 1000 Answer C #### C QUESTION:The average marks scored by Ganesh in English, Science, Mathematics and History is less than 18 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him? options: A)72 B)50 C)60 D)Data inadequate E)None of these SOLUTION:E+H+G+M/4−E+S+M+H/4=18 ⇒ G - S = 72 Answer A #### A QUESTION:xy=1 then what is (6^(x+y)^2) / (6^(x-y)^2) options: A)1296 B)4 C)8 D)16 E)32 SOLUTION:(x+y)^2 - (x-y)^2 (x+y+x-y)(x+y-x+y) (2x)(2y) 4xy 4 6^4 = 1296 Answer A #### A QUESTION:The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 13 percent, what was the annual interest rate last year? options: A)1% B)1.1% C)9.1% D)11.81% E)11.50% SOLUTION:13=1.1*x X=11.81% Answer D) #### D QUESTION:A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 30% while buying and by 10% while selling. What is his percentage profit? options: A)10.22% B)20.22% C)21.22% D)30% E)Can't be calculated SOLUTION:The owner buys 100kg but actually gets 130kg; The owner sells 100kg but actually gives 90kg; Profit: (130-90)/90*100=30% Answer: D. #### D QUESTION:Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank? options: A)10 min. 20 sec. B)11 min. 45 sec. C)12 min. 30 sec. D)14 min. 40 sec. E)15 min. 40 sec. SOLUTION:Take LCM of 15 and 20 and get the total capacity of tank as 60 . Then A will fill 4li in 1 min and B will fill 3 li in 1 min so total will be 7 . A left after 4 min so they worked together for 4 min so 7*4= 28 . now subtract it from 60.(60-38=32). This will be filled by b so time taken would be..10 min 20 sec. ANSWER:A #### A QUESTION:Set #1 = {A, B} Set #2 = {K, L, M, N, O, P} There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel? options: A)1/6 B)1/3 C)7/12 D)2/3 E)5/6 SOLUTION:So Not a vowel in Set-1 : 1/2 And not a vowel in Ser-2:5/6 Now, 1/2∗5/6=5/12 This is for not a vowel. Then for at least one vowel will be = 1−5/12=7/12 Answer will be C. #### C QUESTION:A straight pipe 5 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard? options: A) 1/6 and 1/4 only B) 1/4 and 1/3 only C) 1/6, 1/4, and 1/3 D) 1/12, 1/6 and 1/4 E) 1/12, 1/6, and 1/3 SOLUTION:Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4. In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length). Distinct lengths would be: 3=3/12=1/4, 6-4=2=2/12=1/6meters long pieces. Answer: A. #### A QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)4.1 B)3.6 C)2.6 D)5.0 E)5.5 SOLUTION:B 3.6 In this simple subtraction series, each number decreases by 0.4. #### B QUESTION:The cost price of a radio is Rs.4800 and it was sold for Rs.4400, find the loss %? options: A)8 B)9 C)7 D)6 E)4 SOLUTION:4800 ---- 400 100 ---- ? => 8% Answer: A #### A QUESTION:Sonika bought a V.C.R. at the list price of 18,700. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R. options: A)20,196 B)19,780 C)19,680 D)19,380 E)None of these SOLUTION:Sol. List price of V.C.R. =18,700 Rate of sales tax = 8% ∴ Sales tax = 8% of 18,700 = 8⁄100 × 18700 = 1496 So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,700 + 1496 = 20,196. Answer A #### A <<<Examples ends QUESTION:A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)8 B)9 C)10 D)20 E)30 SOLUTION:x ------- 6 (x + 10) ---- 3 x * 6 = (x + 10)3 x = 10 ANSWER:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C SOLUTION:Let temperature on 4th day be X°C Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1 => X = 41.9 Therefore, temperature on 4th day = 41.9°C. ANSWER:D #### D QUESTION:In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made? options: A)1:4 B)1:3 C)2:3 D)3:4 E)None of these SOLUTION:Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B #### B QUESTION:Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 253 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle? options: A)903 B)2209 C)2878 D)1210 E)1560 SOLUTION:As expected, this question boils down to 2 equation, Consider total number of Balls in Triangle = T and number of balls in last row = x. 1+2+3+...+x = T x(x+1)/2 = T ----(a) As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+253) (x-8)^2 = T+253 -----(b) Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk. We can see that option A fits this criteria in eq (b). Add - 903+253 = 1156 = 34^2 = (x-8)^2 Hence, x = 42. Cross check by putting in eq (a) = x(x+1)/2 = T = > 42*43/2=903 Hence, answer is A. #### A QUESTION:A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? options: A)37 B)38 C)30 D)77 E)27 SOLUTION:US = 25 DS = 35 M = (35 + 25)/2 = 30 Answer:C #### C QUESTION:Pipe A that can fill a tank in an hour and pipe B that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe B is shut 10 minutes before the tank overflows. When will the tank overflow? options: A)37 mins B)35 mins C)40 mins D)32 mins E)36 mins SOLUTION:The last 10 minutes only pipe A was open. Since it needs 1 hour to fill the tank, then in 10 minutes it fills 1/5th of the tank, thus 5/6 of the tank is filled with both pipes open. The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 5/6th of the tank they need (time) = (work)/(rate) = (5/6)/3 = 5/18 hours = 27 minutes. Total time = 10+ 27= 37 minutes. Answer: A. #### A QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:An investor bought two shares of stock, which he sold for $36 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had: options: A)a profit of $5 B)a profit of $3 C)a loss of $3 D)a loss of $5 E)neither a profit nor a loss SOLUTION:The cost of the first stock was 36/1.2=30, so the profit from it is 6. The cost of the second stock was 36/0.8=45, so loss from it is 9. Overall the loss is $3. The answer is C. #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)87 min B)82 min C)86 min D)47 min E)72 min SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:A die is tossed. Find the probability of getting a multiple of 2 ? options: A)1/5 B)2/3 C)1/6 D)1/3 E)1/2 SOLUTION:S = {1,2,3,4,5,6} E= event of getting a multiple of 2 = {2,4,6} P(E) = 3/6 = 1/2 Answer is E #### E QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. options: A)125/128 B)115/122 C)125/126 D)125/122 E)125/112 SOLUTION:Required probability = 1 - 1/126 = 125/126 Answer:C #### C QUESTION:Of the science books in a certain supply room, 50 are on botany, 60 are on zoology, 90 are on physics. 40 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? options: A)81 B)159 C)309 D)285 E)324 SOLUTION:First, you can take all 50 Botany books, all 60 zoology books and all 40 geology books because you're sure to never pick 80 of them. There are still 90 on physics and 110 on chemistry The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry. Minimum number of books picked to reach 80 in the same science should be : 50 + 60 + 40 + 79 +79 + 1 = 309 C #### C QUESTION:How many positive integers will divide evenly into 440? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:520 = 10*13*4 = 8*5*13 = 2^3*5*13 We need to positive integers will divide evenly into 520 or simply the factors of 520 If a number is of the form 2^a*3^b*5^c, Total factors = (a+1)(b+1)(c+1) Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 18 Option D #### D QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(4*90+x)/5=92 x=(5*92)-(4*90) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:Evaluate combination 100C100 options: A)10000 B)1000 C)10 D)1 E)0 SOLUTION:Explanation: nCn=1 100C100=1 Option D #### D QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 15000, then find his savings? options: A)3600 B)3607 C)3608 D)3602 E)3000 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 15000 => x = 3000 Savings = Income - expenditure = 5x - 4x = x So, savings = Rs. 3000. Answer:E #### E QUESTION:A man's age is 125% of what it was 10 years ago, but 83 X 1/3% of what it will be after 10years. What is his present age? options: A)20 B)60 C)50 D)70 E)80 SOLUTION:C 50 Let the age before 10 years =x Then, 125x/100=x+10 ⇒125x=100x+1000 ⇒x=1000/25=40 Present age =x+10=40+10=50 #### C QUESTION:105,100,...,90,85,80,75 Insert the missing number options: A)95 B)78 C)83 D)84 E)none of the above SOLUTION:Missing number : 95 Answer : A #### A QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B QUESTION:In an election between two candidates, one got 55% of the total valid votes. 20% of the votes were invalid. If the total number of votes was 7500, what was the number of valid votes that the other candidate got? options: A)2800 B)2700 C)2100 D)2500 E)3000 SOLUTION:Total no of votes = 7500 20 % invalid =>80% valid tot valid votes = 7500*80/100 =>valid for 2nd candidate got 7500*80/100*45/100 =2700 ANSWER B #### B QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now? options: A)14years B)15years C)16years D)17years E)18years SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years ANSWER:A #### A QUESTION:If P gets 25% more than Q, then by what percent does Q get less than P? options: A)60% B)22% C)12% D)20% E)13% SOLUTION:Let Q get 1 unit. 25% of 1 unit = 1/4 = 0.25 P gets (1 + 0.25) i.e., 1.25 units. Difference = (1.25 - 1) = 0.25 Required percentage = 0.25/1.25 * 100 = 1/5 * 100 = 20% Answer: C #### C QUESTION:An bus covers a certain distance at a speed of 100 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? options: A)500 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (100 x 5) = 500 km. Required speed = 500 km/hr. A #### A QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125 options: A)123 B)143 C)166 D)190 E)210 SOLUTION:28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C #### C QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)16 B)17 C)10 D)18 E)15 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 2 = 26 => x = 8 Deepak's age = 3x = 18 years. Answer: D #### D QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:Tough and Tricky questions: Combinations. Three students - 2 boys and 1 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another? options: A)2 B)4 C)72 D)240 E)720 SOLUTION:2!*1!*2 = 2*1*2 = 4 ways. Ans. B) 4 #### B QUESTION:The average salary of all the workers in a workshop is $1000. The average salary of 5 technicians is $5000 and the average salary of the rest is $500. The total number of workers in the shop is? options: A)25 B)20 C)15 D)30 E)18 SOLUTION:Let the total number of workers be x 1000x = 5000*5 + 500(x-5) x = 25 Answer is A #### A QUESTION:A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)299 B)267 C)269 D)400 E)276 SOLUTION:2*12 : 3*12 : 4*24 1: 3: 4 1/8 * 3200 = 400 Answer: D #### D QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:The number of arrangements that can be made with the letters of the word PETER so that the vowels occupy the even places? options: A)18 B)20 C)40 D)12 E)14 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 4 places in 3! i.e., 24 ways. Hence the total ways are 2 * 6 = 12. Answer:D #### D QUESTION:A single letter is selected at random from the word 'SIMS'. The probability that it is a vowel is..?? options: A)1/4 B)3/11 C)4/11 D)3/7 E)1/2 SOLUTION:total vowels = 1, total number of letters = 4 so probability = 1/4 ANSWER:A #### A QUESTION:2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 20 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A? options: A)15 km/hr B)16 km/hr C)17 km/hr D)18 km/hr E)None of these SOLUTION:Explanation : Total distance covered by B=20*6=120kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=120/8=15 km/hr Answer : A #### A QUESTION:Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take? options: A)40 B)50 C)70 D)80 E)90 SOLUTION:L+M=M+N-40 / N=2L+10 40=M+N-L-M 40=N-L 40=2L+10-L 30=L 2(30)+10=70 C #### C QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)Rs 15 B)Rs 12.10 C)Rs 21.70 D)Rs 16.80 E)None of these SOLUTION:Explanation : Let the cost of the tax items = x Given that tax rate = 6% Cost of tax items, x*(6/100) = 30/100 x = 5 rs Now non taxable item = total cost - cost for taxable item - tax = 27 - 5 - 0.30 =21.70 Answer : C #### C QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)12, 9 B)10, 5 C)12, 7 D)11, 6 E)12, 6 SOLUTION:x – y = 5 4x – 6y = 6 x = 12 y = 7 ANSWER:C #### C QUESTION:If the tens digit of positive integer x is 6 and the tens digit of positive integer y is 6, how many possible values of the tens digit of 2(x+y) can there be? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 60 + p and 60 + q respectively. 2(60+p+60+q)= 240 + 2(p + q). 2(p+q) can range from 0 up to a maximum value of 36 when p=q=9. Then the tens and ones digits of 2(x+y) can range from 40 up to 76. There can be 4 possibilities for the tens digit. The answer is C. #### C QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good? options: A)20/67 B)20/63 C)20/19 D)20/18 E)20/28 SOLUTION:Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63 Answer: B #### B QUESTION:10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)2 B)1 C)7 D)6 E)4 SOLUTION:1 women's 1 day work = 1/70 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/10 + 10/140) = (1/14 + 1/14) = 1/7 5 women and 10 children will complete the work in 7 days. Answer:C #### C QUESTION:A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system correct answer D #### D QUESTION:The ratio between the number of sheep and the number of horses at the Stewart farm is 1 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm? options: A)18 B)28 C)32 D)56 E)8 SOLUTION:Let the number of sheeps and horses be 1x and 7x. Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8 Sheeps = 1x = 1*8 = 8. Hence E #### E QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in? options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr SOLUTION:Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer:D #### D QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION:A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these SOLUTION:Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: C #### C QUESTION:There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle. When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left. So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left. Finally, they woke up the 7th thief and this time the diamonds were divided equally. How many diamonds did they steal in total? options: A)2397 B)2401 C)2411 D)2423 E)None of the above SOLUTION:We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60. Answer B #### B QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)800 B)700 C)750 D)850 E)900 SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265 253/160p=1265==> p =800 ANSWER A #### A QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12*100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=8 and y=6, then x^2-y^2=28 and 28 is divisible only by 4 from the options, thus it must be correct. Answer: B. #### B QUESTION:A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take? options: A)80 B)288 C)4^4 D)576 E)288^2 SOLUTION:The condition that TWO boys or TWO girls cannot be together means they should be alternate.. Total five means 3 of one and 2 of other.. 1) choose 3 girls and arrange them... 4C3*3! = 4!= 24 2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C2*2!= 12 Total ways = 24*12 = 288.. 2) same as above.. 2 girls and 3 boys.. 288 Total 288*2=576 ANS:D #### D QUESTION:In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County? options: A)200 B)210 C)216 D)224 E)235 SOLUTION:The number must be a multiple of both 8 and 7 so the answer is 224. The answer is D. #### D QUESTION:A die is thrown twice and the sum of the numbers appearing is observed to be 6. find the conditional probability that the number 4 has appeared at least once? options: A)2/5 B)3/5 C)3/11 D)3/13 E)3/17 SOLUTION:Let E be the event that ‘number 4 appears at least once’ and F be the event that ‘the sum of the numbers appearing is 6’. Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4)} and F = {(1,5), (2,4), (3,3), (4,2), (5,1)} We have P(E) = 11/36 and P (F) = 5/36 Also EnF = {(2,4), (4,2)} Therefore P(EnF) = 2/36 the required probability P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5. A) #### A QUESTION:What is the area of a square field whose diagonal of length 24 m? options: A)256 B)289 C)200 D)288 E)178 SOLUTION:d2/2 = (24 * 24)/2 = 288 Answer: D #### D QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:A is half good a work man as B and together they finish a job in 32 days. In how many days working alone B finish the job? options: A)98 days B)21 days C)48 days D)18 days E)19 days SOLUTION:WC = 1:2 2x + x = 1/32 => x = 1/96 2x = 1/96 => 48 days Answer:C #### C QUESTION:What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? options: A)s.2.04 B)s.2.08 C)s.3.67 D)s.2.83 E)s.2.42 SOLUTION:C.I. when interest is compounded yearly = [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100] = 9000 * 26/25 * 51/50 = Rs. 9547.2 C.I. when interest is compounded half-yearly = [9000 * (1 + 2/100)2] = (9000 * 51/50 * 51/50 * 51/50) = Rs. 9550.87 Difference = (9550.87 - 9547.2) = Rs.3.67. Answer: C #### C QUESTION:Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? options: A)635.50 B)635.53 C)635.57 D)635.52 E)635.51 SOLUTION:4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 Answer: A #### A QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? options: A)1 B)6 C)7 D)9 E)3 SOLUTION:Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 * 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 = 6 sec. Answer: B #### B QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2 SOLUTION:Solution Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 Answer A #### A QUESTION:21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement. options: A)7/41 B)3/41 C)9/42 D)4/51 E)5/13 SOLUTION:The probability that first toy shows the even number, =1021=1021 Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left. Hence, probability that second toy shows the even number, =920=920 Required probability, =(1021)×(920)=(1021)×(920) =9/42 C #### C QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E QUESTION:Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture? options: A)1 : 9 B)1 by 5 C)1 : 7 D)1 : 3 E)1 : 1 SOLUTION:Selling price of the mixture = 70 and profit = 20% Cost price of the mixture = 70×100120=70×5670×100120=70×56 By applying alligation rule: So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5 Answer:B #### B QUESTION:A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)22 B)20 C)88 D)71 E)10 SOLUTION:x ------- 12 (x + 10) ---- 6 x * 12 = (x + 10)6 x = 10 \Answer: E #### E QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 18 = 6 + 12 - {Both} + 0; {Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: A. #### A QUESTION:A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion? options: A) 81 B) 83 C) 85 D) 86 E) 89 SOLUTION:Overall, there can be 81 minuses. Tus, it is A. #### A QUESTION:On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is: options: A)48759 B)51236 C)47619 D)6974 E)1235 SOLUTION:Explanation: By hit and trial, we find that 47619 x 7 = 333333. ANSWER:C #### C QUESTION:If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of even integers from 30 to 50, inclusive, what is the value of x + y ? options: A)810 B)811 C)830 D)850 E)851 SOLUTION:21 integers from 30 to 50 inclusive so 11th integer is mean, it is 40 21*40=840 from 21 integers 11 ones is even 840+11=851 ANSWER:E #### E QUESTION:A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 55% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight? options: A) 7/12 B) 1/4 C) 1/2 D) 7/24 E) 17/24 SOLUTION:In probability questions the trap answer is just the multiple of the numbers in the question. i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct. C #### C QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 . Number of pages typed by Kumar in 1 hour = 40/5 = 8. Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 . Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours = 8 hours 15 minutes. ANSWER : E #### E QUESTION:The train travels at an average speed of 16km/h, to the top of the hill where the midpoint of the trip is. Going down hill, train travels at an average speed of 8km/h. Which of the following is the closest approximation of train's average speed, in kilometers per hour, for the round trip? options: A)9.6 B)10.6 C)4.3 D)2.5 E)5.3 SOLUTION:Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 16km/hour and 8 km/hour, using a multiple of both 16 and 8 would make the math easiest. Let's set the Distance up the hill at 64 km. So, going uphill, we have.... D = (R)(T) 64 = (16)(T) 64/16 = 4 = T 4 hours to go uphill Going downhill, we have.... D = (R)(T) 60 = (20)(T) 64/8 = 8 = T 8 hours to go downhill Total Distance = 120 km Total Time = 4+8 = 12 hours Average Speed = 128/12 = 10.6 km/hour B #### B QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? options: A)1/48 B)1/42 C)1/40 D)1/41 E)1/43 SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42 Answer: B #### B QUESTION:The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers? options: A)15 B)17 C)19 D)21 E)23 SOLUTION:x,x+2,x+4 are three odd numbers (x+x+2+x+4)/3=12+(x/3) x=15 last no.=x+4=19 ANSWER:C #### C QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? options: A)32 Yrs B)36 Yrs C)40 Yrs D)48 Yrs E)None SOLUTION:Explanation: Let the mother's present age be x years. Then, the person's present age = (2/5)*x years. ((2/5)*x)+8 = (1/2)(x+8) 2(2x + 40) = 5(x + 8) x = 40. Answer: C #### C QUESTION:I. m-14, m, m, m, m+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:5*SP = 7*CP SP = 1.4*CP The profit percent is 40%. The answer is D. #### D QUESTION:a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple? options: A)225 B)228 C)230 D)231 E)235 SOLUTION:CP = 140*2+150*3+160*4+170*1=1540 SP = 1.5*1540=2310 Total no.of kgs=2+3+4+1=10 SP per kg=2310/10=231 ANSWER:D #### D QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? options: A)Rs:567 B)Rs:518 C)Rs:519 D)Rs:500 E)Rs:520 SOLUTION:P - 340 = (P*4*8)/100 P = 500 Answer:D #### D QUESTION:The difference between the ages of two persons is 10 years.Fifteen years ago ,the elder one was twice as old as the younger one.The present age of the elder person is : options: A)25 years B)35 years C)45 years D)55 years E)75 years SOLUTION:Solution Let their ages be x year and (x + 10) years respectively. Then,(x + 10) - 15 = 2 (x - 15) ⇔ x-5 = 2x-30 ⇔ x =25. ∴ Present age of the elder person =(x + 10) =35 years. Answer B #### B QUESTION:There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends? options: A)1 B)10 C)125 D)50 E)20 SOLUTION:25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125 so 125 enrolled for swimming Answer: C #### C QUESTION:The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number? options: A)12 B)20 C)45 D)60 E)52 SOLUTION:Given ratios 5 : 3 4 : 9 20:12:27 The second number = 177/(20+12+27) * 15 = 45 Answer is C #### C QUESTION:On increasing the price of T.V. sets by 40%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? options: A)4 B)5 C)56 D)12 E)7 SOLUTION:Explanation: Let the price be = Rs.100, and number of units sold = 100 Then, sale value = Rs.(100 × 100) = Rs.10000 New sale value = Rs.(140 × 80) = Rs.11200 Increase% = 1200/10000 × 100 = 12% Answer: D #### D QUESTION:0.40 represents what percent of 0.008? options: A)0.05% B)0.5% C)5% D)500% E)5000% SOLUTION:One more method 0.40 represents what percent of 0.008? Adjusting the decimal 400 represents what percent of 8? Divide by 8 50 represents what percent of 1? Answer = 50*100 = 5000% = E #### E QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 13*0 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:The proportion of water to alcohol in Solution A is 5:4 and the proportion of water to alcohol in Solution B is 6:5. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? options: A)40.9% B)41.9% C)42.9% D)43.9% E)44.9% SOLUTION:Let V be the total volume of the new solution. Then a volume of V/2 was added from each solution A and B. The amount of alcohol added to the new solution was: (4/9)(V/2)+(5/11)(V/2)=2V/9+5V/22=89V/198. The concentration of alcohol is 89/198=44.9% The answer is E. #### E QUESTION:A wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face? options: A)52.9% B)55.4% C)58.3% D)61.7% E)64.5% SOLUTION:There are a total of 9*9*9 = 729 cubes. All the exterior cubes will have at least one face painted red. The interior is formed by 7*7*7 = 343 cubes. The number of cubes with at least one side painted red is 729 - 343 = 386 cubes The probability that a cube has at least one side painted red is 386/729 which is about 52.9% The answer is A. #### A QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere? options: A) 6/π B) 9/π C) 6 D) 9 E) 12 SOLUTION:Given Area of the base of a hemisphere is 3 = PI * R^2 Thus R = Sqrt ( 3 / PI ) . Surface area of whole sphere = 4*PI*R^2 . = 4 * PI * 3 / PI = 12 . Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . But the total surface area = 6 + Area of the base of a hemisphere . = 6 + 3 = 9. Answer is D !! #### D QUESTION:If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is options: A)40 B)44 C)80 D)86 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 24 and x2 + y2 = 404. Now, 2xy = (x+y)2 - (x2 + y2) = (24)2 - 404 = 576- 404 = 172 xy = 86. Answer D #### D QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is options: A)277 B)668 C)119 D)177 E)121 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer: C #### C QUESTION:The cube root of what integer power of 2 is closest to 50? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Integer powers of 2 = 2 , 2^2, 2^3, 2^4, 2^5, 2^6, 2^7 etc. Let, Cube root of x is closest to 50 i.e. x is closest to cube of 50 = 50*50*50 = 125000 But x must be equivalent to an Integer power of 2 2^10 = 1024 2^7 = 128 i.e. 2^17 = 128*1024 = 128000 (approx.) i.e. 2^18 = 256*1024 = 256000 (approx.) i.e. 2^16 = 64*1024 = 64000 (approx.) i.e. 2^17 which is closest to 125000 i.e. Integer power of 2 must be 7 Answer: option B #### B QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 5 m wide at the bottom and the area of cross-section is 344 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)40 E)71 SOLUTION:1/2 * d (12 + 5) = 344 d = 40 Answer: D #### D QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/800*1/600=1/4,800. Answer: B. #### B QUESTION:The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 144 metres, what is its area? options: A)1320 sq.metres B)1260 sq.metres C)1280 sq.metres D)1380 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 144 ⇒ x = 6 Area = 7 × 6 × 5 × 6 = 1260 sq.m. Answer B #### B QUESTION:One-third of 600 is what percent of 120 ? options: A)313.2 B)30.1 C)12.24 D)None of these E)166.6 SOLUTION:Answer Let one-third of 600 is N% of 120. ∵ 600/3 = (N x 120)/100 ∴ N = (200x 100) / 120 = 166.6 Correct Option: E #### E QUESTION:Find the circumference and area of radius 13 cm. options: A)124 cm² B)531 cm² C)354 cm² D)584 cm² E)594 cm² SOLUTION:Area of circle = πr² = 22/7 × 13 × 13 cm² = 531 cm² ANSWER:B #### B QUESTION:If the quotient a/b positive, which of the following must be true? options: A)a > 0 B)b > 0 C)ab > 0 D)a-b > 0 E)a+b > 0 SOLUTION:a/b>0 means aa and bb have the same sign, either both are negative or both are positive. Thus, their product will also be positive: ab>0. Answer: C. #### C QUESTION:Which of the following is a prime number ? options: A)27 B)45 C)97 D)98 E)100 SOLUTION:Clearly, 97 is a prime number. #### C QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 300*1 = revenue (eq -1) if he reduced his price by 20% then , 240*(customer) = 125/100*revenue customer = 1.25*300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:Two trains 200m and 160m long run at the speed of 68kmph and 40kmph in opposite directions in parallel tracks. The time which they take to cross each other is? options: A)5.6sec B)8.9sec C)10.8sec D)12 sec E)15sec SOLUTION:Relative speed = 68+40 = 108kmph * 5/18 = 30 m/s Distance covered in crossing each other = 200+160 = 360m Required time = 360*1/30 = 12 sec Answer is D #### D QUESTION:The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is: options: A)12 B)24 C)34 D)48 E)54 SOLUTION:Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. So, the numbers 12 and 16. L.C.M. of 12 and 16 = 48.Answer: Option D #### D QUESTION:Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions? options: A)76 seconds B)16 seconds C)18 seconds D)27 seconds E)19 seconds SOLUTION:Time taken to meet for the first time anywhere on the track = length of the track / relative speed = 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds. Answer: D #### D QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? options: A)60% B)50% C)25% D)20% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 25 + 55 - {both} + 40 {both} = 20%. Answer: D. #### D QUESTION:A milk man has 30 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is: options: A)20% B)25% C)33.33% D)35% E)None of these SOLUTION:Explanation: when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 30 liters of milk. Therefore, profit percentage = 35 %. Answer: D #### D QUESTION:If y exceeds x by 25%, then x is less than y by? options: A)20% B)16 3/3% C)16 2/3% D)12 2/3% E)16 1/3% SOLUTION:X=100 y=125 125------25 100-------? => 20% Answer:A #### A QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)388 B)299 C)266 D)400 E)2871 SOLUTION:2*12 : 3*12 : 4*24 1: 3: 4 1/8 * 3200 = 400.Answer: D #### D QUESTION:If 280 people, constituting 5 percent of the population of a town, ride bicycles, and the others do not, then how many people in the town do not ride bicycles? options: A)5930 B)5600 C)5320 D)5110 E)4980 SOLUTION:5 % of X is 280 5/100 * X = 280 X = 280*100/5 = 5600 So C. 5320 is the correct Answer No. of people Not Riding Bike = 5600 - 280 = 5320 answer is C #### C QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33*100 = 180% of 3.33. Answer: E. #### E QUESTION:Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24 options: A)22 B)62 C)28 D)16 E)11 SOLUTION:Answer:B #### B QUESTION:Two pipes A and B can fill a tank in 15 min and 27 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank? options: A)14 min 19 sec B)14 min 42 sec C)18 min 24 sec D)14 min 40 sec E)14 min 10 sec SOLUTION:: Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15 Remaining part = 1 - 7/15 = 8/15 Part filled by B in 1 minute = 1/27 1/27 : 8/15 :: 1 ; x x = 8/15 * 1 * 27 = 14 2/5 min = 14 min 24 sec. The tank will be full in (4 min. + 14 min. 24 sec) = 18 min 24 sec.Answer: C #### C QUESTION:What percent of 120 are 90? options: A)33 B)66 C)75 D)44 E)31 SOLUTION:(?% /100) * 120 = 90 ? = 75% Answer: C #### C QUESTION:The length of a rectangle is twice its breadth. If its length is decreased by 4 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle. options: A)10/3cm B)20/3cm C)20cm D)16cm E)14cm SOLUTION:Explanation: Let breadth = x. Then, length = 2x. Then, (2x - 4) (x + 5) - 2x * x = 75 => 6x - 25 = 75 => x =20/3. Length of the rectangle = 20/3 cm. Answer: Option B #### B QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Going down = 16 m Going Up = 8 --> Total = 24 Going down = 8 --> Total = 32 Going Up = 4 --> Total = 36 Going down = 4 --> Total = 40 Going up = 2 --> Total = 42 Going down = 2 --> Total = 44 Going up = 1 --> Total = 45 Going down = 1 --> Total = 46 Going up = 0.5 --> Total = 46.5 (Caught) No of going downs = 5 .. ANSWER:A #### A QUESTION:The length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)50 m B)60 m C)65 m D)75 m E)80 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:The ratio between the present ages of P and Q is 5:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)3:4 B)B)8:9 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 5x and 7x years respectively. Then, 7x - 5x = 4 => x = 2 Required ratio = (6x + 4) : (7x + 4) 16 : 18= 8:9 ANSWER:B #### B QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame? options: A)10 B)20 C)30 D)40 E)54 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/3) of that of the painting so Area of frame = (1/3) * a^2 Area of Frame + Painting = a^2 + (1/3)*a^2 = (4/3)*a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2 so, b * sqrt2 = 12 so, b = 6 * sqrt2 b^2 = 72 we know that b^2 = (4/3)*a^2 so, a^2 = (3/4)*b^2 = (3/4)*72 = 54 And area of painting = a^2 = 54 So, answer will be E. #### E QUESTION:Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255 options: A)11 B)8 C)27 D)63 E)127 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong. B #### B QUESTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (4x - 2y) is odd II. xy^2 is an even negative integer III. (y^2 - x) is an odd negative integer options: A)I only B)I,II,III NOT TRUE C)I and II D)I and III E)II and III SOLUTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 2y) is odd 4x - is always negative and EVEN 2y - can be 0, when y=0, or always even integer (positivie or negative) odd integer +/- even integer = always EVEN I statement is always true II. xy^2 is an even negative integer y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true III. (y^2 - x) is an odd negative integer y can be 0 => -x will be positive => III statement is not true basing on above, only I statement will always be true answer is B #### B QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:Which of the following best approximates the percent by which the distance from A to C along a diagonal of square ABCD reduces the distance from A to C around the edge of square ABCD? options: A)30% B)43% C)45% D)50% E)70% SOLUTION:let the sides be 2 units. original distance=2+2=4 units changed distance=2sq.root2 %change=change dist.-original dist./original dist. =(2sq.root 2-4)/4==-.2955 reduced by ~30% Ans A #### A QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7740 km and comes back to the starting point. The total time taken by him is: options: A)914.2 hours B)900 hours C)915 hours D)982.9 hours E)915 hours SOLUTION:Explanation: Speed downstream = (16 + 2) = 18 kmph Speed upstream = (16 - 2) = 14 kmph Total time taken = 7740/18 + 7740/14 = 430 + 552.9 = 982.9 hours Answer: Option D #### D QUESTION:The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result? options: A)600 B)480 C)538 D)650 E)560 SOLUTION:23th result = sum of 45results - sum of 44 results 10*45-16*22+20*22 = 450-352+440 = 538 Answer is C #### C QUESTION:A can run 3 Kms in 3 min 18 sec and B can run same distance in 3 min 40 sec, then by how much distance A can beat B? options: A)300 m B)220 m C)280 m D)195 m E)295 m SOLUTION:Distance travelled=3000m Time taken by A=3 m 18 s Time taken by B=3 m 40 sec=220 sec speed of B=3000m/220 s=150/11 m/s Difference between time of A and B=22 sec when time will be 3 m 18 s A will have travelled 3000m but B need 22 sec more to finish. Distance travelled by B in 22 sec=(150/11)*22=300 m Hence, A beat B by 300 m ANSWER:A #### A QUESTION:The lowest number which should be added to 8247 so that the sum is exactly divisible by 5, 6, 7, 8 and 9 is: options: A)1833 B)1853 C)1733 D)1233 E)1832 SOLUTION:L.C.M. of 5, 6, 7, 8 and 9 = 2520. On dividing 8247 by 2520, the remainder is 687. Number to be added = (2520 - 687) = 1833. Answer: Option 'A' #### A <<<Examples ends QUESTION:The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle? options: A)1: 96 B)1: 98 C)1: 97 D)1: 95 E)1: 91 SOLUTION:Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96. Answer:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:what is the least number. which should be added to 221 to make it a perfect square? options: A)5 B)8 C)4 D)6 E)7 SOLUTION:221+4=225 15^2 ANSWER:C #### C QUESTION:A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.45 B)8.45 C)7.45 D)3.45 E)1.45 SOLUTION:Explanation: 40*(46/100) = 18.4 --- 64 ? --- 12 => Rs.3.45 Answer: D #### D QUESTION:The capacity of a tank of dimensions (8m x 6m x 2.5m)is options: A)120 litres B)1200 litres C)12000 litres D)120000 litres E)None of these SOLUTION:Explanation: capacity of atank =volume of tank = (8 x 100 x 6 x 100 x 2.5 x 100)/1000 litres = 120000 litres Answer: D #### D QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 * 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)45. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (25gray+45other) 85gray+45other Answer:B #### B QUESTION:A starts business with Rs.3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the Capital ? options: A)24887 B)20778 C)23788 D)9000 E)2811 SOLUTION:Explanation: A invested Rs.3500 for 12 months. Let B joined with investment x. And he invested for 12 - 5 = 7 months. So there profit ratio = (3500 × 12) : (7x) = 2 : 3 ⇒ x = 9000 Answer: D #### D QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:SCORE INTERVAL----------------NUMBER OF SCORES 50-59-------------------------- 2 60-69--------------------------10 70-79--------------------------16 80-89--------------------------5 90-99--------------------------2 The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 35 scores? options: A)16th B)20th C)22th D)24th E)18th(70-79) SOLUTION:Total scores= 2+10+16+5+2 = 35, which is odd, therefore the median is the Floor(35/2)+1 = 18th score. And the 18th score is in the 70-79 range, because 50-69 only reference 12 scores. E #### E QUESTION:Virat buys an old car for Rs. 50000 and spends Rs. 6000 on its repairs. If he sells the scooter for Rs. 70000, his gain percent is: options: A)25% B)11 (1/9) % C)12 (2/3) % D)12% E)None of these SOLUTION:Explanation: C.P. = Rs. (50000 + 6000) = Rs. 56000 S.P. = Rs. 70000. Gain% = ( (14000 / 56000) * 100 ) % = 25% ANSWER A #### A QUESTION:A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture? options: A)14 liters B)76 liters C)10 liters D)11 liters E)12 liters SOLUTION:Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters. P liters of water added to the mixture to make water 25% of the new mixture. Total amount of water becomes (30 + P) and total volume of mixture is (150 + P). (30 + P) = 25/100 * (150 + P) 120 + 4P = 150 + P => P =10 liters. Answer: C #### C QUESTION:A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? options: A)66 2/3 % B)33 7/3 % C)33 1/3 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer: A #### A QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)766 m B)156 m C)245 m D)156 m E)156 m SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer: C #### C QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased? options: A) 100% B) 500% C) 300% D) 600% E) 800% SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%. Answer: B. #### B QUESTION:Thomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer? options: A)10 B)14 C)19 D)21 E)25 SOLUTION:The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5 The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0 Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5 The % of profit in selling a single computer=(4545.5/45454.5)*100=10% Answer:A #### A QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)11 2/3% loss C)66 2/3% loss D)12 2/3% loss E)17 2/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss Answer: A #### A QUESTION:If 7a = 2b = 15, then 42ab = options: A)75 B)125 C)675 D)1100 E)1250 SOLUTION:7a * 2b = 15 * 15 = 225 14 ab = 225 i.e. 42 ab = 675 Answer: Option C #### C QUESTION:A car covers a distance of 630 km in 6 hours. Find its speed? options: A)105 B)7778 C)266 D)288 E)121 SOLUTION:624/6 = 105 kmph Answer:A #### A QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)48 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E QUESTION:The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale? options: A)(P-7)*6 B)(P-7)*5 C)(P-7)*2 D)(P-7)*3 E)(P-7)*4 SOLUTION:M/84 =(P-7)/21 M = (P-7)*84/21 =(P-7)*4 E #### E QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)Rs.486 B)Rs.455 C)Rs.487 D)Rs.480 E)Rs.489 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480 Answer: D #### D QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine? options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4 SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine" The above statement is NOT clear Still a solution: For 8 students we have 3 posts one post can be occupied by only one member no two posts can be occupied by the same member probability(P) for a member getting selected for particular 2 of the 3 posts= probable outcomes=1(Caine)+1(Abel)=2 total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8 =2/8=1/4 Probability required for the given case= 1-P=1-1/4=3/4 Answer: E #### E QUESTION:In what ratio should a variety of rice costing $6 per kg be mixed with another variety of rice costing $8.75 per kg to obtain a mixture costing $7.50 per kg? options: A)4/7 B)5/6 C)5/9 D)4/8 E)3/8 SOLUTION:B 5/6 Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6 #### B QUESTION:Adding 30% of x to x is equivalent to multiplying x by which of the following? options: A)12.5 B)1.05 C)1.15 D)1.3 E)1.25 SOLUTION:130x/100= 1.3*x ANSWER:D #### D QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women? options: A)266 B)86400 C)11760 D)5040 E)None of these SOLUTION:Here, 5 men out of 8 men and 6 women out of 10 women can be chosen in 8C5 × 10C6 ways, i.e., 11760 ways. Answer C #### C QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1⁄7 hours B)6 2⁄7 hours C)8 2⁄7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 × 2 = 16 km Distance covered in next two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 – 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. ∴ Time taken = 4⁄12 = 1⁄3 hour. Total time= 6 + 1⁄3 = 6 1⁄3 hour Answer E #### E QUESTION:The present average age of a family of five members is 24 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest) options: A)27.5 years B)17 years C)17.5 years D)16.5 years E)15.5 years SOLUTION:Present total age of the members = 24(5) = 120 years. Present age of the youngest member = 10 years Present total age of the remaining four members = 120 -10 = 110 years Their average age at the time of the birth of the youngest member = [110 - (4 * 10)] / 4 = 17.5 years ANSWER:C #### C QUESTION:A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)50 sec C)44 sec D)49 sec E)60 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 410 + 140 = 550 m Required time = 550 * 2/25 = 44 sec Answer:C #### C QUESTION:Salesperson A's compensation for any week is $350 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation? options: A)$21,000 B)$18,000 C)$15,000 D)$ 14,500 E)$4,000 SOLUTION:sometime, setting up an equation is an easy way to go with: 350 + 0.06 (x - 1000) = 0.08 x x = 14,500 Ans : D #### D QUESTION:If the speed of X meters per second is equivalent to the speed of Y kilometers per minute, what is Y in terms of X? (1 kilometer=1000 meters) options: A)0.06x B)6x/5 C)18x/5 D)60x E)3600000x SOLUTION:x=1000y/60 y = 0.06x Answer : A #### A QUESTION:The radius of a semi circle is 6.3 cm then its perimeter is? options: A)35.4 cm B)32.4 cm C)32 cm D)30 cm E)35 cm SOLUTION:Explanation: 36/7 r = 6.3 = 32.4 ANSWER IS B #### B QUESTION:597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred’s and ten’s places are respectively: options: A)3 and 6 B)7 and 9 C)2 and 6 D)4 and 7 E)None SOLUTION:Solution : Let the given number be 597xy6. Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3 And, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0 => y=x+3 27+x+y) =>(27+x+x+3) =>(30+2x) => x = 3 and y = 6. Answer A #### A QUESTION:Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $752 in total compensation, how many total hours did he work that week? options: A)36 B)40 C)44 D)48 E)52 SOLUTION:For 40 hrs = 40*16=640 Excess = 752-640=112 For extra hours =.75(16)=12+16=28 Number of extra hrs =112/28=28/7=4 Total hrs =40+4=44 Answer C 44 #### C QUESTION:What is the Value given by the equation (-2+a)^2=(a-2)^2? options: A)Indefinite B)Two C)Three D)One E)None SOLUTION:(-2+a)^2=(a-2)^2 Both the equations in RHS and LHS are equal So it give the Value One Option D is answer #### D QUESTION:There are 7 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played? options: A)21 B)30 C)45 D)60 E)90 SOLUTION:7 players are there. two players play one game with one another. so 7C2=7*6/2 =21 SO OPTION A is correct #### A QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:From 6 positive numbers and 6 negative numbers, how many groups F of 4 numbers, yielding a positive product, can be formed? options: A)720 B)625 C)30 D)960 E)255 SOLUTION:Potential combinations of 4 numbers that will yield positive product ++++ 4C6 ---- 4C6 ++-- 2C6*2C6 4C6 + 4C6 + 2C6*2C6 F=15 +15 + 15*15 = 255=E #### E QUESTION:x =3 4 5 y= 27 36 9 then what is the relation between x and y options: A)1*X)^2 B)1*X)^3 C)1*X)^4 D)1*X)^5 E)1*X)^6 SOLUTION:Y=(1*X)^2 9=(1*3)^2 9=9 ANSWER:A #### A QUESTION:A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work? options: A)6 B)5 C)5.5 D)7 E)8 SOLUTION:B's 10 day's work = ( 1 x 10 ) = 2 . 15 3 Remaining work = ( 1 - 2 ) = 1 . 3 3 Now, 1 work is done by A in 1 day. 18 Therefore 1 work is done by A in ( 18 x 1 ) = 6 days. #### A QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform? options: A)39.9 B)37.88 C)35 D)38.88 E)38.09 SOLUTION:Speed = [200 / 42] m/sec = 100/21 m/sec. Let the length of the platform be x meters. Then, x + 200 / 50 = 100/21 21(x + 200) = 5000 è x = 38.09 m. Answer: E #### E QUESTION:A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? options: A)5/6 km/hr B)25 km/hr C)79.2 km/hr D)15 km/hr E)38 km/hr SOLUTION:Explanation: Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr Answer:C #### C QUESTION:In a sequence of 40 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 282, what is the smallest term in the sequence? options: A)2 B)-2 C)0 D)8 E)9 SOLUTION:Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term. An = 282 + (40 - 1)*(-7) An = 282 - 273 = 9 E #### E QUESTION:The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is? options: A)38 B)27 C)75 D)28 E)21 SOLUTION:Explanation: The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75. Answer: C #### C QUESTION:Exactly four sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll? options: A)0.3 B)0.2 C)0.01 D)0.148 E)0.144 SOLUTION:Total no. of sides = 10 Sides that are red = 4 Probability that the die lands with red side up = 4/10 Therefore, Probability that the die does not land with red side up = 1 - 4/10 = 6/10 Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face) = (6/10) X (6/10) X (4/10) = 144/1000 = 0.144 E #### E QUESTION:Sebastian bought a meal at a restaurant and left a 15% tip. With the tip, he paid exactly $35.42. How much did the meal cost without the tip? options: A)$28.98 B)$29.91 C)$30.15 D)$30.60 E)$30.80 SOLUTION:The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip. Thus, 115% of this price equals $35.42: 1.15x = 35.42 Divide both sides by 1.15:=>x=35.42/1.15=30.80 correct answer E)$30.80 #### E QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:Here 10 programmers, type 10 lines within 10 minutes then 60 lines can type within 60 minutes. How many programmers are needed? options: A)16 B)10 C)6 D)60 E)50 SOLUTION:10 10 programmer 10 line 10 mins. 10 programmer 20 line 20 mins. . . . .10 programmer 60 line 60 mins. ANSWER:D #### D QUESTION:In how many different ways can the letters of the word 'CAREER' be arranged? options: A)10 ways B)20 ways C)180 ways D)60 ways E)40 ways SOLUTION:Totally there are 6 letters on the word CAREER. it contains 1C,1A,2R,2E. The no of ways is 6!/2!2!=180 ways. ANSWER:C #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)150 m B)200 m C)240 m D)400 m E)150 m SOLUTION:Answer: Option C Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. #### C QUESTION:18 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place? options: A)144 B)131 C)279 D)90 E)45 SOLUTION:there are 18 business exec and in each handshake 2 business execs are involved. hence 18C2=153 Also, each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake. total=153+126=279 ANS: C #### C QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age 10 years back was: options: A)10 years B)19 years C)33 years D)38 years E)39years SOLUTION:Let the son's present age be x years. Then, (40 - x) = x 2x = 40. x = 20 Son's age 5 years back (20 - 10) = 10 years. Answer:A #### A QUESTION:A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass? options: A)6 B)8 C)10 D)12 E)16 SOLUTION:1)If the two sides are co-prime, SUM of sides -1.. 2)and if not co-prime , Sum of sides - HCF of sides.. the difference is related to the diagonal passing through a vertex of squares at some place.. here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12 ANSWER:D #### D QUESTION:If x is an integer, then x(x – 1)(x – k) must be evenly divisible by six when k is any of the following values EXCEPT options: A)-4 B)-2 C)-1 D)2 E)5 SOLUTION:We have the product of 3 integers: (x-1)x(x-k). Note that the product of 3 integers is divisible by 6 if at least one multiple is divisible by 6. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 6 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 6. Next, if k=2 then we'll have (x-1)x(x-2)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 6. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 6. Answer: D. #### D QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4 options: A)II,III only B)I only C)I,III only D)II only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+4 must be there. if -3 is the starting element the sequence is as follows. S ={-3,1,5,9....} if -3 is not the starting element the sequence is as follows S = {...-7,-3,1,5,9...} By observing the above two sequences we can say that 9 must be there in set S. Answer : B #### B QUESTION:The total of the ages of Amar, Akbar and Anthony is 30 years. What was the total of their ages three years ago ? options: A)20 years B)28 years C)71 years D)21 years E)31 years SOLUTION:Explanation: Required sum = (30 - 3 x 3) years = (30 - 9) years = 21 years. Answer: Option D #### D QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ? options: A)7.2 kg. B)10.8 kg. C)12.4 kg. D)18.0 kg E)None SOLUTION:Answer ∵Weight of 13 m long rod = 23.4 kg ∴ Weight of 1 m long rod = 23.4 / 13 kg ∴ Weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg Option: B #### B QUESTION:Pomes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows? options: A)40 minutes. B)1 hour and 30 minutes. C)1 hour. D)1 hour and 40 minutes. E)2 hours and 15 minutes. SOLUTION:Rate =Output/Time Pomes Rate=25/20=5/4 Dylan Rate=25/60=5/12 Combined rate = 5/4+5/12= 20/12 CombinedRate*CombinedTime= CombinedOutput 20/12*t=150 t=90 mins => 1 hr 30 min #### C QUESTION:A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 60 paise per sq. metre options: A)s510 B)s780 C)s880 D)s480 E)s980 SOLUTION:area of the plot=110m*65m=7150sq.m area of plot excluding gravel=105m*60m=6300sq.m area of gravel =7150sq.m-6300sq.m =850sq.m cost of building it = 850sq.m*60 = 51000p in Rs =51000/100=Rs510 ANSWER:A #### A QUESTION:Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 0.5. What value is exactly 2 standard deviations less than the mean? options: A) 10.5 B) 11 C) 11.5 D) 12 E) 12.5 SOLUTION:The value which is exactly two SD below the mean is: mean-2*SD=13.5-2*0.5=12.5. Answer: E. #### E QUESTION:A work can be finished in 15 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is options: A)4:3 B)3:4 C)2:3 D)3:2 E)5:4 SOLUTION:Work done by 20 women in 1 day = 1/15 Work done by 1 woman in 1 day = 1/(15×20) Work done by 16 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×16) Ratio of the capacity of a man and woman =1/(15×16) : 1/(15×20) = 1/16 : 1/20 = 1/4 :1/5 = 5:4 Answer is E. #### E QUESTION:If 0 < n < 1, what is the median of the values n, n^-1, n^2, n^1/2 and n^3? options: A)n B)n^-1 C)n^2 D)n^1/2 E)n^3 SOLUTION:A. To make the problem less confusing, I picked a number between 0 and 1 such as n = 1/4 and calculate: n = 1/4 n^-1 = 4 n^2 = 1/16 n^(1/2) = 1/2 n^3 = 1/8. From this, rearrange the number and the median is 1/4, which is n. Answer A #### A QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40 SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35 P(at least one graduate) = 1- 1/35 = 34/35 The answer is D. #### D QUESTION:A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)22 B)71 C)54 D)77 E)99 SOLUTION:S = 240/16 * 18/5 = 54 kmph Answer: C #### C QUESTION:If x < y < 0, which of the following must be true? options: A)x/y is a negative integer B)xy is a negative integer C)x+y is a negative integer D)x-y is a positive integer E)(-x)+ (-y) is positive integer SOLUTION:Given x, y are less than 0. So both will be negative integers negative + negative = negative negative * negative = positive negative / negative = positive x-y is false since x<y eg. x=-2, y=-1 then -2-(-1)=-1 So, option E is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers) Answer : E #### E QUESTION:An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)267 B)180 C)287 D)177 E)911 SOLUTION:Angle traced by the hour hand in 6 hours =(360/12)*6 Answer: B #### B QUESTION:How many numbers between 100 and 600 are divisible by 2, 3, and 7 together? options: A)112 B)77 C)267 D)12 E)99 SOLUTION:Explanation: As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42 The limits are 100 and 600 The first number divisible is 42*3 = 126 To find out the last number divisible by 42 within 600: 600/42 = 14.28 Hence, 42*14 = 588 is the last number divisible by 42 within 600 Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12 ANSWER: D #### D QUESTION:Bat is bought for Rs.400 and sold at a gain of 20% find its selling price? options: A)Rs.320 B)Rs.350 C)Rs.370 D)Rs.480 E)None of these SOLUTION:Explanation : 100 % = 400 (100 * 4 = 400)120 % = 480 (120 * 4 = 480)Selling price = Rs.480/- Answer : D #### D QUESTION:A computer program generates a sequence of numbers a1, a2, a3, ... such that a1=1, a2=2, and ak=a(k-2)*4-1 for 2 < k < n for n=10. Find a6. options: A)19 B)27 C)31 D)36 E)41 SOLUTION:a1=1 a2=2 a3=1*4-1=3 a4=2*4-1=7 a5=3*4-1=11 a6=7*4-1=27 27 #### B QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14 SOLUTION:answer isB Total probability=7C3=48 4C3 +4C2*4C1+4C1*4C2=4+24+24=42 therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8 B #### B QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs.7500 B)Rs.7502 C)Rs.7529 D)Rs.7596 E)Rs.7506 SOLUTION:A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs.7500. Answer:A #### A QUESTION:In your classes you counted 120 hands. How many students were at the class? options: A)60 B)61 C)85 D)86 E)88 SOLUTION:Total number of hands = 120 We have 2 hands. To find how many students were at the class, divide the total number of hands by the number of hands we have. We get, divide 120 by 2 220 ÷ 2 = 60 Therefore, there were 60 students at the class. ANSWER IS A #### A QUESTION:In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions? options: A)63 B)48 C)85 D)52 E)47 SOLUTION:In the given word there 6 letters in that there are 2 vowels and 4 consonants no of ways of arranging the vowels=2p2=2 no of ways of arranging the consonants=4p4=24 total number of ways 24*2=48 Answer(B) #### B QUESTION:A 180 meter long train crosses a man standing on the platform in 9 sec. What is the speed of the train? options: A)72 B)108 C)1266 D)188 E)211 SOLUTION:S = 180/9 * 18/5 = 72 kmph Answer: A #### A QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? options: A)25 B)30 C)99 D)88 E)61 SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr. = 72 * 5/18 = 20 m/sec. Time taken to pass the man = 500 * 1/20 = 25 sec. Answer: A #### A QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is: options: A)15 B)18 C)19 D)22 E)23 SOLUTION:explanation: 60-6= 54 ,190-10= 180 Highest number that divides 54 and 180 is HCF of numbers HCF of 54 nad 180= 18 Answer:B #### B QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent? options: A)45 B)35 C)55 D)60 E)66 SOLUTION:Explanation : A : B: C = 10*7 : 12*5 : 15*3 = 2*7 : 12*1 : 3*3 = 14 : 12 : 9 amount that C should pay = 175 * (9/35) = 5*9 = 45. Answer : Option A #### A QUESTION:Convert the 11/36 m/s into kilometers per hour? options: A)2.9 kmph B)1.1 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:11/36 m/s = 11/36 * 18/5 = 11/10 = 1.1 kmph. Answer: B #### B QUESTION:When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction? options: A)5/4 B)4/7 C)5/6 D)6/7 E)None of these SOLUTION:Let the fraction be x/y. When the numerator decreased by 25% and the denominator decreased by 20%. (x * 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5 ANSWER:E #### E QUESTION:In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 5%.what is population of after 2 year. options: A)140 B)141 C)142 D)143 E)146 SOLUTION:next year total population=[150^2+90^2]^.5=174.92=175 man decreased by 5% so total man =150*.95=142.5 women will be= 175-142.5=32.5 so population after two years= [135^2+32.5^2]^.5=146.15=146 so population after two year= 146 ANSWER:E #### E QUESTION:Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is? options: A)7 1/2 sec B)2 sec C)3 sec D)5 sec E)7 sec SOLUTION:70 + 50 = 120 * 5/18 = 100/3 mps D = 150 + 100 = 250 m T = 250 * 3/100 = 15/2 = 7 ½ sec ANSWER A #### A QUESTION:A gardener increased the length of a rectangle-shaped garden by 20 percent and decreased its width by 10 percent. The area of the new garden options: A)has increased by 20 percent B)has increased by 12 percent C)has increased by 8 percent D)is exactly the same as the old area E)cannot be expressed in percentage terms without actual numbers SOLUTION:Let L be the original length and let W be the original width. The original area was L*W. The new area is 0.9W*1.2L = (0.9)(1.2)L*W = 1.08*L*W The answer is C. #### C QUESTION:A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/5 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ? options: A)x + 2000 = 1/3*(x - 3000) B)1/3*(x - 3000) = x C)x + 3000 = 1/3*x D)x - 7000 = 1/3*x E)x - 3000 = 1/5*x SOLUTION:Plane's original altitude = x Plane's new altitude after ascending 2000 ft = x+2000 Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000 So, after two changes plane is at 1/5 its original altitude => x-3000 = x/5 Answer (E) #### E QUESTION:It takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate. If 5 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 1:00 PM, at what time will the machine be complete? options: A)4:30 B)4:45 C)5:00 D)5:15 E)5:30 SOLUTION:3 workers build 1/15 of a machine in one hour. 1 worker builds 1/45 of a machine in one hour. In the first 2 hours, 5 workers build 5*(1/45)*2=10/45 of a machine. From 1:00 to 2:00, 6 workers build another 6/45. The total is 16/45. From 2:00 to 3:00, 7 workers build another 7/45. The total is 23/45. From 3:00 to 4:00, 8 workers build another 8/45. The total is 31/45. From 4:00 to 5:00, 9 workers build another 9/45. The total is 40/45. To build another 5/45, 10 workers need (5/10)*60 minutes which is 30 minutes. The machine is complete at 5:30. The answer is E. #### E QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required ? options: A)34 B)40 C)68 D)88 E)None of these SOLUTION:Solution We have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. ∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D #### D QUESTION:Tanks P and B are each in the shape of a right circular cylinder. The interior of tank P has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank P is what percent of the capacity of tank B? options: A)75% B)80% C)100% D)120% E)125% SOLUTION:B. For P, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi P/B = 160pi/200pi = 0.8 #### B QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same) options: A)1:2 B)3:5 C)1:1 D)3:7 E)2:4 SOLUTION:C 1:1 This is a very simple probability question in a software interview. This question might be a little old to be ever asked again but it is a good warm up. Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method. Number of girls = 0*(Probability of 0 girls) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + … Number of girls = 0*(C*1/2) + 1*(C*1/2*1/2) + 2*(C*1/2*1/2*1/2) + … Number of girls = 0 + C/4 + 2*C/8 + 3*C/16 + … Number of girls = C (using mathematical formulas; it becomes apparent if you just sum up the first 4-5 terms) The proportion of boys to girls is 1 : 1. #### C QUESTION:The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is? options: A)7 B)4 C)5 D)3 E)1 SOLUTION:Explanation: P(1 + 20/100)n > 2P or (6/5)n > 2 Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years. Answer:B #### B QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 *12=45,000*8 1:1 Madhu's share=1/2*60,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:What is the prime factors’ number of 36? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p... So, 24 = 2^2*3^2 prime factors’ number will be 2+2 = 4. Hence, answer is C. #### C QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)None of these SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =((100 x 3000)/(12500 x 4))% = 6% Answer :D #### D QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? options: A)2000 B)2200 C)3000 D)3400 E)3500 SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans Alternative 100+105+110+115=12900 430=12900 100=12900/(430)X100=3000 C #### C QUESTION:If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ? options: A)16 B)1.6 C)0.16 D)0.016 E)None of these SOLUTION:Explanation : (204/12.75) = 16 ⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10) ⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B #### B QUESTION:Which is the following is divisible by 11 options: A)A)4305 B)B)4825 C)C)1635 D)D)4805 E)E)4906 SOLUTION:Explanation: Sum of first 'n' natural numbers = n(n + 1)/2 Sum of first 9 natural numbers = 5(5 + 1)//2 = 5 x 3 = 15 Sum of first 99 natural numbers = 55(55 + 1)//2 = 55 x 30 = 1650 1650 - 15 = 1635 Answer: Option C #### C QUESTION:How many pairs (w, w+1) have one or more prime factors common, where w is an integer and 2 ≤ w ≤9 ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:w and w+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1. Answer: A. #### A QUESTION:If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ? options: A)x-2 B)x-4 C)x+4 D)x-3 E)x-1 SOLUTION:Original Digits=xy i.e. Number=10x+y After reversing the digits: Digits=yx i.e. Number=10y+x 10y+x is 36 more than 10x+y 10x+y+36=10y+x 10x-x+36=10y-y 9x+36=9y x+4=y OR y=x+4 Answer : C #### C QUESTION:I am an odd number; take away an alphabet and I become even. What number am I? options: A)6 B)8 C)9 D)3 E)7 SOLUTION:E 7 (SEVEN-S=EVEN) #### E QUESTION:The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number? options: A)72 B)83 C)45 D)53 E)64 SOLUTION:Sum of all the 13 numbers = 13 * 58 = 754 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 754 = 72. Answer:A #### A QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12*100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:There are two sections C and D of a class, consisting of 18 and 22 students respectively. If the average weight of sections C is 20 kg and that of sections D is 18 kg. Find the average weight of the whole class options: A)18.7 B)18.8 C)18.9 D)19.9 E)None SOLUTION:Solution Total weight of(18+22)Students = (18x20+22x18)Kg = 756 kg. Average weight of the whole class = (756 /40 ) = 18.90. Answer C #### C QUESTION:Which of the following MUST yield an integer when divided by 11? options: A)The sum of eleven consecutive positive integers. B)The square of a prime number. C)The sum of two odd integers. D)The product of three consecutive odd numbers. E)The difference between a multiple of 8 and a multiple of 3. SOLUTION:For option A: Let the numbers be (x-5), (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4), (x+5). Now, (x-5)+(x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4)+(x+5) = 11(x). Hence A is true. No need to check other answers since there can only be one correct answer. So, Ans(A). #### A QUESTION:9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90.5% B)87.5% C)80.5% D)77.5% E)70.5% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.212; 10+0.3} = {9.788; 10.212}. From the 8 listed numbers, 7 are within this range so 6/8=87.5%. Answer: B. #### B QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B QUESTION:Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x? options: A)4 B)5 C)3 D)9 E)6 SOLUTION:9 x + x = 13 + 27 10 x = 40 => x = 4 Answer:A #### A QUESTION:How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest? options: A)2 years B)3 years C)1 year D)4 years E)5 years SOLUTION:Explanation: P = Rs.900 SI = Rs.81 T = ? R = 4.5% T= (100×SI)/PR = (100×81)/(900×4.5) = 2 years Answer: Option A #### A QUESTION:The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination options: A)14 years B)14 years 5 month C)14 years 8 month D)15 years E)15 years 5 month SOLUTION:(d) Let No. of passed candidates are x So, x * 39 + (120 – x) 15= 120 * 35 x = 100 2.(a) Total increase = 8 * 2 = 16 years So, total age of two women = 35 + 45 +16= 96 Average age of two women=96/2=48 years 3(d) Total decrease = 20 * 2 = 40 month = 3 years 4 month So, age of new boy = 18 years – 3 years 4 month = 14 years 8 month C #### C QUESTION:A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent? options: A)35 B)45 C)25 D)15 E)55 SOLUTION:A : B : C =10×7:12×5:15×3 =2×7:12×1:3×3 =14:12:9 Amount that C should pay =175×9/35=5×9=45 Answer is B. #### B QUESTION:A driver goes on a trip of 50 kilometers, the first 25 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour. What is the average speed of the entire trip in kilometers per hour? options: A)35 B)36 C)40 D)42 E)45 SOLUTION:The time for the first part of the trip was 25/60 = 5/12 hours. The time for the second part of the trip was 25/30 = 5/6 hours. The total time for the trip was 5/12 + 5/6 = 15/12 = 5/4 hours. The average speed for the trip was 50 / (5/4) = 40 kph The answer is C. #### C QUESTION:At a party, there were seven times as many females as males and twice times as many adults as children. Which of the following could NOT be the number of people at the party? options: A)384 B)258 C)215 D)120 E)72 SOLUTION:Five times as many females as males --> F = 7M. Three times as many adults as children --> (F + M) = 2C. The number of people at the party = F + M + C = 2C + C = 3C. The number of people at the party must be a multiple of 3. The only answer choice which is NOT a multiple of 3 is C. Answer: C. #### C QUESTION:If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there? options: A)62 B)66 C)70 D)74 E)78 SOLUTION:There are 12 integers from -5 to 6 inclusive. 12C2 = 66. The answer is B. #### B QUESTION:The sum of three consecutive numbers is 87. The greatest among these three numbers is : options: A)22 B)24 C)26 D)30 E)44 SOLUTION:Sol. Let the numbers be x, x + 1 and x + 2. Then, x + (x + 1) + (x + 2) = 87 ⇔ 3x = 84 ⇔ x = 28. Greatest number = (x + 2) = 30. Answer D #### D QUESTION:A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following? options: A)1/6 B)1/9 C)1/18 D)1/24 E)1/36 SOLUTION:There are 6*6 = 36 possibilities. Bob has 2 chances so the probability is 2/36 = 1/18. The answer is C. #### C QUESTION:A grocery shop has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? options: A)4857 B)4184 C)4012 D)4991 E)5291 SOLUTION:Let the sale in the sixth month =x Then (6435+6927+6855+7230+6562+x)/6 =6500 =>6435+6927+6855+7230+6562+x =6×6500 => 34009+x=39000 => x=39000−34009 =4991 ANSWER:D #### D QUESTION:The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)230 B)244 C)245 D)238 E)235 SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X = 235 m. Answer: Option E #### E QUESTION:If 2m + n = 7 and m + 2n = 5, then (2m + n)/2 = options: A) 1 B) 7/2 C) 17/5 D) 18/5 E) 4 SOLUTION:2*(m+2m = 5) equals 2m+4n=10 2m+4n=10 - 2m + n= 7 = 3n=3 Therefore n = 1 Plug and solve... 2m + 1 = 7 2m=6 m=3 (6+1)/2= 7/2 B #### B <<<Examples ends QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these SOLUTION:Reqd ratio 4 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100 = 4 × 140 : 7 × 150 : 8 × 175 = 8 : 15 : 20 Answer C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:John bought 2 shares and sold them for $98 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had options: A) a profit of $10 B) a profit of $8 C) a loss of $4 D) a loss of $10 E) neither a profit nor a loss SOLUTION:$ Profit of the share sold at 20% profit = 120-98 20-? $18 profit on the sale of 1 share. $ Loss of the share sold at 20% loss= 80-98 20-? $22 loss on the sale of 1 share. 18-22=Loss of $4 Answer: C #### C QUESTION:A train 160m long is running at 30kmph. In how much time will it pass a platform 120m long? options: A)15.89 seconds B)24.36 seconds C)15.96 seconds D)14.93 seconds E)22.23 seconds SOLUTION:Distance travelled = 160 + 120m = 280m Speed = 30 * 5/8 = 75/4m Time = 280 * 4/75 = 14.93 Seconds Answer : D. #### D QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c − a? options: A)25 B)70 C)90 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=160 --2 subtracting 1 from 2 we have c-a=70; ANSWER:B #### B QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base * Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 5,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 11.11% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-5,500=4,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/4,500*100=~11.11% of the remaining solution of 4,500 gallons. Answer: E. #### E QUESTION:$378 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share? options: A)$200 B)$208 C)$216 D)$224 E)$232 SOLUTION:Let the shares for A, B, and C be x, 2x, and 4x respectively. 7x = 378 x = 54 4x = 216 The answer is C. #### C QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these SOLUTION:Solution Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr. Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 10000 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×5400 / 12×3) => Rs. 15,000. Answer : C #### C QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:The difference between a two-digit number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number? options: A)4 B)9 C)3 D)Cannot be determined E)None of theses SOLUTION:Let the two-digit number be 10x + y. Then, (10x + y) – (10y + x) = 36 or x – y = 4 Answer A #### A QUESTION:Which of the following is a pair of co–primes? options: A)(16, 62) B)(18, 25) C)(21, 35) D)(23, 92) E)none SOLUTION:Solution H.C.F. of 18 and 25 is 1. So, they are co-primes. Answer B #### B QUESTION:Nil and Ethan are brothers. They left their home at the same time and drove to the same beach. Nil drove at a speed of 30 miles per hour. Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach? options: A)20 miles B)30 miles C)40 miles D)50 miles E)60 miles SOLUTION:Every hour, Nil gets ahead of Ethan 30 - 20 = 10 miles. When Nil arrived at the beach, Ethan is only 20 × 0.5 = 10 miles behind. That tells us they only drove 1 hour when Nil arrived at the beach. The distance between their home and the beach is Nil’s speed × Nil’s time = 30 × 1 = 30 miles. correct answer B #### B QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:Tough and Tricky questions: Distance/Rate. On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 200 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey? options: A)20 B)40 C)50 D)80 E)100 SOLUTION:Say, if speed is 40, 200/40 = 5 hrs and 200/50 = 4 hrs (a reduction of 1 hr -> Correct answer) Answer (B) #### B QUESTION:What number should replace the question mark? 11, 15, 16, 12, 21, 9, ---? options: A)21 B)29 C)28 D)27 E)26 SOLUTION:Answer: E 11, 15, 16, 12, 21, 9, ---? There are two alternate sequences: +5 and -3. #### E QUESTION:A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:A 5 cartons for large boxes = 5 * 6 = 30 boxes 4 cartons for small boxes = 4 * 9 = 36 boxes He will need 9 cartons to place 66 boxes. #### A QUESTION:2/5 of the fish in an aquarium is red and 1/4 of the fish is brown. 1/4of the red fish and 1/5 of the brown fish is male. If the rest of the fish in the aquarium is female, what is the probability that a fish randomly picked from the aquarium is male? options: A)3/20 B)7/30 C)5/16 D)1/3 E)2/5 SOLUTION:Straight method.... 1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20 ANSWER:A #### A QUESTION:Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $12.00 each, what was Company C’s gross profit? options: A) $2,250 B) $2,500 C) $4,100 D) $3,250 E) $4,500 SOLUTION:Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900 Revenue : 500 * 12 = $6000 Profit: 6000 - 1900 = $ 4100 Option C is correct #### C QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) spiders 1:7 Webs 7:1 1 x 7 x x = 7 x 1 x 7 => x= 7 Answer is 7 #### A QUESTION:The income derived from a Rs. 100, 13% stock at Rs. 105, is : options: A)Rs. 5 B)Rs. 8 C)Rs. 13 D)Rs. 18 E)Rs. 19 SOLUTION:Solution Income on Rs. 100 stock = Rs. 13. Answer C #### C QUESTION:A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $752 in total compensation, how many total hours did he work that week? options: A)36 B)40 C)44 D)48 E)52 SOLUTION:For 40 hrs = 40*16=640 Excess = 752-640=112 For extra hours =.75(16)=12+16=28 Number of extra hrs =112/28=28/7=4 Total hrs =40+4=44 Answer C 44 #### C QUESTION:12, 24, 16, 32, 24, 48, ? options: A)31 B)32 C)36 D)37 E)40 SOLUTION:E 40 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2 = 134 m2. answer :E #### E QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A #### A QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 6 years will be options: A)2 : 3 B)7 : 11 C)5 : 4 D)4 : 5 E)11 : 9 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 28 x = 4 Mini’s age = 16 years And Minakshi’s age = 12 years Ratio of their ages after 8 years = (16 + 6) : (12 + 6) = 22 : 18 = 11 : 9 ANSWER:E #### E QUESTION:If 5^29 * 4^15 = 2 * 10^n, what is the value of n? options: A)11 B)21 C)22 D)29 E)32 SOLUTION:My attempt: 5^(29) * 4^(15) = 2*10^p 5^(29) * 2 ^ (30) = 2 * (2*5)^p 5^(29) * 2 ^ (30) = 2 * 2^(p) * 5^(p) 5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p) => (p+1) = 30 => p = 29 Answer: 29 (D) #### D QUESTION:If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since q is an integer so q cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making q^2 as a multiple of 12)) q^2 is divisible by 12 (12 = 2*2*3), So, q should have at least one 2 and one 3 so that q^2 has a 2^2 and two 3 So, q will have a 2 and a 3. Or q will be a multiple of 6 So, largest possible integer than should divide q^3 is 6^3 So, Answer will be D #### D QUESTION:How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ? options: A)3.5 years B)4 years C)4.5 years D)5 years E)None of these SOLUTION:Solution Time =(100*81/450*4.5) years =4 years Answer B #### B QUESTION:A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes? options: A)100 m B)150 m C)190 m D)200 m E)220 m SOLUTION:Explanation: Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr Distance covered in 6 minutes =1/60X6km=1/10km=100m Distance between the thief and policeman = (200 – 100) m = 100 m. ANSWER IS A #### A QUESTION:If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips? options: A)1/8 B)1/16 C)1/32 D)1/64 E)1/128 SOLUTION:P(HHHHTT) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64 The answer is D. #### D QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B #### B QUESTION:If f(x)= 5x^2- 2x+6 and g(y)= 3y-8, then g(f(x)) options: A)82x^2-9x+38 B)15x^2-6x+10 C)58x^2-4x+58 D)87x^2-5x+96 E)98x^2-7x+94 SOLUTION:g(f(x))=3(5x^2-2x+6)-8 =15x^2-6x+18-8 =15x^2-6x+10 the answer is B #### B QUESTION:A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:14x + 75 = 15(x + 3) x = 30 + 3 = 33 Answer:C #### C QUESTION:Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3? options: A)2/5 B)2/7 C)33/83 D)51/250 E)100/249 SOLUTION:SOLUTION The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250. Answer: D #### D QUESTION:In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.0 sec B)2.8 sec C)7.5 sec D)2.3 sec E)1.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 80/40 = 2.0 sec. Answer:A #### A QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:Which of the following must be divisible by 4, given that y is a positive integer? options: A)(y−1)*y*(y+3) B)y^2*(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3) SOLUTION:option A) (y−1)*y*(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A QUESTION:A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in? options: A)days B)days C)days D)1/2 days E)days SOLUTION:Explanation: 10/40 + 10/30 + 10/x = 1 x = 24 days Answer: A #### A QUESTION:jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all? options: A)5 B)10 C)15 D)20 E)14 SOLUTION:10+5=15. Answer is C #### C QUESTION:12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise? (1 litre = 1000cm³) options: A)6 B)8 C)10 D)20 E)40 SOLUTION:we have 1 litre = 1000cm³ (thanks Bunuel) =>12 litres = 12*1000 = 12000cm³ Let call the height of the water is x the breadth and length of the water will equal the aquarium The volume of the water: 50 * 30 * x = 12000cm³ => x = 12000/(50*30) = 8 cm Answer is B #### B QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost? options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800 SOLUTION:1.4x = 2500 x=2500/1.4 so, 1.5X = 2500*1.5/1.4= 2478 Answer:- D #### D QUESTION:A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(13 -8) kmph = 2.5 kmph. Answer A #### A QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)5.14 SOLUTION:Time taken by First tank Fill 1/2 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank =12 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours Answer: option E #### E QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as a(f+l)/2----------------1) a= total no. of terms =80 f= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:On a ferry, there are 32 cars and 8 trucks. The cars have an average mass of 900 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1200 B)1240 C)1280 D)1320 E)1360 SOLUTION:The total mass of the vehicles is 32*900+8*3000=52800 The average mass is 52800/40=1320 The answer is D. #### D QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions? options: A)754 m B)704 m C)708 m D)706 m E)204 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m Answer:B #### B QUESTION:In an examination 60% failed in Math and 40% failed in French. If 10% failed in both. What % of students passed in both. options: A)25% B)15% C)20% D)30% E)10% SOLUTION:Passed in Math = 100 - 60 = 40% Passed in French = 100 - 40 = 60% Students who passed Math or French = 100 -10 = 90% Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-90 =10% ANSWER:E #### E QUESTION:A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? options: A)65 sec B)89 sec C)100 sec D)150 sec E)160 sec SOLUTION:Explanation: Speed =240/24 m/sec = 10 m/sec Required time =(240+650 /10)sec=89sec ANSWER IS B #### B QUESTION:a and b are positive integers less than or equal to 9 and multiple of 4. If a and b are assembled into the seven-digit number abaabab, which of the following must be a factor of abaabab? options: A)3 B)4 C)5 D)7 E)8 SOLUTION:The last two digit of the number are ab. Both a and b are multiple of 4,thus the last two digits are divisible by 4, which makes the number abaabab divisible by 4. Thus 4 is always a factor of abaabab. Answer: B #### B QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:6 B)7:3 C)7:4 D)7:2 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer: B #### B QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Explanation : If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29 If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29 If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27 Hence ,the common number is only 23 so it will be answer. Answer : A #### A QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? options: A)Rs.400 B)Rs.450 C)Rs.550 D)Rs.500 E)Rs.650 SOLUTION:Explanation: P - 340 = (P*4*8)/100 P = 500 ANSWER IS D #### D QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)*28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)? options: A)37 B)41 C)3.5e-05 D)35 E)3.5e-07 SOLUTION:99*0.35=34.65 approx. 35 Answer : B #### B QUESTION:A family made a down payment of $20 and borrowed the balance on a set of encyclopedias that cost $120. The balance with interest was paid in 7 monthly payments of $15.2 each and a final payment of $7. The amount of interest paid was what percent of the amount borrowed? options: A) 6% B) 12% C) 13.4% D) 16% E) 20% SOLUTION:interest paid = 15.2*7+7 - 100 = 13.4 % off the balance = (13.4/100) * 100 = 13.4 % Answer is C. #### C QUESTION:The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother? options: A)39 B)41 C)42 D)43 E)44 SOLUTION:Total age of mother and 6 children = avg x n = 9 x (6+1)= 63 If mother is excluded new average is (9 - 5) = 4 so for 6 children = 6 x 4 =24 so mother's age is 63 - 24 =39 Answer: Option A #### A QUESTION:Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is? options: A)17/65 B)17/29 C)17/21 D)P(EᴜP) =17/20 E)17/212 SOLUTION:n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D #### D QUESTION:The factorial expression 10!/2! is not divisible by which of the following integers? options: A)3 B)5 C)6 D)7 E)None of these SOLUTION:10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3 (A) 3 Can divide 12 or 9 (B) 5 Can divide 10 (C) 6 Can divide 12 (D) 7 can divide 7,21,28 Hence answer will be (E) #### E QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:Walking with 4/5 of my usual speed, I arrive at the bus stop 8 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed? options: A)20 B)24 C)28 D)32 E)36 SOLUTION:Let t = usual time = distance / usual speed t + 8 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4 t = 32 The answer is D. #### D QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:Let S be the set of values which can be written as the sum of 5 consecutive perfect squares. What is the smallest element of S which is divisible by 17? options: A)255 B)355 C)522 D)355 E)664 SOLUTION:Each element of S can be written in the form (x- 2)2 + (x - 1)2 + x2 + (x + 1)2 + (x + 2)2 = x2 + 2x2 + 2 + 2x2 + 8 = 5x2 + 10 = 5(x2 + 2) where x is some positive integer with x 3. By iterating over values of x, we observe that when x = 7, x2 + 2 = 51 = 3 * 17; no smaller value of x exists which satisfies the problem statement. Hence, the solution is 5(x2 + 2) = 5 *51 = 255 correct answer A #### A QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)18 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :D #### D QUESTION:A goods train runs at the speed of 72 kmph and crosses a 250m long platform in 26seconds. what is the length of the goods train? options: A)230 m B)240 m C)260 m D)270 m E)250 m SOLUTION:Speed =(72 *5/18)m/sec= 20 m/sec. then (x+250)/26=20 x+250 =520 x=520-250 then x=270 Answer: D #### D QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1244 B)1532 C)1349 D)1423 E)1543 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:A car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+336*6=448c =>c=336*6/112=18 Answer B. #### B QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2012) = ? options: A)2013 B)2088 C)270 D)1881 E)1781 SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4 .............. f(2012) = 2013 Ans: A #### A QUESTION:Find the remainder of the division (3^33)/7. options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Find the pattern of the remainders after each power: (3^1)/7 remainder 3 (3^2)/7 remainder 2 (3^3)/7 remainder 6 (3^4)/7 remainder 4 (3^5)/7 remainder 5 (3^6)/7 remainder 1 -->this is where the cycle ends (3^7)/7 remainder 3 -->this is where the cycle begins again (3^8)/7 remainder 2 Continuing the pattern to (3^33)/7 gives us a remainder of 6 Final Answer: E) 6 #### E QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)k(n+m+mn)+ k B)(1+n+m+mn)(k+1) C)k^2(mn+n/m) D)kmn(k+m+n) E)None of the above SOLUTION:The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together: (mn + m + n + 1)(k + 1). ANSWER:B #### B QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? options: A)150 B)88 C)270 D)62 E)52 SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 250/20 4X + 480 = 3X + 750 X = 270m Answer: C #### C QUESTION:If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq. m. If the length is creased by 1 m and breadth is decreased by 1m, then the area is decreased by 5 sq. m. The perimeter of the floor is: options: A)27 B)35 C)40 D)49 E)38 SOLUTION:Let length = x meters and breadth = y meters. Then, (x + 1) (y + 1) - xy = 21 x + y = 20 ………………1 And, xy - [(x + 1) (y - 1)] = 5 x - y = 6 ………………..2 Solving (i) and (ii), we get : x = 13 and y = 7 So, length = 13 m and breadth = 7 m. Perimeter = [2 (13 + 7)] m = 40 m. answer : C #### C QUESTION:The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles? options: A)20° B)70° C)60° D)120° E)140° SOLUTION:If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence 3x + 6x = 90 9x = 90 x = 10 Measures of the two acute angles are 3x = 3 × 10 = 30° 6x = 6 × 10 = 60° C #### C QUESTION:If you have 4 New Year greeting cards and you want to send them to 2 of your friends, in how many ways can this be done? options: A)360 B)12 C)16 D)24 E)None SOLUTION:Solution We have to find number of permutations of 2 objects out of 4 objects. This number is 4P2=4(4-1)=4*3=12 Answer B #### B QUESTION:The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 13%? options: A)31.5% B)35.9% C)37.5% D)39.5% E)30.5% SOLUTION:Let marked price = $100. Then, C.P. = $64, S.P. = $87 Gain % = 23/64 * 100 = 35.9%. B #### B QUESTION:If d<0, which of the following represents a positive number? options: A)d|d| B)|d|d C)|d|/d D)-d|d| E)d/ |d| SOLUTION:Answer : D #### D QUESTION:A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? options: A)42.3 B)560.45m C)79m D)26m E)111.12m SOLUTION:Explanation: A runs 1000 m while B runs 900 m and C runs 800 m. The number of meters that C runs when B runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. B can give C = 1000 - 888.88 = 111.12 m. ANSWER E #### E QUESTION:Weights of two friends Ram and Shyam are in the ratio 2:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased? options: A)17% B)10% C)21% D)16% E)None SOLUTION:Solution: given ratio of Ram and Shayam's weight = 2:5 Hence, (x-15)/(15-10) = 2/5 Or, x = 17%. Answer: Option A #### A QUESTION:40 is subtracted from 60% of a number, the result is 50. Find the number? options: A)150 B)140 C)130 D)120 E)110 SOLUTION:(60/100) * X – 40 = 50 6X = 900 X = 150 ANSWER:A #### A QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him? options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7 SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E QUESTION:If the area of a circle is 81pi square feet, find its circumference. options: A)48 B)38 C)51 D)92 E)18 SOLUTION:The area is given by pi pi × r × r = 81 pi r × r = 81 ; hence r = 81 feet The circumference is given by 2 × pi × r = 2 × pi × 9 = 18 pi feet correct answer is E) 18 #### E QUESTION:If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: options: A)0 B)1 C)2 D)None of these E)Cannot be determined SOLUTION:Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3. x = 2. Answer: Option C #### C QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils? options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44 SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p. Selling at a loss: 90 - 90p = 40p --> p = 9/13. (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44. Answer: E. #### E QUESTION:A box contains 3 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors? options: A)1/2 B)3/5 C)7/12 D)2/3 E)7/10 SOLUTION:Total selection ways: 5C2=5!/2!3!=10 Selecting one blue chip out of two: 2C1=2!/1!1!=2 Selecting one red chip out of four: 3C1=3!/2!1!=3 Thus, (2C1*3C1)/5C2=(2*3)/10=6/10=3/5=B #### B QUESTION:A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible? options: A)3 B)Z=4 C)Z=5 D)Z=6 E)Z=8 SOLUTION:The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)} Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with. {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)} Hence 8.E #### E QUESTION:How many 5-digit positive integers exist the sum of whose digits are odd? options: A)36000 B)38000 C)45000 D)90000 E)None SOLUTION:Solution: There are 9�104 = 90000, 5-digit positive integers. Out of these 90000 positive integers, the sum of the digits of half of the numbers will add up to an odd number and the remaining half will add up to an even number. Hence, there are 90000 /2= 45000, 5-digit positive integers whose sum add up to an odd number. Answer: Option C #### C QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:A dragon has 100 heads. A soldier can cut off 15, 17, 20 or 5 heads, respectively with one blow of his sword. In each of these cases, 24, 2, 14, 17 new heads grow on its shoulders. If all heads are cut off, the dragon dies. Can the dragon ever die? options: A)61 B)3 C)5 D)6 E)1 SOLUTION:Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die. Answer:B #### B QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)10987 B)11755 C)17576 D)19775 E)21899 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:For any 5 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3? I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. II. Dividing each of the numbers by 3 and then adding the results together. III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. options: A)I only B)II only C)I and II only D)II and III only E)None of the above SOLUTION:Let the 3 numbers be x, y and z. Question: Which of the following is equivalent to (x + y + z)/3 I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141 II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent Answer: C #### C QUESTION:How much water must be added to a 30 quarts of a 75% acid solution to reduce it to a 15% solution of acid? options: A)120 qts B)220 qts C)320 qts D)420 qts E)520 qts SOLUTION:I’m adding water, so we have WATER + WATER = WATER Starting off with 30 quarts and adding x quarts, we should end up with (30 + x) quarts 30 + x = (30 + x) The problem describes the solution in terms of acid, we have set it up in terms of water. So, we have to change the percentages and put them in the problem. .25(30) + x = .85(30 + x) Again, we multiply both sides of the equation by 100 to get rid of the decimal point. 25(30) + 100x = 85(30 + x) 750 + 100x = 2550 + 85x 15x = 1800 x = 120 qts correct answer A #### A QUESTION:A man swims downstream 40 km and upstream 56 km taking 8 hours each time, what is the speed of the man in still water? options: A)6 B)24 C)8 D)12 E)44 SOLUTION:40 --- 8 DS = 5 ? ---- 1 56 ---- 8 US = 7 ? ---- 1 M = ? M = (5 + 7)/2 = 6 Answer: A #### A QUESTION:Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 36/49, what is the probability that the next one she draws will be pink? options: A)1/7 B)4/7 C)3/7 D)16/49 E)40/49 SOLUTION:The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 36/49 = (6/7) * (6/7) Therefore probability that the next one she draws is pink = 1/7 Option (A) #### A QUESTION:Find the value of (X) in the given equation ? 35% of 1500 + X = 45% of 4200 – 320 options: A)910 B)980 C)1012 D)1045 E)None of these SOLUTION:Explanation: 35% of 1500 + X = 45% of 4200 – 320 (35/100 * 1500) + X = (45/100 * 4200) – 320 525 + X = 1890 – 320 X = 1890 – 320 – 525 X = 1890 – 845 X = 1045 ANSWER: D #### D QUESTION:If y/x is an integer, which of the following must also be an integer? I. xy II. x/y III. x options: A)I alone B)II alone C)None of the above D)I and III E)III alone SOLUTION:Lets take X = 1/6 and Y = 2/3 Then Y/X = 4 which is an integer. But XY = 1/6 * 2/3 = 1/9 --> Not an integer. X/Y = 1/6 divided by 2/3 = 1/4 --> Not an integer. X alone is 1/6. Not an integer. Hence C. None of the above. #### C QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 5%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.15% C)14.95% D)13.33% E)12.52% SOLUTION:(100%+5%)*(100%-19%) = 1.05*.81 = 0.8505. 1-0.8505 = 14.95% lost = -14.95% The Answer is C The organization has lost 14.95% of its total volunteers from fall to spring. #### C QUESTION:The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers? options: A)15 B)17 C)19 D)21 E)23 SOLUTION:x,x+2,x+4 are three odd numbers (x+x+2+x+4)/3=12+(x/3) x=15 last no.=x+4=19 ANSWER:C #### C QUESTION:If a and b are both prime numbers greater than 10, which of the following CANNOT be true? I. ab is an even number. II. The difference between a and b equals 117. III. The sum of a and b is even. options: A)I only B)I and II only C)I and III only D)II and III only E)I, II and III SOLUTION:CONCEPT: Prime Numbers greater than 10 will all be ODD I. ab is an even number - Can't be True because both a and b are ODD II. The difference between a and b equals 117 - Can't be True because both a and b are ODD and Difference of two Odd No. must be EVEN III. The sum of a and b is even - This will be True because both a and b are ODD and Sum of two Odd No. must be EVEN ANSWER:B #### B QUESTION:Two cars cover the same distance at the speed of 50 and 61 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)273 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 61x X = 4.55 60 * 4.55 = 273 km ANSWER:B #### B QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs. 7500 B)Rs. 9000 C)Rs. 9500 D)Rs. 10,000 E)None of these SOLUTION:Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs. 7500. ANSWER IS A #### A QUESTION:John is filling out the office space for his employees. There are 8 people in his office, and he must assign 8 employees to the following positions: 2 next to his cabin, 2 near the gate, 2 in center, and 2 near coffee machine. Only 2 employees are secretary and can sit next to his cabin, and they cannot sit anywhere else. The other employees can sit anywhere they like. How many different groupings are possible? options: A)100 B)90 C)80 D)70 E)60 SOLUTION:Secretary can sit in 2C2 ways = 1 Near the gate we can have 6C2 combinations (2 secretaries are already having a place) In the center we can have 4 C2 employees as 4 already have a place Near coffee machine we can have 2C2 employees as all other place are taken Number of selection = 2C2 * 6C2 * 4C2 * 2C2 = 90 Ans: B #### B QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 30 percent decrease in y would result in which of the following changes in z? options: A)decrease of 7.5% B)decrease of 26.5% C)increase of 16.5% D)increase of 24.5% E)increase of 32.5% SOLUTION:After the changes, z = 1.5x*(0.7y)^2 = (1.5*0.49)xy^2 = 0.735*z The answer is B. #### B QUESTION:If P gets 25% more than Q, then by what percent does Q get less than P? options: A)60% B)22% C)12% D)20% E)13% SOLUTION:Let Q get 1 unit. 25% of 1 unit = 1/4 = 0.25 P gets (1 + 0.25) i.e., 1.25 units. Difference = (1.25 - 1) = 0.25 Required percentage = 0.25/1.25 * 100 = 1/5 * 100 = 20% Answer: C #### C QUESTION:Carol budgeted 18 dollars for gifts for each of the 15 people on her Christmas list. After a disagreement with some of her neighbors, she reduces her Christmas list to 10 people. How much can she spend on each? options: A)20 B)27 C)18 D)23 E)30 SOLUTION:A1*P1=A2*P2 18*15=A2*10 => A2=27 Answer:B #### B QUESTION:How many quarters are equal to 4 dollars? options: A)16 B)8 C)12 D)9 E)7 SOLUTION:4*4 = 16 quarters Answer : A #### A QUESTION:When asked what the time is,a person answered that the amount of time left is 1/5 of the time already completed.what is the time. options: A)2 B)9 C)3 D)8 E)6 SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=15x⇒x=2024−x=15x⇒x=20 Time is 8 PM Answer:D #### D QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 6? options: A)1/4 B)5/36 C)2/11 D)3/13 E)1/5 SOLUTION:n(S) = 6*6 = 36 E = {(1,5),(2,4),(3,3),(4,2),(5,1)} Probability = 5/36 Answer is B #### B QUESTION:Diesel costs Rs.4per lit and petrol costs 5.63 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol. options: A)9 months B)5 months C)6 months D)4 months E)2 months SOLUTION:Explanation : =>In the First Month the price of the diesel would be 4*110/100 = 4.4 =>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84 =>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324 =>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85 which is higher than the price of the petrol! Answer : D #### D QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1100 B)1200 C)1349 D)1430 E)1340 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:131,95,70,54, ? options: A)42 B)45 C)44 D)40 E)39 SOLUTION:131 - 95 = 36 = 6^2 95 - 70 = 25 = 5^2 70 - 54 = 16 = 4^2 so we can write 54 - x = 09 = 3^2 , where x is the next number x = 54 - 9 = 45 so the next number will be 45 ANSWER:B #### B QUESTION:The average (arithmetic mean) of four numbers is 7x + 6. If one of the numbers is x, what is the average of the other three numbers? options: A)9x + 8 B)3x + 3 C)5x + 1 D)5x + 4 E)15x + 12 SOLUTION:If the average of four numbers is 7x + 3, then the sum of all four numbers if 4 * (7x + 6) = 28x + 24. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 24 - x)/3 = (27x + 24)/3 = 9x + 8. Answer is A. #### A QUESTION:Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x – 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a spade and the second card is a jack is? options: A)1/50 B)1/13 C)1/26 D)1/52 E)1/4 SOLUTION:Probability of a spade = 13/52 = 1/4 Probability of a jack = 4/52 = 1/13 Probability of both = P1*P2 = 1/(4*13) = 1/52 Answer is D. #### D QUESTION:Find the base K of the number system, if (524)8 = (664)K ? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:5*8^2 + 2*8^1 + 4*8^0 = 6*K^2 + 6*K^1 + 4*K^0 320 + 16 + 4 = 6(K^2) + 6K + 4 340 = 6(K^2) + 6K + 4 6(K^2) + 6K + 4 - 340 = 0 6(K^2) + 6K - 336 = 0 dividing by 6; (K^2) + K - 56 = 0 solving this quadratic equation we get, K=7 and K=-8 thus K=7 ANSWER:D #### D QUESTION:Which expression is the greatest? options: A)3252/3257 B)3456/3461 C)3591/3596 D)3346/3351 E)3453/3458 SOLUTION:Let 3252/3257 be the original fraction. Notice that it is a positive Proper fraction. Hence adding the same constant to both the numerator and the denominator will increase the fraction as the fraction will move closer to one. Hence we just have to pick the number that adds the greatest value to both the numerator and the denominator. Options can be re-written as (x-5)x => 1-(5/x) A) 1- (5/3257) B) 1- (5/3461) C) 1- (5/3596) D) 1- (5/3351) E) 1- (5/3458) ANSWER:C #### C QUESTION:The ratio of 2 numbers is 2:7 and their H.C.F. is 18. Their L.C.M. is ? options: A)252 B)243 C)521 D)361 E)600 SOLUTION:Let the numbers be 2x and 7x Their H.C.F. = 18 so the numbers are 2*18 , 7*18 = 36,126 L.C.M. = 252 Answer is A #### A QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:Virat buys an old car for Rs. 50000 and spends Rs. 6000 on its repairs. If he sells the scooter for Rs. 70000, his gain percent is: options: A)25% B)11 (1/9) % C)12 (2/3) % D)12% E)None of these SOLUTION:Explanation: C.P. = Rs. (50000 + 6000) = Rs. 56000 S.P. = Rs. 70000. Gain% = ( (14000 / 56000) * 100 ) % = 25% ANSWER A #### A QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 4:3 and B:C = 4:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)20.23 B)20.13 C)30.93 D)20.93 E)10.93 SOLUTION:A:B = 4:3 B:C = 4:5 A:B:C = 16:12:15 12/43 * 75 = 20.93 ANSWER:D #### D QUESTION:The following sets each have a mean of 10 and the standard deviations are given in variable form. Set I = {6, 6, 6, 14, 14, 14}, standard deviation = P Set II = {10, 10, 10, 10, 10, 10}, standard deviation = Q Set III = {7, 8, 9, 11, 12, 13}, standard deviation = R Rank these three standard deviations from least to greatest. options: A)P, Q, R B)P, R, Q C)Q, P, R D)Q, R, P E)R, Q, P SOLUTION:SD is minimum when the terms are closer to the mean. In set 2, we have all terms equal to mean. hence, its SD is 0.(The Lowest) Comparing Set 1 and Set 3, Set 3 has terms more closer to mean than set 1. hence, Set 1 Sd is the highest. So, Answer is D #### D QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles. SOLUTION:Solution: 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 Answer C #### C QUESTION:One computer can upload 100 megabytes worth of data in 4 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 20 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data? options: A) 6 B) 2.5 C) 9 D) 11 E) 13 SOLUTION:Since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4*5=20 seconds it can upload 5*100=500 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-500=800 megabytes worth of data. The second computer can upload 100 megabytes of data in 2.5 seconds. Answer: B. #### B QUESTION:A man has Rs.680 in the denominations of two-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)160 B)40 C)680 D)120 E)180 SOLUTION:Let number of notes of each denomination be x. Then 2x + 5x + 10x = 680 17x = 680 x = 40 Hence, total number of notes = 3x = 120. Answer is D #### D QUESTION:one kilo gram coffee is Rs. 126 and Rs. 135 are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the 3rd variety per kilo gram is? options: A)150 B)133 C)175.5 D)178 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. So, their average price = Rs. 126 + 135 = Rs. 130.50 2 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. By the rule of alligation, we have: Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind Rs. 130.50 Mean Price Rs. 153 Rs. x (x - 153) 22.50 x - 153 = 1 22.50 x - 153 = 22.50 x = 175.50 C #### C <<<Examples ends QUESTION:A carpenter makes 4 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:I believe it is C because if 1C makes 3 beds in 1 day then: 1C's rate = 3/1 So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day. Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed. Time = Amount / Rate Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 4.7 So, in order for the carpenters to be able to finish they need 5 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day. C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole? options: A)16 sec B)18 sec C)19 sec D)10 sec E)17 sec SOLUTION:Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps. The distance to be covered is equal to the length of the train. Required time t = d/s = 100/10 = 10 sec. Answer: D #### D QUESTION:A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars? options: A)500 000 B)1 000 000 C)2 000 000 D)5 000 000 E)250 000 SOLUTION:The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is. 5+3+2 = 10 10/2 = X/100 000 5*100 000 = X 500 000 = X Answer: A) #### A QUESTION:In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true? I) k=0 II) k=−1 III) k=−3 options: A)I only B)III only C)I and II only D)II and III only E)I and III only SOLUTION:Please format the question properly. Per the question, x^2+kx+1=0 with k=constant. For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges. B is the correct answer. #### B QUESTION:Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? options: A)28 B)10 C)28 D)27 E)13 SOLUTION:4/12 + x/15 = 1 x = 10 Answer:B #### B QUESTION:JOHN and ANDREW can finish the work 9 days if they work together. They worked together for 6 days and then ANDREW left. JOHN finished the remaining work in another 6 days. In how many days JOHN alone can finish the work? options: A)30 days B)60 days C)18 days D)80 days E)90 days SOLUTION:Amount of work done by JOHN and ANDREW in 1 day = 1/9 Amount of work done by JOHN and ANDREW in 6 days = 6 × (1/9) = 2/3 Remaining work – 1 – 2/3 = 1/3 JOHN completes 1/3 work in 6 days Amount of work JOHN can do in 1 day = (1/3)/6 = 1/18 => JOHN can complete the work in 18 days Answer : C #### C QUESTION:m:n = 5: 8 , n: p = 6 : 7 , m:n:p = ? options: A)30 : 48 : 54 B)30 : 48 : 56 C)30 : 48 : 50 D)30 : 48 : 52 E)30 : 48 : 58 SOLUTION:m:n = 5: 8 n: p = 6 : 7 m:n:p =30 : 48 : 56 Answer : B #### B QUESTION:At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)720 D)32 E)120 SOLUTION:Has to be C. Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle hence (7-1)! = 6!= 720 #### C QUESTION:In how many different number of ways 5 boys and 4 girls can sit on a bench? options: A)700 B)710 C)720 D)362880 E)740 SOLUTION:npn = n! 9p9 = 9 X 8 X 7 X 6 × 5 × 4 × 3 × 2 × 1 = 362880 D #### D QUESTION:How many integers n are there such that 1< 5n +5 < 40? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:Solution: 1< 5n + 5 < 40 is a compound inequality. Compound inequalities often need to be manipulated, and we can use the rules of algebra that we already know, to do this. Just as with equations, whatever we do to one part of a compound inequality, we must do to all parts of the compound inequality. Let’s first isolate n within the inequality. 1< 5n + 5 < 40 We first subtract 5 from all three parts of the inequality, and we obtain: -4 < 5n < 35 Next, we divide both sides of the inequality by 5 and we get: -4/5 < n < 7 The integers that are greater than -4/5 and less than 4 are 0, 1, 2, and 3. Thus, there are 4 integers that satisfy the inequality 1 < 5n + 5 < 40. The answer is E #### E QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)1 B)2 C)8 D)7 E)0 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer: C #### C QUESTION:A three digit number divisible by 7 becomes divisible by 3 when 7 is added to it. The largest such number is : options: A)891 B)896 C)882 D)867 E)864 SOLUTION:Out of all the 5 options, only 896 is NOT divisible by 3. All others are divisible So Answer = B(No further calculation required) Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3 7 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3 Applying the above rule,It means that the number which we are going to add should be non-divisible by 3 So comes the answer = 896 Answer : B #### B QUESTION:The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score. options: A)172 B)173 C)174 D)175 E)None of the above SOLUTION:Total runs = 40 × 50 = 2000 Let his highest score be = x Then his lowest score = x – 172 Now 200−x−(x−172)/38=48 ⇒ 2x = 2172 – 1824 ⇒ x = 174 Answer C #### C QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:How many integers between 5000 and 6000 that have distinct digits and increase from left to right ? options: A)10 B)48 C)60 D)20 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 545_ --> 4 546_ --> 3 547_ --> 2 548_ --> 1 556_ --> 3 557_ --> 2 558_ --> 1 567_ --> 2 568_ --> 1 578_ --> 1 Number of integers =20 D #### D QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference W between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference W= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:A and B together do a work in 20 days.B and C together in 15 days and C and A in 12 days.so A,B and C together finish same work in how many days? options: A)12 B)15 C)8 D)10 E)11 SOLUTION:(A+B) work in 1 day= 1/20,(B+C) work in 1 days = 1/15.,(C+A) work in 1 days=1/12 (1) adding=2[A+B+C] in 1 day work = [1/20+1/15+1/12]=1/5 (A+B+C) work in 1 day= 1/10 So,all three together finish work in 10 days Answer D #### D QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$824.32 C)$954.26 D)$2472.96 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 30000*(1 + 2/100)^4 = 30000 * 51/50 * 51/50 * 51/50 * 51/50 = $32472.96 C.I. = 32472.96-10000 = $2472.96 Answer is D #### D QUESTION:If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station? options: A)4/5 km B)4/6 km C)4/9 km D)4/1 km E)4/3 km SOLUTION:x/3 – x/4 = 4/60 x = 4/5 km Answer: A #### A QUESTION:If 0.75: x :: 5:12, then x is equal to: options: A)1.12 B)1.16 C)1.8 D)1.3 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *12) X=9/5 = 1.80 Answer: C #### C QUESTION:Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)NOne SOLUTION:Sol. Average = 66 + 65 + 77 + 62 + 75 / 5) = (345 / 5) = 69. Answer B #### B QUESTION:If the price of gold increases by 40%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? options: A)331/8% B)26.67% C)28.5% D)332/3% E)131/3% SOLUTION:100 140 ------ 140-------40 100-------? => 28.5% Answer:C #### C QUESTION:If x is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ? options: A)1 B)2 C)3 D)6 E)12 SOLUTION:Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey x=4n, if it really wanted to convey so. From other questions that I have seen, proper wordings could be: If x is three times as large as n OR simply, If x is three times n.C #### C QUESTION:What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area? options: A)11 + √5 B)11 + √6 C)11 + 4√7 D)11 + √65 E)11 + 3√17 SOLUTION:We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16) = √65 The perimeter is 11 + √65 The answer is D. #### D QUESTION:A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to options: A)the same as one 45 percent discount B)the same as one 38 percent discount C)the same as one 36 percent discount D)the same as one 30 percent discount E)the same as one 28 percent discount SOLUTION:0.9*0.8*x=0.72x from initial value, meaning 0.28 or 36% discount E #### E QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760 SOLUTION:After one year: 1.2 * $2500 After two years: (1.2)^2 * $2500 After three years: (1.2)^3 * $2500 = $4320 The answer is D. #### D QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence? I. w-6,x-6,y-6,z-6 II. 5w,2x,3y,5z III. 5w,5x,5y,5z options: A)II and III B)III only C)I and III D)I and II E)II only SOLUTION:lets look at the three choices... I. w-6,x-6,y-6,z-6 since the difference is constant, it is an arithmetic sequence... II. 5w,2x,3y,5z since the difference is not constant, it is not an arithmetic sequence III. 5w,5x,5y,5z since the difference is constant it is an arithmetic sequence... Answer is A) #### A QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit? options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62 SOLUTION:Explanation: We are given selling price = Rs. 580 and expected profit of 15 % Therefore, we can easily solve this numerical, considering basic formulae of profit and loss. Let cost price = x Selling price = C.P. + Profit S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price) 580 = x + (0.15 x) 580 = 1.15 x Therefore, x = 504.347 Cost Price = Rs. 504.35 Now, we have the cost price and hence, Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65 The trader gets a profit of Rs. 75.65 ANSWER IS A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 B)240 C)288 D)267 E)211 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 24)m = 360 m. Let the length of the platform be x meters. Then, (x + 360)/36 = 15 ==> x + 360 = 540 ==> x = 180 m.Answer: A #### A QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2 = 62 m2. answer :D #### D QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/5 B)1/7 C)1/2 D)1/1 E)1/9 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:The sale price shirts listed for Rs.1000 after successive discount is 15% and 2% is? options: A)338 B)823 C)833 D)337 E)733 SOLUTION:1000*(85/100)*(98/100) = 833 Answer: C #### C QUESTION:A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number. He was afraid of forgetting his PIN. He wrote down the number 125 in his diary to remember his PIN. He also wrote out the way to calculate 125 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 125". Once, Prafull saw his diary in which Pinaki wrote this number 125. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN? options: A)874 B)872 C)876 D)875 E)879 SOLUTION:Explanation : Let, the PIN is x. According to the question, The card number =996 and Remainder =125. Thus, (996 × x)/997=125. =>x= 872. Answer : B #### B QUESTION:How many positive integers less than 250 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)53 E)64 SOLUTION:Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers So required number= 62-20 = 42 Choice C #### C QUESTION:Rs.1210 were divided among 3 person P, Q, R so that P:Q=5:4 and Q: R=9:10. Then R gets the amount. options: A)Rs. 300 B)Rs. 400 C)Rs. 480 D)Rs. 490 E)Rs. 500 SOLUTION:P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9. So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40 Sum of ratio terms is = ( 45 + 36 + 40 ) =121. R share of amount is Rs (1210 x 40 / 121) = Rs. 400. B #### B QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/3*60/55 = 40 min D #### D QUESTION:For how many integers n is 1^n+2 = (n+2)^1? options: A)0 B)1 C)2 D)None of these E)3 SOLUTION:If n=0 1^0+2 = (0+2)^1 1^2 = 1 ; 2^1 =2 not ok If n=1 1^1+2 =1 ; (1+2)^1=3^1=3 not OK So, Answer : D #### D QUESTION:There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3 options: A)I B)II C)III D)II &III E)I &II SOLUTION:Name T = full pool U fills a pool in a days ==> 1 day U fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c 1 day (U+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (U+Y+Z) together fill: T ==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==>d = abc/(ab+bc+ca) d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3 B #### B QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:Three numbers are in the ratio 1:3:5 and their H.C.F is 5. The numbers are? options: A)5, 15, 35 B)5, 15, 30 C)5, 15, 25 D)5, 15, 40 E)5, 15, 20 SOLUTION:Let the required numbers be x, 3x and 5x. Then, their H.C.F = x. So, x = 5. The numbers are 5, 15, 25. Answer: C #### C QUESTION:A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)95 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)56 km/hr SOLUTION:Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr. ANSWER: A #### A QUESTION:There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns? options: A)A)10 B)B)12 C)C)24 D)D)60 E)E)100 SOLUTION:Using anagram method: 4_3_2_1 R_R_B_B so.. 4!/Number of repeated letters (2!)(2!) = 6 ANS:D #### D QUESTION:If x = 3 and y = 2, what is the value of 5(x-y)^2 - xy ? options: A)-8 B)-7 C)-1 D)-2 E)-5 SOLUTION:x = 3 and y = 2 x-y = 3 - 2 = 1 x*y = 3 * 2 = 6 Now we apply it in the equation 5(x-y)^2 - xy =5 (1)^2-6 ==>5*1 -6 = 5-6 =-1 Answer : C #### C QUESTION:What is the sum of all even numbers from 1 to 401? options: A)122821 B)281228 C)281199 D)122850 E)40200 SOLUTION:Explanation: 400/2 = 200 200 * 201 = 40200 Answer: E #### E QUESTION:An article is bought for Rs.700 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 8/3% C)28 4/7% D)35 1/3% E)32 1/3% SOLUTION:700 ---- 200 100 ---- ? => 28 4/7% Answer: C #### C QUESTION:what is the smallest integer that is multiple of 7, 12 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 7, 12 and 20 which is 420 #### E QUESTION:If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a eight-percent vinegar solution, what was the concentration of the original solution? options: A)9.3% B)17.3% C)26.67% D)35.5% E)41.3% SOLUTION:Let X be the quantity of non-vinegar in the strong vinegar solution Thus vinegar quantity will be 12 - X When 50 ounces of water were added the percentage of vinegar becomes 8%, thus (12 - X)/62 = 8/100 From this equation X = 7.04 Answer (12-7.04)/12 = 41.3% ANSWER:E #### E QUESTION:The third proportional to 2 and 6 is? options: A)18 B)17 C)14 D)15 E)13 SOLUTION:(6*6)/2 = 18 Answer:A #### A QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries? options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140 SOLUTION:Probability of basket = 3/5 Probability of no basket = 2/5 Required probability=3* 3/5*2/5*2/5 =36/125 A is the answer . #### A QUESTION:Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B QUESTION:Cara picked a number of pears, each of which she sold, canned, or poached. If she canned 40 percent more than she poached, and she poached 80 percent less than she sold. If there were a total of 111 pears, then how many pears did she sell? options: A)69 B)72 C)75 D)78 E)81 SOLUTION:Let x be the amount of pears that she sold. Then she poached 0.2x. Then she canned 1.4*0.2x=0.28x. The total amount of pears is x+0.2x+0.28x=1.48x The fraction of pears that she sold is 1/1.48=100/148=25/37. The number of pears she sold is (25/37)*111=75. The answer is C. #### C QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2430 * 1/3 = 810 Option B #### B QUESTION:The average age of 30 students in a class is 14 years. If the age of teacher is also included, the average becomes 15 years, find the age of the teacher. options: A)43 B)44 C)45 D)47 E)48 SOLUTION:Explanation: If teacher's age is 14 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 15. Age of teacher = Average age of all + Total increase in age = 15 + (1 x 30 ) = 45 years Answer:C #### C QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)7508 C)7528 D)7527 E)7232 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 Answer:A #### A QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India. Action: I. Pollution committee should immediately take certain measures to control the pollution levels in India. II. Licenses of polluting industries should be cancelled and owners should be put behind the bars. options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided. ANSWER IS A #### A QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? options: A)50 B)75 C)69 D)79 E)82 SOLUTION:number of pens = 100 number of pencils = 50 Required number of students = H.C.F. of 100 and 50 = 50 Answer is A #### A QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50 SOLUTION:Others equal 5650. Answer D #### D QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)40 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers? options: A)1500 B)1600 C)1400 D)1200 E)1000 SOLUTION:Sum of first n even numbers = n(n+1) =1640 Sum of first n odd numbers = n^2 = 40*40 = 1600 (here n=40) Answer : B #### B QUESTION:It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 120 pages? options: A)12 B)18 C)20 D)24 E)36 SOLUTION:If it takes 4 more minutes for A to print 40 pages than it takes B, it takes 5 more minutes for A to print 50 pages than it takes B. Thus if b is the number of minutes than B takes to print 50 pages, we can write: 1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job) 6(2b+5)=b(b+5) b^2-7b-30=0 (b-10)(b+3)=0 b=10 Thus it takes A 15 minutes to print 50 pages and 15*120/50=36 minutes to print 120 pages (ANSWER E) #### E QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:A store reported total sales of $400 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales? options: A)2% B)17% C)25% D)65% E)83% SOLUTION:New Value – Old Value)/Old Value x 100 We are given: February sales this year = 400 million February sales last year = 320 million We need to determine the percent increase between sales from last year to sales this year. Thus, the new value = 400 million and the old value = 320 million. Let’s plug them into our percent change formula. (New Value – Old Value)/Old Value x 100 [(400 – 320)/320] x 100 = 25%. The answer is C. #### C QUESTION:In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group? options: A)12 B)3 C)5 D)8 E)10 SOLUTION:Let the number of buffaloes be x and the number of ducks be y. Then 4x+2y=2(x+y)+24 =>x=12 ANSWER A 12 #### A QUESTION:How many 5-digit positive integers exist the sum of whose digits are odd? options: A)36000 B)38000 C)45000 D)90000 E)None SOLUTION:Solution: There are 9�104 = 90000, 5-digit positive integers. Out of these 90000 positive integers, the sum of the digits of half of the numbers will add up to an odd number and the remaining half will add up to an even number. Hence, there are 90000 /2= 45000, 5-digit positive integers whose sum add up to an odd number. Answer: Option C #### C QUESTION:If (5+k)(5-k)=(5^2)-(2^3),then what is the value of K? options: A)1 B)3 C)4 D)2 E)6 SOLUTION:Obviously,It is in the formula a^2-b^2=(a+b)(a-b) So k is 2 Option D #### D QUESTION:the average age of 56 employees in a company is 35. An employee aged 60 is retired and a fresher of age 20 is taken in. What is the new age average of employees? options: A)25.45 B)32.26 C)33.13 D)34.28 E)35.55 SOLUTION:The sum of age of the employees when the age average is 35 = 35x56 =1960 The sum of ages of the employees of new group= (1960-60)+20 = 1920 The average age of the new group= 1920/56 = 34.28 Answer: D #### D QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)8 B)9 C)7 D)5 E)4 SOLUTION:Explanation: x – y = 5 4x – 6y = 6 x = 12 y = 7 Answer:C #### C QUESTION:The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 10 points after 5 games, what is the least number of the remaining matches it has to win to reach the 45-point mark by the end of the tournament? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:To get 45 points as end of season we need another 35 points or more from remaining 15 matches: Option A= 6*3+9*1=27 Option B=7*3 + 8*1=29 Option C=8*3+7*1=31 Option D=9*3+6*1=33 Option E=10*3+5*1=35 hence option E-10 #### E QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1232? options: A)1000 B)2217 C)1100 D)2777 E)2991 SOLUTION:1232 = P [1 + (5*12/5)/100] P= 1100 Answer: C #### C QUESTION:A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is? options: A)1250m B)1750m C)950m D)1000m E)1300m SOLUTION:Speed = 15*5/18 = 15/18 m/sec Distance covered in 35 minutes = 15/18 *35 *60 = 1750 m Answer is B #### B QUESTION:A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M): m------M---------------W w In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 3*15/60 =15/20 miles and the man walks the distance mM, which is 3*9/60 = 9/20 mile. The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes. Answer B. #### B QUESTION:(8^16)+(16^10)+(4^24) = ? options: A)(4)*(2^29+1) B)(6)*(2^48) C)(9)*(2^49) D)(28)*(2^53) E)2^148 SOLUTION:I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ) So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents. Here's how my brain works with this one, Step 1: Recognize a common base. (8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48) Step 2: Recognize the factor and pull out of the equation. = (2^48)(1 + (2^4) + 1) = (2^48)(1 + 16 + 1) = (2^48)(18) Step 3: Recognize this is not an answer and adapt. (2^48)(18) = (2^48)(2)(9) = 2^148 Answer is E. #### E QUESTION:The value of (10^9-10^2)/(10^7-10^3) is closest to which of the following? options: A)1 B)10 C)10^2 D)10^3 E)10^4 SOLUTION:Because the question asks for what value isclosestthe question invites approximation. Let's look at the numerator: 10^9 - 10^2 10^9 is HUGE compared to 10^2. So 10^9 - 10^2 is very close to 10^9 itself. (Just as 100 - 0.0001 is very close to 100 itself). Likewise, 10^7 is HUGE compared to 10^3. So 10^7 - 10^3 is very close to 10^7. So we have: 10^9/10^7 or 10^(9-7) = 10^2. Choose C. #### C QUESTION:If the selling price of 8 articles is same as the cost price of 10 articles. Find the gain or loss percentage? options: A)25% B)45% C)35% D)65% E)55% SOLUTION:Let the C.P of each article be Re 1. Then, S.P of 8 articles = C.P of 10 articles = Rs. 10 Now, C.P of 8 articles = Rs. 8, S.p of 8 articles = Rs 10 Gain = Rs ( 10 - 8 ) = Rs 2. Gain% = ( 2/8 × 100 ) % = 25% Answer : A #### A QUESTION:Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $45,000 higher than Store B's revenues. In the second month, Store A's revenues were $8,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue? options: A) $14,000 B) $15,000 C) $42,000 D) $47,000 E) $50,000 SOLUTION:Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +45 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +8 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T): (45 + 8 + T)/3 = 2 53 + T = 6 T = -47 Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -47 represents a $47,000 advantage in favor of Store B. Choice (D) is correct. #### D QUESTION:The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:EXPLANATION Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. Answer C #### C QUESTION:A lady bought five books namely A,B,C,D,E to distribute her 3 child. How many ways she can distribute books? options: A)3^3 B)3^4 C)3^5 D)3^6 E)3^2 SOLUTION:3*3*3*3*3 3^5 ANSWER:C #### C QUESTION:In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have? options: A)180 B)45 C)60 D)90 E)135 SOLUTION:We can start with the known quantity and then go on to find the others. Shiny igneous ricks are 40. These are (2/3) of total igneous rocks. (2/3)*Total igneous rocks = 40 Total igneous rocks = 40 * (3/2) = 60 Total sedimentary rocks = 2*Total igneous rocks = 2*60 = 120 Total number of rocks = 60 + 120 = 180 Answer (A) #### A QUESTION:8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged? options: A)A.1296 B)B.1850 C)C.2880 D)D.3546 E)E.4200 SOLUTION:Glue milk and water bottlestogether: {AB}, {CD}. 6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways. Therefore the final answer is 6!*2!*2!=2,880. Answer: C. #### C QUESTION:Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:If 125(5^y) = 1 then y= options: A)–2 B)–1 C)0 D)1 E)-3 SOLUTION:5^x = 1/125 5^x = 1/5^3 5^x= 5^-3 x = -3 E #### E QUESTION:If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? options: A)267 B)766 C)810 D)868 E)812 SOLUTION:12 men 120 acres 36 days 54 men ? 54 days 120 * 54/12 * 54/36 10 * 54 * 3/2 54 * 15 = 810 Answer:C #### C QUESTION:What is the 10th term in this sequence? 3,5,8,15,25,40,67,104,171 options: A)273 B)278 C)279 D)377 E)277 SOLUTION:3+5 =8 +0 =8 8+5 =13+2 =15 15+8 =23+2 =25 25+15=40+0 =40 40+25=65+2 =67 67+35=102+2 =104 104+67=171+0=171 171+104=275+2=277 so 9th term is 277 ANSWER:E #### E QUESTION:If a randomly selected non-negative single digit integer is added to {2, 3, 4, 9}. What is the probability that the median of the set will increase but the range still remains the same? options: A)0.2 B)0.3 C)0.4 D)0.5 E)0.6 SOLUTION:We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes. Hence, the total number of outcomes is 10. We need to find the probability that the median of the set will increase but the range still remains the same. The median of the set is (3 + 4)/2 = 3.5, thus the number selected must be 4 or greater. For the range to remain the same, the number must be between 2 and 9 inclusive. To satisfy both conditions, the number selected must be 4, 5, 6, 7, 8, or 9. The probability is 6/10 = 0.6 The answer is E. #### E QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3×7/36 = 7/12 Remaining work = 1 – 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5 Option A #### A QUESTION:Arun and Varun appeared at an examination. Arun secured 9 marks more than Varun and his marks was 56% of the sum of their marks. What are the marks obtained by them options: A)42, 33 B)42, 36 C)44, 33 D)44, 36 E)44, 37 SOLUTION:Explanation : Let the marks secured by them be x and (x + 9) Then sum of their marks = x + (x + 9) = 2x + 9 Given that (x + 9) was 56% of the sum of their marks =>(x+9)=56/100(2x+9)=>(x+9)=14/25(2x+9) => 25x + 225 = 28x + 126 => 3x = 99 => x = 33 Then (x + 9) = 33 + 9 = 42 Hence their marks are 42 and 33 Answer : A #### A QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is? options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5 SOLUTION:3:1 Answer:B #### B QUESTION:A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result. options: A)0 B)16 C)18 D)1 E)120 SOLUTION:suppose the no is 100 first condition if it mistakenly divided the no by 2/3 ==>100/(2/3)==>150 second condition the no should multiply by 3/2 ==> 100*3/2 ==> 150 hence output should be 150 and mistakenly the output is 150 so pecentage error is zero ANSWER:A #### A QUESTION:A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? options: A)22 B)28 C)25 D)82 E)34 SOLUTION:M = 20 S = 5 DS = 20 + 5 = 20.Answer:C #### C QUESTION:200 is what percent of 40? . options: A)0.2% B)2% C)5% D)20% E)500% SOLUTION:200= x*40/100 x = 500% Ans; E #### E QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value options: A)31 B)32 C)46 D)47 E)48 SOLUTION:- a + b + ((-a)(b)/100) = -25+75+(-25*75)/100 = -25+75-19 =31 ANSWER:A #### A QUESTION:A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed? options: A)32 B)88 C)67 D)11 E)66 SOLUTION:One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10 Remaining work = 7/10 The number of days required for this initial work = 7 days. The total number of days required = 4 + 7 = 11 days. Answer:D #### D QUESTION:A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour? options: A)7 km/hr B)7.2 km/hr C)7.4 km/hr D)7.8 km/hr E)8.9 km/hr SOLUTION:Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B #### B QUESTION:Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other? options: A)1:2 B)2:1 C)1:3 D)3:1 E)1:4 SOLUTION:root (b):root(a) 2:1 ANSWER:B #### B QUESTION:A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)3/5 C)3/8 D)4/9 E)7/10 SOLUTION:The total possible choices are 10C3 = 120 The ways to choose 3 apples: 5C3 = 10 The ways to choose 2 apples: 5C2 * 5C1 = 50 P(at least 2 apples) = 60/120 = 1/2 The answer is A. #### A QUESTION:When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is options: A) 0.005 B) 0.002 C) 0.001 D) 0.0003 E) 0.0002 SOLUTION:It is very easy if x is the diameter, then the magnified length is 1000x. ince 1000x=0.3 then x=0.3/1000=0.0003. The answer is D #### D QUESTION:The sum and the product of two numbers are 16 and 15 respectively, the difference of the number is? options: A)14 B)6 C)7 D)8 E)2 SOLUTION:Explanation: x + y = 16 xy = 15 (x- y)2 = (x + y)2 - 4xy (x- y)2 = 256 - 60 => (x - y) = 14 Answer: A #### A QUESTION:Find (7x + 8y ) / (x-2y) if x/2y = 3/2 ? options: A)24 B)25 C)26 D)27 E)29 SOLUTION:x/2y=3/2 =>x=6y/2=3y =>(7x+8y)/(x-2y)=((7*(3y))+8y)/(3y-2y) =>29y/y=29 ANSWER:E #### E QUESTION:A reduction of 40% in the price of oil enables a house wife to obtain 8 kgs more for Rs.2400, what is the reduced price for kg? options: A)Rs.120 B)Rs.125 C)Rs.130 D)Rs.135 E)Rs.140 SOLUTION:Explanation: 2400*(40/100) = 960 ---- 8 ? ---- 1 => Rs.120 Answer: A #### A QUESTION:Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube? options: A)236 B)256 C)216 D)246 E)206 SOLUTION:Volume of the new cube = [ 5(power)3 + 4(power)3 + 3(power)3 ] Cm(power)3 = 125 + 64 + 27 = 216 Cm(power)3 => a(power)3 = 216 Cm(power)3 Answer is C. #### C QUESTION:A six faced die is so biased that it is twice as likely to show an even number as an odd. It is thrown twice. What is the probability that the sum of the numbers is even? options: A)1/3 B)2/3 C)5/9 D)6/11 E)5/11 SOLUTION:Probability of getting an even number = 2/3 Probability of getting an odd number = 1/3 since the dice is biased. The sum is even if (even,even) or (odd,odd) [P(even).P(even)] + [P(odd).P(odd)] 2/3 * 2/3 + 1/3 * 1/3 = 4/9 + 1/9 = 5/9 ANSWER:C #### C QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A? options: A)3002 B)3000 C)3018 D)3019 E)3012 SOLUTION:60*5:36*6:75*3 100: 72: 75 100/247 * 7410 = 3000 Answer: B #### B QUESTION:A train 320 m long passed a pole in 28 sec. How long will it take to pass a platform 700 m long? options: A)12 sec B)59 sec C)93 sec D)89 sec E)46 sec SOLUTION:Speed = 320/28 = 11 m/sec. Required time = (320 + 700)/11 = 92.7 sec. Answer: C #### C QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs? options: A)11 B)12 C)22 D)24 E)44 SOLUTION:22 times in a day. 12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes) ANSWER:C #### C QUESTION:If a is Negative integers and b is positive integers and a ≠ 0 which of the following equal 0 ? options: A)a-b B)a^2+b^2 C)a*b D)a/b E)a^2-b^2 SOLUTION:All options Except E gives Non-zero answer. a should be negative integers and b should be an positive integers. (E)a^2-b^2 If b=0,a^2-b^2=a^2. a is negative integers. Any square of the negative integers gives us a positive numbers. So The option E is answer #### E QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually. options: A)812 B)712 C)412 D)512 E)612 SOLUTION:Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112. therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612. Answer is E. #### E QUESTION:In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent W of her bushes have only yellow roses? options: A)20 B)30 C)50 D)70 E)80 SOLUTION:let, the number of bushes with only yellow flowers be x so, number of bushes with only yellow flowers will be 1.5x if total number of bushes of flowers= T then total number of bushes with yellow flowers= 0.8T we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers so, W=0.8T+x=T x=0.2T so, 1.5x=0.3T 30% flowers are yellow flowers OA B #### B QUESTION:If 9x^2-16y^2=3x+4y,then what will give the answer? options: A)3x-4y=0 B)3x-4y=2 C)3x-4y=1 D)3x+4y=0 E)3x+4y=1 SOLUTION:9x^2-16y^2=3x+4y (3x+4y)(3x-4y)=3x+4y 3x-4y=(3x+4y)/(3x+4y) 3x-4y=1 Answer is option C #### C QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. options: A)6/63 B)2/63 C)125/126 D)1/126 E)1/63 SOLUTION:Required probability = 1 - 1/126 = 125/126 ANSWER:C #### C QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? options: A)72 min B)25.11628 min C)70 min D)74.11682 min E)76 min SOLUTION:x=time for type B prolems 2x=time for type A problem total time=3hrs=180min 185x+15*2x=180 x=180/215 x=0.837209 time taken for type A problem=15*2*0.837209=25.11628min ANSWER:B #### B QUESTION:A retailer buys 80 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)115 C)112 D)118 E)120 SOLUTION:let the market price of each pen be $1 then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20 profit %=((43.20*100)/36) %=120% Answer E)120 #### E QUESTION:One-third of 1200 is what percent of 236 ? options: A)169.49 B)30 C)120.32 D)125.32 E)15.152 SOLUTION:Answer Let one-third of 1200 is N% of 236. ∵ 1200/3 = (N x 236)/100 ∴ N = (400 x 100) / 236= 169.49 Correct Option: A #### A QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence. options: A)21 B)20 C)40 D)42 E)19 SOLUTION:n for cyclic hand shake and n-1 for linear handshake. so here no of hand shake is 20. ANSWER:B #### B QUESTION:If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is options: A)40 B)49 C)80 D)88 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 22 and x2 + y2 = 386. Now, 2xy = (x+y)2 - (x2 + y2) = (22)2 - 386= 484 - 386= 98 xy = 49. Answer B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)227 B)268 C)240 D)889 E)232 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer:C #### C QUESTION:In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/6 of the absentee ballets were thrown out and 3/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)4,000 D)8,000 E)9,000 SOLUTION:5/6 * 2/5 (total absentee votes) = 1/3 (total votes)=1/3*12000=4000 Answer is C #### C QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:A 10-by-8 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed? options: A)The volume of the cylinder with height 10 is 80/pi cubic inches greater than the volume of the cylinder with height 6. B)The volume of the cylinder with height 8 is 80/pi cubic inches greater than the volume of the cylinder with height 10. C)The volume of the cylinder with height 10 is 80pi cubic inches greater than the volume of the cylinder with height 6. D)The volume of the cylinder with height 8 is 80pi cubic inches greater than the volume of the cylinder with height 10. E)The volume of the cylinder with height 8 is 240/pi cubic inches greater than the volume of the cylinder with height 10. SOLUTION:Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 8 and 10 are the circumference of the base and not the radius. B is the right answer. #### B QUESTION:A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers? options: A)330 B)650 C)729 D)800 E)890 SOLUTION:Choose 4 starters from a team of 11 players. Order is not important. \inline {\color{Black} 11C_{4}}= 330 A #### A QUESTION:A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water? options: A)22 B)37 C)32 D)27 E)18 SOLUTION:US = 25 DS = 39 M = (39 + 25)/2 = 32 Answer:C #### C QUESTION:Two concentric circles form a ring. The inner and outer circumferences of ring are (352/7) m and (518/7) m respectively. Find the width of the ring. options: A)2 B)4 C)6 D)8 E)None of them SOLUTION:Let the inner and outer radii be r and R meters. Then 2(22/7)r = (352/7) = r =((352/7) X (7/22) X (1/2))=8m. 2(22/7)R=(528/7) = R=((528/7) X (7/22) X (1/2))= 12m. Therefore, Width of the ring = (R - r) = (12 - 8) m = 4 m. Answer is B. #### B QUESTION:David covered a distance of 50 miles on his first trip. On a later trip he traveled 75 miles while going six times as fast. His new time compared with the old time was: options: A)twice as much B)three times as much C)the same D)half as much E)a fourth as much SOLUTION:Let t be the time of the first trip. On the later trip, David can travel 300 miles in time t. The trip of 75 miles takes t/4. The answer is E. #### E <<<Examples ends QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. options: A)530 B)675 C)330 D)987 E)854 SOLUTION:Let x e the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8:7 Answer: B #### B QUESTION:If w,x,y,z are consecutive positive integers ; then which of the following is always odd? [1] w*x+(y+2)^2*z [2] w^x + z^y [3] 13x^2 options: A)1 B)2 C)3 D)1 and 2 E)2 and 3 SOLUTION:Plug in some numbers w = 1 x = 2 y = 3 z = 4 Check the options - [1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number } [2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number } [3] 13x^2 = 13*4 =52 even [2] B #### B QUESTION:A cycle is bought for Rs.450 and sold for Rs.520, find the gain percent? options: A)18 B)14 C)20 D)15 E)15.55 SOLUTION:450 ---- 70 100 ---- ? => 15.55% Answer: E #### E QUESTION:Solve below question 2x + 1 = -17 options: A)-8 B)-9 C)9 D)8 E)-7 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? options: A)c is not changed. B)c is halved. C)c is doubled. D)c is multiplied by 4. E)c is multiplied by 16. SOLUTION:a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. E c is multiplied by 16. #### E QUESTION:A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 4, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit? options: A)23/24 B)31/36 C)55/64 D)65/81 E)75/121 SOLUTION:P(no even digits) = 2/3*2/3*2/3*2/3 = 16/81 P(at least one even digit) = 1 - 16/81 = 65/81 The answer is D. #### D QUESTION:A basketball is dropped from a height of 40 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces. options: A)50 B)55 C)110 D)75 E)80 SOLUTION:Initial distance = 40 feet first bounce = 20 feet up + 20 feet down = 40 feet second bouche = 10 feet up + 10 feet down = 20 feet third bounce = 5 feet up and 5 feet down= 10 feet total distance covered = 40+40+20+10= 110 ANSWER IS C #### C QUESTION:Tough and Tricky questions: Number Properties. If (z + 3)/6 is an integer, what is remainder when z is divided by 6? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:6/6=1 Ans B #### B QUESTION:If x and y are integers and x + y = 5, which of the following must be true? options: A)x and y are consecutive integers. B)If x < 0, then y > 0. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:Notice that the question asks which of the following MUST be true, not COULD be true. Given: x + y = 5 A. x and y are consecutive integers: not necessarily true, for example x=1 and y=4; B. If x < 0, then y > 0: if x is negative then y must be positive in order x+y to be positive, so this statement must be true; C. If x > 0, then y < 0: not necessarily true, for example x=1 and y=4; D. Both x and y are even: never true, as the sum of two even numbers is even and can not equal to odd number 5; E. Both x and y are less than 5: not necessarily true, for example x=6 and y=-1; Answer: B. #### B QUESTION:What is the median from the below series 90, 93, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)85 C)93 D)97 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88, 90, 93, 93, 95, 96, 98 The median quiz score was 93. (Four quiz scores were higher than 93 and four were lower.) C #### C QUESTION:A retailer buys 140 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)105 B)155 C)125 D)185 E)285 SOLUTION:let the market price of each pen be $1 then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60 profit %=((102.60*100)/36) %=285% Answer E #### E QUESTION:The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog? options: A)12 B)24 C)30 D)48 E)120 SOLUTION:We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together. Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!*2=48. Answer: D #### D QUESTION:The population of a bacteria colony doubles every day. If it was started 6 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? options: A)512 B)768 C)1024 D)2048 E)128 SOLUTION:2^6(2) = 2^7 = 128 The answer is E. #### E QUESTION:Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train? options: A)270 B)277 C)200 D)257 E)271 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 20 * 10 = 200 m. The length of the faster train = 200 m. Answer: C #### C QUESTION:By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x =30 kmph. Answer: A #### A QUESTION:At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time? options: A)1/3 B)1/4 C)3/8 D)2/9 E)5/18 SOLUTION:Males who did not arrive on time are 1/4*2/3 = 1/6 of the attendees. Females who did not arrive on time are 1/6*1/3 = 1/18 of the attendees. The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9 The answer is D. #### D QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:let no. of right ques be x, then no. of wrong ques will be= 26 - x now, according to ques 8x - (26-x)5 = 0, hence x=10...no. of right ques is 10 ANSWER:B #### B QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)63 B)30 C)36 D)45 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 14) = (x + 7) or x = 21. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63. Answer: A #### A QUESTION:If the price of petrol increases by 44, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? options: A)25% B)20% C)16.67% D)33.33% E)None of these SOLUTION:Explanation : let us assume before increase the petrol will be Rs. 100. After increase it will be Rs (100+44) i.e 144. Now, his consumption should be reduced to :- =(144−100)/144 ∗ 100. Hence, the consumption should be reduced to 30.6%. Answer : E #### E QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:A invested some money in 10% stock at 96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of : options: A)Rs.80 B)Rs.115.20 C)Rs.120 D)Rs.125.40 E)None of these SOLUTION:Explanation: For an income of Rs. 10, investment = Rs. 96. For an income of Rs. 12, investment = (96/10x12) =115.20 Answer: B #### B QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent? options: A)200 B)992 C)772 D)662 E)552 SOLUTION:Profit on first article = 20% of 1000 = 200. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: A #### A QUESTION:Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s amount. At the end of the year 25% profit was earned which was equal to 98,000. What was the amount invested by R? options: A)2,10,000 B)1,05,000 C)1,75,000 D)84,000 E)None of these SOLUTION:Ratio for amount invested by P, Q & R = 5x × 12 : 6x × 12 : 6x × 6 = 60x : 72x : 36x = 5x : 6x : 3x Profit = 98000 = 25% of T where, T = Total amount T = 392000 Amount received by R = 3x /3x+6x+5x(392000) = 84000 Answer D #### D QUESTION:If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true? I. xa= y II. y = 1 III. a and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2). I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2). Answer: A. #### A QUESTION:4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:5|5, 10, 15, 20 2|1, 2, 3, 4 |1, 1, 3, 2 L.C.M of 5, 10, 15, 20 is 60 60 times B #### B QUESTION:Zoey won the lottery and got $7,348,340. she wants to split it among herself and 5 friends evenly. how much money must she add if she wants to split it evenly? options: A)$3 B)$2 C)$9 D)$1 E)$4 SOLUTION:Zoey and her 5 friends is 6 people in all. $7,348,340 must be divisible by 6 if she wants to split it evenly. The money is divisible by 6 if it's divisible by 2 and 3. 7+3+4+8+3+4+0=29. 2 and 3 cant go into 29. Adding 1 dollar makes it 30. 2 and 3 can go into 30 so 6 can also. The answer is D. #### D QUESTION:The price of a laptop . set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)A)19009 B)B)19074 C)C)19008 D)D)19000 E)E)19002 SOLUTION:Explanation: Money paid in cash = R . 1000 Balance payment = (20000 - 1000) = Rs. 19000 Answer: Option D #### D QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)6 E)5 SOLUTION:2x * x = 128 => x= 8 Answer: A #### A QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:The total of the ages of Amar, Akbar and Anthony is 40 years. What was the total of their ages two years ago ? options: A)71 B)44 C)36 D)16 E)18 SOLUTION:Explanation: Required sum = (40 - 3 x 2) years = (40 - 6) years = 36 years. Answer: C #### C QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal? options: A)3377 B)2997 C)3600 D)2799 E)7719 SOLUTION:P = 144(100/5)2 => P = 3600 Answer:C #### C QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively? options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these SOLUTION:Y:Z = 70000 : 30000 = 7:3. ANSWER:C #### C QUESTION:For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| = options: A)ab-4 B)2b-ab-4 C)ab+4 D)ab-2b+4 E)4-ab SOLUTION:Given: |ab| = -ab and |a| = -a Question: |b-4| + |ab-b| = ? **** Looking at |ab| = -ab tells us that either one of a or b is negative. **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: b is positive Let a=-1 and b=1 |b-4| + |ab-b| = |1-4| + |-1-1| = 5 Test a) |ab-4| = |(1)(-1)-4| = |-5|=5 Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1 Test c) ab+4 = -1 + 4 = 3 Test d) ab-2b+4 = -1-2(1)+4=1 test e) 4-1=3 ANSWER=A #### A QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is? options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400 SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4 Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C QUESTION:Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 30 are on geology, and 100 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? options: A)81 B)159 C)166 D)285 E)304 SOLUTION:I solve it using the tough luck technique: According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject. 80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=100>80 Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives. We picked: 50 Botany Books 65 Zoology Books 30 Geology Books Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!! Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick 79*2+1 books Because, we could have picked the books in following order; 1st book picked: Physics 2nd book picked: Chemistry 3rd book picked: Physics Thus, Total= 50+65+30+79*2+1=145+1+158=304 Ans:E #### E QUESTION:The diagonal of a rhombus are 40 m and 30 m. Its area is: options: A)600 B)450 C)350 D)500 E)620 SOLUTION:Area of the rhombus = 1/2 d1d2 = ( 1/2 × 40 × 30) Cm(power)2 = 40 × 15 = 600 Cm(power)2 Answer is A. #### A QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? options: A)10 B)15 C)8 D)12 E)20 SOLUTION:4n+7 > 1 4n> -6 n > -(3/2) n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity) From second constraint 4n+7 < 60 4n< 53 n < 13. 25 n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13) Combining the two -1.5 < n<13.25 n = 1 to 13 (48 integers) and n = -1 and 0 so 15 integers. B #### B QUESTION:The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? options: A)81 : 121 B)81 : 127 C)81 : 191 D)81 : 161 E)81 : 182 SOLUTION:Explanation: Ratio of the sides = ³√729 : ³√1331 = 9 : 11 Ratio of surface areas = 92 : 112 = 81 : 121 Answer: Option A #### A QUESTION:Each student at a certain university is given a four-character identification code, the rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules? options: A)135,200 B)67,600 C)64,000 D)60,840 E)58,500 SOLUTION:First two parts for the code, are digits between 0-9, therefore, 10 options for the first part of the code, and as characters may be repeated, 10 options for the second part as well Therefore, we have 10 X 10 possibilities for the first and second part of the code Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code, and as characters may be repeated, 26 options for the fourth part as well Therefore, we have 26 X 26 possibilities for the third and fourth part of the code so, in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600 Answer B #### B QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d? options: A) 75 and 80 B) 80 and 85 C) 74 and 74 D) 75 and 75 E) 70 and 80 SOLUTION:Ans: C Deviation means spreading of the numbers from one median point value.. as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation. so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value. C #### C QUESTION:The overall age of X and Y is 19 year greater than the overall age of Y and Z. Z is how many decades younger that X? options: A)11 B)15 C)12 D)19 E)20 SOLUTION:D 19 (X + Y) – (Y + Z) = 19 X – Z = 19 #### D QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time? options: A)s. 53.30 B)s. 53.22 C)s. 51.219 D)s. 53.18 E)s. 51.10 SOLUTION:Explanation: Sum = (52 * 100) / (2 * 5) = Rs. 520 Amount = [520 * (1 + 5/100)2] = Rs. 573.3 C.I. = (573.3 - 520) = Rs. 53.30. Answer:A #### A QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)42 8/7% B)42 6/4% C)42 6/7% D)42 3/7% E)42 6/9% SOLUTION:SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/6 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 5*x Hence, a1+a2+..+a20+n = 25x So, the fraction asked = 5x/25x = 1/5 Answer C #### C QUESTION:The perimeter of a rectangular yard is completely surrounded by a fence that measures 36 meters. What is the length of the yard if the area of the yard is 40 meters squared? options: A)12 B)10 C)8 D)14 E)16 SOLUTION:Perimeter of rectangular yard = 2(l + b) = 36 --> l + b = 18 Area = l * b = 40 b = 18 - l l(18 - l) = 40 18l - l^2 = 40 l^2 - 18l + 40 = 0 Upon simplifying we get l = 5 or 8. Only 8 is there in the answer choice. Answer: C #### C QUESTION:12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise? (1 litre = 1000cm³) options: A)6 B)8 C)10 D)20 E)40 SOLUTION:we have 1 litre = 1000cm³ (thanks Bunuel) =>12 litres = 12*1000 = 12000cm³ Let call the height of the water is x the breadth and length of the water will equal the aquarium The volume of the water: 50 * 30 * x = 12000cm³ => x = 12000/(50*30) = 8 cm Answer is B #### B QUESTION:Find the number which is nearest to 3105 and is exactly divisible by 21 options: A)1208 B)3108 C)241 D)217 E)3147 SOLUTION:On dividing 3105 by 21, we get 18 as remainder. Number to be added to 3105 = (21 - 18) - 3. Hence, required number = 3105 + 3 = 3108. ANSWER B 3108 #### B QUESTION:Tom can hit a target 3 times in 6 shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4shots. What is the probability that at least 2 shots hit the target ? options: A)1/2 B)2/5 C)2/3 D)3/7 E)3/11 SOLUTION:Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by Karan hits tha target and Raja not hit the target. or Karan does not hit the target and Raja hits the target. or. Karan hits the target and Raja hits the target = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6 = 24/36 = 2/3 C #### C QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:Find the length of the wire required to go 12 times round a square field containing 104976 m2. options: A)15840 B)3388 C)2667 D)8766 E)15552 SOLUTION:a2 = 104976 => a = 324 4a = 1296 1296 * 12 = 15552 Answer: E #### E QUESTION:Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is: options: A)Rs. 1000 B)Rs. 2000 C)Rs. 2500 D)Rs. 3000 E)Rs. 3500 SOLUTION:Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y. Then, 4x + 9y = 13400 -- (i) And, 10% of 4x + 20% of 9y = 1880 2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii) Solving (i) and (ii), we get : x = 2000 and y = 600. Cost price of each horse = Rs. 2000. ANSWER:B #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? options: A)15hrs B)20hrs C)25hrs D)30hrs E)32hrs SOLUTION:Part filled by A in 1 hour = 1/50 part filled by B in 1 hour = 1/75 Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30 Both the pipes will together will fill the tank in 30 hours. Answer is D #### D QUESTION:If KING is coded as 17 and MASS is coded as 29 Then DON is coded as options: A)12 B)16 C)18 D)None E)cannot be determined SOLUTION:Explanation : KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17 MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29 DON = 4+14+15=33 i.e(3*3)+(3*3)=18 Hence (C) is correct Answer : C #### C QUESTION:The volume of a cube is 3375 cc. Find its surface. options: A)1350 B)1150 C)1456 D)1254 E)1489 SOLUTION:a3 = 3375 => a = 15 6a2 = 6 * 15 * 15 = 1350 Answer: A #### A QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between? options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2 SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest. Answer (E) #### E QUESTION:The price of a certain painting increased by 30% during the first year and decreased by 20% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price? options: A)102% B)105% C)120% D)135% E)104% SOLUTION:Easiest thing to do: Assume that price is 100 Price at the end of yr 1: 100+ 30 = 130 Price at the end of year 2 = 130 - 130*0.20 = 130*0.80 = 104 Hence required answer = (104/100)*100% = 104% Answer is E. #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)12 B)18 C)22 D)24 E)none of these SOLUTION:Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x 27 * x = 36 * 18 x = (36 * 18)/27 x = 24. Answer is D. #### D QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speed∗Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)Rs 15 B)Rs 12.10 C)Rs 21.70 D)Rs 16.80 E)None of these SOLUTION:Explanation : Let the cost of the tax items = x Given that tax rate = 6% Cost of tax items, x*(6/100) = 30/100 x = 5 rs Now non taxable item = total cost - cost for taxable item - tax = 27 - 5 - 0.30 =21.70 Answer : C #### C QUESTION:The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.2.0 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? options: A)s.1014 B)s.1332 C)s.999 D)s.1085 E)s.1020 SOLUTION:a2 = 3136 => a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.0 = 1332 ANSWER:B #### B QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members 51* 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:Nelly made a part payment of $875 toward buying a brand new refrigerator, which represents 25% of the total cost of the refrigerator, how much remains to be paid? options: A)$2225 B)$2782 C)$1625 D)$2629 E)$2625 SOLUTION:Explanation: Let's start with what the total price of the refrigerator would be. If 25% is equal to $875 then 100% equals $x. We just have to multiply $875 by 4 to get total amount=$3500. Out of this amount we then need to deduct the amount already paid which was $875 so we have $3500-$875=$2625 Answer: Option E #### E QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 B)1 C)8 D)6 E)9 SOLUTION:100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer:D #### D QUESTION:if log 7 = 0.845098, the number of digits in 7128 is options: A)100 B)120 C)109 D)280 E)110 SOLUTION:Explanation: log(7128) = 128log(7) = 128 × 0.845098 ≈ 108.17 ie, its characteristic = 108 Hence, number of digits in 2128 = 108+1 = 109 Answer: Option D #### D QUESTION:The wages earned by Robin is 40% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? options: A)14% B)23% C)30% D)50% E)100% SOLUTION:Let wage of Erica = 10 Wage of Robin = 1.4*10 = 14 Wage of Charles = 1.6 *10 = 16 Percentage by which wage earned by Charles is more than that earned by Robin = (16-14)/14 * 100% = 2/14 * 100% =14% Answer A #### A QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)40 E)55 SOLUTION:Total = 75 books. 65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned. Now, there are 66 books, thus 76-68=7 books are NOT returned. {loaned out}*0.30=7 --> {loaned out}=30. Answer: B. #### B QUESTION:Given two fair dice, what is the probability G that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. G=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ? options: A)500 B)1000 C)1500 D)2000 E)3000 SOLUTION:Explanation: Let the cost of a table and that of a chair be Rs. x and Rs, y respectively. Then, 2x + 3y = 3500 ...(i) and 3x + 2y = 4000 .....(ii) solving (i) and (ii) we get x = 1000, y = 500 ANSWER IS B #### B QUESTION:A sum of Rs.4000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)2888 B)3120 C)2877 D)2600 E)1277 SOLUTION:Let A be the amount received at the end of the three years. A = 4000[1 + 10/100][1 + 20/100][1 + 25/100] A = (4000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.6600 So the interest = 6600 - 4000 = Rs.2600 Answer: D #### D QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items? options: A)15% B)12.16% C)13.4% D)20.2% E)None of these SOLUTION:Explanation : Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively. And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively. Overall loss percentage of the 1st two items = 14.33% =>(0.21p+0.11q)/(p+q)=0.1433 =>p/q=1/2. Overall loss percentage of the 2nd and 3rd item =10.4% =>(0.11q+0.1r)/(q+r)=0.104. =>q/r=2/3. Therefore, the overall loss percentage is : =>(0.21p+0.11q+0.1r)x100/(p+q+r). =>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3). =>0.1216×100. =>12.16%. Answer : B #### B QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence? options: A)−164 B)0 C)16 D)32 E)64 SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term) sum of 64 terms = 32 ANSWER:D #### D QUESTION:Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die. options: A)1/2 B)1/6 C)0 D)5/6 E)1 SOLUTION:Determine if E and F are independent. P(E|F) = the probability of event E occurring given that event F has already occurred P(E|F) ≠ P(E) as P(E) is changed if it is given that F occurs. Consequently, P(E∩F) ≠ P(E)P(F) since the events are not independent. As a result, P(E∩F) ≠ 1/4 = P(E)P(F) We must use the more complex formula for finding the intersection of E and F: P(E∩F) = P(F)P(E|F) P(F) = the probability of event F occurring The probability of rolling a 1, 2, or 3 is 3/6 = 1/2 P(E|F) = the probability of event E occurring given that event F has already occurred If event F already occurred, we are limited to the numbers 1, 2, or 3. Within this range of 3 possible numbers, only one number--namely, 2--is an even number. Therefore, P(E|F) = 1/3 P(E∩F) = P(F)P(E|F) = (1/2) * (1/3) = 1/6 Answer B #### B QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B QUESTION:A tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth? options: A)20 B)22 C)24 D)26 E)28 SOLUTION:Let the original side of the square be x. (x-12)*(x-10) = 120 = 10*12 x = 22 The answer is B. #### B QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables w are there in the warehouse? options: A)6 B)8 C)10 D)15 E)30 SOLUTION:Total number of ways to choose 2 chairs from 5 w= 5C2=10 Total number of combination=150 That means we need get 15 combinations from the selection of tables.... Screening through the answers.... 6C2=15..... 15*10=150 Answer is 6... A #### A QUESTION:In how many K ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6*6*6*6= 1296 ------(1) Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2) therefore required value K= (1)-(2)= 1296-360=936.D #### D QUESTION:A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 15 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder? options: A) $204 B) $216 C) $220 D) $230 E) $240 SOLUTION:Wholesale cost of video recorder = 200 $ Video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 15 Emlpoyee paid = .85 * 240 = 204 $ Answer A #### A QUESTION:There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)675 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 10C2 Number of ways of selecting 2 non fiction books = 6C2 10C2 * 6C2 = 45 * 15 = 675 Answer: C #### C QUESTION:In a manufacturing plant, it takes 48 machines 4 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders? options: A)3 B)6 C)8 D)9 E)12 SOLUTION:the choices give away the answer.. 48 machines take 4 hours to fill 8 standard orders.. in next eq we are doubling the machines from 48 to 72, but the work is not doubling(only 1 1/2 times), = 4*48/72*12/8 =4 Ans A #### A QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 210 sq. feet, how many feet of fencing will be required? options: A)34 B)41 C)68 D)88 E)None SOLUTION:EXPLANATION We have: l = 20 ft and lb = 210 sq. ft. So, b = 10.5 ft. Length of fencing = (l + 2b) = (20 + 21) ft = 41 ft. Answer B #### B QUESTION:What is the 10th term in this sequence? 3,5,8,15,25,40,67,104,171 options: A)273 B)278 C)279 D)377 E)277 SOLUTION:3+5 =8 +0 =8 8+5 =13+2 =15 15+8 =23+2 =25 25+15=40+0 =40 40+25=65+2 =67 67+35=102+2 =104 104+67=171+0=171 171+104=275+2=277 so 9th term is 277 ANSWER:E #### E QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years? options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 % SOLUTION:Let sum = x. Then, S.I. = x. Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11) = 100/11 = 9.09 % ANSWER:A #### A QUESTION:The average of first six multiples of 3 is options: A)10.5 B)6 C)9 D)12 E)15 SOLUTION:Solution Average = 3(1+2+3+4+5+6) / 6 = 63 / 6. = 10.5. Answer A #### A QUESTION:A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)80 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B #### B QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)12% C)22% D)24% E)21 SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer:A #### A QUESTION:How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed options: A)5040 B)1254 C)4510 D)1203 E)4510 SOLUTION:'LOGARITHMS' contains 10 different letters Required number of words = Number of arrangements of 100 letters taking 4 at a time = 10P4 = 10 * 9 * 8 * 7 = 5040 Ans: A #### A QUESTION:Find the fourth proportion to 2,4,6 options: A)18 B)12 C)9 D)6 E)8 SOLUTION:Explanation: 2:4 :: 6:x => 2/4= 6/x => x = 24/2 => x = 12 Answer:B #### B QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 78. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 81 C)(c) 82 D)(d) 65 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (78-6)/6+1=13 such multiples. So, final number of sets is 13*5=65 Answer: D #### D QUESTION:A sum of money at simple interest amounts to $ 980 in 3 years and to $1024 in 4 years. The sum is: options: A)$153 B)$848 C)$398 D)$549 E)$675 SOLUTION:B $848 S.I. for 1 year = $(1024 - 980) = $44. S.I. for 3 years = $(44 x 3) = $132. Principal = $(980 - 132) = $848. #### B QUESTION:At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A? options: A)12 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:After t hours the distances D1 traveled by car A is given by D1 = 40 t Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by D2 = 60 (t-1) When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives 40 t = 60 (t-1) Solve the above equation for t to find t = 3 hours Car B passes car A at 9 + 3 = 12 pm Answer A #### A QUESTION:John began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after John? options: A)35 B)55 C)39 D)40 E)60 SOLUTION:Carla starts 30 minutes later and it takes 3 hr for carla to meet John So John total time travelled = 3hr + 30 minutes John distance = 30 * (3 1/2) = 105 so carla need to travle 105 to meet John in 3 hrs speed of carla = 105/3 = 35 miles per hour Answer is A #### A QUESTION:A right triangle has sides of a, b, and 7, respectively, where a and b are both integers. What is the value of (a + b)? options: A)40 B)42 C)46 D)48 E)49 SOLUTION:LET a= hypotenuse , b =base ,7 = perpendicular . therefore a^2 -b^2 =7^2 or (a+b)(a-b) = 49 a+b =49/a-b ' a-b cannot be zero ..therefore a+ b =49 where a-b is equal to 1 E #### E QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed? options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr SOLUTION:Let the speed be x km/hr 50x-50* 9/10 *x = 450 50x - 45x = 450 x = 90km/hr Answer is E #### E QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly? options: A)4 B)6 C)10 D)12 E)24 SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5∗150=90 2nd Question : four fifths of the remainder answered the second question correctly so 4/5∗(150−90)=4/5∗60=48 total students who answered at least one Q correct =90+48=138 so students who answered BOTH incorrectly = 150−138=12 ANSWER:D #### D QUESTION:Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.90? options: A)426 B)430 C)443 D)480 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones. Having 7.9$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.9 $ left. so we buy 1 pack of 50 for 1$. We now have 0.9$ left, so we buy 30 individual envelopes. If we add up the numbers, we get 400+50+30=480 envelopes. Answer D #### D QUESTION:When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[8] = ? options: A)[22] B)[44] C)[75] D)[88] E)[90] SOLUTION:[7]*[8]=(7*2+1)(8/2+1) =[75]. Ans -C #### C QUESTION:How many four-digit positive integers can be formed by using the digits from 1 to 9 so that two digits are equal to each other and the remaining two are also equal to each other but different from the other two ? options: A)400 B)1728 C)108 D)216 E)432 SOLUTION:The number of ways u can chose two digits from 9 digits is 9C2=(9*8)/2. And the no of ways u can arrange two digits like asked is 4C2=(4*3)/2. total ways is 36*6=216. Answer : D #### D QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following numbers? options: A)4 B)3 C)7 D)6 E)9 SOLUTION:Let the consecutive even integers are n and (n + 2) difference of the squares = (n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4 = 4(n + 1) which is divisible by 4 Answer is A #### A QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z? options: A)50% B)40% C)37.5% D)331⁄3% E)25% SOLUTION:Work with fraction of brand Z in the tank. 1st step: brand Z is 1 2nd step: brand Z is 1/2 3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4 4th step: brand Z is (1/2)*(3/4) Q= 3/8 = 37.5% Answer (C) #### C QUESTION:P and Q are the only two applicants qualified for a short-term research project that pays 300 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage? options: A)$5 B)$10 C)$15 D)$20 E)$25 SOLUTION:Let Q's hourly wage be x, then P's hourly wage is 1.5x Let T be the number of hours that Q needs, then P needs T-10 hours to do the job. Since they both are paid an equal total amount of $300: x*T=1.5x*(T-10) T = 30 hours and Q's hourly wage is 300/30 = $10 P's hourly wage is 300/(T-10) = $15 which is $5 per hour more. The answer is A. #### A QUESTION:In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? options: A)48400 B)48000 C)48100 D)48500 E)48600 SOLUTION:Assume that investment of C =x Then, investment of A =2x Investment of B =4x/3 A:B:C =2x:(4x)/3:x =2:4/3:1=6:4:3 B's share =157300×4/(6+4+3) =157300×4/13=12100×4=48400 Answer is A. #### A QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 2 rows or 7 rows or 9 rows, then no tree will be left. Find the least number of trees required options: A)22 B)60 C)126 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(2, 7, 9) = 126 Answer: C #### C QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer C #### C QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? options: A)176 m B)198 m C)197 m D)150 m E)168 m SOLUTION:Let the length of the train be x meters and its speed be y m/sec. They, x / y = 15 => y = x/15 x + 100 / 25 = x / 15 x = 150 m. Answer:D #### D QUESTION:If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s? options: A)8 B)2 C)− 2 D)− 3 E)− 5 SOLUTION:Given: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x - 5)(x + 3) = (x + r)( x + s) Rewrite as: (x + -5)(x + 3) = (x + r)( x + s) So, it's possible that r = -5 and s = 3 Here, r - s = (-5) - 3 = -8 Try REVERSING the factorization: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x + 3)(x - 5) = (x + r)( x + s) Rewrite as: (x + 3)(x + -5) = (x + r)( x + s) So, it's possible that r = 3 and s = -5 Here, r - s = 3 - (-5) = 8 Answer: A #### A QUESTION:A mixture contains milk and water in the ratio 6:3. On adding 10 litters of water, the ratio of milk to water becomes 6:5. The quantity of milk in the original mixture is? options: A)90 B)45 C)110 D)40 E)50 SOLUTION:Explanation: milk:water = 6:3 6x : 3x + 10 = 6 : 5 5[6x] = 6[3x + 10] 30x = 18x + 60 30x - 18x = 60 12x = 60 x = 5 The quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9 9x = 45 Short cut method - 2 : for Only milk problems milk : water 6 : 3 6 : 5 milk ratio same but water ratio 2 part incress per 10 liters 2 part of ratio -------> 10 liters 9part of ratio -------> 45 liters Answer: Option B #### B QUESTION:The sum of three consecutive integers is 102. Find the lowest of the three? options: A)18 B)67 C)98 D)33 E)26 SOLUTION:Three consecutive numbers can be taken as (P - 1), P, (P + 1). So, (P - 1) + P + (P + 1) = 102 3P = 102 => P = 34. The lowest of the three = (P - 1) = 34 - 1 = 33. Answer: D #### D QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters? options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n SOLUTION:C is the answer. To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra. Given - tank was already 1/3 full. - When n ltr added, it became 5/9 So 1/3 + n = 5/9 n = 5/9 - 3/9 n = 2/9 capacity of the tank is full fraction . i.e. 1 i.e. 9/9 so the question is 9/9 is how much times n = 9/9 = 1 = xn so x = 9/2 and total = 9/2n #### C QUESTION:On the x-y coordinate plane there is a parabola, y=x(4-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis? I. (1, 4) II. (2, 3) III. (4, 1) options: A)I only B)II only C)III only D)I and II E)I, II, and III SOLUTION:Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive. When x = 1, y = 3 lies on the parabola, so (1, 4) will not be enclosed by the parabola and x axis. When x = 2, y = 4 lies on the parabola, so (2, 3) will lie below it and this point will be enclosed by the parabola and x axis. When x = 4, y = 0 lies on the parabola, so (4, 1) will not be enclosed by the parabola and x axis. The answer is B. #### B QUESTION:Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 4 = f(3x – 6) options: A)3 B)4 C)6 D)7 E)13 SOLUTION:Answer = A = 3 f(x) = 3x – 5 2*[f(x)] – 4 = f(3x – 6) 2(3x-5) -4 = 3 (3x-6) - 5 6x - 14 = 9x - 23 x = 3 #### A QUESTION:What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive? options: A)90 B)80 C)100 D)105 E)110 SOLUTION:10 and 190 inclusive would mean there are 17 terms. No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170 The middle term is the average which is the tenth term = 80 B is the answer. #### B QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5? options: A)3 B)16 C)75 D)24 E)26 SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens. 2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers). 3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers. 4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left! 6) Answer choice E. #### E QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. After how much time will the trains meet? options: A)20/8 sec B)20/4 sec C)5/2 sec D)22/7 sec E)60/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (54 + 90)*5/18 = 8*5 = 40 mps. The time required = d/s = 100/40 = 5/2 sec.Answer:C #### C QUESTION:a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream options: A)13 km/hr. B)12 km/hr. C)9 km/hr. D)15 km/hr. E)11 km/hr. SOLUTION:Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph. So,2x=24 or x=12. Rate upstream=12 km/hr,rate downstream=36 km/hr. Hence,rate of stream=1/2(36-12)km/hr=12 km/hr. Answer is B. #### B QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B QUESTION:.05% of cans of beans that go down a conveyor belt are sealed improperly and must be disposed of. How many cans of beans must pass down a conveyor belt for 5 cans to be sealed improperly? options: A)500 B)5000 C)4000 D)2500 E)10000 SOLUTION:Let the number of total cans of beans be x Then, .05% of x=5 (5/100)*(1/100)*x=5 x=10000 Answer is E #### E QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.899] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ? options: A)0 B)1 C)27 D)54 E)0 SOLUTION:K=[lCM of 80 and 45] * (any integer) however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer for value of k(60) * any integer unit value will be always zero . E #### E QUESTION:A set of 11 positive integers has an average of 20. Which of the following is the greatest possible value for the median of this set? options: A)25 B)30 C)35 D)45 E)46 SOLUTION:for the median to bé max , we should take all the values below meadian to be the lowest and the remaining values to be the same.. here 1 is the lowest value(positive int) số thẻ lowest 5 int will equal 5.. remaining 6= 20*11-5=215.. therefore each valueof these 6 int =215/6=35 ans C #### C QUESTION:The average age of three boys is 40 years and their ages are in proportion 6:10:8. What is the age in years of the youngest boy? options: A)8 B)10 C)7 D)6 E)5 SOLUTION:6x + 10x + 8x = 40 x =1.6 6x = 10 Answer:B #### B QUESTION:If x percent of 400 is 20 percent of 700, then x = options: A)200 B)350 C)700 D)400 E)1,400 SOLUTION:x/100(400) = 2/10(700) x = 400. Option D. #### D <<<Examples ends QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Solution Start with 11 coins. Sharon takes 3 coins from you: 11 - 3 = 8 coins. Steven takes 4 coins from you: 8 - 4 = 4 coins. So you have 4 at the end. Correct answer : C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1 SOLUTION:(4*6 + 8*6): (4*12) 72:48 => 3:2 Answer:C #### C QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) spiders 1:7 Webs 7:1 1 x 7 x x = 7 x 1 x 7 => x= 7 Answer is 7 #### A QUESTION:For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is? options: A)between 2 and 20 B)between 10 and 20 C)between 20 and 30 D)between 30 and 40 E)greater than 40 SOLUTION:SOL: Lets consider h(100): => 2*4*6*8.........*98*100 => (2*1) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50) => (2^50) * (1*2*3*4........*49*50) => h(100) = (2^50) * (50!) We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100). But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50; ANSWER:E #### E QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)201 SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111 Answer : Option C #### C QUESTION:You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg. And each emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What should you collect to get the maximum wealth? options: A)20 rubies and 15 emeralds B)40 rubies C)28 rubies and 9 emeralds D)None of these E)Cannot be determined SOLUTION:Explanation : The limits our wealth is the capacity of bag which is 12 Kg. So we should make each unit of weight to worth the max. Rubee: 0.3 Kg worth 4 Crore, so 1 Kg of Rubee is worth 4/(0.3) = 40/3 = 13.33 Crore. Emerald: 0.4 Kg worth 5 crore so 1 Kg of Emerald is worth 5/(0.4) = 50/4 = 12.5 Crore. As value per kilogram is more for Rubee we should pick max rubees for max wealth. Here we can accomadate the whole 12Kg with 40 rubees which is worth 160 Crore. Answer : B #### B QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)1 B)2 C)8 D)7 E)0 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer: C #### C QUESTION:A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent? options: A)27% B)20% C)80% D)30% E)25% SOLUTION:900 ---- 225 100 ---- ? => 25% Answer: E #### E QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 4 candidates are there to fill the 4 positions? options: A)420 B)770 C)840 D)165 E)315 SOLUTION:1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer None of the 4 chosen people can be in more than one departments. We can choose any of the 7 candidates for the math dep., which gives as 7 selections. We can choose 3 of the 10 candidates for the computer dep., which gives us 3 selections and 7 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /3!*7!= 120 We are multiplying our individual selections: 7*120 = 840 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans C #### C QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am SOLUTION:In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours. Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am. Answer: D #### D QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job? options: A)6 B)13 1⁄2 C)17 D)Data inadequate E)None of these SOLUTION:12 M × 18 = 12 W × 18 × 3/1 \ w = 1/3 M 10M + 8W = 10M + 8 × 1/3M = 12 2/3 M \12 2/3 men can complete the same work in 12×18/12 2/3=17days Answer C #### C QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? options: A)6 hrs 21 min B)6 hrs 91 min C)6 hrs 01 min D)6 hrs 23 min E)3 hrs 21 min SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs. Number of stoppages = 600/75 - 1 = 7 Total time of stoppages = 3 * 7 = 21 min Hence, total time taken = 6 hrs 21 min. Answer:A #### A QUESTION:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of t feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(x/t) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet. The number of revolutions = distance/circumference = 5,280x/t. Answer: A. #### A QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3% SOLUTION:Let 100 is the enrollment in 1990. Enrollment in 1980= 83.3 % increase= (Increase from 1980 to 1990)/Enrollment in 1983 =>16.7*100/83.3 =20% ANSWER:C #### C QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 15000, then find his savings? options: A)3600 B)3607 C)3608 D)3602 E)3000 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 15000 => x = 3000 Savings = Income - expenditure = 5x - 4x = x So, savings = Rs. 3000. Answer:E #### E QUESTION:Two consecutive traffic signals each show either red or green. How many different arrangements of the two signals are possible? (Note: “Red-green” is different from “green-red.”) options: A)10 B)9 C)8 D)7 E)4 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 2 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 2 signals are possible. Total Options: 4 Final Answer: E #### E QUESTION:30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there? options: A)800 B)1000 C)1200 D)1500 E)1800 SOLUTION:800score Official Solution: People who do both hunting and fishing make 30% of fishermen and 20% of hunters. There are 1500 hunters so 1500 × 20% = 300 pers. do both hunting and fishing. Same people make 30% of all fishermen.30% of fishermen = 300 pers. Fishermen = (300 / 30) × 100 pers. = 1000 pers. The correct answer is choice (B). #### B QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:A mixture of 85 kg contains milk and water in the ratio 27 : 7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:1? options: A)5 kg B)6.5 kg C)7.5 kg D)8 kg E)9 kg SOLUTION:Milk in 85 kg of mix = 85* (27/34) = 135/2 kg. Water in it = 85-135/2 = 35/2 kg. Let x kg of water be added to it. Then, (135/2)/(35/2 + x) = 3/1; 135/(35 +2x) = 3/1; 105 + 6x = 135 ; 6x = 30; x = 5 The quantity of water to be added = 5 kg ANSWER:A #### A QUESTION:I have a three digit number in my mind. In that number, the tens digit is seven more than the ones digit and the hundreds digit is six less than the tens digit. What is the number? options: A)281 B)239 C)254 D)276 E)277 SOLUTION:A 281 #### A QUESTION:A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in? options: A)12 B)13 C)13 5/7 D)13 ¾ E)None of these SOLUTION:Explanation: (A+B)’s 2 day work = 1/16 + 1/12 = 7/18 work done in 6 pairs of days=7/48 x 6 = 7/8 remaining work = 1/8 work done by A on 13th day =1/16 remaining work = 1/16 on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day total time taken =13 ¾ days Answer: Option D #### D QUESTION:factor: 3y (x-3)-2(x-3) options: A)(x-3)-2(x-3) B)(x-3)power2 C)(x-3)(3y-2) D)3y(x-3) E)x-3 SOLUTION:3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C) #### C QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:P = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of P = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:The difference between a number and its three-fifths is 50.What is the number? options: A)75 B)100 C)125 D)Cannot be determined E)None of these SOLUTION:Suppose the number is N. Then N - 3⁄5N = 50 ⇒ 2N⁄5 = 50 ∴ N=50×52=125 Answer.C #### C QUESTION:The average weight of 5 person's increases by 4 kg when a new person comes in place of one of them weighing 50kg. What is the weight of the new person? options: A)70 B)86.5 C)80 D)88.5 E)75 SOLUTION:Total increase in weight =5 × 4=20 If x is the weight of the new person, total increase in weight = x−50 => 20= x - 50 => x = 20+50= 70 ANSWER:A #### A QUESTION:What least no. must be subtracted from 5026 so that remaining no.is divisible by 5? options: A)3 B)4 C)5 D)6 E)1 SOLUTION:Explanation: On dividing 5026 by 5 we get the remainder 1, so 1 should be subtracted Option E #### E QUESTION:A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 35 instead of 99 then find the correct average marks up to two decimal places. options: A)73.41 B)74.31 C)72.43 D)73.43 E)73.82 SOLUTION:Total marks = 35 x 72 =2520 Corrected total marks = 2520 - 35 + 99 =2584 Correct Average = 2584/35 = 73.82 Answer : E #### E QUESTION:Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:Let x be the number of guests. Number of muffins prepared = 5x + 2 Number of muffins eaten + Number of muffins remaining = Number of muffins prepared 6(x - 1) + 4 = 5x + 2 6x - 4 = 5x + 2 x = 6 Answer: D #### D QUESTION:If there is exactly one root of the equation x^2 + ax - b, where a and b are positive constants, what is b in terms of a? options: A)a/2 B)a C)-a^2/4 D)a^2/2 E)a^2/4 SOLUTION:one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1 Here b = a c= b a = 1 substituting these values in 1, we have a^2 = -4b => b =-a^2/4 Answer is C. #### C QUESTION:8500 + (1600 ÷ ?) of 1/5 = 8501 options: A)310 B)312 C)320 D)325 E)345 SOLUTION:Explanation: => 8500 + (1600/?) × 1/5 = 8501 => 1600/? × 1/5 = 8501 - 8500 = 1 => ? = 1600/5 = 320 Answer: Option C #### C QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame? options: A)12 B)20 C)30 D)40 E)50 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so Area of frame = (1/2) * a^2 Area of Frame + Painting = a^2 + (1/2)*a^2 = (3/2)*a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2 so, b * sqrt2 = 6 so, b = 3 * sqrt2 b^2 = 18 we know that b^2 = (3/2)*a^2 so, a^2 = (2/3)*b^2 = (2/3)*18 = 12 And area of painting = a^2 = 12 So, answer will be A. #### A QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? options: A)90 B)2,700 C)3,300 D)5,400 E)324,000 SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 110*30=3,300 copies. Answer: C. #### C QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? options: A)610 B)720 C)825 D)920 E)650 SOLUTION:Explanation: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA). Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters =5!=5×4×3×2×1=120=5!=5×4×3×2×1=120 All the 3 vowels (OIA) are different Number of ways to arrange these vowels among themselves =3!=3×2×1=6=3!=3×2×1=6 Hence, required number of ways =120×6=720 ANSWER IS B #### B QUESTION:If w persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job? options: A)z B)x C)x/y D)z/x E)y/z SOLUTION:the Q doesn't seem to be having the any correct answer as a choice.. since we are looking for days, lets keep days in end and work out a solution.. w person can do z jobs in y days.. so w person can do 1 job in y/z days.. and 1 person can do 1 job in y^2/z days.. so y person can complete 1 job in y^2/zy=y/z.. so the answer should be y/z=E #### E QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:A man buys an item at Rs. 750 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 600 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 750 = 80/100 * 750 = 600 Option C #### C QUESTION:When a merchant imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $94.50, what was the total value of the item? options: A)$2,350 B)$2,850 C)$3,250 D)$3,400 E)$3,750 SOLUTION:Let x be the value in excess of $1,000. 0.07x = 94.5 x = $1,350 The total value was $1,350 + $1,000 = $2,350. The answer is A. #### A QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads? options: A)1 B)2 C)8 D)31 E)30 SOLUTION:Total outcome is 2^3 = 8 Favourable cases = H_ H The second place can be occupied by either H or T There are 2^1 =2 ways that can be done. Hence, the correct option is B #### B QUESTION:On a map the distance between two mountains is 310 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain? options: A)14.83 B)14.81 C)14.91 D)14.82 E)14.12 SOLUTION:Explanation: Since 310 inch = 136 km So 1 inch = 136/310 km So 34 inch = (136 × 34)/ 310 = 14.91 km Answer: C #### C QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 40*9/40 = 9 seconds. Answer: C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94 SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8. Thus when n is even, this whole expression will be divisible by 8. from 1 to 96, there are 47 even integers. Now when (n+1) is multiple by 8, we have 12 such values for (n+1) probability that n(n+1)(n+2) will be divisible by 8 = (47 + 12)/94 = 59/94 = 5/8 Ans is E #### E QUESTION:In how many ways can the letters of the word ARRANGED be arranged in a row so that the vowels appear in alphabetic order? options: A)6720 B)5280 C)6240 D)5202 E)4020 SOLUTION:three letters can be arranged in 3! ways. only one combination AEI is required. 8 letters can be arranged in 8! ways. thus 8!/ 3! * 1 = 6720. A #### A QUESTION:A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 60 kmph. When and at what distance from Mumbai do the two trains meet? options: A)187 B)279 C)120 D)278 E)379 SOLUTION:When the second train leaves Mumbai the first train covers 40 * 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (60 -40) = 2 hours So, the two trains meet at 12 a.m. The two trains meet 2 * 60 = 120 km away from Mumbai. Answer:C #### C QUESTION:The price of lunch for 10 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? options: A)11.73 B)12 C)13.8 D)14 E)18 SOLUTION:Clearly E is the answer I used POE here Lets consider option (E) 10*18= 180 now 180(115/100)=207 => possible ANSWER IMO E #### E QUESTION:What is the greatest of 3 consecutive integers whose sum is 27 ? options: A)6 B)7 C)8 D)9 E)11 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 27; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: E #### E QUESTION:There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends? options: A)1 B)10 C)125 D)50 E)20 SOLUTION:25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125 so 125 enrolled for swimming Answer: C #### C QUESTION:Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once? options: A)9/100 B)1/10 C)11/100 D)19/100 E)1/5 SOLUTION:Probability = No of balls with exactly one 1 / total number of balls = {1,10,12 to 19, 21,31,41,51,61,71,81,91,100}/100 = 19/100 Answer is D #### D QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)77 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get? options: A)57% B)57.3% C)65% D)90% E)80% SOLUTION:total votes are 20280 ( sum of votes obtained by 3 candidates) percentage of the total votes recd by the winning candidate = 100*11620/20280 = 57.3% ANSWER:B #### B QUESTION:575.104 x 15.98 ÷ 9.001 + 21.25 = ? options: A)983.578 B)1043.65 C)1033.65 D)656.112 E)456.512 SOLUTION:Explanation: ? = 575.104 x 15.98 ÷ 9.001 + 21.25 ≈ (575.104 x 16/9) + 21.25 ≈ 1022.40 + 21.25 ≈ 1043.65 Answer: Option B #### B QUESTION:In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase? options: A)16.67% B)25% C)20.45% D)31.56% E)40% SOLUTION:Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67% Answer is A #### A QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:1) Draw a simple cube 2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes. 3) Remember that the OUTSIDE of the cube is the part that's painted.... The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. J=4 + 4 + 4 = 12. Answer A #### A QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:For: (2^(3x+3)+3)/3 Let n = 3x + 3 2^n 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, .... Rule: x^(m+n) = (x^m)(x^n) (2^(3x))(2^3) Rule: x^(mn) = (x^m)^n ((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1. Answer: B #### B QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)7/8 C)3/8 D)5/6 E)9/11 SOLUTION:Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E)=n(E)/n(S) =7/8 The answer should be B #### B QUESTION:man is 36 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)34 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 36) + 2 = 2(x + 2) x + 38 = 2x + 4 x = 34. answer :D #### D QUESTION:In how many K ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6*6*6*6= 1296 ------(1) Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2) therefore required value K= (1)-(2)= 1296-360=936.D #### D QUESTION:In an examination, 25% of total students failed in Hindi, 50% failed in English and 25% in both. The percentage of these who passed in both the subjects is : options: A)23 B)37 C)28 D)40 E)50 SOLUTION:Explanation: Formula n(a∪b) = n(a) + n(b) − n(a∩b) Fail in Hindi or English = 25 + 50 – 25 = 50 Therefore students who passed = 100 – 50 = 50. Answer: E #### E QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:How many of the integers between 25 and 45 are even ? options: A)21 B)20 C)11 D)10 E)9 SOLUTION:Number start between 25 to 45 is 20 numbers half of them is even..which is 10 ANSWER:D #### D QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 asquotient and the 15 as remainder? options: A)1245 B)1567 C)1678 D)1335 E)1635 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Large number = 270+1365 = 1635 E #### E QUESTION:Jim and Reneey will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneey have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win? options: A)5/6 B)2/3 C)1/2 D)5/12 E)1/3 SOLUTION:1/3 probability of jim winning is basically the sum of three probabilities: probability of jim picking rock and reneey picking scissors = 1/3*1/3 = 1/9 probability of jim picking scissors and reneey picking paper = 1/3*1/3=1/9 probability of jim picking paper and reneey picking rock = 1/3*1/3=1/9 1/9 + 1/9 + 1/9 = 3/9 = 1/3=E #### E QUESTION:A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? options: A)32 B)55 C)6 D)78 E)81 SOLUTION:S = (100 + 300)/45 = 400/45 * 18/5 = 32 Answer: A #### A QUESTION:A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed? options: A)10.21 days B)10.23 days C)18.25 days D)10.25 days E)40.25 days SOLUTION:Explanation: A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work. => In one day A came complete 1/9th of the task(x/9) => In one day B can complete 1/12th of the job.(x/12) First day x/9th work will be done next day x/12th and so on: Together A and B can do x/9 + x/12 work. =>(x/9) + (x/12) = 7/36th work done In 10 days 35/36th of the work will be done. On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work. So, 1/36th work will be done in 1/4 days. =>10.25 days ANSWER: D #### D QUESTION:In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 35 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class ? options: A)22 B)27 C)75 D)29 E)271 SOLUTION:Explanation: Let the number of students in the class be 100 and let this required average be x. Then, (10 * 95) + (20 * 90) + (70 * x) = (100 * 80) => 70x = 8000 - (950 + 1800) = 5250 => x = 75. Answer: C) 75 #### C QUESTION:If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true? I. c - a = 2 II. abc is an odd integer. III. (a + b + c)/3 is an integer. options: A) I only B) II only C) I and III only D) II and III only E) I, II, and III SOLUTION:Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true. Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is false. Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well. Answer: C. #### C QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.9 sec C)3.5 sec D)7.5 sec E)5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 200/40 = 5 sec. Answer: E #### E QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)*(100%-19%) = 1.07*.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D QUESTION:A, B and C rents a pasture for Rs.638. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay? options: A)270 B)198 C)676 D)156 E)122 SOLUTION:12*8 :16*9 = 18*6 8: 12: 9 9/29 * 638= 198 Answer: B #### B QUESTION:How many 3-digit even numbers are possible such that if one of the digits is 4, the next/succeeding digit to it should be 7? options: A)305 B)5 C)365 D)405 E)495 SOLUTION:470, 472, 474, 476, and 478, so total 5. Hence Option B. #### B QUESTION:Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions? options: A)54 B)432 C)864 D)2,916 E)148,824 SOLUTION:We have the rectangle with dimensions 9*4 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis. Choose the (x,y) coordinates for vertex A: 9C1*4C1; Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A); Choose the y coordinate for vertex B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A). 9C1*4C1*8C1*3C1=864. Answer: C. #### C QUESTION:Three distinct single-digit numbers. A,B,C are in GP. If abs(x) for real x is the absolute value of x(x if x is +ve or 0 and -x if x is -ve), then the number of different possible values of abs(A+B+C) is options: A)5 B)6 C)3 D)4 E)7 SOLUTION:A,B,C may be (1,2,4) & (4,2,1) (1,3,9) & (9,3,1) (2,4,8) & (8,4,2) (4,6,9) & (9,6,4) find abs(A+B+C) for these 8 GPs 7,13,15,19 So,we get 4 different values ANSWER:D #### D QUESTION:Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 22 boys and 38 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic. Table method is shown above; here is how you will use logic: There are 6 happy boys. There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys. We have 6 happy boys and 6 sad boys. Total we have 22 boys. So 22 - 6 - 6 = 10 boys must be neither happy nor sad. Answer (E) #### E QUESTION:The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? options: A)27 B)30 C)31 D)33 E)34 SOLUTION:The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 A #### A QUESTION:A fruit seller sells mangoes at the rate of Rs.14 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 15%? options: A)Rs.11.81 B)Rs.12 C)Rs.18.94 D)Rs.12.31 E)None SOLUTION:Solution 85 : 14 = 115 : x x= (14×115/85) = Rs.18.94 Hence, S.p per Kg = Rs.18.94 Answer C #### C QUESTION:John has taken four (4) tests that have an average of 81. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade? options: A)87 B)90 C)92 D)94 E)99 SOLUTION:87-81=6*4=24 points 2*87=174 174+24=198 points to be scored in the 2 tests. Avg of 2 tests = 198/2=99 Answer: E Traditional Method: Total scored till now 81*4=324 Total score to avg 87 in 6 tests = 87*6=522 Total to be scored on 2 tests = 522-324=198 Avg on 2 tests = 198/2 = 99 Answer E #### E QUESTION:At 15:00 there were 22 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ? options: A)7 B)14 C)25 D)27 E)32 SOLUTION:Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) - 8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44) 20 + 3*14 -8 * 4 = 32 E #### E QUESTION:What is the remainder when 1014*1047*1050*1053 is divided by 33? options: A)3 B)6 C)30 D)21 E)18 SOLUTION:OA is 'C'. OE: take the remainder from each of 1044/33, 1047/33 and so on.. 1014/33 gives remainder = 24 1047/33 gives remainder = 24 1050/33 gives remainder = 27 1053/33 gives remainder = 30 the net remainder is the product of above individual remainders. i.e = 24*24*27*30 break them into pairs 24*24/33 gives remainder 15 and 27*30/33 gives remainder 18 so 15*18/33 gives remainder 6. B #### B QUESTION:Which of the following is greatest? options: A)1/2 B)1/4 C)1/3 D)1/6 E)1/7 SOLUTION:simply we know that 1/2 is greater than all others. So, Answer : A #### A QUESTION:A can do a piece of work in 13 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in? options: A)15 10/11 days B)10 10/11 days C)12 10/11 days D)19 10/11 days E)13 10/11 days SOLUTION:B (x – 5)/13 + x/20 = 1 x = 10 10/11 days #### B QUESTION:Find the odd man out 864, 420, 200, 96, 40, 16, 6 options: A)420 B)200 C)96 D)40 E)6 SOLUTION:6x2+4=16 16x2+8=40 40x2+12=92 92x2+16=200.. and so on. ANSWER:C #### C QUESTION:The sector of a circle has radius of 35 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)91.8 cm D)92.5 cm E)152.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 35) + 2(35) = 49.5 + 70 = 152.5 cm Answer:E #### E QUESTION:[1/(1.2.3)] + [1/(2.3.4)] + [1/(3.4.5)] + [1/(4.5.6)] is equal to options: A)7 / 30 B)11 / 30 C)13 / 30 D)17 / 30 E)None SOLUTION:Answer Given Exp. = [(4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3)] / [(2 x 3 x 4 x 5 x 6)] = 168 / (24 x 30) = 7 / 30 Correct Option: A #### A QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is? options: A)14 years 8 months B)15 years C)13 years 8 months D)17 years 10 months E)17 years SOLUTION:Total decrease = (20 x 2) months = 3 years 4 months Age of the new boy = 17 years - 3 years 4 months. = 13 years 8 months. ANSWER:C #### C QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)78% D)48% E)11% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 13000, then the share of B is? options: A)6000 B)12000 C)18000 D)24009 E)24002 SOLUTION:Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 13000 Share of B = 6/13 (13000) = Rs. 6000 Answer: A #### A QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. options: A)32 B)15 C)18 D)20 E)25 SOLUTION:Relative speed = (420/18)m/s = (420/18)*(18/5) = 84 kmph speed of goods train = 84-64 = 20 kmph Answer is D #### D QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 300*1 = revenue (eq -1) if he reduced his price by 20% then , 240*(customer) = 125/100*revenue customer = 1.25*300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:A division of a company consists of four men and eight women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)7/11 B)7/33 C)14/33 D)7/66 E)14/66 SOLUTION:The total number of ways to choose two representatives is 12C2=66. The number of ways to choose two females is 8C2=28. P(choosing two female representatives)=28/66=14/33 The answer is C. #### C QUESTION:The cost price of 20 articles is equal to the selling price of 25 articles. The loss percent in the transaction is options: A)5 B)20 C)25 D)30 E)None of these SOLUTION:Let C.P. of 1 article = 1 then C.P. of 25 articles = 25 and S.P. of 25 articles = 20 ∴ loss % = 25−20/20×100=25% Answer C #### C QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace? options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525 SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that the card drawn is an ace. Clearly, we have to find P (QQA) Now P(Q) = 4/52 Also, P (Q|Q) is the probability of second queen with the condition that one queen has already been drawn. Now there are three queen in (52 - 1) = 51 cards. Therefore P(Q|Q) = 3/51 P(A|QQ) is the probability of third drawn card to be an ace, with the condition that two queens have already been drawn. Now there are four aces in left 50 cards. Therefore P(A|QQ) = 4/50 By multiplication law of probability, we have P(QQA) = P(Q) P(Q|Q) P(A|QQ) = 4/52 × 3/51 × 4/50 = 2/5525. A) #### A QUESTION:There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to? options: A)7!*1! B)7!*2! C)6!*2! D)8!*2! E)6!*2! SOLUTION:Total number of ways = 7!*2!. B #### B QUESTION:A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle? options: A)2.5π B)3π C)5π D)4π E)10π SOLUTION:If a rectangle is inscribed in a circle, then the diagonal of the rectangle = diameter of the circle. In this case, diagonal = (9 + 16)^(1/2) = 5 Hence the radius = 2.5 Circumference = 2πr = 2π*2.5 = 5π Correct Option: C #### C QUESTION:A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in options: A)18 sec B)12 sec C)15 sec D)20 sec E)13.5 sec SOLUTION:Length of train = 12 × 15 = 180 m. Then, speed of train = 180⁄18 = 10 m/s Now, length of train = 9 × 15 = 135m ∴ Required time = 135⁄10 = 13.5 sec. Answer E #### E QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.2 x = 3.2 Alternate solution: Try to backsolve. Initial volume = 3.2 After one hour --> (1/4)3.2 = 0.8 After two hours --> (1/4)0.8 = 0.2 Answer: B #### B QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is options: A)10√2 m B)100 m C)100√2 m D)200 m E)None SOLUTION:Solution Let the altitude of the triangle be hïand base of each be b. Then , (½ ×b× h1) where h2 = 100 m. = h1 = 2h2 = ( 2 x 100) m = 200 m. Answer D #### D QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,700 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Price in 96 = 22000 Price decrease each year = 2.5/100*22000 = 550 Price in 97 = 22000 - 550 Price in 98 = 22000 - 2*550 Price in 99 = 22000 - 3*550 Price in 00 = 22000 - 4*550 Price in 01 = 22000 - 5*550 Price in 02 = 22000 - 6*550 = 18700 Investment in the car = 1000 Net price of the car in 02 = 18700 + 1000 = $19700 Correct Option: B #### B QUESTION:In a certain village, 200 litres of water are required per household per month. At this rate, if there are 5 households in the village, how long (in months) will 2000 litres of water last? options: A)9 B)5 C)6 D)2 E)4 SOLUTION:I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p: In a certain village,m 200 litres of water are required per household per month. At this rate, if there aren 5 households in the village, how long (in months) willp2000litres of water last? Water required is 200*5=1000 (m*n) Water available is 2000 (p) It will last 2 months (p/m*n) Ans : D #### D QUESTION:835, 734, 642, 751, 853, 981, 532 options: A)751 B)853 C)981 D)532 E)None of these SOLUTION:Solution In each number except 751,the difference of third and first digit is the middle one. Answer A #### A QUESTION:There are 8 people and 5 chairs. In how many different ways people can occupy the chairs? options: A)1640 B)1650 C)1660 D)1670 E)1680 SOLUTION:number of ways = 8*7*6*5 = 1680 Answer is E #### E QUESTION:For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? options: A)12% B)26% C)29% D)32% E)60% SOLUTION:In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated. In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated. Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%. Answer: D. #### D QUESTION:A can do a piece of work in 8 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? options: A)8.7 days B)2.0 days C)6.6 days D)7.7 days E)4.8 days SOLUTION:C = 1/2 - 1/8 - 1/8 = 5/24 => 4.8 days Answer: E #### E QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table? options: A)6925 B)6887 C)6728 D)6725 E)2871 SOLUTION:: CP = SP * (100/(100 + profit%)) = 8587(100/124) = Rs. 6925. Answer: A #### A QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many digits does this integer consists of? options: A)150 B)339 C)342 integers D)359 E)362 SOLUTION:1-digit integers Number of 1-digit integers (1 to 9) = 9 - 1 + 1 = 9 Number of digits used = (9)(1) = 9 2-digit integers Number of 2-digit integers (10 to 99) = 99 - 10 + 1 = 90 Number of digits used = (90)(2) = 180 3-digit integers Number of 3-digit integers (100 to 150) = 150 - 100 + 1 = 51 Number of digits used = (51)(3) = 153 TOTAL # of digits uses = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:According to a recent survey report issued by the Commerce Ministry, Government of India, 30% of the total FDI goes to Gujarat and 20% of this goes to rural areas. If the FDI in Gujarat, which goes to urban areas, is $72 m, then find the size of FDI in rural Andhra Pradesh, which attracts 50% of the FDI that comes to Andhra Pradesh, which accounts For 20% of the total FDI? options: A)30m B)40m C)35m D)38m E)50m SOLUTION:30% of total FDI given to Gujarat is $90m. so,100% is $300m. 20%of 300m=60m. 50%of 60m=30m. ANSWER:A #### A QUESTION:A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 60% above the original cost per share of stock, then interns of m for how many dollars was each share sold? options: A)a) 2m/300 B)b) m/300 C)c) 5m/900 D)d) m/300 + 50 E)e) 350/m SOLUTION:Let Cost of 300 shares be $ 3000 So, Cost of 1 shares be $ 10 =>m/300 Selling price per share = (100+60)/100 * m/300 Or, Selling price per share = 5/3 * m/300 => 5m/900 Hence answer will be (C) #### C QUESTION:Walking with 4/5 of my usual speed, I arrive at the bus stop 8 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed? options: A)20 B)24 C)28 D)32 E)36 SOLUTION:Let t = usual time = distance / usual speed t + 8 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4 t = 32 The answer is D. #### D QUESTION:Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I? options: A)111 B)145 C)110 D)119 E)120 SOLUTION:There are five letters in the given word. Consider 7 blanks .... The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways. The number of words = 5! = 120. Answer:E #### E QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n? options: A)-200 B)-130 C)-104 D)51 E)305 SOLUTION:2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151: -51 < c < 151 -51 < n < 151 -102 < c+n < 302. Only option D is in this range. Answer: D. #### D QUESTION:An elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children? options: A)40: 20 B)42: 21 C)50: 100 D)15: 25 E)It cannot be determined by the information given. SOLUTION:While you can figure out most of this question, there is not enough information to completely tell. the answer is E. #### E QUESTION:A football matches has been organized in such a fashion, every participating team plays a match against every other team once and only once. If 36 matches are totally played, how many teams participated? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:For a match u need 2 teams. Suppose there are totally 'n'teams. Now we have to choose 2 teams out of 'n' teams. nC2 = 36; Solve to get n=9. n(n-1)/2 = 36 9(9-1)/2 = 36 9(8)/2 = 36 72/2 = 36 So, answer is 9 If 36 matches are totally played. ANSWER:C #### C QUESTION:A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen? options: A)Rs.6.40 B)Rs.10 C)Rs.9.6 D)Rs.10.2 E)None of the above SOLUTION:4 dozens of bananas cost is rs12 then 4*12=48 6 dozens of bananas cost is rs8 then 6*8=48 48+48/4+6=96/10=9.6 ANSWER:C #### C QUESTION:A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance? options: A)21 (1/3) kmph B)25 (1/3) kmph C)29 (1/3) kmph D)20 (1/3) kmph E)24 (1/3) kmph SOLUTION:A Let the total distance be x km total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64 Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph. #### A QUESTION:The operation # is defined for all nonzero x and y by x#y = x + x/y. If S>0, then 1#(1#S) = options: A)S B)S+1 C)S/(S+1) D)(S+2)/(S+1) E)(2S+1)/(S+1) SOLUTION:x#y = x + x/y. If S>0, then 1#(1#S) = You can see that a stands for y and 1 stands for x. I like to work with numbers so I did x=1 S=2 and S=y so y=2 1#S= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3 So now you can check by filling in S, which is 2: A. S --> 2 B. S+1 --> 2+1=3 C. S/(S+1)-->2/(2+1)=2/3 D. (S+2)/(S+1)-->(2+2)/(2+1)=4/3 E. (2S+1)/(S+1)-->(2*2+1)/(2+1)=5/3 So E is the answer. #### E QUESTION:What is 35% of 4/13 of 845? options: A)58 B)69 C)80 D)91 E)102 SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 845, or 1/9 of 845. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate. The number 845 is a bit more than 810, so (1/9)*845 will be a bit more than 90. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently. The closest answer is 91, so this is the answer to choose. The answer is C. #### C QUESTION:In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? options: A)48400 B)48000 C)48100 D)48500 E)48600 SOLUTION:Assume that investment of C =x Then, investment of A =2x Investment of B =4x/3 A:B:C =2x:(4x)/3:x =2:4/3:1=6:4:3 B's share =157300×4/(6+4+3) =157300×4/13=12100×4=48400 Answer is A. #### A QUESTION:Applying VBODMAS rule options: A)31/120 B)31/129 C)31/1276 D)31/122 E)31/111 SOLUTION:Answer:A #### A QUESTION:A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job? options: A)77 days B)21 days C)88 days D)55 days E)44 days SOLUTION:WC = 1:2 2x + x = 1/14 => x = 1/42 2x = 1/21 => 21 days Answer: B #### B QUESTION:How many multiples of 5 are there between 5 to 95? options: A)9 B)18 C)17 D)16 E)15 SOLUTION:As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the unit’s place). So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. Answer C #### C QUESTION:The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by? options: A)2.0% B)3.2% C)3.9% D)4% E)5.1% SOLUTION:Net growth on 1000 = 32-10 = 20 Net growth on 100 = 20*100/1000 = 2.0% Answer is A #### A QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C? options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480 SOLUTION:Explanation : Amount of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400 Answer : Option D #### D <<<Examples ends QUESTION:Two sides of a triangle have lengths q and y and meet at a right angle. If the perimeter of the triangle is 4q, what is the ratio of q to y ? options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1 SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8q = 6y --> q/y = 3/4. Actually B is the right answer. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:John and Jacob set out together on bicycle traveling at 12 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible) options: A)3 B)2 1/3 C)3 1/2 D)4 E)4 1/2 SOLUTION:John's speed - 12 miles/hr Jacob's speed - 9 miles/hr After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles. Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles. Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr. Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours Answer B #### B QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. options: A)530 B)675 C)330 D)987 E)854 SOLUTION:Let x e the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. #### B QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)15,2 B)15, 4 C)15, 8 D)15, 5 E)15,7 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer:D #### D QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (36 + 36)*5/18 = 4*5 = 20 mps. The time required = d/s = 100/20 = 5 sec. Answer : C #### C QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph? options: A)21.4 sec B)77 sec C)25 sec D)18 sec E)17 sec SOLUTION:D = 100 + 150 = 250 S = 42 * 5/18 = 11.7 mps T = 250/11.7 = 21.4 sec Answer:A #### A QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3*1*10+3*10*10 = 330 ANSWER:A #### A QUESTION:The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is : options: A)120 B)123 C)125 D)128 E)130 SOLUTION:Time from 11 May to 10 September, 1987 =21+30+31+31+10 = 123 days Time : 123 days = 123/365 year S.I =(7300x123x5)/(365x100)=Rs.123 answer :B #### B QUESTION:In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/6 of the absentee ballets were thrown out and 3/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)4,000 D)8,000 E)9,000 SOLUTION:5/6 * 2/5 (total absentee votes) = 1/3 (total votes)=1/3*12000=4000 Answer is C #### C QUESTION:Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together? options: A)6 B)7 C)7.5 D)8 E)9 SOLUTION:Each day, Molly can do 1/15 of the task. Each day, Sandy can do 1/10 of the task. Each day, they can do 1/15 + 1/10 = 1/6 of the task. The task will be completed in 6 days. The answer is A. #### A QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:D is the set of all the multiples of 5 between 20 and 100. E is the set of all the factors of 999. Set D and Set E have how many numbers in common? options: A)2 B)1 C)3 D)0 E)12 SOLUTION:D is a set of multiples of 5. 999 is NOT a multiple of 5, hence none of its factors is a multiple of 5. Therefore, those two sets won't have any overlap. Answer: D #### D QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec time = (360+140)/25/2 = 500*2/25 =40sec ANSWER:A #### A QUESTION:The navy pilots are practicing flight formations. 200 pilots are practicing flying in rectangles. They want to make a rectangular formation with X planes in a row and Y planes in a column. If the number of airplanes in a row is no less than 5 and no more than 40, how many different combinations of rectangular shapes are possible? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:firstly factors of 200 = 1,2,4,5,8,10,20,25,40,50,100,200 the question says each row will have airplanes not less than 5 and not more than 40, therefore, we should be interested in the factors starting from 5 til 40 (inclusive) 5(in each row) * 40(number of columns) =200, similarly 8 * 25 10 * 20 20 * 10 25 * 8 40 * 5 total possibilities = 6 option A #### A QUESTION:The entire contents of a full sack of flour can be used to make 15 cupcakes and 10 pizzas. The same full sack of flour can be used to make 7 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made? options: A)10 B)21 1/2 C)18 3/4 D)19 E)19 1/4 SOLUTION:15x+10y=7x+14y x=1/2y. Answer B #### B QUESTION:A train running at the speed of 30 km/hr crosses a pole in 6 sec. What is the length of the train? options: A)20 m B)70 m C)50 m D)Cannot be determined E)None of these SOLUTION:Speed = 30 * 5/18 = 25/3 m/sec Length of the train = speed * time = 25/3 * 6 = 50 m ANSWER:C #### C QUESTION:In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole? options: A)16 sec B)18 sec C)19 sec D)10 sec E)17 sec SOLUTION:Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps. The distance to be covered is equal to the length of the train. Required time t = d/s = 100/10 = 10 sec. Answer: D #### D QUESTION:Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home? options: A)6 B)7 C)8 D)10 E)11 SOLUTION:It's a simple geometry problem. Look at the diagram below: Answer: E. #### E QUESTION:A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle? options: A)96 km B)100 km C)106 km D)116 km E)126 km SOLUTION:Distance covered in first two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in next two hours = 14 × 2 = 48 km Distance covered in first six hours 20 + 24 + 48 = 92 km Remaining distance = 8 km 92 + 8 = 100 km Answer B #### B QUESTION:A man buys s cycle for $100 and sells it at a loss of 30%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 70% of the $100 = 70/100 * 100 = $70 Answer is C #### C QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 78. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 81 C)(c) 82 D)(d) 65 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (78-6)/6+1=13 such multiples. So, final number of sets is 13*5=65 Answer: D #### D QUESTION:If three sides of the triangle are 8 , 15 and A respectively then the how many values can A ? options: A)[A] 6 B)[B] 7 C)[C] 8 D)[D]9 E)[E] infinite number of values SOLUTION:Needed: How many Values can A take Concept: Sum of any two sides of a triangle is greater then the third side. Case 1: 8+5 > A => A<13 Case 2: 5+A > 8 => A >3 Case 3: 8+A > 5 => A > -3 (Always true since A is one side of a Triangle) Finally, 3 < A < 13. So, we can have infinite number of sides between 3 and 13. Answer = E PS: If question said A can take only integer value, the A = 9. Answer choice D. #### D QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places? options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5 SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset. Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300 Number CA possible = 1C1 = 1 Number FL possible = 1C1 = 1 Number HI possible = 1C1 = 1 Number other possible = 47C1 = 47 Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes) P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900 Answer: D #### D QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008? options: A)Monday B)Tuesday C)Wednesday D)Friday E)Sunday SOLUTION:The year 2007 is an ordinary year. So, it has 1 odd day. day of the year 2007 was Monday day of the year 2008 will be 1 day beyond Monday Hence, It will be Tuesday. answer : B #### B QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $280. Find the original price of petrol? options: A)$11 B)$5 C)$45 D)$400 E)$6.2 SOLUTION:Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 280/45=$6.2 Answer: E. #### E QUESTION:There are two bridges running parallel over river Kauvery, and they are 1 KM apart. A man started rowing the boat upstream under first bridge, his hat fell into river while he was exactly under second bridge. He realized that after 15 mts, and started rowing in opposite direction, he eventually caught his hat under First Bridge. What is the speed of river Kauvery? options: A)5km/h B)4km/h C)3km/h D)1km/h E)2km/h SOLUTION:Let the upstream velocity=xkm/h so he goes first 1 km then 15 min with this velocity so total goes=x*15/60+1 km=x+4/4 km and now he in downstream cover this distance in 15 min so his downstream velocity=x+4/4*15=x+4/60 now speed of river=1/2[downstream speed-upstream speed] =1/2[x+4/60-x/60]km/min =2km/h ANSWER:E #### E QUESTION:Which of the following is(are) true for a@b=b@a? I. a@b=b+ba II. a@b=(a+b)(a-b) III. a@b=(a/b)+(b/a) options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X). If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O). If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O). Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4? options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3 SOLUTION:We can have 6 different outcomes on a dice. Total outcomes on two dices = 6*6 We need only the cases where total sum of the numbers on the dices is 4 They can be {1, 3}, {2, 2}, {3, 1} A total of 3 outcomes Probability = favorable outcomes/ total outcomes = 3/36 = 1/12. Option A #### A QUESTION:A train 280 m long, running with a speed of 63 km/hr will pass a tree in? options: A)18 sec B)16 sec C)19 sec D)11 sec E)12 sec SOLUTION:: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec Answer: B #### B QUESTION:A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long? options: A)38 sec B)35 sec C)44 sec D)40 sec E)50 sec SOLUTION:Explanation: Speed = 45 km/hr = 45×(10/36) m/s = 150/12 = 50/4 = 25/2 m/s Total distance = length of the train + length of the platform = 360 + 140 = 500 meter Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds Answer: Option D #### D QUESTION:An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? options: A)520 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (240 x 5) = 1200 km. Speed = Distance/Time Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours] Required speed = 1200 x 3 km/hr = 720 km/hr. 5 E #### E QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 90 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)32 E)40 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 90 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 90 = 110. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 60 = 40. Thus E is the correct answer choice #### E QUESTION:In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 6 consecutive days in Rwanda? options: A)4/7 B)3/7 C)15/64 D)4/28 E)28/135 SOLUTION:using Binomial. theorem nCr (p)^r (q)^n-r 6C4 (1/2)^4 (1/2)^r which is 15/64 Answer is C. #### C QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is: options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (30 x 3) = 90 …. (i) A + B = (25 x 2) = 50 …. (ii) B + C = (28 x 2) = 56 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 106 …. (iv) Subtracting (i) from (iv), we get : B = 16. B’s weight = 16 kg. Answer E #### E QUESTION:Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: options: A)175.5 B)170 C)169.5 D)180 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. average price = 126+135/2 = 130.50 o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x - 153 = 22.50 x = 175.50 ANSWER A #### A QUESTION:What is the greatest prime factor of (11!10!) + (11!12!)? options: A)11 B)17 C)19 D)23 E)29 SOLUTION:11!10! + 11!12! = 11!10! (1+11*12) = 12!11!(133) = 12!11!(7*19) The greatest prime factor is 19. The answer is C. #### C QUESTION:If 5^29 * 4^15 = 2 * 10^n, what is the value of n? options: A)11 B)21 C)22 D)29 E)32 SOLUTION:My attempt: 5^(29) * 4^(15) = 2*10^p 5^(29) * 2 ^ (30) = 2 * (2*5)^p 5^(29) * 2 ^ (30) = 2 * 2^(p) * 5^(p) 5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p) => (p+1) = 30 => p = 29 Answer: 29 (D) #### D QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={13,13,13...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)a) k(n+m+mn)+ k B)b) (1+n+m+mn)(k+1) C)c) k^2(mn+n/m) D)d) kmn(k+m+n) E)e) None of the above. SOLUTION:a) how many 2's are included? b) how many 3's are included? and c) how many 11's are included? For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers. NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations. The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together: (mn + m + n + 1)(k + 1). Mike B #### B QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:Tharak covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph? options: A)3 hours 12 minute B)2 hours C)4 hours 40 minutes D)3 hours 20 minutes E)3 hours 18 minute SOLUTION:Let x be no. Of hours, and he travelled at 20kmph. And balance distance (8-x)hr at 70kmph. Total distance=20x+(8-x)hr =400 20x+(8-x)70=400 20x+560-70x=400 20x-70x=400-560 -50x=-160 x=3.2 =3 hr 12minutes ANSWER:A #### A QUESTION:The remainder obtained when a prime number greater than 4 is divided by 4 is options: A)a) 1 or 3 B)b) 1 or 5 C)c) 3 or 5 D)d) 4 or 5 E)e) 5 SOLUTION:The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 4, i.e. 7 and 5: 7/4 = 1 + remainder of 3 5 / 4 = 1 + remainder of 1 This is already sufficient to see that answer choice a) is correct. A #### A QUESTION:In how many ways the word "KIT" can be arranged? options: A)6 B)8 C)18 D)21 E)24 SOLUTION:Explanation : The required number of ways = 3! = 6 Answer : A #### A QUESTION:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there. It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week). We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat). => 3* odd is again odd. 2 * age of students is always even. So final equation is even +odd = odd. Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer A. #### A QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? options: A)671.5 B)600 C)672.5 D)673 E)773.5 SOLUTION:Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds; Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours; So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time). Answer: B. #### B QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)42 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/5 = 3x => x = 20/3. So, speed of the faster train = 40/3 = 40/3 * 18/5 = 42 km/hr. Answer:D #### D QUESTION:If n is an integer, which of the following CANNOT be a factor of 3n+4? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well. Answer: C. #### C QUESTION:A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system correct answer D #### D QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow? options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10% So 8100+15100⋅x+10100⋅(8100−x)=9100 Therefore 8100+320x+110(8100−x)=9100 120x=190 x=3800 Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres correct answer is D)4370 lt #### D QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 20:50:80. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)520 B)640 C)700 D)750 E)800 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 20:50:80 Initial soap:alcohol = 20/50 =20:50 after doubled soap:alcohol =2* 20/50 = 40:50 Initial soap:water = 20/80=20:80 after halved soap:water: 1/2 * 20/80 = 10/80 = 10:80 After soap: alcohol:water --> 40:50:320-->4:5:32 given alcohol 100 cubic centimeter. ratio is 80:100:640(4:5:32) For 100 cubic centimeter of Alcohol --- 640cubic cm water is required. Answer-B #### B QUESTION:There are 12 cans in the refrigerator. 8 of them are red and 4 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)460 B)490 C)493 D)455 E)424 SOLUTION:Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator = total ways to pick 4 can out of 12 - ways to pick 4 red out of 8 red - ways to pick 4 blue out of 4 blue 12C4−8C4−4C4=495−70−1=424 ANSWER:E #### E QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A. options: A)256 B)388 C)379 D)277 E)122 SOLUTION:Explanation: (3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 672 = 256 Answer: A #### A QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:If a^2+b^2=177and ab=54 then find the value of a+b/a-b? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:(a+b)^2=a^2+b^2+2ab=117+2*24=225 a+b=15 (a-b)^2=a^2+b^2-2ab=117-2*54 a-b=3 a+b/a-b=15/3=5 Answer is C. #### C QUESTION:Which of the following is an integer? I. 9! / 6! II. 9! / 8! III. 9! / 7!5! options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:9!/6! = 9*8*7 which is an integer. 9!/8! = 9 which is an integer. 9!/7!5! = 9*8 / 5*4*3*2 = 3/5 which is not an integer. The answer is D. #### D QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)37.5 B)40 C)50 D)48 E)52 SOLUTION:Dividend on 1 share = $(10/100*50) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(100*2/25*5)=40 Thus, cost of 1 share =$40 ANSWER B #### B QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds? options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these SOLUTION:First cart speed will be 24/3=8 Second cart speed is 120/2=60 So, ratio is 8/60=2/15 ANSWER:A #### A QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:A division of a company consists of six men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/11 D)5/12 E)7/15 SOLUTION:Total number of ways to select 2 members = 11C2 = 55 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/55 = 2/11 The answer is C. #### C QUESTION:If the sum of 5 consecutive integers is y, which of the following must be true? I. y is an even number II. y is an odd number III. y is a multiple of 5 options: A) I only B) II only C) III and II only D) I and III E) III only SOLUTION:I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true. II. Same as above. This need not be always true. III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4) = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases. Therefore E is the answer. #### E QUESTION:Find the invalid no.from the following series 15 46 63 71 75 77 78 options: A)32 B)35 C)46 D)49 E)67 SOLUTION:In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46 C #### C QUESTION:Mark drove for 1/2 of the trip, and Justin drove for 1/4 of the trip. Gina and Kaitlyn divided the rest of the driving evenly between them. If the entire trip was 128 miles, how many miles did Kaitlyn drive? options: A)26 miles B)16 miles C)20 miles D)18 miles E)17 miles SOLUTION:1/2 x 128 = 64 miles Mark drove 1/4 x 128 = 32 miles Justin drove 64 + 32 = 96 miles driven 128 - 96 = 32 miles left 32 ÷ 2 = 16 miles driven by Kaitlyn correct answer B #### B QUESTION:One out of every 4000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch? options: A)450 B)900 C)90,000 D)1800,000 E)900,000 SOLUTION:(D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 4000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/4000 = 450/y. Solve for y and you will get the total number of chips in the batch: 1800,000. The answer is (D). #### D QUESTION:Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 30 are on geology, and 100 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? options: A)81 B)159 C)166 D)285 E)304 SOLUTION:I solve it using the tough luck technique: According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject. 80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=100>80 Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives. We picked: 50 Botany Books 65 Zoology Books 30 Geology Books Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!! Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick 79*2+1 books Because, we could have picked the books in following order; 1st book picked: Physics 2nd book picked: Chemistry 3rd book picked: Physics Thus, Total= 50+65+30+79*2+1=145+1+158=304 Ans:E #### E QUESTION:Find the compound interest on $1000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$82.43 C)$954.26 D)$745.69 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 1000*(1 + 2/100)^4 = 1000 * 51/50 * 51/50 * 51/50 * 51/50 = $1082.43 C.I. = 1082.43-1000 = $82.43 Answer is B #### B QUESTION:A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 5 inches B)b) 6 inches C)c) 7 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 25=5*5 35=5*7 GCF = 5 P.S you can make squares with side of 5 Answer : A #### A QUESTION:Mr. Sane invested a total amount of 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was 3,620, what was the amount invested in scheme B? options: A)8,000 B)8,600 C)8,150 D)Data inadequate E)None of these SOLUTION:% interest on total amount per annum = 3620×100/16500×2=362/33% Now, use Alligation method. Hence, ratio of amount invested in schemes A and B = (12 - 362⁄33) : (362⁄33 - 10) = 17 : 16 Hence, amount invested in B = 16×16500/(17+16)=8000 Answer A #### A QUESTION:If (2/3)^n=(3/2)^3, what is the value of n? options: A)-3 B)-2 C)-1 D)0 E)1 SOLUTION:(2/3)^n = (3/2)^3 = (2/3)^-3 n = -3 (Answer = A) #### A QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)Rs.7288 B)Rs.2542 C)Rs.2522 D)Rs.2625 E)Rs.6271 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)376 C)1267 D)198 E)621 SOLUTION:624/6 = 104 kmph Answer: A #### A QUESTION:What is the median from the below series 92, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)82 C)92.25 D)98 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88,92, 93, 95, 96, 98 The median quiz score was 92.25 (Four quiz scores were higher than 92.25 and four were lower.) C #### C QUESTION:The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area? options: A)1:1 B)1:9 C)1:3 D)1:4 E)1:3 SOLUTION:1:4 Answer: D #### D QUESTION:The average age of the district level hockey team of eleven is 35 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ? options: A)43 yrs. B)44 yrs. C)45 yrs. D)47 yrs. E)46 yrs. SOLUTION:Explanation: Total age of players in team = 35 x 11 = 385 When coach is included, total members = 12, Avg age increases by one becomes 23 Total age when coach is included = 36x12 = 432 Age of coach = 432-385 = 47 yrs. Answer:D #### D QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train? options: A)7:00 B)8:00 C)9:00 D)10:00 E)11:00 SOLUTION:In one hour and thirty minutes the first train travels 105 km. The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h. The second train will catch the first train in 105/10 = 10.5 hours, so at 9:00 pm. The answer is C. #### C QUESTION:Out of a classroom of 6 boys and 5 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions? options: A)2/33 B)4/33 C)2/165 D)4/165 E)7/165 SOLUTION:The number of ways to choose three people is 11C3=165. The number of ways to choose three girls is 5C3=10. P(only girls are chosen)=10/165=2/33 The answer is A. #### A QUESTION:The average successfull Search time for sequential search on n items is options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1 SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison. Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons. Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons. so we can write total search time will be: (1+2+3+........+n) average search time will be (1+2+3+........+n)/n NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2 ANSWER: C #### C QUESTION:If each day a tree loses half its remaining leaves, what fraction of its leaves will it have lost after 4 days ? options: A)X-1/8 B)X-1/16 C)X/8 D)X/16 E)X/32 SOLUTION:LET NO OF LEAVES IX X ..IST DAY X/2 ..2ND DAY X/4 ..3RD DAY X/8 , FOURTH DAY X/16 , 5TH DAY X/32 , 6TH DAY X/64 SO ON SO FOURTH. FINALLY ON LEAVE WILL BE LEFT ..SO ON 3RD DAY LEAVE LOST IS X-1/16 ANSWER B #### B QUESTION:A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many art books were there at the starting? options: A)1355 B)1350 C)1450 D)1600 E)2000 SOLUTION:science books sold = 2x × 0.2 = 0.4x science books unsold = 2x – 0.4x = 1.6x art books sold = 5x × 0.2 = x art books unsold = 5x – x = 4x total books unsold = 1.6x + 4x = 5.6x 5.6x = 2240 x = 400 2x science = 800 and 5x art books = 2000 E #### E QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 8 years? options: A)3 : 2 B)1 : 3 C)2 : 3 D)3 : 1 E)1 : 4 SOLUTION:Explanation : Simple Interest = PRT/100 Here Principal(P) and Rate of Interest (R) are constants Hence, Simple Interest ∝ T Required Ratio = Simple Interest for 2 years/Simple Interest for 8 years =T1/T2 =2/8 =1/4 =1:4 Answer : Option E #### E QUESTION:If 16% of 40% of a number is 3, then the number is options: A)200 B)225 C)46.875 D)320 E)None of these SOLUTION:Explanation: Let 16/100×40/100×a=3 a = 3×100×100/16×40=46.875 Correct Option: C #### C QUESTION:A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)30 B)60 C)75 D)90 E)105 SOLUTION:Answer : A Let number of notes of each denomination be x. Then, x + 5x + 10x = 160 16x = 160 x = 10. Hence, total number of notes = 3x = 30. #### A QUESTION:A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 95, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? options: A)74 B)75 C)76 D)77 E)81 SOLUTION:ratio is 4:6:5 , numbers are 4x, 6x, 5x total scores of each class is (65*4x + 6x * 95 + 77*5x) = 260x+570x+385x = 1215x total number of students = 15x average = 1215x/15x = 81 E is the answer #### E QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 2/5 Km B)3 1/5 Km C)3 1/7 Km D)4 1/5 Km E)4 2/5 Km SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km B) #### B QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)100 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer C, 50 cans #### C QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = p*r*t/100 = 1000000*4*3/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is options: A)280 B)285 C)290 D)295 E)275 SOLUTION:Explanation: As the month begin with sunday, so there will be five sundays in the month. So result will be: =(510×5+240×25 / 30)=(8550 / 30)=285 Option B #### B QUESTION:If w persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job? options: A)z B)x C)x/y D)z/x E)y/z SOLUTION:the Q doesn't seem to be having the any correct answer as a choice.. since we are looking for days, lets keep days in end and work out a solution.. w person can do z jobs in y days.. so w person can do 1 job in y/z days.. and 1 person can do 1 job in y^2/z days.. so y person can complete 1 job in y^2/zy=y/z.. so the answer should be y/z=E #### E QUESTION:In an election between two candidates, the winner has a margin of 10% of the votes polled. If 3000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election? options: A)23000 B)22000 C)20000 D)25000 E)30000 SOLUTION:Winner - Looser 55% - 45% If 3000 people change their mind and vote for the loser: Winner - Looser 45% - 55% Thus 3,000 people compose 10% of all voters, which means that the total number of votes is 30,000. Answer: E. #### E QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good. options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980 SOLUTION:Let actual price was 100. After three successive discount this will become, 100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4 Now Compare, 68.4 = 6400 1 = 6400/68.4 100 = (6400*100)/68.4 = Rs. 9357. Answer: Option D #### D QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 7 C) 5 D) 9 E) 12 SOLUTION:If x=6 and y=4, then x^2-y^2=20and 20 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:If a positive odd integer N has p positive factors, how many positive factors will 3N have ? options: A)p B)2p C)P+1 D)2p+1 E)Cannot be determined SOLUTION:I have added some extra text to make this question more GMAT-like: Let's TEST some values of N Try N = 3 The factors of 3 are {1, 3}. Here, p =2 So, 2N = (2)(3) = 6 The factors of 6 are {1, 2, 3, 6}. So, we have a total of4 Now check the answer choices: A) p =2No good. We want an output of4. ELIMINATE B) 2p = (2)(2) = 4. PERFECT! KEEP B C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE E) Cannot be determined. POSSIBLE. KEEP E Let's TEST another value of N Try N = 7 The factors of 7 are {1, 7}. Here, p =2 So, 2N = (2)(7) = 14 The factors of 14 are {1, 2, 7, 14}. So, we have a total of4 Now check the REMAINING answer choices: B) 2p = (2)(2) =4. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E Let's TEST one more (non-prime) value of N Try N = 9 The factors of 9 are {1, 3, 9}. Here, p =3 So, 2N = (2)(9) = 18 The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6 Now check the REMAINING answer choices: B) 2p = (2)(3) =6. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E At this point, it SEEMS LIKELY that the correct answer is C #### C QUESTION:A certain elevator has a safe weight limit of 1950 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 190 pounds and the average weight of the others being 200 pounds? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Lets assume there are 2X people. Half of them have average weight of 190 and other half has 200. Maximum Weight is = 1950 So 190*X + 200*X = 1950 => 390X = 1950 => X is approximately equal to 5. So total people is 2*5 = 10 Answer D. #### D QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 40 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)96 C)100 D)125 E)250 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 5.6 , so radius is 2.8 New area = 7.84π Increase in area is 3.84π % increase in area = 3.84/4*100 So, % increase is 96% Answer will be (B) #### B QUESTION:Median H of price of the car is 52,000. which could be the median of the other two. 35000, 44000, x, y, 57000. options: A)38000 B)47000 C)48000 D)51,000 E)56,000 SOLUTION:Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits H is 56,000.E #### E QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M? options: A)278 B)2890 C)270 D)2702 E)1050 SOLUTION:504/M = 384/800 (504 * 800) / 384 = M M = 1050 Answer:E #### E QUESTION:One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met? options: A)38.07 B)40 C)42 D)39 E)40.07 SOLUTION:Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows 9t + 8(t + 1) = 80 9t + 8t + 8 = 80 17t = 72 T = 4.23 (hours) Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A. #### A QUESTION:Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen options: A)44/221 B)55/221 C)76/221 D)45/221 E)63/221 SOLUTION:WE HAVE N(S)=52C2=(52*51)/(2*1)=1326. LET A=EVENT OF GETTING BOTH BLACK CARDS B=EVENT OF GETTING BOTH QUEENS AB=EVENT OF GETTING QUEEN OF BLACK CARDS N(A)=26C2=(26*25)/(2*1)=325, N(B)=4C2=(4*3)/(2*1)=6 AND N(AB)=2C2=1 P(A)=N(A)/N(S)=325/1326; P(B)=N(B)/N(S)=6/1326 AND P(AB)=N(AB)/N(S)=1/1326 P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221 Option: B #### B QUESTION:The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January? options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500 SOLUTION:Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8600 = 34400 ----(2) (2)-(1) i.e. May - Jan = 2400 Salary of May is Rs.6500 Salary of January = Rs.4100 Answer:A #### A QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? options: A)10 hours B)17 hours C)19 hours D)16 hours E)27 hours SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:The line CD is parallel to AB and crosses the angle BOA so that O,B,D lie on the same line and so do O,A,C. If OA=2, AC=4 and BD=6, determine the length of OB. options: A)3 B)4 C)5 D)6 E)7 SOLUTION:Solution: The lines AB and CD are parallel, so by the intersect theorem, we have OB/BD=OA/AC, or OB=OA/AC.BD=2/4.6=3 Answer A #### A QUESTION:The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5/18 = 30 m/s Hence time taken to cover 330 m = 330/30 = 11 seconds. Answer: A #### A QUESTION:If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ? options: A)16 B)1.6 C)0.16 D)0.016 E)None of these SOLUTION:Explanation : (204/12.75) = 16 ⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10) ⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B #### B QUESTION:Next number in the series is 1 , 2 , 4 , 13 , 31 , 112 , ? options: A)221 B)222 C)223 D)224 E)225 SOLUTION:In Base 5 1 (1), 2(2) , 4(4) , 13(8) , 31(16) , 112(32) ,224(64) ANSWER:D #### D QUESTION:A group of tourists wants to visit at least three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary. options: A)24 B)36 C)48 D)60 E)64 SOLUTION:The number of ways to choose three cities is 4C3=4. The number of itineraries for each group of 3 cities is 3!. So the number of itineraries to three cities is 4*3!=24. The number of ways to choose four cities is 4C4=1. The number of itineraries for the group of 4 cities is 4!. So the number of itineraries to four cities is 4!=24. The total number of itineraries is 24+24=48. The answer is C. #### C QUESTION:A dragon has 100 heads. A soldier can cut off 15, 17, 20 or 5 heads, respectively with one blow of his sword. In each of these cases, 24, 2, 14, 17 new heads grow on its shoulders. If all heads are cut off, the dragon dies. Can the dragon ever die? options: A)61 B)3 C)5 D)6 E)1 SOLUTION:Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die. Answer:B #### B QUESTION:Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/10 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now? options: A)$110 B)$152.3 C)$180 D)$220 E)$260 SOLUTION:Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition. A-E = 1/10*(A+E) ==> 9A = 11E ------------ (1) Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E 1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2) Substituting (1) in (2): 11E/9*11 = 220+12E or (121/9-12) E = 220 or 13/9 E =220 E = 220*9/13 =152.3 B #### B QUESTION:In how many ways can a cricket eleven be chosen out of a batch of 15 players ? options: A)1365 B)5263 C)4512 D)7845 E)1549 SOLUTION:Required number of ways = 15c11 = 15c(15-11) = 11c4 = 15x14x13x12/4x3x2x1 = 1365. Ans: A #### A QUESTION:Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood? options: A)a) 90 B)b) 100 C)c) 110 D)d) 130 E)e) 140 SOLUTION:C. 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3rd piece (sorted in increasing length) length = 140 (median) for sum of first 2 wood length to become max, last two should be least. let 4th, 5th wood also have length 140 each. total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220/2 = 110 Answer C #### C QUESTION:David obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? options: A)75 B)27.6 C)66.6 D)16.5 E)11 SOLUTION:Explanation: Average = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6. Answer:C #### C QUESTION:On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price Q per glass on the second day? options: A) $015 B) $0.20 C) $0.30 D) $0.40 E) $0.45 SOLUTION:On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade; On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade; So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3. We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day. Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4. Answer: D. #### D QUESTION:A fruit seller had some oranges. He sells 40% oranges and still has 300 oranges. How many oranges he had originally? options: A)420 B)700 C)220 D)500 E)None of these SOLUTION:Explanation : He sells 40% of oranges and still there are 300 oranges remaining => 60% of oranges = 300 ⇒ (60 × Total Oranges)/100 = 300 ⇒ Total Oranges/100 = 5 ⇒ Total Oranges = 5 × 100 = 500 Answer : Option D #### D QUESTION:he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person ? options: A)75 kg B)55 kg C)80 kg D)85 kg E)25 kg SOLUTION:Explanation: Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (60 + 20) kg = 80 kg. Answer: C #### C QUESTION:Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is? options: A)98% B)56% C)96% D)964% E)16% SOLUTION:I II III 120 125 100 125----------120 100-----------? => 96% Answer:C #### C QUESTION:A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting? options: A)12 B)22 1/2 C)37 1/2 D)88 E)80 SOLUTION:(16/2) ( 2+3) * 2 = 80=E #### E QUESTION:The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 30 brand B widgets, 30 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x? options: A)0.02 B)0.095 C)0.03 D)0.0275 E)0.4 SOLUTION:Given probability of defective items in each brand, So, the number of items defective in brand A=x*40, in brand B=0.06*30 and brand C=0.08*30 Total number of widgets=40+30+30=100 the probability that the widget selected is defective is 0.053=(x*40+0.06*30+0.08*30)/100 => 40x+1.8+2.4 =5.3 =>40x=1.1 >x=1.1/40=0.0275 Ans D #### D QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14 SOLUTION:answer isB Total probability=7C3=48 4C3 +4C2*4C1+4C1*4C2=4+24+24=42 therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8 B #### B QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1⁄7 hours B)6 2⁄7 hours C)8 2⁄7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 × 2 = 16 km Distance covered in next two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 – 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. ∴ Time taken = 4⁄12 = 1⁄3 hour. Total time= 6 + 1⁄3 = 6 1⁄3 hour Answer E #### E QUESTION:There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends? options: A)1 B)10 C)125 D)50 E)20 SOLUTION:25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125 so 125 enrolled for swimming Answer: C #### C QUESTION:The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 252° of the circle, what percentage of MegaTek employees are in manufacturing? options: A)20% B)25% C)30% D)35% E)70% SOLUTION:ANSWER: E 252° divided by 360° equals 0.7, therefore the sector is equal to 70% of the total #### E QUESTION:The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to x% of stall’s revenue and accounted for y% of sales of juice tetra packs. Which of the following expresses x in terms of y? options: A)100y/(150 – y) B)200y/(250-y) C)200y/(300-y) D)250y/(400-y) E)300y/(500-y) SOLUTION:1. Let the number of units sold be 100. Then y units of A are sold and (100-y) units of B are sold. Total revenue= Revenue due to A + Revenue due to B = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B) = y *1 + (100-y) *1.5 = y + (150-1.5y) --- (1) 2. But we know, revenue due to A = x%. of the total revenue --- (2) 3. To express x in terms of y we need to relate (1) and (2) 4. x% = y / ( y + (150-1.5y)) or x= 100y / 150-0.5y = 200y/(300-y) C #### C <<<Examples ends QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article? options: A)2777 B)2987 C)1200 D)1240 E)1671 SOLUTION:CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 Answer: D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds? options: A)186 B)130 C)180 D)181 E)120 SOLUTION:LCM of 9, 12, 15 and 18 is 180 LCM=180 ANSWER:C #### C QUESTION:A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? options: A)A B)B C)C D)all alike E)None of these SOLUTION:Let B = 100 A = 50 C * (150/100) = 50 3C = 100 C = 33.3 then 'C' Cheapest ANSWER:C #### C QUESTION:It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number X? options: A)a. 2^96 + 1 B)b. 2^16 - 1 C)c. 2^16 + 1 D)d. 7 * 2^33 E)e. 2^64 + 1 SOLUTION:a³ + b³ =(a+b)(a² -ab +b²) Now, let (2^32 + 1) be (a+b) a³ + b³ = (2^96 + 1) Now, as mentioned in formula above, a³ + b³ is always divisible by (a+b) So any factor of X=(a+b) is a factor of (a³ + b³) Henca A #### A QUESTION:At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? options: A)5% B)3 1/2% C)4% D)5 1/2 % E)6% SOLUTION:150 = (750*5*R)/100 R = 4% Answer :C #### C QUESTION:Shopkeeper rise price by 32% and gives successive discount of 10% and 15%. What is overall % gain or loss? options: A)0.98% B)4.98% C)3.95% D)6.98% E)7.98% SOLUTION:Let d initial price be 100 32 % rise now price = 132/100*100 = 132 10% discount Then price = 132 * 90/100 = 118.8 15 % discount Then price = 118.8 * 85/100 = 100.98 So Gain = 100.98 - 100 = 0.98 Gain % = Gain * 100 /CP ==> 0.98* 100 /100 = 0.98% ANSWER:A #### A QUESTION:A student got twice as many sums wrong as he got right. If he attempted 27 sums in all, how many did he solve correctly ? options: A)12 B)16 C)18 D)9 E)12 SOLUTION:Explanation: Suppose the boy got x sums right and 2x sums wrong. Then, x + 2x = 27 3x = 27 x = 9. Answer:D #### D QUESTION:The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? options: A)c is not changed. B)c is halved. C)c is doubled. D)c is multiplied by 4. E)c is multiplied by 16. SOLUTION:a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. E c is multiplied by 16. #### E QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? options: A)112 B)50 C)77 D)14 E)12 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B #### B QUESTION:A train 310 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? options: A)4 B)6 C)5 D)17 E)13 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [310 * 3/55] sec = 17 sec ANSWER:D #### D QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.3 x = 4.8 Alternate solution: Try to backsolve. Initial volume = 4.8 After one hour --> (1/4)4.8 = 1.2 After two hours --> (1/4)1.2 = 0.3 Answer: C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? options: A)150 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer: A #### A QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:If the President and Vice President must sit next to each other in a row with 2 other members of the Board, how many different seating arrangements are possible? options: A)10 B)16 C)18 D)12 E)18 SOLUTION:We need to take President and VP as one unit. Therefore we have 3 people to arrange=3! ways Also, we both President and VP can be arranged in 2 ! ways. Reqd no of ways=3!*2!=12 ways Answer D #### D QUESTION:The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A? options: A)81 B)65 C)75 D)89 E)90 SOLUTION:A + B + C = 3 *70 = 210 A + B + C + D = 4 * 70 = 280 ---- (i) So, D = 70& E = 70 + 3 = 73 B + C + D +E =68 * 4 = 272 --- (ii) From Eq. (i) & (ii) A-E = 280 –272 = 8 A = E +8 = 73 + 8 = 81 Answer : A #### A QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)30% B)70% C)100% D)250% E)300% SOLUTION:cp = 100 profit = 320 ans SP = 420 new CP = 125% of RS 100 = Rs 125 New SP = 420 profit = (420-125) = 295 req % (295/420*100)% = 1475/21% = 70% ANSWER B #### B QUESTION:#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6? options: A)–108 B)–44 C)10 D)16 E)18.25 SOLUTION:#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer. #### E QUESTION:3x^2 + 5x - 2 = options: A)(3x-1)(x+2) B)(3x-4)(x+2) C)(3x-4)(x-2) D)(3x-2)(x+4) E)none of above SOLUTION:3x^2 + 5x - 2 = 3x^2 + 6x - x - 2 = 3x (x + 2) - (x+2) = (3x-1) (x+2) Option A #### A QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rajan? options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000 =>4:5:3 =>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...] => 12:5:6 Share of Rajan => 4600*12/23 = 2400 ANSWER:E #### E QUESTION:A committee of 3 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee? options: A)1/28 B)3/28 C)1/14 D)4/28 E)3/14 SOLUTION:3/8*4/7*1/6*3! = 3/14. We are multiplying by 3! because we can choose secretary, economist, and accountant is several way: SEA, SAE, ESA, EAS, ASE, AES. Answer: E. #### E QUESTION:In May Mrs Lee's earnings were 50 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ? options: A)55 B)56 C)34 D)78 E)23 SOLUTION:Lets say the Family Income is 100 In May, lee earned 50Family income is 50 In june, Lee earned 20% more than May, so it is (50+20*50/100 = 60) Family Income is same 50 In June Lee's Income percent is 60*100/110 ~ 55 Ans is A #### A QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)Rs.18000 B)Rs.15000 C)Rs.17000 D)Rs.14000 E)NONE SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 ANSWER:D #### D QUESTION:For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? options: A)12% B)26% C)29% D)32% E)60% SOLUTION:In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated. In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated. Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%. Answer: D. #### D QUESTION:A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? options: A)10 B)15 C)21 D)36 E)42 SOLUTION:Since the order in which we select the socks does not matter, we can use combinations. We can select 2 socks from 5 socks in 5C2 ways. 5C2 = 10 Answer : A #### A QUESTION:The area of a triangle is with base 12m and height 5m? options: A)88 m2 B)30 m2 C)66 m2 D)77 m2 E)31 m2 SOLUTION:1/2 * 12 * 5 = 30 m2 Answer: B #### B QUESTION:Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck. options: A)150 B)160 C)170 D)180 E)190 SOLUTION:Let the 1st paycheck be x (integer). Dawson got a weekly raise of $ 160. So after completing the 1st week she will get $ (x+160). Similarly after completing the 2nd week she will get $ (x + 160) + $ 160. = $ (x + 160 + 160) = $ (x + 320) So in this way end of every week her salary will increase by (B)$ 160. #### B QUESTION:A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 60% above the original cost per share of stock, then interns of m for how many dollars was each share sold? options: A)a) 2m/300 B)b) m/300 C)c) 5m/900 D)d) m/300 + 50 E)e) 350/m SOLUTION:Let Cost of 300 shares be $ 3000 So, Cost of 1 shares be $ 10 =>m/300 Selling price per share = (100+60)/100 * m/300 Or, Selling price per share = 5/3 * m/300 => 5m/900 Hence answer will be (C) #### C QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points T is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points T is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years? options: A)35 years B)77 years C)55 years D)44 years E)33 years SOLUTION:Let the present ages of X and Y be 5x and 6x years respectively. Then, (5x + 7)/(6x + 7) = 6/7 7(5x + 7) = 6(6x + 7) => x = 7 X's present age = 5x = 35 years.Answer: A #### A QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:20000*2+8*x=15665*10 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A)$140 B)$141 C)$142 D)$147 E)$145 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer D)$147 #### D QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is options: A)10% B)50% C)25% D)17.6% E)None of these SOLUTION:Explanation: cost price = (225 + 30) = 255 sell price = 300 gain = (45/255)*100 = 17.6%. Answer: D #### D QUESTION:In a group of 70 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there? options: A)1140 B)1160 C)1180 D)1200 E)1040 SOLUTION:Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12. Number of sweets 80 children got = 70 * 12 = 840. Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20. Number of sweets 10 youngsters got = 10 * 20 = 200. Total number of sweets = 840 + 200 = 1040. E) #### E QUESTION:If p ≠ 1 and if qp/(q - p) = 1, what is the value of q in terms of p? options: A)(p+1)/p B)(p - 1)/p C)p/(p + 1) D)p/(1-p) E)(1 - p)/p SOLUTION:This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator. Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one. Final Answer: D #### D QUESTION:M and N invested in a shop. The profits were divided in the ratio of 4 : 5 respectively. If M invested Rs. 40,000, the amount invested by N is: options: A)35000 B)40000 C)50000 D)60000 E)None SOLUTION:Suppose N invested Rs. x. Then, 40000/x = 4/5 or y = [40000 x 5/ 4] = 50000. Answer C #### C QUESTION:Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)18 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 2 = 26 => x = 6 So Deepak age is = 3(6) = 18 Option B #### B QUESTION:For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| = options: A)ab-4 B)2b-ab-4 C)ab+4 D)ab-2b+4 E)4-ab SOLUTION:Given: |ab| = -ab and |a| = -a Question: |b-4| + |ab-b| = ? **** Looking at |ab| = -ab tells us that either one of a or b is negative. **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: b is positive Let a=-1 and b=1 |b-4| + |ab-b| = |1-4| + |-1-1| = 5 Test a) |ab-4| = |(1)(-1)-4| = |-5|=5 Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1 Test c) ab+4 = -1 + 4 = 3 Test d) ab-2b+4 = -1-2(1)+4=1 test e) 4-1=3 ANSWER=A #### A QUESTION:21 goats eat as much as 15 cows. How many goats eat as much as 35 cows? options: A)49 B)32 C)36 D)41 E)45 SOLUTION:Explanation: 15 cows ≡ 21 goats 1 cow ≡ 21/15 goats 35 cows ≡ 21×35/15 goats ≡ 21×7/3 goats ≡ 7 × 7 goats ≡ 49 goats Answer: Option A #### A QUESTION:How many different positive integers are factors of 196 ? options: A) 1 B) 2 C) 3 D) 49 E) 36 SOLUTION:15, 14×15, 14=7^2 × 2^2 So total factors = (6+1)(6+1) = 49 Answer: D #### D QUESTION:In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can? options: A)52 B)56 C)60 D)64 E)68 SOLUTION:Let C be the capacity of the can. (5/8)*(C-20)+20=(3/4)*C 5C-100+160=6C C=60 The answer is C. #### C QUESTION:In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions? options: A)63 B)48 C)85 D)52 E)47 SOLUTION:In the given word there 6 letters in that there are 2 vowels and 4 consonants no of ways of arranging the vowels=2p2=2 no of ways of arranging the consonants=4p4=24 total number of ways 24*2=48 Answer(B) #### B QUESTION:A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office? options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h SOLUTION:u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27 \inline \Rightarrow 1.5k = 27 \inline \Rightarrow k=18km/h E #### E QUESTION:If BAT = 58 HAT = 52 CAT = 57 then whats RAT = ? options: A)42 B)45 C)34 D)76 E)25 SOLUTION:A 42 #### A QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? options: A)176 m B)198 m C)197 m D)150 m E)168 m SOLUTION:Let the length of the train be x meters and its speed be y m/sec. They, x / y = 15 => y = x/15 x + 100 / 25 = x / 15 x = 150 m. Answer:D #### D QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest? options: A)49% B)90% C)60% D)40% E)41% SOLUTION:8 = (1*20*R)/100 R = 40% Answer:D #### D QUESTION:The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers? options: A)15 B)17 C)19 D)21 E)23 SOLUTION:x,x+2,x+4 are three odd numbers (x+x+2+x+4)/3=12+(x/3) x=15 last no.=x+4=19 ANSWER:C #### C QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:In a consumer survey, 88% of those surveyed liked at least one of three products: 1, 2, and 3. 55% of those asked liked product 1, 40% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:55 + 40 + 20 = 115 This number includes some people counted twice and some people counted three times. 115 - 88 = 27, and this number represents people counted twice or three times. 7% of the people are counted two extra times. The percentage of people counted one extra time is 27 - 7(2) = 13. The percentage of people who liked more than one product is 7% + 13% = 20%. The answer is B. #### B QUESTION:Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king? options: A)1/13 B)2/15 C)4/13 D)3/17 E)1/19 SOLUTION:Here, n(S) = 52 There are 13 cards that are diamond (including one king) and there are 3 more kings. Let E = event of getting a diamond or a king. Then, n(E) = (13 + 3) = 16 P (E) = 16 / 52 = 4/13 C #### C QUESTION:Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Ram's tour programme is options: A)28 Days B)24 Days C)22 Days D)20 Days E)None of these SOLUTION:Solution: Let Ram under takes a tour of x days. Then, expenses for each day = 360/x 360/x+4=360/x−3 x=20x=20 and −24−24 Hence, x= 20 days. Option(D) #### D QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)15 bukets B)17 bukets C)18 bukets D)19 bukets E)None of these SOLUTION:Explanation: Capacity of the tank = (12*13.5) litres = 162 litres Capacity of each bucket = 9 litres. So we can get answer by dividing total capacity of tank by total capacity of bucket. Number of buckets needed = (162/9) = 18 buckets Option C #### C QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)18 B)24 C)42 D)81 E)28 SOLUTION:Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 * 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. ANSWER:B #### B QUESTION:A certain country had a total annual expenditure of $1.2x10^12. If the population of the country was 240 million last year, what was the per capita expenditure? options: A)$500 B)$1000 C)$2000 D)$3000 E)5000 dollar SOLUTION:Explanation: In scientific notation 240 million is 2.4x10^8. So the per capita expenditure was: ($1.2x10^12)/(2.4x10^8)=($1.2)/(2.4)x10^12-8=$0.5x10^4=$5000 Answer: Option E #### E QUESTION:In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the A share of profit? options: A)10600 B)10400 C)10200 D)12200 E)14200 SOLUTION:Given A=45000 B=30000 C=22500 A:B:C= 450:300:225 As A withdrew its half of capital after 4 months,it can withdraw 22500 rupees But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost 9+4=13 months.For that 9 months, the capital for A is half of its original capital, So A= 450*4+ 225*9= 1800+2025= 3825 Similarly, B= 300*13=3900 Similarly,C= 225*13= 2925 Therefore, ratio of A:B:C= 3825: 3900 : 2925= 51:52:39 A's share=51/142(28400)=10200 ANSWER:C #### C QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following numbers? options: A)4 B)3 C)7 D)6 E)9 SOLUTION:Let the consecutive even integers are n and (n + 2) difference of the squares = (n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4 = 4(n + 1) which is divisible by 4 Answer is A #### A QUESTION:A train 320 m long passed a pole in 28 sec. How long will it take to pass a platform 700 m long? options: A)12 sec B)59 sec C)93 sec D)89 sec E)46 sec SOLUTION:Speed = 320/28 = 11 m/sec. Required time = (320 + 700)/11 = 92.7 sec. Answer: C #### C QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:What is the greatest prime factor of 4^16 - 2^30? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:4^16 - 2^30 =(2^2)^16 - 2^30 = 2^32 - 2^30 = 2^30 (2^2 -1) = 2^30 * (4-1) = 2^30 * 3 The greatest prime factor is 3. The answer is B. #### B QUESTION:The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000 SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=4500pi r=15 so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx) E #### E QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted? options: A)3 B)6 C)2 D)12 E)27 SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black. But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2. Answer: C. #### C QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:If the speed of the boat in still water is 12km/hr and the speed of the stream is 5km/hr. Find the time taken to travel 34kms down stream. options: A)4 hrs. B)1 hrs. C)3 hrs. D)2 hrs. E)5 hrs. SOLUTION:DS =speed of the boat + speed of the stream 5+12 =17km/hr. Time taken to cover 34km down stream =34/17 =2hrs. Answer : D #### D QUESTION:A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water? options: A)32 kmph B)34 kmph C)30 kmph D)50 kmph E)65 kmph SOLUTION:US = 45 DS = 55 M = (45 + 55)/2 = 50 Answer:D #### D QUESTION:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:p is a positiveeveninteger with apositive units digit--> the units digit of p can be 2, 4, 6, or 8 --> In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6. Intersection of values is 6, thus the units digit of p + 2 is 6 + 2 = 8. Answer: B. #### B QUESTION:A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result? options: A)132 B)127 C)125 D)152 E)112 SOLUTION:C 125 96 passes out of 125 give an average of 76.8% #### C QUESTION:A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 8, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? options: A)20 B)22 C)24 D)27 E)30 SOLUTION:Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes Answer: D. #### D QUESTION:A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars? options: A)500 000 B)1 000 000 C)2 000 000 D)5 000 000 E)250 000 SOLUTION:The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is. 5+3+2 = 10 10/2 = X/100 000 5*100 000 = X 500 000 = X Answer: A) #### A QUESTION:The number 0.650 is how much greater than 1/8 ? options: A)½ B)21/40 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .65-1/8=x 65/100-1/8=x x=21/40 ans B #### B QUESTION:Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age? options: A)12 years B)13 years C)15 years D)14 years E)18 years SOLUTION:Let MTomy's present age be 'x' years. x+ 16 = 3(x- 4) => 2x = 28 => x = 14 years. D #### D QUESTION:A man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water? options: A)11 B)77 C)30 D)88 E)35 SOLUTION:US = 25 DS = 45 M = (45 + 25)/2 = 35 Answer:E #### E QUESTION:Median H of price of the car is 52,000. which could be the median of the other two. 35000, 44000, x, y, 57000. options: A)38000 B)47000 C)48000 D)51,000 E)56,000 SOLUTION:Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits H is 56,000.E #### E QUESTION:The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet? options: A)33 B)37 C)27 D)28 E)23 SOLUTION:Explanation: Other side = = = = 6 ft Area of closet = (6 x 4.5) sq. ft = 27 sq. ft. Answer: C) 27 #### C QUESTION:If the selling price of 8 articles is same as the cost price of 10 articles. Find the gain or loss percentage? options: A)25% B)45% C)35% D)65% E)55% SOLUTION:Let the C.P of each article be Re 1. Then, S.P of 8 articles = C.P of 10 articles = Rs. 10 Now, C.P of 8 articles = Rs. 8, S.p of 8 articles = Rs 10 Gain = Rs ( 10 - 8 ) = Rs 2. Gain% = ( 2/8 × 100 ) % = 25% Answer : A #### A QUESTION:The fourth proportional to 5, 8, 15 is: options: A)15 B)5 C)24 D)8 E)28 SOLUTION:Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : 15 : x = 5x = (8 x 15) x = (8 x 15)/5= 24. Answer is C. #### C QUESTION:Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? . options: A)20 B)30 C)50 D)80 E)100 SOLUTION:150 employees 80 are full-time 100 have worked at company X for at least a year 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? 150-80=70 employees not full time 70-20= 50 employees not full time who worked over a year 100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year ANSWER:C #### C QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)8 B)15 C)16 D)18 E)None SOLUTION:Solution Capacity of the tank = (12×13.5) litres = 162 litres. Capacity of each bucket = 9 litres. Number of buckets needed = (162/9) ‹=› 18. Answer D #### D QUESTION:The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %? options: A)18% B)20.5% C)30% D)45% E)12% SOLUTION:1800 ---- 370 100 ---- ? => 20.5% Answer:B #### B QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:A certain ski shop sells pairs of gloves in 11 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color? options: A)1/144 B)1/143 C)1/21 D)1/23 E)1/12 SOLUTION:there are 11 different colours sothere are 11 pairs of gloves dropped.. first can be any of 22..so 22/22.. second has to be its pair, which will be just one out of remaining 21.. 1/21.. overall prob=22/22*1/21= 1/21.. C #### C QUESTION:Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase? options: A)3 B)4 C)6 D)9 E)10 SOLUTION:We have 5, 10, 10 and 20 to work with From least to greatest, we have... 5 (the least) 10 15 20 25 30 35 40 45 (the greatest) Total options = 9 Final Answer:D #### D QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts and we should calculate how many sandwiches holds 1 part: 120 / 20 = 6 sandwiches in one part For bologna we have 7 parts so: 5* 6 = 30 Answer is B #### B QUESTION:The G.C.D. of 1.08, 0.33 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.33 and 0.90. H.C.F. of 108, 33 and 90 is 3, H.C.F. of given numbers = 0.03. Answer A #### A QUESTION:David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house? options: A)$96,000 B)$94,000 C)$88,000 D)$75,000 E)$40,000 SOLUTION:Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer. #### B QUESTION:The average of eleven ten prime numbers which are odd is? options: A)17.72 B)18.52 C)19.63 D)16.53 E)15.63 SOLUTION:Explanation: Sum of first 11 prime no. which are odd = 195 Average = 195/11 = 17.72 Answer:A #### A QUESTION:Three types of tea the a,b,c costs Rs. 95/kg,100/kg and70/kg respectively.How many kgs of each should be blended to produce 100 kg of mixture worth Rs.90/kg, given that the quantities of band c are equal options: A)70,15,15 B)50,25,25 C)60,20,20 D)40,30,30 E)20,30,30 SOLUTION:given quantities of b and c are equal . therefore instead of considering them as a different quantities take average of both and consider it as a single entity . so the cost of the mixture "D" (equal quantities of "B" and "C") is 170/2=85rs/kg now the tea contains only "A" of 95 rs/per and "D" of 85 rs/kg. it is clearly seen that "A" is 5 more and "D" is 5 less than the required cost per kg . therefore 50/50 will go well . A=50kg and D=50kg. (D= B&C in equal ratio). therefore B&C=25kg each . (A:B:C)=(50,25,25) ANSWER:B #### B QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)767 m B)240 m C)187 m D)176 m E)186 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m. Answer:B #### B QUESTION:At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day? options: A) 100 B) 1,800 C) 1,090 D) 200 E) 1,000 SOLUTION:Let the total number of sunlasses produced be x % of high quality sunglasses = 70% % of low quality sunglasses = 25% % of sunglasses defective = 100% - 95% = 5% But this number is given as 50 so 5% of x = 50 and x = (50)(100/5)) x = 180 Therefore there a total of 1,000 sunglasses made per day. Correct answer - E #### E QUESTION:Which number is the odd one out? 159 248 963 357 951 852 options: A)154 B)248 C)536 D)645 E)135 SOLUTION:B 248 In the rest there is the same difference between each digit, eg: 8 (–3) 5 (–3) 2. #### B QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number? options: A)9 B)11 C)17 D)13 E)15 SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7. Given (x + 1) + (x + 7) = 28 => 2x + 8 = 28 => x = 10 The third number = x + 3 = 10 + 3 = 13. Answer: D #### D QUESTION:A can do a piece of work in 13 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in? options: A)15 10/11 days B)10 10/11 days C)12 10/11 days D)19 10/11 days E)13 10/11 days SOLUTION:B (x – 5)/13 + x/20 = 1 x = 10 10/11 days #### B QUESTION:A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5% options: A)Rs 6.56 B)Rs 9.56 C)Rs 10.56 D)Rs 11.56 E)None of these SOLUTION:Explanation: 80 : 5 = 105 : x x= (5×105/80) = Rs 6.56 Option A #### A QUESTION:Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers? options: A)21, 12 B)9, 0 C)15, 6 D)10, 1 E)14, 5 SOLUTION:the larger number: x the smaller number: y twice the larger: 2x three more than five times the smaller: 5y + 3 relationship between ("is"): 2x = 5y + 3 four times the larger: 4x three times the smaller: 3y relationship between ("sum of"): 4x + 3y = 71 Now I have two equations in two variables: 2x = 5y + 3 4x + 3y = 71 I will solve, say, the first equation for x: x = (5/2)y + (3/2) Then I'll plug the right-hand side of this into the second equation in place of the "x": 4[ (5/2)y + (3/2) ] + 3y = 71 10y + 6 + 3y = 71 13y + 6 = 71 13y = 65 y = 65/13 = 5 Now that I have the value for y, I can solve for x: x = (5/2)y + (3/2) x = (5/2)(5) + (3/2) x = (25/2) + (3/2) x = 28/2 = 14 Answer: E #### E QUESTION:The line CD is parallel to AB and crosses the angle BOA so that O,B,D lie on the same line and so do O,A,C. If OA=2, AC=4 and BD=6, determine the length of OB. options: A)3 B)4 C)5 D)6 E)7 SOLUTION:Solution: The lines AB and CD are parallel, so by the intersect theorem, we have OB/BD=OA/AC, or OB=OA/AC.BD=2/4.6=3 Answer A #### A QUESTION:A committee of 7 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed? options: A)308 B)700 C)1404 D)2620 E)3510 SOLUTION:The only cases possible are : 1. 2 men and 5 women : 8C2 * 5C5 = 28 2. 4 men and 3 women: 8C4*5C3 = 280 Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed) Total possible combinations = 28+280 = 308. Thus A is the correct answer. #### A QUESTION:If x > 0 and m is x percent of y, then, in terms of x, y is what percent of m? options: A)a) 100m B)b) 1/100m C)c) 1/m D)d) 10/m E)e) 10,000/x SOLUTION:m= x/100 * y So y= 100/x *m So y= (10000/x)/100 * m E #### E QUESTION:Evaluate: |7 - 8(3 - 12)| - |5 - 11| = ? options: A)40 B)50 C)73 D)70 E)80 SOLUTION:According to order of operations, inner brackets first. Hence |7 - 8(3 - 12)| - |5 - 11| = |7 - 8*(-9)| - |5 - 11| According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence = |7 + 72| - |5 - 11| = |79| - |-6| = 79 - 6 = 73 correct answer C)73 #### C QUESTION:If n = 20! + 15, then n is divisible by which of the following? I. 15 II. 17 III. 19 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:15 divides 20! so 15 also divides 20! + 15. 17 and 19 divide 20! so they do not divide 20! + 15. The answer is A. #### A QUESTION:Two trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ? options: A)10.7 Seconds B)10.8 Seconds C)10.9 Seconds D)11.8 Seconds E)None of these SOLUTION:Explanation: Relative Speed = 60+40 = 100 Kmph = 100*(5/18) = 250/9 m/sec Distance to be covered = 140 + 160 = 300 metres Time = Distance/Speed Time=300∗9/250=54/5=10.8 seconds Option B #### B QUESTION:One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ? options: A)Rs. 130,000 B)Rs. 150,000 C)Rs. 160,000 D)Rs. 140,000 E)None SOLUTION:EXPLANATION Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then, 1/3x=1/2(350000-x) => x/3 + x/2 = 175000 => 5x/6 = 175000 => x= 175000 x 6 /5= 210000 Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000 Answer D #### D QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/4 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)7/12 B)29/60 C)17/30 D)19/30 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/2*1/3=x/6 Platinum card unspent limit is= x-1/4x=3/4x So if gold card balance is transferred then the rest unspent will be 3/4x-x/6=7/12x So the ans is A #### A QUESTION:If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true? I. xa= y II. y = 1 III. a and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2). I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2). Answer: A. #### A QUESTION:Twelve telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of five members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? options: A)120 B)126 C)792 D)1200 E)1260 SOLUTION:My ans is 12C5 = 792 C #### C QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)42 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/5 = 3x => x = 20/3. So, speed of the faster train = 40/3 = 40/3 * 18/5 = 42 km/hr. Answer:D #### D QUESTION:7, 10, 8, 11, 9, 12, ___ options: A)10 B)11 C)12 D)13 E)14 SOLUTION:10= 7+3 8 = 10-2 11= 8+3 9 = 11-2 12 =9+3 Similarly 12-2=10 ANSWER:A #### A QUESTION:In the xy-plane, line k passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line k? options: A)3x+2y-5=0 B)3x+2y+5=0 C)2x-3y-12=0 D)2x+3y=0 E)4x+3y-6=0 SOLUTION:If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line k should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A. #### A QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 --> 2x = 20 --> x = 10. --> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. Answer : C. #### C QUESTION:In the faculty of Reverse-Engineering, 100 second year students study numeric methods, 100 second year students study automatic control of airborne vehicles and 25 second year students study them both. How many students are there in the faculty if the second year students are approximately 50% of the total? options: A)340 B)335 C)370 D)360 E)350 SOLUTION:Total number of students studying both are 100 + 100 - 25 = 175 (Subtracting the 25 since they were included in the both the other numbers already). So 50% of total is 175, so 100% is 350 Answer is E #### E QUESTION:Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 450 or over 650. If the individual ranges of the three people's scores in those 4 practice tests were 30, 80 and 110, what is the difference between the maximum and minimum possible ranges of all their scores put together. options: A)90 B)120 C)50 D)70 E)100 SOLUTION:According to the information in the question the maximum range would be between 450 and 650(200). The minimum range would be the greatest range for any one individual, which is listed in the problem as 110. So the difference between these would be 200-110 or 90. Answer: A #### A QUESTION:A merchant marks his goods up by 50% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)21% B)25% C)69% D)35% E)19% SOLUTION:Let the price be 100. The price becomes 150 after a 50% markup. Now a discount of 10% on 150. Profit=135-100 35% answer D #### D QUESTION:The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)40% D)62% E)80% SOLUTION:We need multipliers. multiplier for a 10% increases = 1 + 0.10 = 1.1 multiplier for a 20% decreases = 1 – 0.20 = 0.8 multiplier for a 50% increases = 1 + 0.50 = 1.5 Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3 (0.8)*(1.5) = (0.4)*(3) = 1.2 Now, multiply this by 1.1 1.2*1.1 = 1.32 Thus, the three percent changes combined produce a 32% increase. Answer = (B). #### B QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:Sagar was riding bike towards north,turned left road 1 km turnes towrds left &road 2km found himself 1km west of starting how far did he road north? options: A)2km in north. B)2km in south. C)2km in east. D)2km in west. E)4km in north. SOLUTION:He travelled total distance of 3km. From which he travelled 1km in west. Hence in all he travelled total 2km in north. ANSWER:A #### A QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.2200, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.5500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 2200 …(i) and 4x – 2y = 2200 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 2200 -> x = 1100 P1’s income = Rs 5*1100 = Rs.5500 ANSWER:D #### D QUESTION:A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.2 hours, then the distance covered at 40 kmph is options: A)130 km B)120km C)100km D)124km E)none of these SOLUTION:Let the partial distance covered at 40 kmph be X Let the another partial distance covered at 60 kmph be (250 - x) Thus, x/40 - (250 - x)/60 = 5.2 or, x/40 + (250 - x)/60 = 5.2 or, (3x + 500 - 2x)//120 = 5.2 or 500 + x = 624 x=124 ANSWER:D #### D QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:Jerry wrote down all the positive integers that have at most 7 digits and contain only the digits 0 and 1. How many times did he write down the digit 1 ? options: A)128 B)224 C)288 D)448 E)512 SOLUTION:Jerry wrote down a total of 27 − 1 = 127 numbers (0 is missing). Add 0 to the numbers Jerry wrote. We divide the resulting 128 numbers in pairs. If x is one of the numbers Jerry wrote then we put it in pair with 1111111 − x (whose digits are also 0s and 1s). For example 1100101 is paired with 11010. In this way, we divide the numbers into 64 distinct pairs so that each number appears exactly once. Note that there are exactly 7 digits 1 in each pair. So, Jerry wrote the digit 1 exactly 64 × 7 = 448 times. correct answer D #### D QUESTION:What percent is 20% of 25%? options: A)20% B)30% C)50% D)60% E)80% SOLUTION:Required percentage = 20%/25% * 100 = 20/25 * 100 = 80% Answer is E #### E QUESTION:Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 15% and its breadth is decreased by 10%? options: A)3.5 percent increase B)9.5 percent increase C)1.5 percent increase D)3.9 percent increase E)3.5 percent increase SOLUTION:let L and B be 100 each 100 * 100 = 10000 L increase by 15% = 115 B decrease by 10% = 90 115 * 90 = 10350 3.5 percent increase ANSWER:E #### E QUESTION:If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers? options: A)108 B)99 C)128 D)135 E)143 SOLUTION:Let the 2 positive numbers x and y x+ y = 20 -- 1 x^2 - y^2 = 40 => (x+y)(x-y)=40 -- 2 Using equation 1 in 2 , we get => x-y = 2 -- 3 Solving equation 1 and 3 , we get x= 11 y= 9 Product = 11*9 = 99 Answer B #### B QUESTION:If (x-13)(x-3) < 0, which of the following must be true? options: A)x^2 + 5x + 6 < 0 B)x^2 + 5x + 6 > 0 C)5 - x < 0 D)x - 5 < 0 E)13 - x > 0 SOLUTION:(x-13)(x-3)<0 can be written as (13-x)(x-3)>0 So,to inequality hold true multiple of (13-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<13 Answer Choice E matched which says 13-x>0 or x<13,which must be true (I started to look from E to A for making easy decision first) Correct Answer E #### E QUESTION:A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)126 Kmph B)136 Kmph C)172 Kmph D)128 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 700/20 S = 35 M/Sec Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 126 Kmph Answer: A #### A QUESTION:Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology? options: A)30 B)90 C)120 D)168 E)188 SOLUTION:I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168 Using your analysis: We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168 = 232 So, in the image we know that the number of students in the zone with the black boundary = 232 Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize) And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w Since the total number of students = 400, we can write: 232 +b+w= 400 Or,b+w= 400 - 232 = 168 That is,b= 168 -w So, the maximum value ofbwill happen forw= 0 This is how we get, the maximum value ofb= 168 D #### D QUESTION:At what rate percent per annum will a sum of money double in 8 years. options: A)12.5% B)13.5% C)11.5% D)14.5% E)21.5% SOLUTION:Let principal = P, Then, S.I.=P and Time=8 years Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum. Answer: A #### A QUESTION:What is the range of all the roots of |x^2 - 5| = x ? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:we get 2 quadratic equations here .. 1) x^2-x-5=0 ....... roots 2 , -1 2) x^2+x-5=0 ........ roots -2, 1 Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations . So value of x for given equation .... x=5 or x=1 I guess range is 5-1 =4 A #### A QUESTION:The area of a triangle is with base 5.5m and height 6m? options: A)11 m2 B)16.5 m2 C)18.5 m2 D)19.5 m2 E)12 m2 SOLUTION:1/2 * 5.5* 6 = 16.5 m2 Answer: B #### B QUESTION:The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is options: A)0.4869 B)0.5904 C)0.6234 D)0.5834 E)0.2952 SOLUTION:P(winning prize atleast on one ticket) = 1 - P("Losing on all tickets") = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2) = (1.64)(0.36) = 0.5904 ANSWER:B #### B QUESTION:Which of the following is NOT the sum of the squares of two integers? options: A)36 B)37 C)65 D)146 E)147 SOLUTION:List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. (A) 36 - 9+25. NO. (B) 37 - 1+36. NO. (C) 65 - 1+64. NO. (D) 146 - 25+121. NO. (E) - must be the answer. ANSWER:E #### E <<<Examples ends QUESTION:Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window? options: A)a 100 B)b 112 C)c 90 D)d 120 E)e 30 SOLUTION:D David's position is fixed. Now we need to arrange all others around David. There are 5x4x3x2x1= 120 ways to arrange five people. #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:A monkey ascends a greased pole 12 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ? options: A)21st B)22nd C)23rd D)24th E)None of these SOLUTION:In 2 minutes, he ascends = 1 metre ∴ 10 metres, he ascends in 20 minutes. ∴ He reaches the top in 21st minute. Answer B #### B QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000*(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:For a certain exam,a score of 86 was 5 standard deviations above mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam? options: A)50 B)55 C)48 D)42 E)49 SOLUTION:Mean+5SD=86 Mean+2.5SD=67 By solving above equations we get, SD (absolute value)=7.6 Mean=48 ANS. C #### C QUESTION:The difference between simple and compound interest on Rs. 1600 for one year at 10% per annum reckoned half-yearly is? options: A)8 B)3 C)9 D)4 E)2 SOLUTION:S.I. = (1600 * 10 * 1)/100 = Rs. 160 C.I. = [1600 * (1 + 5/100)2 - 1600] = Rs. 164 Difference = (164 - 160) = Rs.4. Answer:D #### D QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:A can complete a project in 20 days and B can complete the same project in 20 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed? options: A)18 days B)27 days C)26.67 days D)16 days E)15 days SOLUTION:Let X = the number of days taken to complete the project. The amount of work done by A is (x-10) * (1/20). The amount of work done by B is (x) * (1/30). (1/20)*(x-10) + (1/20)*(x) = 1 (x/20) + (x/20) - (10/20) = 1 x/10 = 3/2 x = 15 Therefore, the answer is E: 15. #### E QUESTION:Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)21 C)25 D)26 E)24 SOLUTION:Solution Given Data 3 positive integers Average of a, b, and c = 20. So, a+b+c3a+b+c3 = 20 or a + b + c = 60 a ≤ b ≤ c Median = (a + 11) Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c Therefore, b = a + 11 Objective To find the least value of 'c' Theoretically, the least value of c is when c = b. Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11) Or 3a = 38 or a = 12.66 So, b = c = 12.66 + 11 = 23.66 However, we know that these numbers are all integers. Therefore, a, b, and c cannot take these values. So, the least value for c with this constraint is NOT likely to be when c = b Let us increment c by 1. Let c = (b + 1) In this scenario, a + (a + 11) + (a + 12) = 60 Or 3a = 37. The value of the numbers is not an integer in this scenario as well. Let us increment c again by 1. i.e., c = b + 2 Now, a + (a + 11) + (a + 13) = 60 Or 3a = 36 or a = 12. If a = 12, b = 23 and c = 25. The least value for c that satisfies all these conditions is 25. Correct answer is choice C. #### C QUESTION:A word is defined as a sequence of five dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed? options: A)124 B)150 C)212 D)243 E)316 SOLUTION:3^5 = 243 The answer is D. #### D QUESTION:What is the smallest possible common multiple of three integers, all larger than 53? options: A)27. B)54. C)846. D)19,656. E)21,924. SOLUTION:The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54. Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer B. #### B QUESTION:When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number? options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these SOLUTION:Let the first and the second numbers be x and y respect then y + 30% of x = 140% of y or, y + 0.3x = 1.4y or, 0.3x = 0.4y ∴ x : y = 0.4 : 0.3 = 4 : 3 Answer B #### B QUESTION:The sector of a circle has radius of 20 cm and central angle 135o. Find its perimeter? options: A)91.5 B)87.1 C)91.7 D)91.3 E)91.1 SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 20) + 2(20) = 47.1 + 40 = 87.1 cm Answer:B #### B QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A QUESTION:The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is options: A)112 B)22 C)56 D)27 E)35 SOLUTION:Explanation: Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4. So, the numbers 16 and 28. L.C.M. of 16 and 28 = 112. Answer: Option A #### A QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? options: A)2000 B)2200 C)3000 D)3400 E)3500 SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans Alternative 100+105+110+115=12900 430=12900 100=12900/(430)X100=3000 C #### C QUESTION:The reflex angle between the hands of a clock at 10.25 is: options: A)180º B)192 1/2 º C)195º D)197 1/2 º E)197 º SOLUTION:Angle traced by hour hand in 125/12 hrs ={(360/12)x(125/2)}º = 312 1/2 º . Angle traced by minute hand in 25 min =(360/60)x 25 º= 150º. Reflex angle = 360º -(312 1/2- 150º )= 360º - 162 1/2º= 197 1/2º . Answer: D #### D QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? options: A)35 B)36 C)37 D)43 E)39 SOLUTION:James worked for 41 hours hence he earned 40*x+5*2x=50x dollars; We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours. Answer: D. #### D QUESTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? options: A)2443200 B)3643200 C)5443200 D)1443200 E)2163200 SOLUTION:Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? A. 24 B. 36 C. 72 D. 144 E. 216 Choosing the digit for p - 9 ways; Choosing the digit for q - 8 ways; Choosing the digit for r - 7ways; Choosing the digit for s - 6ways; Choosing the digit for t - 5ways; # of permutations of 3 digits in ppqrst - 6!/2! Total: 9*8*7*6*5*6!/2!=5443200. Answer: C. #### C QUESTION:The average successfull Search time for sequential search on n items is options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1 SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison. Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons. Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons. so we can write total search time will be: (1+2+3+........+n) average search time will be (1+2+3+........+n)/n NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2 ANSWER: C #### C QUESTION:P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last? options: A)5 days B)10 days C)14 days D)22 days E)26 days SOLUTION:Explanation : Work done by P in 1 day = 1/10 Work done by Q in 1 day = 1/6 Work done by P in 2 days = 2 × (1/10) = 1/5 Remaining work = 1 – 1/5 = 4/5 Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15 Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3 Total days = 2 + 3 = 5 Answer : Option A #### A QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)198 E)200 SOLUTION:185 Answer is B #### B QUESTION:The average age of 29 students in a group is 15 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years? options: A)31 B)36 C)29 D)53 E)57 SOLUTION:age of the teacher=(29*16-29*15) =29 years. ANSWER:C #### C QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 6? options: A)1/4 B)5/36 C)2/11 D)3/13 E)1/5 SOLUTION:n(S) = 6*6 = 36 E = {(1,5),(2,4),(3,3),(4,2),(5,1)} Probability = 5/36 Answer is B #### B QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20 SOLUTION:Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(30-10) = 10 kmph => Rate in still water = 1/2(30+10) = 20 kmph Option E #### E QUESTION:The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)16 seconds B)34 seconds C)14 seconds D)18 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5/18 = 10/3 m/s Hence time taken to cover 60 m = 60*3/10 = 18 seconds. Answer: D #### D QUESTION:The average age of a husband and his wife was 23 years at the time of their marriage.After 5 years they have a one year old child.The average of the family is now? options: A)18 years B)23 years C)29 years D)26 years E)19 years SOLUTION:sum of the present age of husband, wife and child =(23*2+5*2)+1 = 57 years required average = 57/3 = 19 years. Answer :E #### E QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6500? options: A)Rs. 5870 B)Rs. 5991 C)Rs. 8870 D)Rs. 6850 E)None of these SOLUTION:Explanation: Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130 Therefore, required sale = Rs. [(6500 * 6) – 30,130] = Rs. (39000 – 30,130) = Rs. 8870 ANSWER C #### C QUESTION:The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green? options: A)21/55 B)28/55 C)34/55 D)5/8 E)139/220 SOLUTION:Prob of selecting one blue and two green is (4*8*7/12*11*10) one blue and two green can be arranged in 3!/2! ways hence the prob becomes 3*4*8*7/12*11*10=28/55 Correct answer is B #### B QUESTION:log3 N+log12 N what is 3 digit number N that will be whole number options: A)6291 B)7292 C)1728 D)1929 E)1727 SOLUTION:No of values N can take is 1 12^3=1728 ANSWER:C #### C QUESTION:Evaluate: |4 - 8(3 - 12)| - |5 - 11| = options: A)49 B)55 C)69 D)70 E)82 SOLUTION:According to order of operations, inner brackets first. Hence |4 - 8(3 - 12)| - |5 - 11| = |4 - 8*(-9)| - |5 - 11| According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence = |4 + 72| - |5 - 11| = |76| - |-6| = 76 - 6 = 70 correct answer D)70 #### D QUESTION:he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person ? options: A)75 kg B)55 kg C)80 kg D)85 kg E)25 kg SOLUTION:Explanation: Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (60 + 20) kg = 80 kg. Answer: C #### C QUESTION:If x and y are integers such that (x+1)^2 is less than or equal to 16 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy? options: A) -16 B) -10 C) 0 D) 14 E) 16 SOLUTION:(x+1)^2 <= 16 x <= 3 x >= -5 (y-1)^2< 64 y < 9 y > -7 Max possible value of xy is -5 × -6 = 30 minimum possible value of xy is -5 × 8 = -40 -40 + 30 = -10 Answer : B #### B QUESTION:The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).? options: A)180.27 cm B)180.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 182 cm. Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm = 182 cm - 1.71 cm = 180.29 cm. Answer: B #### B QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)16 SOLUTION:1. We need to find out the time taken by 7 workers after day 1. 2. total no.of wokers * total time taken = time taken by 1 worker 3. Time taken by 1 worker = 16*8 = 128 days 4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job. 5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7* total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days. 6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days. The answer is choice E #### E QUESTION:Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately. options: A)12 , 18 B)8 , 10 C)18 , 20 D)20 , 25 E)None of these SOLUTION:Explanation : Let speed of ram and shakil be x and y resp. Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute. 2000/x - 1800/y= -60 2000/x= 1800/y -60---------------------(1) Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters 1000/x = (2000- 360y)/y------------------(2) Solve equation 1 and 2 to obtain x and y Answer is x = 8 minutes, y = 10 minutes Hence (B) is the corret answer. Answer : B #### B QUESTION:If y is an integer, then the least possible value of |23 - 4y| is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We know that 4y is a multiple of 4, so let’s first look at the multiples of 4 closest to 23. We have “20” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 4y = 20, y is 5 and when 4y = 24, y is 5. Let’s start with letting y = 4. |23-4(5)| |23-20| |3| = 3 Next, let’s let y equal 5. |23-4(6)| |23-24| |-1| = 1 We see that the smallest possible value of |23-4y| is 1. Answer A. #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)227 B)268 C)240 D)889 E)232 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer:C #### C QUESTION:The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 360 metres, what is its area? options: A)1320 sq.metres B)4260 sq.metres C)6870 sq.metres D)7875 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 360 ⇒ x = 15 Area = 7 × 15 × 5 × 15 = 7875 sq.m. Answer D #### D QUESTION:Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group? options: A)87 B)67 C)23 D)75 E)25 SOLUTION:Let the initial number of members in the group be n. Initial total weight of all the members in the group = n(48) From the data, 48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23 Therefore there were 23 members in the group initially. Answer: C #### C QUESTION:Which number should replace both the asterisks in (* /18) x (*/162) = 1 ? options: A)27 B)36 C)54 D)72 E)90 SOLUTION:Let (y/18) x (y/162) = 1 y^2 = 18 x 162 = 18 x 18 x 9 y = (18 x 3) = 54 The answer is C. #### C QUESTION:Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many T applicants majored in political science and had a GPA higher than 3.0? options: A)5 B)10 C)15 D)25 E)35 SOLUTION:Total applicants = 40 Political science = 15 and Non political science = 40 - 15 = 25 GPA > 3.0 = 20 and GPA <= 3.0 = 20 10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0 GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5 Answer: A #### A QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:Jemma takes 2 hours to swim the 4 miles from buoy A to buoy B. Tired from her swim, she then continues to buoy C at half her previous speed. If buoy C is 6 miles away from buoy B, how many more hours will pass before Jemma reaches Buoy C? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Time taken for Jemma to reach buoy B is 2 hours. The distance between the buoys is 4 miles. Distance travelled/time taken = Average speed Hence the average speed to travel the distance is 2m/hr Now, she would have to travel 6 miles . However as she is tired the speed is half or 1m/hr Hence, it will take her 6 hours (Option C) #### C QUESTION:A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ? options: A)650 meter B)555 meter C)500 meter D)458 meter E)None of these SOLUTION:Explanation: Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time =>800+x=65/3∗60 =>800+x=20∗65=1300 =>x=1300−800=500 So the length of the tunnel is 500 meters. Option C #### C QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:It takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate. If 5 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 1:00 PM, at what time will the machine be complete? options: A)4:30 B)4:45 C)5:00 D)5:15 E)5:30 SOLUTION:3 workers build 1/15 of a machine in one hour. 1 worker builds 1/45 of a machine in one hour. In the first 2 hours, 5 workers build 5*(1/45)*2=10/45 of a machine. From 1:00 to 2:00, 6 workers build another 6/45. The total is 16/45. From 2:00 to 3:00, 7 workers build another 7/45. The total is 23/45. From 3:00 to 4:00, 8 workers build another 8/45. The total is 31/45. From 4:00 to 5:00, 9 workers build another 9/45. The total is 40/45. To build another 5/45, 10 workers need (5/10)*60 minutes which is 30 minutes. The machine is complete at 5:30. The answer is E. #### E QUESTION:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold? options: A) 11 B) 13 C) 15 D) 17 E) 19 SOLUTION:(x+5)*150 +x*85=2160 =>x=6 total lens=6+(6+5)= 17 Answer D #### D QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:The fourth proportional to 5, 8, 15 is options: A)18 B)19 C)20 D)24 E)None SOLUTION:Sol. Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : : 15 : x ⇔ 5x = (8x15) ⇔ x = (8x15) / 5 = 24. Answer D #### D QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12 SOLUTION:Explanation: Given numbers are 1.08 , 0.42 and 0.90 H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F] therefore H.C.F of given numbers = 0.06 Answer: C) #### C QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. options: A)12 B)14 C)15 D)16 E)17 SOLUTION:d = (D-R)/Q = (109 - 1)/9 = 108/9 = 18 A #### A QUESTION:What is the sum of the different positive prime factors of 960? options: A)5 B)10 C)15 D)17 E)21 SOLUTION:Prime factorization of 960 =96 * 10 =16*6 * 10 =4*4 * 2*3 * 2*5 =2*2 * 2*2 * 2* 3 * 2*5 =2^6 * 3 * 5 Sum of the different positive prime factors of 960 = 2+3+5 =10 Answer B #### B QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is? options: A)39yr B)42yr C)45yr D)32yr E)50yr SOLUTION:Let B's present age = x years Then A's present age = x+9 years x+9+10 = 2(x-10) x + 19 = 2x - 20 x = 39years Answer is A #### A QUESTION:The rate of Interest on a sum of money is 11% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is options: A)1,000 B)2,000 C)2,100 D)2,250 E)2,540 SOLUTION:Explanation: I1 = (P x 3 x 11)/100 = P/3 I2 = (P x 4 x 4)/100 = 4P/25 I3 = (P x 1 x 5)/100 = P/20 P/3 + 4P/25 + P/20 = 540 27P/50 = 540 P = 1000 Answer: Option A #### A QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together? options: A)16 days B)12 days C)3 days D)5 days E)9 days SOLUTION:Sol. (A + B)'s 1 day's work = (1/18) (B + C)'s 1 day's work = (1/24) and (A + C)'s 1 day's work = (1/36) Adding, we get: 2 (A + B + C)'s 1 day's work =¬(1/18 + 1/24 + 1/36) =9/72 =1/8 (A +B + C)'s 1 day's work =1/16 Thus, A, Band C together can finish the work in 16 days. Ans: A #### A QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member? options: A)13.5 B)14 C)15 D)12.5 E)None SOLUTION:Solution: At present the total age of the family = 5*20 =100. The total age of the family at the time of the birth of the youngest member, =[100−10−(10*4)]=50. Therefore, average age of the family at the time of birth of the youngest member, = 50/4 = 12.5. Answer: Option D #### D QUESTION:If, 1 * 3 * 5 = 16 3 * 5 * 7 = 38 Then find, 15 * 17 * 19 =? options: A)89 B)49 C)68 D)38 E)338 SOLUTION:E 338 (19 * 17) + 15 = 338 #### E QUESTION:A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route? options: A)12km B)15km C)18km D)24km E)Data Inadequate SOLUTION:time=distance/speed so, let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so, (x/4+y/3)+(y/6+x/4)=6 x+y=12 km. ANSWER:A #### A QUESTION:A can do a piece of work in 8 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? options: A)8.7 days B)2.0 days C)6.6 days D)7.7 days E)4.8 days SOLUTION:C = 1/2 - 1/8 - 1/8 = 5/24 => 4.8 days Answer: E #### E QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)6 E)5 SOLUTION:2x * x = 128 => x= 8 Answer: A #### A QUESTION:(3x + 2) (2x - 1) = ax^2 + kx + n . What is the value of a - n + k ? options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Expanding we have 6x^2 - 3x + 4x -2 6x^2 + x - 2 Taking coefficients, a = 6, k= 1, n = -2 Therefore a - n + k = 6 - (-2) +1 = 8 + 1 = 9 The answer is C. #### C QUESTION:The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i options: A)70 B)72 C)75 D)78 E)80 SOLUTION:Income of 6 months = (6 × 85) – debt = 510 – debt Income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ Income of 10 months = 780 Average monthly income = 780 ÷ 10 = 78 Answer D #### D QUESTION:Four of the following five numbered parts (a), (b), (c), (d) and (e) are equal. The number of the part which is not equal to the other four parts is the answer. options: A)115 × 8 ÷ 10 + 8 B)425 ÷ 17 × 4 C)36 × 5 ÷ 6 + 17 × 4 D)2(6) + √256 + 20 E)35 × 12 ÷ 14 + 14 × 5 SOLUTION:All others are equal to 100. But option (c) gives a value equal to 98. Answer C #### C QUESTION:0.9*0.007= ­­­­­­­­­­_________ options: A)0.063 B)0.0063 C)0.63 D)0.00063 E)63 SOLUTION:9*7=63 Sum of decimal places= 4 So, 0.9*0.007= 0.0063 ANSWER:B #### B QUESTION:Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:When m is divided by 9, the remainder is 8. When m is divided by 13, the remainder is 1. If 1 < m < 200, what is the greatest possible value of m? options: A)47 B)65 C)103 D)117 E)170 SOLUTION:Looking at the choices, options BD can be eliminated as they are divisible by 13 Starting from the highest number 164; 170 = 162 + 8 (162 divisible by 9) 170 = 169 + 1 (169 divisible by 13) it fits the result Answer = E #### E QUESTION:The equation of line s is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line s? options: A)48 B)50 C)60 D)75 E)100 SOLUTION:This can be solve in two steps and without any complex calculation. Given : equation of line s as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.5*100*75=0.5*125* x => x=60; SO answer is 60=C #### C QUESTION:If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ? options: A)500 B)1000 C)1500 D)2000 E)3000 SOLUTION:Explanation: Let the cost of a table and that of a chair be Rs. x and Rs, y respectively. Then, 2x + 3y = 3500 ...(i) and 3x + 2y = 4000 .....(ii) solving (i) and (ii) we get x = 1000, y = 500 ANSWER IS B #### B QUESTION:One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish. options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Fast's 1 hr work = 1/2 slow's 1 hr work = 1/3 1/2 + 1/3 = 5/6 they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins ANSWER:C #### C QUESTION:What is the sum of the numbers between 1 and 20, inclusive? options: A)310 B)200 C)215 D)285 E)210 SOLUTION:Sol. 1+2+3...17+18+19+20 answer. E #### E QUESTION:Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary? options: A)RS.3500 B)Rs.1500 C)Rs.4500 D)Rs.2500 E)Nill SOLUTION:Answer: Option D Let's anil's salary be Rs. 100. Money spent on Rent = 40% of 100 = Rs. 40. Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18. Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40 anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60 for 33.6 ---> 100 ; 840 ---> ? Required salary = 840/33.6 * 100 = Rs. 2500 #### D QUESTION:In an election between two candidates, the winner has a margin of 10% of the votes polled. If 3000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election? options: A)23000 B)22000 C)20000 D)25000 E)30000 SOLUTION:Winner - Looser 55% - 45% If 3000 people change their mind and vote for the loser: Winner - Looser 45% - 55% Thus 3,000 people compose 10% of all voters, which means that the total number of votes is 30,000. Answer: E. #### E QUESTION:A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)28 sec B)16 sec C)36 sec D)18 sec E)17 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 240 + 120 = 360 m. Time taken = 360/10 = 36 sec. Answer:C #### C QUESTION:Which of the following CANNOT be the median of the 3 positive integers a, b, and c? options: A)a B)c C)a+c D)(a+c)/2 E)(a+c)/3 SOLUTION:The median of a set with odd number of terms is justa middle term, so it's a, b or c. Eliminate A and B right away. Now, the median can also be (a+c)/2 and (a+c)/3 (for example: {1, 2, 3} and {1, 2, 5}). But since a, b, and c are positive integers then it no way can be a+c . Why? Because a middle term (the median) cannot possibly be greater than two terms (a and c) in a set with 3 terms. Answer: C. #### C QUESTION:The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income, what is the ratio of the savings of P, Q and R ? options: A)15 : 8 : 2 B)19 : 7 : 9 C)7 : 15 : 10 D)12 : 9 : 17 E)None of these SOLUTION:Explanation: Let the incomes of P, Q, R be 6x, 8x, 11x and expenditure be 5y, 8y and 12y respectively. Therefore, savings are : (6x – 5y), (8x – 8y) and (11x – 12y) Now, 6x – 5y = 1/4(6x) 24x – 20y = 6x 18x = 20y x/y = 20/18 = 10 / 9 Savings of P / Savings of Q = 6x – 5y / 8x – 8y = [6(x/y) – 5] / [8(x/y) – 8] = [(6 * 10/9) – 5] / [(8 * 10/9) – 8] = 15/8 Savings of Q / Savings of R = 8x – 8y / 11x – 12y = [8(x/y) – 8] / [11(x/y) – 12] = (8 * 10/9) – 8 / (11* 10/9) – 12 = 8/2 Ratio of savings of P : Q : R = 15 : 8 : 2 ANSWER: A #### A QUESTION:Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) options: A)8/3 B)3/8 C)8/5 D)12/5 E)5/3 SOLUTION:Distance traveled by Eddy = 540 km Time taken by Eddy = 3 hours Average speed of Eddy = 540/3 = 180 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 180/75 = 12/5 Answer D #### D QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? options: A)10 hours B)17 hours C)19 hours D)16 hours E)27 hours SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is : options: A)12 B)11 C)10 D)27 E)22 SOLUTION:Explanation: Total employees = \inline \frac{(25-10)\times 20}{10}=30 Hence number of educated employees = 30-20 = 10 Answer: C) 10 #### C QUESTION:The perimeters of two squares are 80 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares? options: A)76 cm B)24 cm C)88 cm D)55 cm E)73.2 cm SOLUTION:We know perimeter of square = 4(side) So Side of first square = 80/4 = 20 cm Side of second square = 32/4 = 8 cm Area of third Square = 20*20 - 8*8 = 336 cm So side of third square = 18.3 [because area of square = side*side] Perimeter = 4*Side = 4*18.3 = 73.2 cm Answer:E #### E QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:A = {0, 1, -3, 6, -8, -10} B = {-1, 2, -4, 7, 6, -9} If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0? options: A)1/4 B)1/3 C)5/13 D)5/12 E)1/2 SOLUTION:For the product of 2 numbers to be negative either of them must be positive or negative: P(positive, negative) = 2/6*3/6 = 6/36; P(negative,positive ) = 3/6 * 3/6 = 9/36 P = 6/36 + 9/36 P = 15/36 P = 5/12 Answer: D #### D QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:The ratio of flour to water to sugar in a recipe is 11:8:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 4 cups of water, how much sugar is required? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:The ratio of flour to water is 22:8=11:4. The ratio of flour to sugar is 5.5:1=11:2. The new ratio of flour to water to sugar is 11:4:2 If we need 4 cups of water, then we need 2 cups of sugar. The answer is D. #### D QUESTION:A mixture contains milk and water in the ratio 3:2. On adding 10 liters of water, the ratio of milk to water becomes 2:3. Total quantity of milk & water before adding water to it? options: A)30 B)40 C)20 D)10 E)25 SOLUTION:milk:water = 3:2 after adding 10 liters of water milk:water = 2:3 Olny water patrs increase when mixture of water milk:wate = 3:2 = 2*(3:2) = 6:4 after adding 10 liters of water milk:water = 2:3 = 3*(2:3) = 6:9 Option 'C' #### C QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.8 sec C)5 sec D)2.2 sec E)4.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 200/40 = 5 sec. Answer:C #### C QUESTION:4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 weavers in 10 days? options: A)10 B)15 C)20 D)25 E)30 SOLUTION:1 weaver can weave 1 mat in 4 days. 10 weavers can weave 10 mats in 4 days. 10 weavers can weave 25 mats in 10 days. The answer is D. #### D QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? options: A)90 B)2,700 C)3,300 D)5,400 E)324,000 SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 110*30=3,300 copies. Answer: C. #### C QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:In case N is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)O and P E)T and U SOLUTION:O and P should serve on A ANSWER:D #### D QUESTION:Six children — A, B, C, D, E and F— are going to sit in six chairs in a row. The children B & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children? options: A)240 B)720 C)1440 D)4320 E)4800 SOLUTION:for such questions , we can treat both as one then total person=5. these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways BF or FB.. so ans =5!*2=240 ans A #### A QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:If 5a + 7b = n, where a and b are positive integers, what is the largest possible value of n for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5*a1 + 7*b1 = n 5*a2 + 7*b2 = n 5*(a1 - a2) = 7*(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 to a we will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 from a, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it? options: A)600 B)602 C)604 D)606 E)608 SOLUTION:The nth term is 2+3*(n-1). The 201st term is 2 + 3(200) = 602 The answer is B. #### B QUESTION:Twelve telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of five members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? options: A)120 B)126 C)792 D)1200 E)1260 SOLUTION:My ans is 12C5 = 792 C #### C QUESTION:A father was as old as his son's present at the time of your birth. If the father's age is 44 years now, the son's age 5years back was? options: A)10 years B)12 years C)14 years D)16 years E)17 years SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22. Son's age 5 years back (22 - 5) = 17 years. E #### E QUESTION:By selling a house for Rs.45000, it was found that 1/2 of the outlay was gained, what ought the selling to price to have been in order to have lost 2 p.c? options: A)38020 B)38000 C)38028 D)29400 E)38192 SOLUTION:CP + CP/2 = 45000 CP = 30000 SP = 30000*(98/100) =29400 Answer:D #### D QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x? options: A)16 B)28 C)15 D)13 E)18 SOLUTION:HCF x LCM = Product of Numbers 2 x 144 = 16 x x x = (2 x 144) / 16 x = 18 ANSWER : E #### E QUESTION:How many positive integers less than 250 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)53 E)64 SOLUTION:Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers So required number= 62-20 = 42 Choice C #### C QUESTION:The watch store down the street from Wendy's house has 2 leather watches, 1 gold watch, and 1 silver watch. How many watches does the store have in all? options: A)10 B)19 C)04 D)12 E)07 SOLUTION:Add the numbers of watches. 2 + 1 + 1 =4. Answer is C. #### C QUESTION:Baby Isabel plays with blocks. Each block is 3.9 inches tall. She has a collection of 32 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be? options: A)67" B)124.8" C)106" D)120" E)151.7" SOLUTION:3.9"*32=124.8". Answer is B. #### B QUESTION:How many numbers from 10 to 10000 are exactly divisible by 9? options: A)900 B)1000 C)1110 D)1200 E)1400 SOLUTION:10/9 = 1 and 10000/9 = 1111 ==> 1111 - 1 = 1110. Therefore 1110 Answer : C #### C QUESTION:Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0 options: A)If x>y B)If x>=y C)If x<y D)If x<=y E)x=y or relationship cannot be established SOLUTION:Solution:- Solving we get X= -2/3 or -2 Y= 3/4 or 4 C) #### C QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum z of all the even integers between 99 and 301? options: A)10,100 B)20,200 C)22,650 D)40,200 E)45,150 SOLUTION:I would solve it in a different way. First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101 Average = (301+99)/2 = 400/2 = 200 Sum z= Average*total count = 200*101 = 20,200 Answer is B #### B QUESTION:A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule? options: A)18 B)81 C)56 D)72 E)24 SOLUTION:IMO 'E' is the answer. Matches will be in multiples of 5x+4. The answer that satisfies this condition is E #### E QUESTION:The ages of Charlie and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is: options: A)15 years B)16 years C)135 years D)21 years E)18 years SOLUTION:A 15 years Charlie’s age = 3A and Vaibhav’s age = 5A { (3A + 9)/(5A + 9) }=3/4 => 4 (3A + 9) = 3 (5A + 9) => A = 3 Therefore, Vaibhav’s age = 15 years. #### A QUESTION:Gary had an average score of 70 on his first four quizzes. He had an average score of 75 on his first five quizzes. What score did he receive on his fifth quiz? options: A)90 B)95 C)65 D)42 E)43 SOLUTION:The sum of Gary's first 4 scores is 4 · 70 and the sum of his first 5 scores is 5 · 75, so he received 5 · 75 − 4 · 70 on his 5th quiz. You can do the arithmetic or note that the answer ends in a 5 and eliminate answer C because it is lower than the average. The correct answer is B. #### B QUESTION:A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train? options: A)metres B)metres C)metres D)metres E)metres SOLUTION:Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s Time taken to cross, t = 18 s Distance Covered, d = vt = (400/36)× 18 = 200 m Distance covered is equal to the length of the train = 200 m Answer: Option C #### C QUESTION:Which of these lines in the xy-plane does not contain any point with two negative coordinates? options: A)y = 4x B)y = x + 6 C)y = x^2 - 5 D)y = x^3 + 3x E)y = 2x^4 SOLUTION:2x^4 is 0 when x is 0 and positive for all other values of x. The answer is E. #### E QUESTION:C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used? options: A)months B)months C)months D)months E)months SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 ANSWER:D #### D QUESTION:If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals? options: A)4:3 B)4:0 C)4:5 D)4:7 E)4:2 SOLUTION:Explanation: a1:a2 = 4:3 d1:d2 = 4:3 Answer: Option A #### A QUESTION:The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? options: A)4538 B)2778 C)2608 D)4530 E)2001 SOLUTION:Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs. 4530 Answer:D #### D QUESTION:A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? options: A)155 m B)150 m C)187 m D)177 m E)186 m SOLUTION:Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 => y = x/15 (x + 100)/25 = x/15 => x = 150 m. Answer: B #### B QUESTION:Josh spends a total of $5.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following? options: A)99 B)100 C)101 D)109 E)140 SOLUTION:Let x be the number of single bubblegums and y be the number of bubblegum pack. then 5x+50y=550 or x+10y=110 or x=110-10y Now, let y=0, then x= 110 and N=x+y or N=0+110 =110. let y=1, then x=100 and N=100+1= 101 (given in the options) let y=2, then x= 90 and N=92 the value will further decrease and hence we do not need to calculate anymore values. ANSWER:- C #### C QUESTION:If 3x - y = 6 and x+2y = 8, then what is the value of 4x + y? options: A)1/7 B)14 C)15 D)52/7 E)60/7 SOLUTION:3x-y=6 ...equation 1 x+2y=8 ...equation 2 adding both the equations 4x+y=14 correct answer option B #### B QUESTION:What should come in place of the question mark (‘?) in the following equation? 18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16 options: A)2764.44 B)2864.34 C)1864.44 D)2684.44 E)None of these SOLUTION:? = 8697.32 – 3058.16 – 92⁄5 × 150.8 = 5639.16 – 2774.72 = 2864.44 Answer E #### E QUESTION:The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination options: A)14 years B)14 years 5 month C)14 years 8 month D)15 years E)15 years 5 month SOLUTION:(d) Let No. of passed candidates are x So, x * 39 + (120 – x) 15= 120 * 35 x = 100 2.(a) Total increase = 8 * 2 = 16 years So, total age of two women = 35 + 45 +16= 96 Average age of two women=96/2=48 years 3(d) Total decrease = 20 * 2 = 40 month = 3 years 4 month So, age of new boy = 18 years – 3 years 4 month = 14 years 8 month C #### C QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)288 B)2609 C)245 D)298 E)221 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer:C #### C QUESTION:A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck? options: A)2:1 B)3:4 C)4:3 D)1:4 E)5:6 SOLUTION:Given; 4 duck = 3 hen; Or, duck/hen = 3/4; Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter. Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''Answer: 2:1; #### A QUESTION:The CI on Rs 30000 at 7% per annum for a certain period is 4347.The period is ? options: A)2 B)3 C)1 D)6 E)5 SOLUTION:I year 2100 II year 2100+147=2247 2100+2247=4347 So 2 Years Answer A #### A QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:6 B)7:3 C)7:4 D)7:2 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer: B #### B QUESTION:A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is: options: A)42 B)43 C)46 D)47 E)49 SOLUTION:A 42 After 10 days : 150 men had food for 35 days. Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion) 125 : 150 :: 35 : x 125 x x = 150 x 35 x = (150 x 35)/125 x = 42 #### A <<<Examples ends QUESTION:A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum? options: A)22887 B)2677 C)2987 D)8925 E)17711 SOLUTION:Principal = (100 * 4016.25) / (9 * 5) = Rs. 8925. Answer:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? options: A)15% B)25% C)35% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(300) / 1000 = 15% The answer is A. #### A QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:Three (rather lazy) men A, B and C working together can do a work in 5 days. They start the work together and A works for 1 day and takes rest on the second day, B works for 2 days and takes rest on the next two days and C works for 2 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate) options: A)7 days B)8 days C)9 days D)10 days E)11 days SOLUTION:Total work is 3*5 = 15 units. A does 1 day of work every 2 days. B does 2 days of work every 4 days. C does 2 days of work every 5 days. Test the options. In 7 days: A will do 1*3 + 1 = 4 units (3 complete cycles and 1 day of work). B will do 2*1+ 2= 4 units (1 complete cycle, 2 days of work, and 1 day of rest). C will do 2*1 + 2 =4 units (1 complete cycle and 2 days of work). Total = 4 + 4 + 4 = 12 units. In 8 days: A will do 1*4 = 4 units (4 complete cycles). B will do 2*2= 4 units (2 complete cycles). C will do 2*1 + 2 =4 units (1 complete cycle, 2 days of work, and 1 day of rest). Total = 4 + 4 + 4 = 12 units. In 9 days: A will do 1*4 + 1 = 5 units (4 complete cycles and 1 day of work). B will do 2*2+ 1 = 4 units (2 complete cycles and 1 day of work). C will do 2*1 + 2 = 4 units (1 complete cycle, 2 days of work, and two days of rest). Total = 5 + 5 + 4 = 14 units. In 10 days: A will do 1*5 = 5 units (5 complete cycles). B will do 2*2+ 2= 6 units (2 complete cycle and 2 days of work). C will do 2*2 =4 units (2 complete cycles). Total = 5 + 6 + 4 = 15 units. Therefore, the answer is D. #### D QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:A bat is bought for Rs.400 and sold at a gain of 30% find its selling price? options: A)s.460/- B)s.480/- C)s.500/- D)s.520/- E)s.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 130 % ------> 520 (130 * 4 = 520) Selling price = Rs.520/- Option 'D' #### D QUESTION:What distance (in meters) will be covered by a bus moving at 54 km/hr in 15 seconds? options: A)175 B)200 C)225 D)250 E)275 SOLUTION:54 km/hr = 54 * 5/18 = 15 m/s distance = 15 * 15 = 225 meters The answer is C. #### C QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)288 B)2609 C)245 D)298 E)221 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer:C #### C QUESTION:A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there? options: A)15 B)30 C)28 D)24 E)32 SOLUTION:number of workers = 10* (25-10)/10 = 15 Answer is A #### A QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:Find all integers x NOT EQUAL TO 3 such that X-3|X^3-3 options: A)1,2,3,4,5 B)-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 C)1 D)6 E)-1,0,1 SOLUTION:Let x-3=t. Thus, t is an integer not equal to such'that t|(t+3)^2-3, which is equivalent to the condition t|3^3-3, or t|24. Therefore, it is necessary and sufficient for t to be an integer divisor of 24, hence t must be equal to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x = t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7, 9, 11, 15, and 27. Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 #### B QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: options: A)14 B)17 C)19 D)22 E)24 SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer : A #### A QUESTION:What is the smallest positive integer x, such that 1944x is a perfect cube? options: A)4 B)3 C)8 D)12 E)18 SOLUTION:Take out the factors of 1944 that will come 2^3*3^3 *3^2. for perfect cube you need every no. raise to the power 3. for 1944 to be a perfect cube, need 1 3 that means =3 B is the answer. #### B QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod? options: A)22.8 kg B)26.6 kg C)28 kg D)26.5 kg E)None of these SOLUTION:Explanation : Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion) => 11.25 : 7 :: 42.75 : x => 11.25 x x = 7 x 42.75 => x = (7 x 42.75) / 11.25 => x = 26.6 Answer : B #### B QUESTION:Jar X is 1/4 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity? options: A)2/5 B)1/4 C)1/3 D)1/2 E)2/3 SOLUTION:Let P be the capacity of Jar X. The amount of water in Jar Y is 1/2*P/2=P/4 Then the total amount in Jar X is P/4+P/4=P/2 The answer is D. #### D QUESTION:A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target? options: A)175/256 B)451/365 C)312/456 D)156/754 E)164/784 SOLUTION:The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes. So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes. The event of not hitting the target even once is the complement of the event of hitting the target at least once. The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾ Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256 The probability that he will hit the target at least in one of the four shots=1-81/256 =175/256 Ans:A #### A QUESTION:If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it? options: A)8 B)24 C)32 D)56 E)192 SOLUTION:let AABBCCDD is the group with same letter representing a sibling pair. total # ways to select 3 from 8 is 8C3=56 Qtn: committee of 3 NOT having siblings in it = Total (56) - committee of 3 with siblings in it committee of 3 with siblings = select 2As and one from rem. 6. This can be done in 4 ways as 4 different letters A,B,C and D = 4 * (2C2*6C1) = 24 Hence Answer = 56-24 = 32 ANS:C #### C QUESTION:The C.P of 10 pens is equal to the S.P of 15 pens. Find his gain % or loss%? options: A)loss 16 2/8% B)loss 16 6/3% C)loss 16 2/3% D)loss 18 2/3% E)loss 33.33% SOLUTION:10 CP = 15 SP 15 --- 5 100 --- ? => 33.33% (Loss) Answer:E #### E QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 24 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)4 D)6 E)8 SOLUTION:C 24 As stated 4=24 => 24=4 Answer is C #### C QUESTION:The sale price sarees listed for Rs.150 after successive discount is 20% and 10% is? options: A)187 B)120 C)108 D)178 E)175 SOLUTION:150*(80/100)*(90/100) = 108 Answer:C #### C QUESTION:What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 6), (x, 6)? options: A)64 B)81 C)125 D)196 E)225 SOLUTION:To find the area of a square, knowing the length of one side is sufficient. From the coordinates given, we can see that one side equals 14. The area is 14*14 = 196. The answer is D. #### D QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:John professes to sell his goods at the cost price but he made use of 800 grams instead of a kg, what is the gain percent? options: A)12 1/3% B)12 1/4% C)12 2/3% D)12 2/1% E)12 1/2% SOLUTION:800 --- 100 100 --- ? => 12 1/2% Answer:E #### E QUESTION:What is the probability that a leap year has 53 Sundays and 52 Mondays? options: A)1/9 B)1/8 C)1/3 D)1/7 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:D #### D QUESTION:A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is? options: A)200 B)150 C)455 D)300 E)600 SOLUTION:Amount = (15000)* (1 + (3/4*100))^4 Amount = 15000 * (1+ 0.0075)^4 = 15455 ------(for investment in 1st month) Interest = 15455-15000 = 455.............. Ans -C #### C QUESTION:The ages of two persons differ by 16 years. If 6 years agao, the elder one be 3 times as old as the younger one, find their present ages. options: A)20 years. B)30 years. C)40 years. D)50 years. E)60 years. SOLUTION:Sol. Let the age of the younger person be x years. Then, age of the elder perosn = (x + 16) years. ∴ 3(x - 6) = (x + 16 - 6) ⇔ 3x - 18 = x + 10 ⇔ 2x = 28 ⇔ x = 14 Hence, their present ages are 14 years and 30 years. Answer B #### B QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:TOM traveled the entire 60 miles trip. If he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour? options: A)20mph B)24mph C)30mph D)40mph E)42mph SOLUTION:avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (12+48) / ((12/24)+(48/48)) = 60*2/3 = 40mph D #### D QUESTION:For a certain set of numbers, if x is in the set, then x - 4 is also in the set. If the number 1 is in the set , which of the following must also be in the set ? a) 4 b) -3 c) -6 options: A)a only, B)b only, C)c only, D)a and b only E)b and c only SOLUTION:Notice that the question asks which of the following MUST be in the set, not COULD be in the set. Since 1 is in the set, then so must be 1-4=-3. Similarly, since -3 is in the set, then so must be -3-3=-6. Could 4 and -1 be in the set? Certainly, but we don't know that for sure. Answer: E. Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set. #### E QUESTION:Given two fair dice, what is the probability G that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. G=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members 51* 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:Two trains running in opposite directions cross a man standing on the platform in 20 seconds and 18 seconds respectively and they cross each other in 19 seconds. The ratio of their speeds is: options: A)1 : 1 B)3 : 2 C)3 : 8 D)3 : 25 E)3 : 4 SOLUTION:Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 20 x meters, and length of the second train = 18 y meters. (20 x + 15 y) / (x + y) = 19 ==> 20 x + 18 y = 19 x + 19 y ==> x = y ==> x/y = 1/1 Answer: Option A #### A QUESTION:Which of the number is odd one out ? options: A)84129 B)32418 C)47632 D)36119 E)67626 SOLUTION:C 47632 as 32*32 !=476 #### C QUESTION:John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)17 B)18 C)19.7 D)21 E)27 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 C) #### C QUESTION:From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? options: A)16 B)24 C)60 D)120 E)150 SOLUTION:Answer=E=150 No of 4 person committees that can be formed=5C2*6C2=150 Answer E #### E QUESTION:Find the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114. options: A)2 or ½ B)2/3 or 3/2 C)¾ or 4/3 D)4 or ¼ E)5 or 1/5 SOLUTION:Let the terms be a/r, a , ar a/r *a * ar = a 3 =216, a =6 (a/r*a )+ (a*ar) + (ar*a/r ) =114, a 2/r + a 2 r + a 2 =114 a 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114 6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0, On solving, r = 2/3 or 3/2 ANSWER:B #### B QUESTION:There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3 options: A)I B)II C)III D)II &III E)I &II SOLUTION:Name T = full pool U fills a pool in a days ==> 1 day U fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c 1 day (U+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (U+Y+Z) together fill: T ==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==>d = abc/(ab+bc+ca) d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3 B #### B QUESTION:Which number is the odd one out? 159 248 951 357 122 582 options: A)951 B)246 C)325 D)147 E)852 SOLUTION:A 951 In the rest there is the same difference between each digit, eg: 9(–4) 5 (–4)1 #### A QUESTION:Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)18 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 2 = 26 => x = 6 So Deepak age is = 3(6) = 18 Option B #### B QUESTION:A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $335,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment? options: A)$1,395 B)$1,733 C)$3,466 D)$13,333 E)$20,796 SOLUTION:0.04x + 0.09y = 335000 [1] 0.04x = 0.80 * 335000 = 268000 [2] 268000 + 0.09y = 320000 --> 0.09y = 67000 [3] 268000 / 12 = 22333.3333 [4] 67000 / 12 = 5583.333 [5] Adding [4,5] we get: 27916 [6] Dividing [6] / 2 to get an average we get 1.395,ANS A #### A QUESTION:An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share? options: A)8877 B)3000 C)7787 D)1799 E)1711 SOLUTION:4 --- 2000 5 --- ? => 3000 Answer: B #### B QUESTION:A number x is 8 times another number y. The percentage that y is less than x is options: A)12.5% B)87.5% C)80% D)11% E)1% SOLUTION:Say y=1 and x=8. Then y=1 is less than x=8 by (8-1)/8*100=7/8*100=87.5%. Answer: B. #### B QUESTION:Thomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer? options: A)10 B)14 C)19 D)21 E)25 SOLUTION:The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5 The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0 Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5 The % of profit in selling a single computer=(4545.5/45454.5)*100=10% Answer:A #### A QUESTION:A sum of Rs. 12500 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)4% B)5% C)6% D)8% E)14% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000/- Rate = (100 * 3000) / (12500 * 4) = 6% ANSWER:C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? options: A)150 meter B)299 meter C)666 meter D)155 meter E)144 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer: A #### A QUESTION:If a quarter kg of onions costs 80 paise, how many paise will 100 gm cost? options: A)32 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 80 : x 250 * x = (100 * 80) x = (100 * 80) / 250 x = 32 ANSWER: A #### A QUESTION:One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in: options: A)180 min B)160 min C)280 min D)18 min E)190 min SOLUTION:Let the slower pipe alone can fill the tank in x minutes Then the faster pipe can fill the tank in x/4 minutes Part filled by the slower pipe in 1 minute = 1/x Part filled by the faster pipe in 1 minute = 4/x Part filled by both the pipes in 1 minute = (1/x)+(4/x) Answer is A It is given that both the pipes together can fill the tank in 36 minutes ⇒ Part filled by both the pipes in 1 minute = 1/36 (1/x)+(4/x)=1/36 5/x=1/36 x=5×36=180 i.e.,the slower pipe alone fill the tank in 180 minutes #### A QUESTION:A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is? options: A)A)$58 B)B)$42 C)C)$65 D)D)$48 E)E)$62 SOLUTION:avg = sum of observations/number of observations avg income=(45+50+60+65+90)/5 = 62 Answer is E #### E QUESTION:If 4a = 16b and 8b = 13c, Find a:b:c? options: A)52:13:8 B)13:7:52 C)7:13:52 D)7:13:54 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (8b = 13c ==> b/c = 13/8) ==> a:b = 16:4 and b:c = 13:8 a:b:c = 52:13:8 Answer: Option A #### A QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. options: A)12 B)14 C)15 D)16 E)17 SOLUTION:d = (D-R)/Q = (109 - 1)/9 = 108/9 = 18 A #### A QUESTION:How many of the positive factors of 19 are not factors of 29? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 19 - 1, 19 factors of 29- 1, 29 Comparing both, we have three factors of 19 which are not factors of 29- 19, The answer is B #### B QUESTION:4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)4 days B)6 days C)7 days D)9 days E)1 days SOLUTION:1 women's 1 day work = 1/28 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/28 + 10/140) = 1/4 5 women and 10 children will complete the work in 4 days. Answer: A #### A QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. options: A)4 km B)5 km C)6 km D)7 km E)8 km SOLUTION:time=distance/speed let total distance travelled be x in 84/60 hrs 2/3 rd of x travelled in 4 km/hr 1/3 rd of distance travelled in 5 km/hr 2x/(3*4)+x/(3*5)=84/60 x=6 km ANSWER:C #### C QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be . options: A)90 seconds B)150 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B #### B QUESTION:From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The distance traveled by Ferry P is 18 km. Then the distance traveled by Ferry Q is 54 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 54/9 = 6 hours, which is 3 hours more than Ferry P. The answer is C. #### C QUESTION:The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit? options: A)$3000 B)$1000 C)$2000 D)$5000 E)$6000 SOLUTION:C $2000 Let C.P. be $x. Then, (1920 - x)/x * 100 = (x - 1280)/x * 100 1920 - x = x - 1280 2x = 3200 => x = 1600 Required S.P. = 125 % of $1600 = 125/100 * 1600 = $2000. #### C QUESTION:The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%? options: A)16 2/7% B)16 2/6% C)16 2/3% D)16 7/3% E)12 2/3% SOLUTION:10 CP = 12 SP 12 --- 2 CP loss 100 --- ? => 16 2/3% Answer: C #### C QUESTION:A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the president? options: A) 1/720 B) 1/5 C) 1/10 D) 1/9 E) 1/6 SOLUTION:This question is much easier than it appears. Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the president is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the president is 1/10+1/10=2/10. Answer: B #### B QUESTION:There are 20,6 and 9 rupees notes. you have to form 99 rupees with minimum number of notes.At what minimum number of notes you can achieve this? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:20*3 = 60 6*2 = 12 9*2 = 18 9*1 = 9 9 notes ANSWER:A #### A QUESTION:If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks. options: A)120 MILES B)130 MILES C)140 MILES D)150 MILES E)160 MILES SOLUTION:LET ORIGINAL SPEED BE V AND TIME TAKEN BE T... AS DISTANCE BETWEEN TWO POINTS IS CONSTANT, 30*(T-1)=20*(T+1)=V*T HENCE, V=24MILE/HR T=5 HRS DISTANCE BETWEEN TWO POINTS IS 120 MILES ANSWER:A #### A QUESTION:A man buys milk at 6 per litre and adds one third of water to it and sells mixture at 7.20 per litre. The gain is options: A)40% B)80% C)60% D)25% E)None of these SOLUTION:C.P. of one litre = 6 After adding water to it One has to pay 7.20 for 2⁄3 litre of milk. So S.P. of 2⁄3 litre of milk = 7.20 ⇒ S.P. of 1 litre of milk = 7.20×3/2=10.80 ∵ S.P. > C.P. Hence gain = 10.80−6/6×100=4.80/6×100 = 0.80 × 100 = 80% Answer B #### B QUESTION:Seven people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: options: A)7/8 B)1/8 C)1/3 D)1/6 E)1/9 SOLUTION:Original share of 1 person =1/7 New share of 1 person =1/6 Increase =1/6 - 1/7 =1/42 Required fraction = (1/42)/(1/7)=1/6 Answer is D. #### D QUESTION:A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)7 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph Answer:D #### D QUESTION:The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas. options: A)5:25 B)4:25 C)3:15 D)7:15 E)6:15 SOLUTION:Let the diagonals of the squares be 2x and 5x respectively. Ratio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2 = 4x2: 25x2 = 4 : 25. ANSWER B 4:25 #### B QUESTION:What is the remainder when 3990990900032 is divided by 32 ? options: A)0 B)8 C)4 D)2 E)3 SOLUTION:Though i was unaware of the divisibility test for 32 but i guessed the pattern!! divisibility rule for 4- last two digits must be divisible by 4 divisibility rule for 8- last three digits must be divisible by 8 similarly, divisibility rule for 32 - last five digits must be divisible by 32 Hence, Ans A #### A QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:Two pipes can fill a tank in 14 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ? options: A)5.5 Hours B)7.5 Hours C)8.5 Hours D)9.5 Hours E)6.5 Hours SOLUTION:In 1 hour it fill 1/14 + 1/12 - 1/20 = 2/19 So fill tank fill up in 19/2= 9.5 Hours ANSWER:D #### D QUESTION:A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? options: A)7/11 B)6/7 C)1/5 D)2/7 E)None of these SOLUTION:Explanation : Let, the vessel initially contains 8 litres of liquid. Let x litres of this liquid be replaced with water then quantity of water in new mixture =>3−(3x/8)+x litres. Quantity of syrup in new mixture =5−5x/8 litres. Therefore, =>3−(3x/8)+x=5−5x/8. =>5x+24=40−5x. =>x=8/5. So part of the mixture replaced, =>(8/5)×(1/8)=1/5. Answer : C #### C QUESTION:In a certain store, the profit is 350% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)72.2% B)70% C)100% D)250% E)120% SOLUTION:Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 450 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420 Profit = 450 - 125 = Rs. 325 Required percentage = 295/420 * 100 = 72.2% ANSWER:A #### A QUESTION:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ? options: A)23/30 B)11/15 C)7/10 D)1/6 E)2/15 SOLUTION:Let total Housing Units = 5x. As per question, Equipped with Cable TV = x Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6. So, Cable TV + VCR = x + x/6 = 7x/6 No Cable TV and VCR = 5x - 7x/6 = 23x/6. Fraction = 23x/(6 * 5x) = 23/30. Hence, A #### A QUESTION:6% of customers that enter a store on any given day must not pay tax. If 1000 people shop every day, how many people pay taxes in the store every week options: A)6500 B)6580 C)7200 D)7120 E)6800 SOLUTION:6% of customers do not pay taxes. 6/100 * 1000 customers do not pay taxes. 6/100 * 1000 = 60 Therefore 1000 - 60 customers do pay taxes. 1000 - 60 = 940 940 * 7 days per week = 6580 B) #### B QUESTION:David is able to sell a hand-carved statue for $1150 which was a 15% profit over his cost. How much did the statue originally cost him? options: A)$496.30 B)$512.40 C)$1000 D)$574.90 E)$588.20 SOLUTION:Cost price = 1150/115*100 = 1000 Answer : C #### C QUESTION:What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”? options: A)5 B)7 C)49 D)20 E)25 SOLUTION:The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum). C #### C QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age? options: A)22 B)15 C)77 D)21 E)182 SOLUTION:Present age is 4x and 3x, => 4x + 6 = 34 => x = 7 So Deepak age is = 3(7) = 21 Answer: D #### D QUESTION:45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:45 workers * 8 hours / 30 meters = x * 6 / 55 x = 110 total workers 110 - 45 = 65 new workers The answer is D. #### D QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? options: A)230 B)288 C)267 D)256 E)298 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer: A #### A QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178? options: A)2277 B)2669 C)2200 D)2766 E)2998 SOLUTION:Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178. => (90%) of (110%) of x = Rs. 2178. => (90/100)(110/100)x = 2178 => x = (2178 * 100)/(9 * 11) => x = Rs. 2200 Answer: C #### C QUESTION:If an average hard drive had a capacity of 0.1 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)768 D)1024 E)1536 SOLUTION:0.1*2^10=0.1*1024=102.4 The answer is D. #### D QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.400 when the rate to profit rises from 5 to 7 percent. Find the Capital of C? options: A)3377 B)2899 C)5000 D)2778 E)1991 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 400 C's capital = 30000*1/6 = 5000 Answer: C #### C QUESTION:How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number. options: A)1875 B)2000 C)2375 D)2500 E)3875 SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375 ANSWER:C #### C QUESTION:In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made? options: A)1:4 B)1:3 C)2:3 D)3:4 E)None of these SOLUTION:Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B #### B QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? options: A) 4 B) 2 C) 2 D) 10 E) 12 SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. Answer A #### A QUESTION:A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business? options: A)2400 B)2880 C)2787 D)3087 E)0728 SOLUTION:1200 * 12: x * 9 = 2:3 x = 2400 Answer: A #### A QUESTION:A school has received 30% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 60% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$250 C)$100 D)$350 E)$875 SOLUTION:Let us suppose there are 100 people. 60% of them donated $30000 ( 500 * 60 ) $30000 is 30% of total amount. So total amount = 30000 * 100/60 Remaining amount is 70% of total amount. 70% of total amount = 30000 * (100/60) * (70/100) = 35000 This amount has to be divided by 40 ( remaining people are 40 ) So per head amount is 35000/40 = $875; ANSWER:E #### E QUESTION:Sandy had $231 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? options: A)$270 B)$290 C)$310 D)$330 E)$350 SOLUTION:Let the money Sandy took for shopping be x. 0.7x = 231 x = 330 The answer is D. #### D QUESTION:John has taken four (4) tests that have an average of 81. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade? options: A)87 B)90 C)92 D)94 E)99 SOLUTION:87-81=6*4=24 points 2*87=174 174+24=198 points to be scored in the 2 tests. Avg of 2 tests = 198/2=99 Answer: E Traditional Method: Total scored till now 81*4=324 Total score to avg 87 in 6 tests = 87*6=522 Total to be scored on 2 tests = 522-324=198 Avg on 2 tests = 198/2 = 99 Answer E #### E QUESTION:A pharmaceutical company received $3 million in royalties on the first $25 million in sales of and then $9 million in royalties on the next $130 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $25 million in sales to the next $130 million in sales? options: A)8% B)15% C)35% D)42% E)56% SOLUTION:(9/130)/(3/25) = 15/26 = 57.7% it means that 9/130 represents only 57.7%. Therefore a decrease of 42%. Answer D #### D QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:An bus covers a certain distance at a speed of 100 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? options: A)500 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (100 x 5) = 500 km. Required speed = 500 km/hr. A #### A QUESTION:If b does not equal zero, and ab = b/2, what is the value of a? options: A)A)1/8 B)B)1/4 C)C)1/3 D)D)1/2 E)of the above SOLUTION:Explanation: To solve for a, divide both sides of the equation by b: ab = b/2 (ab)/b = (b/2)/b a = (b/2)*1/b a = 1/2 Answer: (D). #### D QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 * 58 = Rs. 2784. Answer:A #### A QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:During a trip on an expressway, Son drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip? options: A)8.5% B)50% C)x/12% D)60/x% E)500/x% SOLUTION:so Son drove (x-5) miles at 60mph and 5 miles at 30mph: (x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance if the entire trip @60mph than time = x/60 so to get percent [(X+5)/60 ]/[x/60] x100 =(x+5)/x *100 =100+500/x so increase of 500/x%[/u]=E #### E QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 4 cm. What is the length of the wire? options: A)116 cm B)144 cm C)168 cm D)173 cm E)189 cm SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(4)^2 * h = (4/3)π (12)^3 => h = 144 cm Answer:B #### B QUESTION:The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 guards will be available to patrol the fairgrounds on the following Saturday night? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:For any given day, only the guards patrolling on the previous day won't be available. So, 3 guards who patrolled on Friday won't be available. We are thus left with 4 guards. To choose 3 out of 4, we will have 4C3 = 4 different groups. The answer is B. #### B QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)11 B)408 C)2881 D)287 E)221 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 13 + 21 = 34 T = 12 D = 34 * 12 = 408 Answer:B #### B QUESTION:On flipping 3 coins together what is the outcomes for exactly one head and one tail? options: A){HHH, HTH, THH, TTH, THT, HTT} B){HHT, HTH, THH, TTH, THT, TTT} C){HHT, HTH, THH, TTH, THT, HTT} D){HHT, HTH, THH, TTH, THT, TTT} E)None SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for one head and one tail and favorable outcomes for more than one head and one tail. = {HHT, HTH, THH, TTH, THT, HTT} C #### C QUESTION:A bowl of fruit contains 14 apples and 23 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples? options: A)3 B)6 C)14 D)17 E)20 SOLUTION:Number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70% of pieces of fruit in bowl will be apples = x Total number of fruits after x oranges are removed = 14+(23-x) = 37-x 14/(37-x) = 7/10 =>20 = 37-x =>x= 17 Answer D #### D QUESTION:find value for x from below equation? x + 1 = 3 options: A)-5 B)-4 C)4 D)3 E)2 SOLUTION:1. Subtract 1 from both sides: x + 1 - 1 = 3 - 1 2. Simplify both sides: x = 2 E #### E QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 6*6 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)30 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:A person says that their speed while going to a city was 10mph however while returning as there is no much traffic they came with a speed of 15mph. what is their average speed? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:Avg speed= 2xy/x+y Hence Ans: 12 ANSWER:A #### A QUESTION:there are 15 cars and 16 trucks? which is greater15 or 16? options: A)15 B)14 C)12 D)17 E)16 SOLUTION:E #### E QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 15 years? options: A)2:6 B)3:5 C)1:4 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×9/100) /(P×R×15/100)]=9PR/15PR=9/15=3:5 Answer B #### B QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5. O=12.5*6 = 75=E #### E QUESTION:A man's age is 125% of what it was 10 years ago, but 83 X 1/3% of what it will be after 10years. What is his present age? options: A)20 B)60 C)50 D)70 E)80 SOLUTION:C 50 Let the age before 10 years =x Then, 125x/100=x+10 ⇒125x=100x+1000 ⇒x=1000/25=40 Present age =x+10=40+10=50 #### C QUESTION:There are three foam generators in the factory, each of the first two can generate 8 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)146. D)154. E)115 SOLUTION:Let the foam generators capacity be - A = 8 lit/hr B = 8 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 34 lit ( 8 + 8 + 18 ) ; since in 1 and 1/2 hr they will generate 34 + 17 => 51 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 8 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 52 litres {2 (8+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 8 => 12 litres So, total foam generated will be 115 Litres ( 51 + 52 + 12 ) ; hence answer will be (E) #### E QUESTION:On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is: options: A)48759 B)51236 C)47619 D)6974 E)1235 SOLUTION:Explanation: By hit and trial, we find that 47619 x 7 = 333333. ANSWER:C #### C QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 19.7%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)26% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 19.70 Let marked price be Rs. x. Then, 95/100 x = 119.70 x = 11970/95 = Rs. 126 Now, S.P. = Rs. 126, C.P. = Rs. 100 Profit % = 26%. Answer: B #### B QUESTION:In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:Let x be the number of cars and let y be the number of cars parked illegally. 4%*x = 20%*y y/x = 1/5 = 20% The answer is A. #### A QUESTION:In a two-digit number, the digit in the unit’s place is four times the digit in ten’s place and sum of the digits is equal to 10. What is the number? options: A)14 B)41 C)41 D)None of these E)Cannot be determined SOLUTION:Solution Let the ten's digits be x. Then, unit's digit = 4x. ∴ x + 4x = 10 ⇔ 5x = 10 ⇔ x = 2. So, ten's digit = 2, unit's digit = 8. Hence, the required number is 28. Answer D #### D QUESTION:Two 6 faced dice are thrown together. The probability that all the three show the same number on them is? options: A)1/32 B)1/6 C)1/33 D)1/38 E)1/34 SOLUTION:The three dice can fall in 6 * 6 = 36 ways. Hence the probability is 6/36 = 1/6 Answer: B #### B QUESTION:A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get: options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these SOLUTION:Explanation: Ratio of working days of A : B = 10 : 15 Therefore, their wages ratio = reverse ratio = 15 : 10 Therefore, A will get 15 units of ratio Total ratio = 25 1 unit of ratio =3100/25 = 124 So, A’s amount = 124 × 15 = Rs.1860. Answer: Option C #### C QUESTION:If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars? options: A)3⁄20 B)11⁄60 C)9⁄40 D)1⁄5 E)2⁄15 SOLUTION:Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car. Half of them are men, and the other half are women, more precisely 60. It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total. Answer E #### E QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] Q=z-x = x+9-x= 9 Ans:D #### D QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A? options: A)3002 B)3000 C)3018 D)3019 E)3012 SOLUTION:60*5:36*6:75*3 100: 72: 75 100/247 * 7410 = 3000 Answer: B #### B QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)50 SOLUTION:Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec t=500*3/50=30sec ANSWER:B #### B QUESTION:For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6? options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4. SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6 = 6*0 + 2*7.2 + 8 - 6.6 = 0 +14.4 +1.4 15.8 Answer B #### B QUESTION:If x > 3 and y < -3, then which of the following must be true ? options: A)x/y > 1 B)x/y < -1 C)x/y < 0 D)x + y > 0 E)xy > 0 SOLUTION:Pick x=3, y = -3 A) x/y > 1 - Incorrect as x/y = -1 B) x/y < -1 - Incorrect as x/y = -1 C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0 D) x + y > 0 - Incorrect. x + y = 0 E) xy > 0 - Incorrect. XY = -9 which is less than zero. D should be the answer. #### D QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd? options: A)45 B)50 C)30 D)60 E)55 SOLUTION:90 numbers between - 10 and 100 Out of which half would be even, half odd. Number of odd unit digit number = 45. correct option is A #### A <<<Examples ends QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially? options: A)16 B)24 C)32 D)28 E)54 SOLUTION:after 7 girls left remaining 7 girls now boys 14 are twice as many as remaining girls. initially boys=14 and girls=14. ANSWER:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:L * W = 750 : area , L is the length and W is the width. 2 L + 2 W = 110 : perimeter L = 55 - w : solve for L (55 - W) * W = 750 : substitute in the area equation W = 25 and L = 30 correct answer E #### E QUESTION:If 5% more is gained by selling an book for $ 350 than by selling it for $ 340, the cost of the book is: options: A)160 B)210 C)200 D)227 E)220 SOLUTION:C 200 Let C.P. be $ x. Then, 5% of x = 350 - 340 = 10 x/20 = 10 => x = 200 #### C QUESTION:Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)Rs.7000 B)Rs.8000 C)Rs.8500 D)Rs.8600 E)Rs.8700 SOLUTION:The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000. B) #### B QUESTION:10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them. options: A)1628.4 B)1534 C)1492 D)240 E)None of these SOLUTION:Solution: Let average expenditure of 10 people be x. then, 10x = 20*5+5*(x+4); Or, 10x = 20*5+5x+20; Or, x = 24; So, total money spent = 24*10 = Rs. 240. Answer: Option D #### D QUESTION:In an entrance exam, 3 marks is awarded for every correct answer and (-1) for every wrong answer. If a student gets 38 marks after attempting all questions, find the number of questions answered correctly if the total questions were 70. options: A)27 B)88 C)26 D)29 E)71 SOLUTION:Explanation: Let x be the number of questions answered correctly. Hence, number of questions whose answer were wrong = (70 – x) 3*x + (70 – x)*(-1) = 38 4x = 38 + 70 = 108 x = 27 ANSWER:A #### A QUESTION:A data set with a mean of 60 has a standard deviation of 1.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)53 B)56 C)58 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=60-1.5=58.5 to{mean}+{deviation}=60+1.5=61.5. The smallest number within this range from the options is 58. Answer: C. Hope this helps. #### C QUESTION:(A% of 5B + B% of A) is equal to ? options: A)A% of B B)B% of A C)6% of AB D)AB% of 3 E)None SOLUTION:Answer A% of 5B + B% of A =5AB/100 + AB/100 = 6AB/100 = 6% of AB Correct Option: C #### C QUESTION:A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work? options: A)5 days B)21 days C)15 days D)25 days E)30 days SOLUTION:Explanation: WC = 2:1 2x + x = 1/14 => x = 1/42 2x = 1/21 A can do the work in 21 days. Answer: B #### B QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)90 B)70 C)50 D)80 E)60 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 480 16x = 480 x = 30. Hence, total number of notes = 3x = 90. Answer is A. #### A QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? options: A)21 B)36 C)39 D)60 E)65 SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96. Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room. Therefore there are 3/8*96=36 people in the room under the age of 21. Answer: B. #### B QUESTION:Pure milk costs 3.60 per litre. A milkman adds water to 25 litres of pure milk and sells the mixture at 3 per litre. How many litres of water does he add? options: A)2 litres B)5 litres C)7 litres D)11 litres E)None of these SOLUTION:In mixture, Quantity of pure milk /Quantity of water=3−0/3.6−3=3/0.6=5/1 Since in every 5 litres of milk, he adds 1 litre of water. ∴ In every 25 litres of milk, he adds 5 litres of water. Answer B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)99 B)277 C)48 D)99 E)22 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer:C #### C QUESTION:There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure y in inches of the width of the foil covered prism? options: A)4 B)6 C)8 D)9 E)10 SOLUTION:If the width is w, then length and height would be w/2. So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3) => w = 2*4 = 8 in. Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes = 8 +2 =y=10 Ans E. #### E QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ? options: A)24 B)17 C)18 D)9 E)11 SOLUTION:Explanation: Less Men, means more Days {Indirect Proportion} Let the number of days be x then, 72 : 36 :: 18 : x x = 9 Answer: D) 9 days #### D QUESTION:The positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true? I. c > a II. c = a III. c < a options: A)I only B)II only C)III only D)I and II only E)II and III only SOLUTION:Let q = 10% then l = 100/11 % let b = 100 then a = 110 after increasing a by l and decreasing b yq we get c= 108 therefore c<a C it is answer #### C QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book? options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20 SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations: m + p + c = 20 (since 4/5 of the 25 spots are full of books) m = 2p p = 4 + c From that, you can use Substitution to get everything down to one variable. c = p - 4 m = 2p p = p Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf. With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E QUESTION:Find the total number of divisors of 1728(including 1 and 1728) options: A)28 B)29 C)30 D)31 E)32 SOLUTION:1728=2^6*3^3 no. of divisors = (6+1)*(3+1)=28 ANSWER:A #### A QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre. options: A)$8250 B)$8350 C)$8650 D)$8450 E)$8500 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $400 Hence, total cost =5.5×3.75×400= $8250 A #### A QUESTION:The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid. options: A)9: 8 B)9: 5 C)9: 1 D)9: 2 E)9: 4 SOLUTION:a1 : a2 = 3 : 1 6 a12 : 6 a22 = 9: 1 Answer:C #### C QUESTION:A chair is bought for Rs.200/- and sold at Rs.310/- find gain or loss percentage options: A)15% loss B)20% gain C)25% gain D)30% gain E)55% gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (310- 200)/200= 55% gain E #### E QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:There are 36 students in a certain geometry class. If one third of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)9 B)12 C)18 D)24 E)27 SOLUTION:Total Students = 36 One third of the students are boys = 1/3*36 = 12 Three fourths of the boys are under six feet tall = 3/4*12 = 9 ... Therefore Number of boys in the class under six feet tall = 9 ... Answer A.... Alternatively... Number of boys in the class under six feet tall = 3/4 of 1/3 of Total Students = 3/4*1/3*36 = 9... Answer A #### A QUESTION:Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent? options: A)16% B)17% C)18% D)58% E)23% SOLUTION:Total CP = Rs. 36000 + Rs. 15000 = Rs. 51000 and SP = Rs. 62900 Profit(%) = (62900 - 51000)/51000 * 100 = 23% Answer: E #### E QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1244 B)1532 C)1349 D)1423 E)1543 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l * l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:A right circular cylinder has a height of 25 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? options: A)500(π – 3) B)500(π – 2.5) C)500(π – 2) D)500(π – 1) E)625(π – 1.5) SOLUTION:[quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? The square base has sides of sqrt(50) due to the 45-45-90 triangle 25*25*pi - 15*sqrt(50)^2 =625(π – 1.5) E. 500(π – 1.5) #### E QUESTION:The average value of property of Mittal, Ambani and Singhania is Rs.11111 crore. The property of Singhania is as less than the property of Mittal is greater than the average property of both the Singhania and Mittal. The value of property of Ambani is? options: A)Rs. 17111 crore B)Rs. 11121 crore C)Rs. 11111 crore D)Rs. 12111 crore E)Rs. 11611 crore SOLUTION:Explanation: {M+A+S}{3}=11111 {S+M}{2}=11111 (\inline \because M - 11111 = 11111 - S) Rightarrow A = 11111 Answer: C #### C QUESTION:A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle? options: A)Rs.1148 B)Rs.1160 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 82% of Rs.1400 = Rs.(82/100×1400) Rs.1148. Answer A #### A QUESTION:Given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km? options: A)22754.3 B)22254.2 C)25754.2 D)22753.2 E)22254.2 SOLUTION:2 * 22/7 * 3.62 * x = 22754.3 x = 1000 Answer: A #### A QUESTION:Solve x^2 – 7x = 0 options: A)(0,7) B)(0,3) C)(0,2) D)(0,5) E)(0,6) SOLUTION:This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved x^2 – 7x = 0 x(x – 7) = 0 x = 0 or x – 7 = 0 x = 0 or x = 7 The solution is x = 0, 7 Ans: A #### A QUESTION:Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there? options: A)20 toys B)30 toys C)40 toys D)60 toys E)50 toys SOLUTION:x : the total number of toys x/10 : the number of toys for first child x/10 + 12 : the number of toys for second child x/10 + 1 : the number of toys for the third child 2(x/10 + 1) : the number of toys for the fourth child x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x x = 30 toys : solve for x correct answer B #### B QUESTION:In an election between two candidates, the winner has a margin of 10% of the votes polled. If 3000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election? options: A)23000 B)22000 C)20000 D)25000 E)30000 SOLUTION:Winner - Looser 55% - 45% If 3000 people change their mind and vote for the loser: Winner - Looser 45% - 55% Thus 3,000 people compose 10% of all voters, which means that the total number of votes is 30,000. Answer: E. #### E QUESTION:The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 51st term in the sequence? options: A)9 B)8 C)7 D)6 E)4 SOLUTION:Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below 02,07,22,67, 202, 607, 1822, 5467... Observe the last two digits of the sequence which have the cyclicity of4and the last two digits repeat in the order {02, 07, 22, 67} Also 51st Term =6*8 +3 i.e. 51th Terms will have same Last two digits as 3rd term of the sequence = 22 i.e. Sum of lat two digits of 35th Term = 2+2 = 4 E #### E QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ? options: A)3700 B)3890 C)88798 D)2789 E)2891 SOLUTION:Explanation: Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700. Answer: A) 3700 #### A QUESTION:A store has 10 bottles of juice, including 5 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 4 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. options: A)2/7 B)3/11 C)4/15 D)5/21 E)6/25 SOLUTION:The total number of ways to sell 6 bottles from 10 is 10C6 = 210. The number of ways to sell 4 bottles of apple juice is 5C4*5C2 = 5*10 = 50 P(selling 4 bottles of apple juice) = 50/210 = 5/21 The answer is D. #### D QUESTION:In a group of 28 junior high school students, 7 take French, 9 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish? options: A)7 B)6 C)9 D)4 E)8 SOLUTION:E 8 Add 7 + 9 + 4 to get 20. Then subtract 21 from the total students ⇒ 28 – 20 = 8. Answer is E #### E QUESTION:Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 120 players took part in that tournament. How many matches were played? options: A)99 matches. B)88 matches. C)77 matches. D)66 matches. E)119 matches. SOLUTION:Solution: 119 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 119 matches were played. Answer E #### E QUESTION:A man can do a piece of work in 6 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? options: A)7 days B)6 days C)5 days D)4 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/3−1/6)=(6−3)/18=1/6 So son will do whole work in 6 days Answer: B #### B QUESTION:Before a salary increase, the weekly salary of a worker for 44 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:Let x be the original salary per hour. Let y be the salary per hour after the increase. 40y=44x y=(44/40)x=1.1x The salary increased 10%. The answer is D. #### D QUESTION:At what rate of interest is an amount doubled in two years, when compounded annually? options: A)41.4% B)43.4% C)31.4% D)30% E)21.4% SOLUTION:Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4% ANSWER:A #### A QUESTION:The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)75 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 2.5) kg = 25 kg. Weight of new person = (50 + 25) kg = 75 kg. Answer: C #### C QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent? options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these SOLUTION:Let CP of an book = 100 MP of an book = 120 Discount 30 % on 120 = 36 SP of the book = 120 - 36 = 84 loss = 16% Answer : C #### C QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 5400 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)30000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 5400 ( 18 × 300 = 5400) 100% -------> 30000 votes (100 × 300 = 30000) C #### C QUESTION:If |x^2 − 12| = x, which of the following could be the value of x? options: A)-4 B)-3 C)1 D)2 E)3 SOLUTION:|x2−12|=x|x2−12|=x |x2−12||x2−12|cannot be negative; anything that comes out of mod is always positive so |x2−12|>0|x2−12|>0 Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0 Now only Option C=1 or D=2 or E=3 are contenders for right answers. A quick Cursory crude calculation will tell you that E is the right choice |−32−12|=3|−32−12|=3 |9−12|=3|9−12|=3 |−3|=3|−3|=3 3=33=3 ANSWER IS E #### E QUESTION:At what rate of annual simple interest,a certain sum will amount to four times in 15 year? options: A)15% B)17.5% C)20% D)25% E)35% SOLUTION:r=? t=15 yrs SI=p*r*t/100 Amount = SI+p = 4p (p*r*15/100)+p = 4p p(15r/100 + 1) = 4p 15r + 100 = 400 15r = 300 r = 20% ANSWER:C #### C QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.) options: A)96 B)240 C)E=256 D)E=384 E)E=480 SOLUTION:Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers.... We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes. This means, at the minimum, we have... 1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C.... The difference in the number of boxes MUST be 16 though, so we could have.... 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc. With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer.... 284+28 = 312 312+28 = 340 340+28 = 368 368+28 = 396 At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof.... 396+28 = 424 424+28 = 452 452+28 = 480 Final Answer: E #### E QUESTION:A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:if average of 3 is 9 so sum of 3 should be 27 3 recording can be from 0-10 inclusive to find one smallest other two should be highest so, lets assume three var are a,b,c say a is smallest and give b and c greatest readings say 10 and 10 so a has to be 7 E #### E QUESTION:A 2-year certificate of deposit is purchased for R dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years? options: A)k(1.06)^2 B)k(1.06)^8 C)k(1.015)^2 D)R(1.015)^8 E)k(1.03)^4 SOLUTION:Annual Rate of interest= 6% Quaterly rate of interest= 6/4% = 1.5% Now, periods of compounding in 2 years= 8 (8 quarters) Thus R(1.015)^8 Answer: D #### D QUESTION:The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? options: A)8 : 9 B)21 : 22 C)17 : 18 D)12 : 20 E)Cannot be determined SOLUTION:Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x). (120/100 x 7x) and (110/100 x 8x) 42x/5 and 44x/5 The required ratio = (42x/5 : 44x/5)= 21 : 22. ANSWER B #### B QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:If the population of a certain country increases at the rate of 1 person every 60 seconds, by how many persons does the population increase in 2 Hours? options: A)120 B)80 C)100 D)150 E)140 SOLUTION:Answer = 1 * 120(2 hour = 120 minutes)= 120 Answer = A #### A QUESTION:A sum of money becomes 7/6 of itself in 6 years at a certain rate of simple interest. The rate per annum is? options: A)50/9 B)50/13 C)50/17 D)25/9 E)5 5/1 SOLUTION:Let sum = x. Then, amount = 7x/6 S.I. = 7x/6 - x = x/6; Time = 6 years. Rate = (100 * x) / (x * 6 * 6) = 25/9 %. Answer:D #### D QUESTION:There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible? options: A)435 B)367 C)361 D)297 E)261 SOLUTION:Explanation: Total number of persons = n = 30 Shakehands involve only 2 persons = r = 2 Number of shakehands = nCr = 30C2 30C2 = (30 * 29) /(2 * 1) = 435 nCr = (n!) / r! (n – r)! = 30! / 2! 28! = 435 ANSWER:A #### A QUESTION:If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? options: A)30 B)33 1/3 C)35 D)25 E)20 SOLUTION:100---150 150----50 100-----? ==>33 1/3 ANSWER B #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)180 metres SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50 x 9/3 m = 150 m. ANSWER : OPTION D #### D QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot? options: A)1 B)17 C)88 D)12 E)15 SOLUTION:Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer: B #### B QUESTION:Line W has the equation 3x + y = 7. Which of the following lines is perpendicular to Line W? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line W as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line W? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:number of ways by which 4digit no made where aless than b,bless than c,c less than d where all lies between 1 to 9 options: A)1290 B)1296 C)1380 D)1480 E)1580 SOLUTION:we have to make 4 digit number in which the format is d> c > b > a __ __ __ __ 1st position can be filled by 6 digits(9, 8, 7, 6, 5, 4) 2nd position can be filled by 6 digits(8, 7, 6, 5, 4, 3) 3rd position can be filled by 6 digits(7, 6, 5, 4, 3, 2) 4th position can be filled by 6 digits(6, 5, 4, 3, 2, 1) hence every place can be filled by 6 digits, 6* 6* 6* 6 = 1296 ANSWER:B #### B QUESTION:A furniture dealer purchased a desk for $120 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? options: A)$40 B)$60 C)$80 D)$90 E)$100 SOLUTION:Purchase price = 120 Selling price = x 120 + 0.4*x = x 0.6*x = 120 x = 200 Profit = 200 - 150 = 50 ANSWER:A #### A QUESTION:There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic? options: A)70 % B)75 % C)80 % D)85 % E)90 % SOLUTION:Chance of no picnic+chance of picnic= 100% ... (i) Chance of picnic=100%-Chance of no picnic ... (ii) Chance of no picnic= 50% of 30%= 15% Therefore, According to (ii), Chance of picnic= 100%-15%= 85%. Answer D #### D QUESTION:A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 7 minutes less than they can row it in still water. How long would they take to row down with the stream options: A)45 or 23 minutes B)73 or 12 minutes C)77 minutes D)19 minutes E)25 minutes SOLUTION:A method has been discussed here to nullify the calculations though. All I can input here is, speed of a crew in still water = 1/2 ( speed upstream + speed downstream) approximating this for time, t = 1/2(84+ (t-7)) giving t = 77 C #### C QUESTION:In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have? options: A)180 B)45 C)60 D)90 E)135 SOLUTION:We can start with the known quantity and then go on to find the others. Shiny igneous ricks are 40. These are (2/3) of total igneous rocks. (2/3)*Total igneous rocks = 40 Total igneous rocks = 40 * (3/2) = 60 Total sedimentary rocks = 2*Total igneous rocks = 2*60 = 120 Total number of rocks = 60 + 120 = 180 Answer (A) #### A QUESTION:If both 5^2 and 3^3 are factors of n x (2^5) x (12^2) x (7^3) x (10), what is the smallest possible positive value of n? options: A)15 B)45 C)75 D)125 E)150 SOLUTION:(2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and one appearance of 5 (in the 10). Thus n must include at least 3 * 5 = 15 The answer is A. #### A QUESTION:A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation? options: A)20 B)30 C)37 D)40 E)39 SOLUTION:There are three ladies and five gentlemen and a committee of 5 members to be formed. Number of ways such that two ladies are always included in the committee = ⁶C₃ = (6 * 5 * 4)/6 = 20. Answer:A #### A QUESTION:Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -7 then by what factors will the Mean,Variance and Standard Deviation respectively change ? options: A)-7,-7,-7 B)-7,7,7 C)1,1,1 D)-7,49,7 E)7,7,49 SOLUTION:Mean: If all values are multiplied by -7 then their sum will also be multiplied by -7 so Mean will also get -7 Variance: Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values When we multiply all the values by -7 then the difference between the mean and the individual values also gets multiplied by -7 and the square of that difference becomes 49. So, the variance gets multiplied by a factor of 49 SD: Standard Deviation is the square root of variance so sqrt(49)=7. So SD gets multiplied by a factor of 7. So, answer will be D. #### D QUESTION:The length of a rectangle is twice its breadth. If its length is decreased by 4 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle. options: A)10/3cm B)20/3cm C)20cm D)16cm E)14cm SOLUTION:Explanation: Let breadth = x. Then, length = 2x. Then, (2x - 4) (x + 5) - 2x * x = 75 => 6x - 25 = 75 => x =20/3. Length of the rectangle = 20/3 cm. Answer: Option B #### B QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/800*1/600=1/4,800. Answer: B. #### B QUESTION:If x > 3 and y < -3, then which of the following must be true ? options: A)x/y > 1 B)x/y < -1 C)x/y < 0 D)x + y > 0 E)xy > 0 SOLUTION:Pick x=3, y = -3 A) x/y > 1 - Incorrect as x/y = -1 B) x/y < -1 - Incorrect as x/y = -1 C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0 D) x + y > 0 - Incorrect. x + y = 0 E) xy > 0 - Incorrect. XY = -9 which is less than zero. D should be the answer. #### D QUESTION:Find the value of 1/(3+1/(3+1/(3-1/3))) options: A)21/89 B)89/27 C)27/89 D)1/14 E)1/56 SOLUTION:1/[3 + (1/(3+1/(3 - 1/3)))] => 1/[3 + 1/(3 + 1/(8/3))] => 1/[3 + 1/(3 + 3/8)] => 1/[3 + 8/27] => 1/(89/27) => 27/89 C #### C QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class? options: A)45 B)40 C)35 D)30 E)50 SOLUTION:Explanation: Let the total number of students = x The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks. But total increase in the marks = 1/2×x=x/2 Hence we can write as x/2=20 ⇒x=20 x 2=40 Answer: Option B #### B QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)? options: A)2 B)4 C)7 D)9 E)10 SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3. Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9. The answer is D. #### D QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100 x 3000)/(12500 x 4)% = 6% answer :D #### D QUESTION:If there are 10 apples and 20 oranges, what is the ratio of apples to oranges? options: A)10:20 B)2:4 C)1:2 D)4:8 E)It cannot be determined from the information given SOLUTION:A ratio should be reduced to the lowest common denominator. 10:20 means 10x:20x which can be written as 1(10):2(10)... ANSWER:C #### C QUESTION:How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ? options: A)3.5 years B)4 years C)4.5 years D)5 years E)None of these SOLUTION:Solution Time =(100*81/450*4.5) years =4 years Answer B #### B QUESTION:A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 B)(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2 C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D)(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.1 Probability of Tail, P(T) = 0.9 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2*(0.1)^3*(0.9)^2 1 Tail and 4 Heads, Probability = 5C1*(0.1)^4*(0.9)^2 0 Tail and 5 Heads, Probability = (0.1)^5 Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 Answer: option A #### A QUESTION:A,B,C can complete a piece of work in 24,8,12 days. Working together, they complete the same work in how many days? options: A)4 B)4/5 C)7/9 D)10 E)24/7 SOLUTION:A+B+C 1day work = 1/24 + 1/8 + 1/12 = 6/24 = 1/4 A,B,C together will complete the job in 4 days Answer is A #### A QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is options: A)70 B)71 C)72 D)73 E)74 SOLUTION:Explanation: Let the second number is x, then first is 2x, and third is 1/3(2x) =>2x+x+2x/3=264 <=>11x/3=264 =>x=72 Answer: Option C #### C QUESTION:Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is options: A)2 : 3 B)4 : 3 C)6 : 7 D)9 : 16 E)None SOLUTION:Sol. Let us name the trains as A and B. Then, (A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3. Answer B #### B QUESTION:What could be the range of a set consisting of odd multiples of 3? options: A)21 B)24 C)35 D)62 E)70 SOLUTION:Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 3*(2n+1) where n is any positive integer. Range = 3*(2m + 1) - 3*(2n + 1) = 3*2*(m-n) = 6 * (m-n). m, n - any positive integers The answer must be divisible by 6, which is only 24. The correct answer is B #### B QUESTION:If the height of a right cone C is 3 and the diameter of the base of C is 8, what is the distance from the apex of C to any point on the circumference of the base of C? options: A)3√2 B)5 C)5√2 D)√(67) E)√(73) SOLUTION:height of cone=3 radius of base=4 so the distance from the apex of C to any point on the circumference of the base of C will be a right angled triangle Hence the distance is sqrt(3^2+4^2)= 5 ANSWER:B #### B QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION:What is the tens digit of 7^1415? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401 7^5 = 16807 7^6 = 117649 We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit ) 0 , 4 , 4 , 0 . 1415= 4*353 + 3 The ten's digit will be 4 . Answer E #### E QUESTION:The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ? options: A)6 years B)7 years C)8 years D)9 years E)None SOLUTION:Answer Let the age of youngest child be y. so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12 ⇒ 4y + 24= 48 ∴ y = 6 years Correct Option: A #### A QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)25 SOLUTION:Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER IS A #### A QUESTION:Sonika bought a V.C.R. at the list price of 18,700. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R. options: A)20,196 B)19,780 C)19,680 D)19,380 E)None of these SOLUTION:Sol. List price of V.C.R. =18,700 Rate of sales tax = 8% ∴ Sales tax = 8% of 18,700 = 8⁄100 × 18700 = 1496 So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,700 + 1496 = 20,196. Answer A #### A QUESTION:A ship sails out to a mark at the rate of 15 kmph. and sails back at the rate of 10 kmph. The average rate of sailing is ? options: A)5 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None SOLUTION:Answer Average = ( 2uv / u +v ) km/hr = ( 2 x 15 x 10 ) / (15 +10 ) km/hr. = 12 km/hr. Correct Option: B #### B QUESTION:One pipe can fill a pool four times faster than a second pipe. When both pipes are opened, they fill the pool in eight hours. How long would it take to fill the pool if only the faster pipe is used? options: A)5 hr B)8 hr C)10 hr D)16 hr E)20 hr SOLUTION:fast pipe + slow pipe = together One pipe fills the pool four times faster than the other pipe so, hourly fill rates: 1/x + 1/4x = 1/8 Let x = number of hours it would take the fast pipe to fill the pool thus, x=10 hours Answer: C #### C QUESTION:If f(x) = (x^2 - 1)/(x), what is f(1/x) in terms of f(x)? options: A)-1*f(x) B)f(x) C)1/f(x) D)-1/f(x) E)2*f(x) SOLUTION:f(1/x) = ((1/x)2 - 1) / ((1/x)) = ((1/x^2) - 1) / (1/x) = ((1-x^2)/(x^2)) / (1/x = (1-x^2)/(x^2) = - ( (x^4) -1) / (x) = -1* f(x) Answer is A. #### A QUESTION:In the xy-coordinate system, line k passes through points (-7m, 0) and (0, 3m). Which of the following is a possible equation of line k? options: A)y = -7/3*x + 3m B)y = 3/7*x - 7m C)y = 7/3*x + 3m D)y = 3/7*x + 3m E)y = -3/7*x - 7m SOLUTION:The slope of the line is 3m/7m=3/7. The y-intercept is 3m. the equation of the line is: y = 3/7*x +3m The answer is D. #### D QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)k(n+m+mn)+ k B)(1+n+m+mn)(k+1) C)k^2(mn+n/m) D)kmn(k+m+n) E)None of the above SOLUTION:The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together: (mn + m + n + 1)(k + 1). ANSWER:B #### B QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 6? options: A)1/4 B)5/36 C)2/11 D)3/13 E)1/5 SOLUTION:n(S) = 6*6 = 36 E = {(1,5),(2,4),(3,3),(4,2),(5,1)} Probability = 5/36 Answer is B #### B QUESTION:If n is an integer greater than 8, which of the following must be divisible by 8 ? options: A)n(n + 5)(n – 6) B)n(n + 2)(n – 1) C)n(n + 1)(n – 4) D)n(n + 3)(n – 5) E)n(n + 5)(n – 6) SOLUTION:If n= 9 , then (n-1) is divisible by 8 . B #### B QUESTION:If p is a natural number and p! ends with w trailing zeros, then the number of zeros that (5p)! ends with will be options: A)a) (p+w) trailing zeros B)b) (5p+y) trailing zeros C)c) (5p+5y) trailing zeros D)d) (p+5y) trailing zeros E)e) none of them above SOLUTION:Let p = 1. p! = 1! = 1, which means w= 0 (5p)! = 5! = 120, trailing zeros = 1 1 = 1 + 0 = p + w Answer (A). #### A QUESTION:A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 25 per kg, then his gain percent is options: A)12% B)33% C)14% D)15% E)16% SOLUTION:Explanation: Suppose he bought 5 kg and 3 kg of tea. Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150. Selling price = Rs. (8 x 25) = Rs. 200. Profit = 200 - 150 = 50 So, Profit % = (50/150) * 100 = 33% Option B #### B QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(6200*5*3)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,700 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Price in 96 = 22000 Price decrease each year = 2.5/100*22000 = 550 Price in 97 = 22000 - 550 Price in 98 = 22000 - 2*550 Price in 99 = 22000 - 3*550 Price in 00 = 22000 - 4*550 Price in 01 = 22000 - 5*550 Price in 02 = 22000 - 6*550 = 18700 Investment in the car = 1000 Net price of the car in 02 = 18700 + 1000 = $19700 Correct Option: B #### B QUESTION:Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.90? options: A)426 B)430 C)443 D)480 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones. Having 7.9$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.9 $ left. so we buy 1 pack of 50 for 1$. We now have 0.9$ left, so we buy 30 individual envelopes. If we add up the numbers, we get 400+50+30=480 envelopes. Answer D #### D QUESTION:At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.50. What is the price of 2 doughnuts? options: A)$ 0.55 B)$ 1.00 C)$ 1.10 D)$ 1.30 E)$ 1.50 SOLUTION:3D + C = 2.25......(1) 2D + C = 1.5........(2) (1) - (2) --> D = 0.75 --> 2D = 1.5 Answer: E #### E QUESTION:If you are given $5, and the amount doubles every day, how much money will you have after 4 days? options: A)$256 B)$512 C)$1024 D)$625 E)$720 SOLUTION:5^4=625 The answer is D #### D QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? options: A)52% B)64% C)72% D)76% E)80% SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A QUESTION:A dragon has 100 heads. A soldier can cut off 15, 17, 20 or 5 heads, respectively with one blow of his sword. In each of these cases, 24, 2, 14, 17 new heads grow on its shoulders. If all heads are cut off, the dragon dies. Can the dragon ever die? options: A)61 B)3 C)5 D)6 E)1 SOLUTION:Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die. Answer:B #### B QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet. The number of revolutions = distance/circumference = 5,280z/y. Answer: A. #### A QUESTION:In a certain village, 200 litres of water are required per household per month. At this rate, if there are 5 households in the village, how long (in months) will 2000 litres of water last? options: A)9 B)5 C)6 D)2 E)4 SOLUTION:I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p: In a certain village,m 200 litres of water are required per household per month. At this rate, if there aren 5 households in the village, how long (in months) willp2000litres of water last? Water required is 200*5=1000 (m*n) Water available is 2000 (p) It will last 2 months (p/m*n) Ans : D #### D QUESTION:If a - b = 3 and a^2 + b^2 = 31, find the value of ab. options: A)12 B)15 C)10 D)11 E)13 SOLUTION:2ab = (a^2 + b^2) - (a - b)^2 = 31 - 9 = 22 ab = 11. Answer is D. #### D QUESTION:X is an even number and Y is a positive odd number. Which of the following expressions cannot be even? options: A)(XY)^Y B)X^3Y^3 C)X^3 D)XY E)Y^2 SOLUTION:If x is even, let x = 0 and see what happens. A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE) B. 0³Y³ = 0 (EVEN - ELIMINATE) C. 0³ = 0 (EVEN - ELIMINATE) D. (0)Y = 0 (EVEN - ELIMINATE) E. Y² Answer:E #### E QUESTION:What is the different between the place value and face value of 6 in the numeral 5468? options: A)45 B)54 C)60 D)36 E)44 SOLUTION:place value of 6 = 6 * 10 = 60 face value of 6 = 6 60 - 6 = 54 Answer is B #### B QUESTION:In how many ways can 6 apples (identical) be distributed among 5 children? (Some children may get no apples.) options: A)124 B)210 C)128 D)130 E)132 SOLUTION:Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1. n=6 r= 5 10C4 =210 Answer : B #### B QUESTION:Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side? options: A)20,25 B)21,25 C)27,23 D)28,25 E)30,25 SOLUTION:Let the two parallel sides of the trapezium be a cm and b cm. Then, a-b = 4 ------ (1) And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2) Solving 1 and 2, we get: a=27,b=23 So, the two parallel sides are 27 cm and 23 cm. C #### C QUESTION:Machine Z takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Z to make 40 widgets? options: A) 5 B) 6 C) 8 D) 10 E) 12 SOLUTION:i approached this one by plugging in numbers...started with C. if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Z is 4, and time of B is 2. rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and A reduces the time - the total # of widgets made will be even higher. now between D and E -> try only one ..if it doesn't work, then the other one is the answer. i picked E: 12h to make 40 widgets, and 6 hours to make 20. this is the time of Z. time of B=4 hours. 20/6 + 20/4 = 10/3 + 20/4 find LCM of 3 and 4 = 12. multiply first by 4, and second by 3: 40+60/12 = 100/12 divide by 4: 25/3 so this is the rate given. E is the correct answer #### E QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed? options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5! SOLUTION:Explanation: Total number of letters = 5 Using these letters the number of 5 letters words formed is 5!. Answer: Option E #### E QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)? options: A)0 B)20 C)75 D)5 E)10 SOLUTION:Explanation : Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0 Answer : A #### A QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? options: A)26 B)39 C)42 D)65 E)156 SOLUTION:Here 156 has three two's two three's and one 13 rest of them must be in w so w= 13*3*4 = 156 Answer: E #### E QUESTION:A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 80 percent of the drive from the center, what percent of the round-trip has the technician completed? options: A)5% B)75% C)25% D)40% E)50% SOLUTION:The complete round trip consists of driving to the service center and then back home again. So, once the technician drives to the service center he/she has already competed 50% of the entire trip. Since the technician completes a portion of the trip back home,the correct answer must be greater than 50% Only one answer choice works. Answer: B #### B QUESTION:A man spends Rs. 1900 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income? options: A)2075 B)2175 C)2275 D)2375 E)2475 SOLUTION:Explanation: Total expenditure for the first 3 months = 3 × 1900 = 5700 Total expenditure for 4 months = 4 × 1550 = 6200 Total expenditure for 5 months = 5 × 1800 = 9000 Total expenditure and saving (which is income for one year) = 5700 + 6200 + 9000 + 5200 = Rs. 25200 So, Average monthly income = 26100/12 = Rs. 2175 Answer B #### B QUESTION:In the faculty of Reverse-Engineering, 240 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total? options: A)515. B)545. C)661. D)644. E)666. SOLUTION:Answer is C :661 Solution : Total number of students studying both are 423 + 240 - 134 = 529 (Subtracting the 134 since they were included in the both the other numbers already). So 80% of total is 529, so 100% is approx. 661. #### C QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 5 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)153602 D)60000 E)153604 SOLUTION:Perimeter = Distance covered in 5 min. =(12000/60) x 5m = 1000 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1000 or x = 100. Length = 300 m and Breadth = 200 m. Area = (300 x 200) m2 = 60000 m2. Answer: D #### D QUESTION:If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: options: A)0 B)1 C)2 D)None of these E)Cannot be determined SOLUTION:Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3. x = 2. Answer: Option C #### C QUESTION:A pharmaceutical company received $3 million in royalties on the first $25 million in sales of and then $9 million in royalties on the next $130 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $25 million in sales to the next $130 million in sales? options: A)8% B)15% C)35% D)42% E)56% SOLUTION:(9/130)/(3/25) = 15/26 = 57.7% it means that 9/130 represents only 57.7%. Therefore a decrease of 42%. Answer D #### D QUESTION:Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 31.5 kg of zinc has been consumed in it? options: A)58 kg B)60 kg C)64 kg D)70 kg E)None SOLUTION:Sol. For 9 kg Zinc, mixture melted = (9+11) kg. For 31.5 kg Zinc, mixture, melted = [20/9 x 31.5] kg = 70 kg. Answer D #### D <<<Examples ends QUESTION:A train 310 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? options: A)4 B)6 C)5 D)17 E)13 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [310 * 3/55] sec = 17 sec ANSWER:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:At an international conference, “Yellow” world countries and “Blue” world countries are the only participants. The ratio of “Yellow” world participants to “Blue” world participants is 3:2. If one-third of “Yellow” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed? options: A)7 B)7/15 C)5/8 D)9/2 E)4/6 SOLUTION:Yellow: Blue = 3:2 Let Yellow = 3x and Blue = 2x 1/3 of Yellow are left handed => 1/3 * 3x = 3x/3 Yellow left handed 2/3 of Blue are left handed => 2/3 *2x = 4x/3 blue left handed fraction of participants who are left handed = total left handed/ total participants = (yellow left handed + blue left handed)/total participants = (3x/3 + 4x/3)/(3x+2x) = (7x/15x) = 7/15 Answer : B #### B QUESTION:Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent? options: A)705 B)655 C)656 D)657 E)658 SOLUTION:total cost 940 940*25/100=235 so the cut in amount is 235 the less amount to be spend is 940-235=705 ANSWER:A #### A QUESTION:A man can row upstream at 10kmph and downstream at 24 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)7 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(24 -10) kmph = 7 kmph. Answer C #### C QUESTION:A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water? options: A)2 kmph B)8 kmph C)16 kmph D)4 kmph E)6 kmph SOLUTION:30 --- 3 DS = 10 ? ---- 1 18 ---- 3 US = 6 ? ---- 1 M = ? M = (10 + 6)/2 = 8 ANSWER:B #### B QUESTION:What number should replace the question mark? 11, 15, 16, 12, 21, 9, ---? options: A)21 B)29 C)28 D)27 E)26 SOLUTION:Answer: E 11, 15, 16, 12, 21, 9, ---? There are two alternate sequences: +5 and -3. #### E QUESTION:3, 5, 7, 11, 13, 17, 19, ____ options: A)25 B)36 C)23 D)49 E)27 SOLUTION:The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23.... Answer : C. #### C QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:A school has received 30% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 60% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$250 C)$100 D)$350 E)$875 SOLUTION:Let us suppose there are 100 people. 60% of them donated $30000 ( 500 * 60 ) $30000 is 30% of total amount. So total amount = 30000 * 100/60 Remaining amount is 70% of total amount. 70% of total amount = 30000 * (100/60) * (70/100) = 35000 This amount has to be divided by 40 ( remaining people are 40 ) So per head amount is 35000/40 = $875; ANSWER:E #### E QUESTION:A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg? options: A)s.7.7 B)s.7.4 C)s.7.5 D)s.7.1 E)s.7.9 SOLUTION:100*(20/100) = 20 --- 10 ? --- 1 => Rs.2 300 --- 80 ? --- 2 => Rs.7.5 Answer:C #### C QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast? options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2 SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes. Answer: C. #### C QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is? options: A)22772 B)24000 C)23877 D)23789 E)28222 SOLUTION:Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs. 24000 Answer: B #### B QUESTION:After a mathematics exam, 20 percent of the students reported that they didn't study, while 20 percent of the students who didn't study refused to admit they hadn't studied. What percent of the students didn't study? options: A)15% B)50% C)35% D)20% E)25% SOLUTION:Statement: 20% of Students (S) Reported they Didn't Study (RDS). Of the students who didn't study (DS) 20% refused to admit they didn't study (notRDT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RDS/S = 20% notRDS/DS = 20% => 100% - 20% => RDS/DS = 80% DS/S = (20)/(80)% = 25% Answer: E #### E QUESTION:If x ≠ 1 and if yx/(y - x) = 1, what is the value of y in terms of x? options: A)(1-x)/x B)(x - 1)/x C)x/(x + 1) D)(x + 1)/x E)x/(1-x) SOLUTION:This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator. Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one. Final Answer: E #### E QUESTION:What is the units digit of (3^5)(4^13)? options: A)2 B)4 C)6 D)7 E)8 SOLUTION:-> The ones place of (~3)^n repeats after 4 times like 39713. The ones place of (~4)^n repeats after 2 times like 464. Then, 3^5=3^4*1+13^1., 4^13=4^2*6+1=4^1=~4 which is (3^5)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is A. #### A QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C QUESTION:Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved? options: A)56% B)64% C)62.2% D)68% E)61% SOLUTION:If initial cost is Rs 100, then Final cost will be 100*0.7*0.6*0.9 = Rs. 37.8 savings = 100-37.8=62.2 so 62.2% ANSWER:C #### C QUESTION:A wooden box of dimensions 4 m x 2 m x 4 m is to carry rectangularboxes of dimensions 4 cm x 2 cm x 2 cm. The maximum number ofboxes that can be carried in the wooden box, is options: A)9800000 B)2000000 C)7500000 D)1200000 E)None of these SOLUTION:Explanation: Number = (400*200*400)/4*2*2 = 2000000 Answer: B #### B QUESTION:Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)? options: A)670 B)710 C)750 D)790 E)830 SOLUTION:total pay = 40*$12.50 + $0.16*x = 620 x = 120 / 0.16 = 750 The answer is C. #### C QUESTION:John had a stock of 700 books in his bookshop. He sold 50 on Monday, 82 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold? options: A)26.5% B)50% C)46.5% D)56.5% E)60% SOLUTION:Let N be the total number of books sold. Hence N = 50 + 82 + 64 + 78 + 135 = 280 Let M be the books NOT sold M = 700 - N = 700 - 280 = 420 Percentage Books not sold / total number of books = 420/700= 0.60 = 60% correct answer E #### E QUESTION:Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? options: A)654 B)655 C)656 D)588 E)658 SOLUTION:total cost 840 840*30/100=252 so the cut in amount is 252 the less amount to be spend is 840-252=588 ANSWER:D #### D QUESTION:If 18 is 15 percent of 25 percent of a certain number, what is the number? options: A)9 B)36 C)480 D)81 E)400 SOLUTION:Let the certain number be x. => (15/100)*(25/100)*x = 18; => x=480; Ans is (C). #### C QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)190 C)109 D)278 E)211 SOLUTION:Explanation: 624/6 = 104 kmph Answer:C #### C QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)30 C)42 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 45, 100%= 45*100/60= 75.. ans 40% of 75 =30 B #### B QUESTION:A furniture manufacturer has two machines, but only one can be used at a time. Machine W is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine W can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? options: A)14 B)13 C)11 D)9 E)7 SOLUTION:'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days. To finish a work Machine W say you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D #### D QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1400. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ? options: A)3600 B)3890 C)88798 D)2789 E)3500 SOLUTION:Explanation: Manager's monthly salary Rs. (1500 * 21 - 1400 * 20) = Rs. 3500. Answer: E #### E QUESTION:Two trains 141 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? options: A)7.16 B)7.59 C)7.12 D)7.15 E)7.11 SOLUTION:T = (141 + 165)/ (80 + 65) * 18/5 T = 7.59 Answer: B #### B QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? options: A)14 B)144 C)777 D)992 E)221 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways. Hence the total ways are 24 * 6 = 144. Answer:B #### B QUESTION:If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p? options: A)p B)2p C)5p D)7p E)p^2 SOLUTION:Y=30p other number is 5p then GCF(30p,5P)=5P; C is the correct answer #### C QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:A certain list has an average of 6 and a standard deviation of B (B is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than B? options: A)(-6;0) B)(0;0) C)(0;6) D)(0;12) E)(6;6) SOLUTION:Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. E) #### E QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)1 B)7 C)3 D)8 E)5 SOLUTION:40*(40/100) = 16 --- 64 ? --- 12 => Rs.3 Answer: D #### D QUESTION:How many keystrokes are needed to type numbers from 1 to 1000? options: A)2704 B)2890 C)2893 D)3001 E)None of these SOLUTION:1-9 9 digits 10-99 There are 90 2-digit numbers (90)(2) = 180 digits 100-999 There are 900 3-digit numbers (900)(3) = 2700 digits 1000 4 digits 9 + 180 + 2700 + 4 = 2893 Answer: C #### C QUESTION:A data set with a mean of 60 has a standard deviation of 1.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)53 B)56 C)58 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=60-1.5=58.5 to{mean}+{deviation}=60+1.5=61.5. The smallest number within this range from the options is 58. Answer: C. Hope this helps. #### C QUESTION:Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 32 percent ryegrass, what percent of the weight of this mixture is X ? options: A) 10% B) 33.33 % C) 46.66% D) 50% E) 66.66 % SOLUTION:---------------->Ryegrass X--------------> 40% Y--------------> 25% M(mixture)---->32% 0.4X + (M-X)0.25 = 0.32M 0.15X = 0.07M X = 0.4666M X = 46.66% of M C #### C QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => |x-2| < 6. Hence, answer is D #### D QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum? options: A)8 B)2 C)9 D)4 E)6 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96 15000[(1 + R/100)2 - 1 - 2R/100] = 96 15000[(100 + R)2 - 10000 - 200R]/10000 = 96 R2 = (96 * 2)/3 = 64 => R = 8 Rate = 8% Answer: Option A #### A QUESTION:If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30? I. wb + b^2 II. (w+ b)^2 III. w + b options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30. I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK; II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD; III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK. Answer: B. #### B QUESTION:A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together? options: A)120 B)110 C)105 D)140 E)135 SOLUTION:we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together so 8C6 + (8C5 * 2C1) this is 28 + 112=140 Answer : D #### D QUESTION:Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is? options: A)7 1/2 sec B)2 sec C)3 sec D)5 sec E)7 sec SOLUTION:70 + 50 = 120 * 5/18 = 100/3 mps D = 150 + 100 = 250 m T = 250 * 3/100 = 15/2 = 7 ½ sec ANSWER A #### A QUESTION:In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year? options: A)74 B)75 C)76 D)77 E)78 SOLUTION:let the age is 'x' so after 1st yr 2x=40 and x=20 after 2nd year (now age become 21) 2*21+ 20=62 grades after 3rd year(now age becomes 22) 2*22+31=75 ANSWER:B #### B QUESTION:What is the smallest number which when diminished by 24, is divisible 5, 10, 15 and 20? options: A)276 B)84 C)88 D)90 E)342 SOLUTION:Required Number = (LCM of 5, 10, 15 and 20) + 24 = 60 + 24 = 84 Option B #### B QUESTION:If x+1/x=5 then find out the value of x^5+1/x^5=? options: A)2515 B)2525 C)2535 D)2545 E)2555 SOLUTION:given,(x+ 1/x) = 5 x^2 + 1/x^2 = (x+ 1/x)^2 - 2*x*1/x = 5^2 - 2 = 23 -------(1) x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2) multiplying (1)& (2), we get =>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110 => x^5 + 1/x + x + 1/x^5 = 2530 => x^5 + 1/x^5 + (x+ 1/x)= 2530 => x^5 + 1/x^5 + 5 = 2530 => (x^5+ 1/x^5)= 2525 ANSWER:B #### B QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 40*9/40 = 9 seconds. Answer: C #### C QUESTION:In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner? options: A)$9 x 10^4 B)$9.90 x 10^6 C)$1.00 x 10^7 D)$1.05 x 10^7 E)$9.90 x 10^7 SOLUTION:The max product of any two balls can be 9 * 10 = 9900 = 9 * 10 If we multiply it by $1000 the max amount will be 9 * 10^4. A #### A QUESTION:In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way? options: A)5 sec B)4 sec C)3 sec D)6 sec E)1 sec SOLUTION:T = 30/36 * 18/5 = 3 sec Answer: C #### C QUESTION:How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible? options: A)4C3+4 B)4C3+9 C)4C3+2 D)4C3 E)4C3+6 SOLUTION:So 4C3 for abcd - 4 choices 3 more for dd(b,c or a) 3 more for bb(a,c or d) 3 more for cc(a,b or d) total 4C3+9 Ans : B #### B QUESTION:The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability T that the next couple the maitre 'd seats will not order dessert? options: A) 20% B) 25% C) 40% D) 60% E) 75% SOLUTION:could you use a venn diagram and just go with the number 100. 60 people order dessert and coffee... which is the union of D and C. T=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither. B 25% #### B QUESTION:Jenna rode her bike to school at 5 kph, but rode home at 15 kph. What was her average speed traveling to and from school? options: A)5 kph B)7 kph C)10 kph D)13 kph E)15 kph SOLUTION:(5 kph +15 kph)/2 =10 kph Correct answer is: C #### C QUESTION:Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics? options: A) 20% B) 42% C) 44% D) 66% E) 84% SOLUTION:You are correct. People who cover local politics are a subset of people who cover politics. 25% of reporters who cover politics do not cover local politics so 75% DO cover local politics. Reporters covering local politics= 75% of reporters covering politics= 25% of all reporters Reporters covering politics/All Reporters = 25/75 = 1/3 Reporters not covering politics/All Reporters = 2/3 = 66%=D #### D QUESTION:A 16% stock yielding 10% is quoted at : options: A)83.33 B)110 C)112 D)120 E)160 SOLUTION:Solution To earn Rs. 10, money invested = Rs. 100. To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160. ∴ Market value of Rs. 100 stock =Rs. 160 Answer E #### E QUESTION:In case N is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)O and P E)T and U SOLUTION:O and P should serve on A ANSWER:D #### D QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most? options: A)3 B)1 C)0 D)19 E)20 SOLUTION:Average of 20 numbers = 0 Sum of 20 numbers / 20=0 => Sum of 20 numbers = 0 Hence at the most, there can be 19 positive numbers. (Such that if the sum of these 19 positive numbers is x, 20th number will be -X) ANSWER:C #### C QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1055 B)1065 C)1070 D)1075 E)1080 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 A #### A QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 => 675 675 * 2 = Rs.1350 Answer:A #### A QUESTION:The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought? options: A)42. B)38. C)33. D)22. E)20. SOLUTION:Let X pizzas of 2 slices and Y pizzas of 4 slices. 2X + 4Y. Lets check options wise. A. 42 => 2(15) + 4(3) B. 38 => 2(15) + 4(2) C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out. D. 22 => 2(10) + 4(3) E. 20 => 2(6) + 4(2) Answer: correct option is C #### C QUESTION:In a class, there are 21 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ? options: A)8 B)14 C)18 D)24 E)26 SOLUTION:Explanation: Let the number of boys be x. Then, (3/4)x = 21 or x = 21 x(4/3) = 28. If total number of students is y, then (2/3) y = 28 or y = 28 x (3/2) = 42. Therefore Number of girls in the class = (42 - 28) = 14. Answer: B #### B QUESTION:#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6? options: A)–108 B)–44 C)10 D)16 E)18.25 SOLUTION:#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer. #### E QUESTION:In a recent head-to-head run-off election, 10,000 absentee ballets were cast. 2/3 of the absentee ballets were thrown out and 2/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000 SOLUTION:1/3 * 3/5 (total absentee votes) = 1/5 (total votes)=1/5*10000=2000 Answer is A #### A QUESTION:At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? options: A)5% B)3 1/2% C)4% D)5 1/2 % E)6% SOLUTION:150 = (750*5*R)/100 R = 4% Answer :C #### C QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? options: A)10 hours B)17 hours C)19 hours D)16 hours E)27 hours SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 50 paisa and Z gets 40 paisa. If the share of X is RS. 30, what is the total amount? options: A)67 B)55 C)62 D)47 E)57 SOLUTION:x:y:z = 100:50:40 10:5:4 10 --- 30 19 --- ? => 57 Answer: E #### E QUESTION:Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is? options: A)10 B)30 C)40 D)50 E)60 SOLUTION:Let the numbers be 3x,4x and 5x their L.C.M. = 60x 60x =600 x = 10 The numbers are 3*10 , 4*10 , 5*10 Hence required H.C.F. = 10 Answer is A #### A QUESTION:If Jenee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased? options: A)1/4 B)1/5 C)1/10 D)3/50 E)1/20 SOLUTION:Perhaps it is also easy to just translate the % into fractions: 6%: 6/100 = 3/50 7%: 7/100 8%: 8/100 = 4/50 =2/25 9%: 9/100 Only 3/50 exists in the answer choices, so ANS D #### D QUESTION:A car dealership has 40 cars on the lot, 15% of which are silver. If the dealership receives a new shipment of 80 cars, 30% of which are not silver, what percentage of total number of cars are silver? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:The number of silver cars is 0.15*40 + 0.3*80 = 30 The percentage of cars which are silver is 30/120 = 25% The answer is B. #### B QUESTION:Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X? options: A)25% B)40% C)50% D)60% E)75% SOLUTION:34% is 9%-points above 25% and 6%-points below 40%. Thus the ratio of mixture Y to mixture X is 2:3. The percent of mixture X is 3/5 = 60%. The answer is D. #### D QUESTION:Evaluate: 20 - 12÷4×2 = options: A)A)12 B)B)24 C)C)36 D)D)48 E)E)60 SOLUTION:According to order of operations, 12÷4×2 (division and multiplication) is done first from left to right 12÷4×2 = 3 × 2 = 6 Hence 20 - 12÷4×2 = 20 - 6 = 14 correct answer is B) 22 #### B QUESTION:In a bag, there are 4 white, 1 brown and 5 red pens. One pen is picked up randomly. What is the probability that it is neither white nor red? options: A)1/5 B)1/10 C)1/2 D)1/3 E)1/4 SOLUTION:Explanation : Neither white nor red means the pen drawn is brown. Total number of outcomes = (4+1+5) = 10. Number of Favourable outcomes = 1 = Number of brown pens. Hence, Probability of the event = 1/10. Answer : B #### B QUESTION:If 1 persons can do 1 times of a particular work in 1 day, then, 7 persons can do 7 times of that work in ? options: A)3 days B)1 day C)9 days D)11 days E)15 days SOLUTION:That is, 1 person can do one time of the work in 1 day. Therefore, 7 persons can do 7 times work in the same 1 day itself. Option 'B' #### B QUESTION:Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3? options: A)2/5 B)2/7 C)33/83 D)51/250 E)100/249 SOLUTION:SOLUTION The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250. Answer: D #### D QUESTION:What simple interest will produce Rs.84000 as in 4 years at 3 1/2 percent? options: A)11500 B)12660 C)15220 D)11760 E)16520 SOLUTION:(84000*4*7/2)/100 = i i = 11760 Answer: D #### D QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:Shaun is starting a new diet plan that offers him the choice of fruit or yogurt for breakfast, 6 different entrees for lunch, and 9 different entrees for dinner. If Shaun chooses an Italian entree for lunch, he always chooses an Italian entree for dinner. If Shaun chooses a Chinese entree for lunch, he never chooses a Chinese entree for dinner. If there are 2 Italian entrees and 2 Chinese entrees among the lunch choices, and 3 Italian entrees and 3 Chinese entrees among the dinner choices, from how many different daily menus can Shaun choose? options: A)24 B)36 C)72 D)90 E)108 SOLUTION:Let the Breakfast set be {F , Y} Lunch be {I ,I , C,C , L1,L2} Dinner be {I,I,I , C,C,C, D1,D2,D3} There are only 2 restrictions, Italian Lunch has to go with Italian Dinner and Chinese Lunch cannot go with Chinese dinner. So the set of Breakfast, Lunch and Dinner will {Any BF, Italian Lunch, Italian Dinner } = 2 * 2 * 2 {Any BF, Chinese Lunch, Not Chinese Dinner} = 2 * 2 * 6 {Any BF, Not Italian or Chinese Lunch, Any Dinner} = 2 * 2 * 9 Adding all these gives 72. Answer is C #### C QUESTION:If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is? options: A)22 B)65 C)78 D)33 E)25 SOLUTION:Given that, cost price of 50 article is equal to selling price of 40 articles. Let cost price of one article = Rs. 1 Selling price of 40 articles = Rs. 50 But Cost price of 40 articles = Rs. 40 Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25% Answer:E #### E QUESTION:John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit as the cost price? options: A)Rs.12 B)Rs.8 C)Rs.16 D)Rs.20 E)None of these SOLUTION:Explanation : CP=20×8.5+35×8.75=170+306.25=476.25Profit=40%SP=(100+Profit%)100×CP=(100+40)100×476.25=140 100×476.25=1404×19.05=35×19.05Total quantity = 20 + 35 = 55 KgSP per Kg=35×19.0555=7×19.0511≈7×1911≈13311≈12 Answer : Option A #### A QUESTION:In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class? options: A)12 Years B)12.6 Years C)13.6 Years D)14 Years E)14.5 Years SOLUTION:Total age of 50 students (30X 13+20 X 12) = 630 Average = 630/50 = 12.6 Years \ B #### B QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n? options: A)10 B)12 C)16 D)22 E)24 SOLUTION:The average of the numbers in set S is 10. If we increase the mean by 10%, the new mean is 11. Thus, on average, 5 numbers increase by 1. Therefore n = 11+5 = 16 The answer is C. #### C QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value D of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] D=z-x = x+9-x= 9 Ans:D #### D QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1994. She ended on her options: A)thumb B)the index finger C)the middle finger D)the ring finger E)the little finger SOLUTION:Notice the pattern. The thumb lands up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1994 has to be the index finger Answer is B #### B QUESTION:A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 85, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? options: A)74 B)75 C)76 D)77 E)78 SOLUTION:ratio is 4:6:5 , numbers are 4x, 6x, 5x total scores of each class is (65*4x + 6x * 85 + 77*5x) = 260x+510x+385x = 1155x total number of students = 15x average = 1155x/15x = 77 D is the answer #### D QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)80 km/hr B)81 km/hr C)85 km/hr D)84 km/hr E)83 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y-4.5)(10/36) ---(1) x/8.5 = (y-5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y-4.5)/ (y-5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4 .1y = 8.5×5.4 - 8.4×4.5 => .1y = 45.9-37.8 = 8.1 => y = 81 km/hr Answer is B. #### B QUESTION:A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 680 dollars, and, in a third, loses 80. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ? options: A)-280 B)300 C)-350 D)-380 E)None SOLUTION:In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -. Let x = the sum required. Then according to the statement x + 680 - 80 = 250 And x = -350. Answer C #### C QUESTION:5 blue marbles, 3 red marbles and 4 purple marbles are placed in a bag. If 4 marbles are drawn without replacement, what is the probability that the result will not be 2 blue and 2 purple marbles? options: A)4/33 B)(5/36)^2 C)1/2 D)(31/36)^2 E)29/33 SOLUTION:Answer is 29/33. The probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33. Subtracting the above from 1 we get 29/33 E #### E QUESTION:What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5? options: A) 94 B) 99 C) 26 D) 73 E) None of the Above SOLUTION:Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 5 = 10x +y = x^2 y^2 -10 Thus 2xy +5 = x^2 + y^2 - 10 x^2 + y^2 -2xy = 15 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 15 or 94 Thus the answer is A #### A QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 6*8.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)9 D)2 E)9 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept? Assume there are 82 unique alphanumeric case sensitive characters. options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6) SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways ) =82^4(1+ 82) =82^4 * 83 Answer B #### B QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? options: A)30 B)33 1/3 C)35 D)25 E)20 SOLUTION:100---150 150----50 100-----? ==>33 1/3 ANSWER B #### B QUESTION:The cost of 100 articles is equal to selling price of 90. Find the gain or loss percent? options: A)11% B)20% C)27% D)32% E)49% SOLUTION:C.P. of each article be $1 C.P. of 90 articles = 100 gain% = 10/90*100 = 11% approximately Answer is A #### A QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ? options: A)1000 B)1100 C)1200 D)1300 E)1400 SOLUTION:let profit rate of b = x acc to question profit rate of a becomes 5/3 x and that of c= 1/3 x which is given as 10% 1/3 x= 10 therefore x=30 now b=30% , a=50% now we will find out c's price- 11/10 * price = 2145 price = 1950 in similar way we will find out b's price as we know that profit is 30% therefore 130/100 * price = 1950 so b 's price =1500 similarly for a ('profit is 50%) 150/100 * price = 1500 on solving it we get a's price = 1000 ANSWER:A #### A QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)*(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)*(r+4)/(y+r+6) D)(y+3)/(y+r+7)*(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is? options: A)72 kmph B)88 kmph C)54 kmph D)18 kmph E)19 kmph SOLUTION:S = 120/6 * 18/5 = 72 kmph Answer: A #### A QUESTION:a, b, c and d are four consecutive numbers. If the sum of a and dis 111, what is the product of b and c? options: A)2652 B)2578 C)2534 D)3080 E)4234 SOLUTION:Here d = a + 3 a + a + 3 = 111 2a = 108 a = 54 So, numbers are 54, 55, 56 and 57 ∴ b × c= 55 × 56 = 3080 D #### D QUESTION:The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is? options: A)7 B)4 C)5 D)3 E)1 SOLUTION:Explanation: P(1 + 20/100)n > 2P or (6/5)n > 2 Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years. Answer:B #### B QUESTION:In how many ways can the letters of the word STATE be arranged? options: A)60 B)1348 C)2520 D)3000 E)3478 SOLUTION:STATE has 5 words, but T is repeated two times. Thus ways = 5! / 2! = 60 ways A #### A QUESTION:If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station? options: A)4/5 km B)4/6 km C)4/9 km D)4/1 km E)4/3 km SOLUTION:x/3 – x/4 = 4/60 x = 4/5 km Answer: A #### A QUESTION:A carpenter makes 4 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:I believe it is C because if 1C makes 3 beds in 1 day then: 1C's rate = 3/1 So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day. Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed. Time = Amount / Rate Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 4.7 So, in order for the carpenters to be able to finish they need 5 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day. C #### C QUESTION:The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people C who purchased only book A? options: A)250 B)500 C)750 D)1000 E)1500 SOLUTION:This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, C=1000 purchased A only. (This is much simpler to solve using the Venn diagram). Correct answer is D. 1000 #### D QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A. options: A)Rs.240 B)Rs.350 C)Rs.340 D)Rs.390 E)Rs.370 SOLUTION:Explanation: (3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 630 = 240 ANSWER IS A #### A QUESTION:The length of a rectangle is halved, while its breadth is tripled. What is the % change in area? options: A)30% B)40% C)50% D)60% E)65% SOLUTION:Let original length = x and original breadth = y. Original area = xy. New length = x . 2 New breadth = 3y. New area = x x 3y = 3 xy. 2 2 Increase % = 1 xy x 1 x 100 % = 50%. 2 xy C #### C QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number T of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:T=7 is the correct answer. Good solution Buneul.B #### B QUESTION:The sum of three consecutive integers is 102. Find the lowest of the three? options: A)18 B)67 C)98 D)33 E)26 SOLUTION:Three consecutive numbers can be taken as (P - 1), P, (P + 1). So, (P - 1) + P + (P + 1) = 102 3P = 102 => P = 34. The lowest of the three = (P - 1) = 34 - 1 = 33. Answer: D #### D QUESTION:In an election between the two candidates ,The candidates who gets 60% of votes polled is winned by 280 votes majority. What is the total number of votes polled? options: A)1200 B)1400 C)1600 D)1500 E)1540 SOLUTION:Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %) 20 % = 60 % - 40 % 20% -----> 280 (20×14 = 280 ) 100% -----> 1400 (100×14 = 1400) Option 'B' #### B QUESTION:Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D? options: A)(5,10) B)(-3,2) C)(-1,7) D)(-1,2) E)(-3,1) SOLUTION:The slope of the line is -ve, the only point that makes the slope -ve is D. (5 - 2)/(-2 + 1) = 3/-1 Answer - D #### D QUESTION:2 is what percent of 50 options: A)2% B)4% C)6% D)8% E)10% SOLUTION:Explanation: 2/50 * 100 = 1/25 * 100 = 4 % Answer: Option B #### B QUESTION:When N is divided by T, the quotient is S and the remainder is M. Which of the following expressions is equal to N? options: A)ST B)S + V C)ST + M D)T(S+V) E)T(S – V) SOLUTION:Using the rule dividend = Quotient * divisor + remainder =>ST + M C is correct #### C QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)58 km/hr SOLUTION:Speed of the train relative to man = 125/10 m/sec = 25/2 m/sec. 2 = 25/2 x 18/5 km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 x = 50 km/hr. Option B #### B QUESTION:What is the are of an equilateral triangle of side 8 cm? options: A)64√5 B)64√9 C)16√3 D)64√3 E)64√2 SOLUTION:Area of an equilateral triangle = √3/4 S2 If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2; Answer: C #### C QUESTION:A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-38 E)36-37 SOLUTION:5%(35.5) = 1.775 8%(35.5) = 2.84 total amount could have been 35.5+1.775 and 35.5+2.84 => could have been between 37.275 and 38.34 => approximately between 37 and 38 Answer is B.D #### D QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)88% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,11 = 11/100 x= 80*11/100 x= 8.8 8.8/10 = 0.88 = 88%, Answer C #### C QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 11220, how much money did he borrow? options: A)11000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 11220 18x + 45x + 39x = (11220 * 100) 102x = 1122000 => x = 11000. Answer:A #### A QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)Rs.486 B)Rs.455 C)Rs.487 D)Rs.480 E)Rs.489 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480 Answer: D #### D QUESTION:Which of the following is(are) true for a@b=b@a? I. a@b=b+ba II. a@b=(a+b)(a-b) III. a@b=(a/b)+(b/a) options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X). If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O). If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O). Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A QUESTION:A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 30% profit on the cost of the item? options: A)18 B)21.6 C)22 D)25.7 E)27 SOLUTION:Producer price = $15; The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 30% of the final price --> (final price)*0.7 = $18 --> (final price) = $25.7. Answer: D. #### D QUESTION:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required? options: A)18 B)20 C)24 D)36 E)42 SOLUTION:Use weighted average: 2% and 12% solutions mix to give 5% solution. w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3 You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution. If total 5% solution is actually 60 litres, you need 7*6 = 42 litres of 2% solution and 3*6 = 18 litres of 12% solution. Answer (E) #### E QUESTION:If Mason is now twice as old as Gunther was 5 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now? options: A)3G+14 B)3G+8 C)3G+15 D)3G+10 E)3G+9 SOLUTION:G is Gunther's current age. Let Mason's current age be M. given M = 2(G-5). four years from now Mason's age will be = 2(G-5) + 10 = 2G four years from now Gunther's age will be = G+10 Sum of ages of Mason and Gunther's after 4 years = 2G+G+10 = 3G+10 Ans : D #### D QUESTION:Submarine M and Submarine N are equipped with sonar devices that can operate within a 4,000 yard range. Submarine M remains in place while Submarine N moves 3,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West options: A)I,II only B)II,III only C)II only D)I and III only E)III only SOLUTION:It's evident if we make a diagram for the Movement of N respect to M. From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range. Thus it can only move north or west or anything in that curve. Answer : D #### D <<<Examples ends QUESTION:Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)491 B)481 C)471 D)441 E)445 SOLUTION:Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 3*7/100*2100 = 441. D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The average weight of 5 person's increases by 4 kg when a new person comes in place of one of them weighing 50kg. What is the weight of the new person? options: A)70 B)86.5 C)80 D)88.5 E)75 SOLUTION:Total increase in weight =5 × 4=20 If x is the weight of the new person, total increase in weight = x−50 => 20= x - 50 => x = 20+50= 70 ANSWER:A #### A QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches were made? options: A)84 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 240 / 20 = 12 sandwiches in one part For bologna we have 7 parts so: 7 *12 = 84 Answer is A #### A QUESTION:835, 734, 642, 751, 853, 981, 532 options: A)751 B)853 C)981 D)532 E)None of these SOLUTION:Solution In each number except 751,the difference of third and first digit is the middle one. Answer A #### A QUESTION:10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)90 B)98 C)35 D)99 E)80 SOLUTION:Though 2*(10C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used. The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches. Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches. This continues like this and the total matches are 18+16+14...+2 18+16+...+2 = 2(9+8+...+1) = 2((9*10)/2) = 9*10 = 90. ANSWER:A #### A QUESTION:What is the units digit of (12^3)(15^4)(31^7)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8. The units digit of 15^4 is the units digit of 5^4 which is 5. The units digit of 31^7 is the units digit of 1^7 which is 1. The units digit of 8*5*1 is 0. The answer is A. #### A QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = p*r*t/100 = 1000000*4*3/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:Of the 11 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 11 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man? options: A)22 B)35 C)60 D)70 E)105 SOLUTION:another approach : one scenario : [WWWM] now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women. and 6 ways to select one man so 5*4*3*6 = 360 now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways hence 360/3!= 360/6= 60 C #### C QUESTION:A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 5 hours. During that time, the faster car traveled 2/3 of the distance XY. How long would it take the slower car to travel the distance XY? options: A)6 hours B)8 hours C)10 hours D)12 hours E)15 hours SOLUTION:If one car travelled 2/3, then the other car must have travelled only 1/3, as they are meeting after 5 hours in a certain point. So: (1/3)XY= 4*y --> It took the car 5 hours to travel 1/3 of the distance at a constant speed y. So if we solve this last equation: XY= 3*5*y= 15*y --> It will take this car 15 hours in total to reach its final destination. Answer: E #### E QUESTION:The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is? options: A)10 years B)11 years C)12 years D)13 years E)14 years SOLUTION:Total age of 3 boys = 24*3 =72 ratio of their ages = 1:2:3 Age of the youngest = 72*1/6 = 12 years Answer is C #### C QUESTION:10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day? options: A)4 days B)10 days C)20 days D)25 days E)26 days SOLUTION:Explanation: 10*12*15/20 = 24*20*x/32 X=4 Answer: Option A #### A QUESTION:A parking garage rents parking spaces for $10 per week or $42 per month. How much does a person save in a year by renting by the month rather than by the week? options: A) $14 B) $16 C) $22 D) $24 E) $26 SOLUTION:10$ per week! An year has 52 weeks. Annual charges per year = 52* 10 = 520$ 30$ per month! An year has 12 months. Annual charges per year = 12 * 42 = 504$ 520 - 504 = 16 Ans B #### B QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is: options: A)22 B)50 C)99 D)35 E)12 SOLUTION:Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr.Answer: D #### D QUESTION:If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in? options: A)7 days B)3 days C)9 days D)8 days E)2 days SOLUTION:C 9 days C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C QUESTION:Which of the following must be true? 1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1 2) Every prime number greater than 5 can be written as 4n+1 or 4n-1 3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number. options: A)1,2,3 B)2,3 C)1,2 D)only 1 E)only 2 SOLUTION:Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible. 3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1. C #### C QUESTION:A cube of side one meter length is cut into small cubes of side 5 cm each. How many such small cubes can be obtained? options: A)2878 B)8000 C)1000 D)2997 E)2701 SOLUTION:Along one edge, the number of small cubes that can be cut = 100/5 = 20 Along each edge 5 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 20 * 20 * 20 = 8000 Answer: B #### B QUESTION:The list price of a watch is 160. A retailer bought the same watch 122.40. He got two successive discounts one at 10% and the other at a rate which was not legible. What is the second discount rate? options: A)12% B)14% C)15% D)18% E)None of these SOLUTION:Retailer price = list price (1−d1/100)(1−d2/100) ⇒ 122.40 = 160(1−10/100)(1−d2/100) ⇒ 1−d2/100=122.40×100/160×90=0.85 ⇒ d2 = (1 - 0.85) × 100 = 15% Answer C #### C QUESTION:A train 250 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)150m B)200m C)250m D)270m E)300 m SOLUTION:D = 72 * 5/18 = 25 = 500 – 250 = 250m ANSWER:C #### C QUESTION:In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Roslin played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Roslin could have gotten? options: A)30 B)25 C)20 D)15 E)10 SOLUTION:There are two conditions: 1. Roslin got at least one score of each of 1, 2, 3, 4, and 5. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Roslin could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30. Answer: A. #### A QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)99 B)277 C)48 D)99 E)22 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer:C #### C QUESTION:The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be options: A)12 years B)20 years C)25 years D)28 years E)None SOLUTION:Solution Let the present ages of son and father be x and (60 - x) years respectively. Then, (60 - x) - 6 = 5(x - 6) = 54 - x = 5x - 30 ‹=›6x = 84 ‹=›x= 14. ∴Son's age after 6 years = (x + 6) = 20 years. Answer B #### B QUESTION:A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 30% profit on the cost of the item? options: A)18 B)21.6 C)22 D)25.7 E)27 SOLUTION:Producer price = $15; The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 30% of the final price --> (final price)*0.7 = $18 --> (final price) = $25.7. Answer: D. #### D QUESTION:Sandy bought 65 books for $1480 from one shop and 55 books for $920 from another shop. What is the average price that Sandy paid per book? options: A)$38 B)$18 C)$99 D)$27 E)$20 SOLUTION:average price per book = (1480 + 920) / (65 + 55) = 2400 / 120 = $20 The answer is E. #### E QUESTION:Zeynep (the lady of the rings) has 10 identical gold, 10 identical silver and 10 identical bronze rings. (total of 30) She always wears exactly 3 rings on each of her 10 fingers in a particular sequence: first gold, then silver and last bronze. In how many different orders can she wear her 30 rings? options: A)(10!)^3 / 2^10 B)(10!)^3 / 3^10 C)30! / 2^10 D)30! / 3^10 E)30! / 6^10 SOLUTION:By convention, the answer choice letters are typically listed as capital letters, not lower case. Also, professional math notation is always preferable to plain text shortcuts. 30! / 6^10 ANSWER:E #### E QUESTION:A toy RC car goes 3 feet per second. A boy wants to add an updated part to his RC that will allow the RC car to travel at 6 feet per second. How far will the upgraded car travel in 1 minute? Round to the nearest hundredth. options: A)200 feet B)250 feet C)300 feet D)360 feet E)400 feet SOLUTION:6 feet per sec x 60= 360 feet Answer D #### D QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? options: A)22 days B)77 days C)24 days D)17 days E)18 days SOLUTION:B = 1/8 – 1/2 = 1/24 => 24 days Answer: C #### C QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive? options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000 SOLUTION:There are 5 people inheriting the money. We have to take the total of the inheritance and divide it by 5 for each person receiving money. $527,500 / 5 = $105,500. Therefore the correct answer is D. #### D QUESTION:Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144? options: A) 0 B) 25 C) 49 D) 81 E) 100 SOLUTION:144 =12 *12 (1!)^3=1 2!=2, therefore (2!)^3=2*2*2=8 3!=6, therefore (3!)^3=6*6*6=216 4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144 thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0 now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144 now remainder when 225 is divided by 144 is 81. hence answer should be D #### D QUESTION:A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 210, how much must C pay as his share of rent? options: A)45 B)50 C)54 D)65 E)none SOLUTION:Sol. A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9. ∴ C’s rent = Rs. [210* 9/35] = Rs. 54. Answer C #### C QUESTION:There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ? options: A)120ways B)220ways C)420ways D)720ways E)520ways SOLUTION:By kept 3boys together(1) and arranging 4 girls with them 5! = 5*4*3*2*1 = 120ways. (i.e., 4+1 =5) Possible arrangements of 3 boys in following ways 3! = 3*2*1 = 6ways Now, arrange all with the boys together 120*6 = 720ways ANSWER:D #### D QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rajan? options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000 =>4:5:3 =>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...] => 12:5:6 Share of Rajan => 4600*12/23 = 2400 ANSWER:E #### E QUESTION:A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit? options: A)39:40 B)39:45 C)39:40 D)39:41 E)39:42 SOLUTION:3: 4 A = 3/7*210 = 90 390: 400 39:40 Answer: A #### A QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%? options: A)20% B)28% C)29% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 86 2/3 SP1 = 86 SP1 = 129 100 --- 29 => 29% Answer:C #### C QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 130*4=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture? options: A)12 liters B)10 liters C)4 liters D)2 liters E)3 liters SOLUTION:70 * (10/100) = 7 Wine Water 87 1/2% 12 1/2% 87 1/2% ------- 63 12 1/2% -------? => 9-7=2 ANSWER:D #### D QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ? options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours SOLUTION:Explanation: We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as Work done for 1 hour without leak = 1/3 Work done with leak = 3 1/2=7/2 Work done with leak in 1 hr=2/7 Work done by leak in 1 hr=1/3=2/7=1/21 So tank will be empty by the leak in 21 hours. ANSWER IS D #### D QUESTION:A right triangle has sides of a, b, and 7, respectively, where a and b are both integers. What is the value of (a + b)? options: A)40 B)42 C)46 D)48 E)49 SOLUTION:LET a= hypotenuse , b =base ,7 = perpendicular . therefore a^2 -b^2 =7^2 or (a+b)(a-b) = 49 a+b =49/a-b ' a-b cannot be zero ..therefore a+ b =49 where a-b is equal to 1 E #### E QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third smallest sector? options: A)1/72 B)1/36 C)1/18 D)1/12 E)1/9 SOLUTION:Its an AP question .... it is given clearly in the question . Let the smallest angle be a and the circle has 8 sectors and hence 8 angle with a common difference d hence all the angles can be written in AP form with Cd as d , a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d, given that a+7d = 80 --------1 also a + a+d + a+2d + a+3d + a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360) which is 8a + 28d = 360 --------2 solving 1 and 2 we get a=10 We are almost done , now the question ask what fraction of the wheel’s area is represented by the smallest sector ? (30/360)( pie r*r)/ (pie r*r) = 30/360= 1/12 D ans .... #### D QUESTION:Which number should replace both the asterisks in (* /21) x (*/84) = 1 ? options: A)21 B)42 C)63 D)72 E)168 SOLUTION:Let (y/21) x (y/84) = 1 y^2 = 21 x 84 = 21 x 21 x 4 y = (21 x 2) = 42 The answer is B. #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)267 B)240 C)166 D)111 E)121 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? options: A)45% B)47% C)57% D)48% E)50% SOLUTION:Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = 11628/20400 * 100 = 57% C #### C QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes? options: A)18 B)21 C)35 D)42 E)56 SOLUTION:Note that each handshake includes two people. The total number of handshakes is 14*3/2 = 21 The answer is B. #### B QUESTION:3889 + 13.952 - ? = 3854.002 options: A)48.95 B)49.75 C)45.97 D)47.59 E)45.79 SOLUTION:Let 3889 + 13.952 - x = 3854.002. Then x = (3889 + 13.952) - 3854.002 = 3902.952 - 3854.002 = 48.95. Answer is A #### A QUESTION:When asked what the time is,a person answered that the amount of time left is 1/5 of the time already completed.what is the time. options: A)2 B)9 C)3 D)8 E)6 SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=15x⇒x=2024−x=15x⇒x=20 Time is 8 PM Answer:D #### D QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^a*q^b no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:Find the odd man out 32, 34, 42, 46, 58, 59, 60, 66 options: A)31 B)41 C)67 D)59 E)61 SOLUTION:as 59 is only odd number. ANSWER:D #### D QUESTION:In an election between two candidates, one got 55% of the total valid votes. 20% of the votes were invalid. If the total number of votes was 7500, what was the number of valid votes that the other candidate got? options: A)2800 B)2700 C)2100 D)2500 E)3000 SOLUTION:Total no of votes = 7500 20 % invalid =>80% valid tot valid votes = 7500*80/100 =>valid for 2nd candidate got 7500*80/100*45/100 =2700 ANSWER B #### B QUESTION:A book is bought for $60 and sold for $75. What is the profit in percentage? options: A)12 B)15 C)20 D)25 E)30 SOLUTION:75/60 = 1.25 The answer is D. #### D QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid? options: A)$2.25 B)$3.25 C)$2.00 D)$3.50 E)$3.00 SOLUTION:Explanation: 3 1 2 $3.00 $2.50 $4.00 $9.00 + $2.50 + $8.00 = $19.50/6 = $3.25 B #### B QUESTION:There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to? options: A)7!*1! B)7!*2! C)6!*2! D)8!*2! E)6!*2! SOLUTION:Total number of ways = 7!*2!. B #### B QUESTION:The price of pulses has fallen by 18%. How many quintals can be bought for the same amount which was sufficient to buy 16 quintals at the higher price? options: A)20.5 B)22.5 C)19.5 D)18.4 E)32.5 SOLUTION:80% of original price can buy = 16 quintals. Therefore, he can buy ( 16 x 100 )/ 82 = 19.5 quintals at the lower price. ANSWER:C #### C QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? options: A)336 B)425 C)275 D)235 E)689 SOLUTION:B 425 (68 ÷ 16) × 100 #### B QUESTION:Which of the following number is divisible by 24 ? options: A)3100000 B)3115832 C)3115800 D)3125832 E)3125834 SOLUTION:31214 is not divisible by 3 and 8 => 31214 is not divisible 24 61212 is not divisible by 8 though it is divisible by 3 => 61212 is not divisible 24 512216 is not divisible by 3 though it is divisible by 8 => 512216 is not divisible 24 3125832 is divisible by 3 and 8 => 3125832 is divisible 24 D) #### D QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:Let J – John’s weight S – Susan’s weight M – Mark’s weight A – Sam’s weight L – Lynn’s weight J = 2S S = 0.6A M = 0.5L L = 1.9J Let us convert these weights to one variable S = J/2 A = S/0.6 = J/1.2 = 5J/6 L = 1.9J M = 0.5 * 1.9J = 0.95J So Susan has the least weight. Answer - B #### B QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33*100 = 180% of 3.33. Answer: E. #### E QUESTION:A division of a company consists of six men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/11 D)5/12 E)7/15 SOLUTION:Total number of ways to select 2 members = 11C2 = 55 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/55 = 2/11 The answer is C. #### C QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long? options: A)65sec B)70sec C)74sec D)80sec E)85sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 500)/10 = 74 sec. Answer:C #### C QUESTION:A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get: options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these SOLUTION:Explanation: Ratio of working days of A : B = 10 : 15 Therefore, their wages ratio = reverse ratio = 15 : 10 Therefore, A will get 15 units of ratio Total ratio = 25 1 unit of ratio =3100/25 = 124 So, A’s amount = 124 × 15 = Rs.1860. Answer: Option C #### C QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet? options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am SOLUTION:meet x hrs after 8 a.m. (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330 ==>60x+75(x-1) = 330 x=3. So,they meet at (8+3). i.e 11a.m. ANSWER A #### A QUESTION:On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every six minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period? options: A)25% B)50% C)75% D)100% E)150% SOLUTION:Dolphin once in 3 min; Beluga once in 6 min; So, dolphin comes up 2 times frequently than beluga, which is 150% (6-3)/2*100. Answer: E. #### E QUESTION:The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 51st term in the sequence? options: A)9 B)8 C)7 D)6 E)4 SOLUTION:Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below 02,07,22,67, 202, 607, 1822, 5467... Observe the last two digits of the sequence which have the cyclicity of4and the last two digits repeat in the order {02, 07, 22, 67} Also 51st Term =6*8 +3 i.e. 51th Terms will have same Last two digits as 3rd term of the sequence = 22 i.e. Sum of lat two digits of 35th Term = 2+2 = 4 E #### E QUESTION:Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C? options: A)127 B)150 C)177 D)167 E)122 SOLUTION:A+B+C = 590 5A = 6B = 8C = x A:B:C = 1/5:1/6:1/8 = 24:20:15 15/59 * 590 = Rs.150 Answer:B #### B QUESTION:A vendor bought Headphones at 5 for Rs 100.How many for Rs 100 must he sell to gain 50%? options: A)8 B)3 C)5 D)6 E)None SOLUTION:C.P. of 9 Headphones= Rs100 S.P. of 9 Headphones = 150% of Rs 100 = Rs150 For Rs.150 , Headphones sold = 9. For Rs. 100,Pens sold=(9/150)*100=6 Answer: Option D #### D QUESTION:What is the greatest positive integer x such that 5^x is a factor of 125^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:125^10 = (5^3)^10 = 5^30 ANSWER:E #### E QUESTION:If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is? options: A)18 B)11.2 C)14 D)12 E)91 SOLUTION:2 * 22/7 * 15 * x = 1056 => x = 11.2 Answer: B #### B QUESTION:A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day? options: A)2880. B)4860. C)5780 D)4320 E)6380. SOLUTION:Normal Day = 600 kw/h Stormy Day = 600*1.2=720 kw/h 3 windmills for 2 hours on stormy day 720*3*2=4320 Answer: D #### D QUESTION:A boy has thirteen trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)186 ways B)177 ways C)188 ways D)195 ways E)189 ways SOLUTION:The boy can select one trouser in thirteen ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 13 * 15 = 195 ways. Answer:D #### D QUESTION:A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 50 paisa and Z gets 40 paisa. If the share of X is RS. 30, what is the total amount? options: A)67 B)55 C)62 D)47 E)57 SOLUTION:x:y:z = 100:50:40 10:5:4 10 --- 30 19 --- ? => 57 Answer: E #### E QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)375 SOLUTION:Explanation: Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. ANSWER IS C #### C QUESTION:A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum? options: A)22887 B)2677 C)2987 D)8925 E)17711 SOLUTION:Principal = (100 * 4016.25) / (9 * 5) = Rs. 8925. Answer:D #### D QUESTION:Insert the missing number 100,91,....,76,70 options: A)82 B)83 C)84 D)81 E)80 SOLUTION:Missing number: 83 Answer: B #### B QUESTION:What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x options: A)2450 B)2560 C)3200 D)3400 E)3158 SOLUTION:12 12 × 3 + 2 = 38 38 × 3 + 2 = 116 116 × 3 + 2 = 350 350 × 3 + 2 = 1052 1052 × 3 + 2 = 3158 E #### E QUESTION:The ratio of 2 numbers is 2:7 and their H.C.F. is 18. Their L.C.M. is ? options: A)252 B)243 C)521 D)361 E)600 SOLUTION:Let the numbers be 2x and 7x Their H.C.F. = 18 so the numbers are 2*18 , 7*18 = 36,126 L.C.M. = 252 Answer is A #### A QUESTION:In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ? options: A)100 B)72 C)110 D)135 E)145 SOLUTION:Explanation : Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x. .'. 60% of x = 36 +5/6 *36 =>60/100 * x = 66 =>x = 110 Answer : C #### C QUESTION:Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Tuesday, how many croissants will Marina eat on the 24th of that month? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:She eat as follow Mon - 1 Tue - 2 Wed - 3 Thr - 5 Fri - 1(since she had more than 4 previous day) sat - 6 sunday - 1 (since she had more than 4 previous day) so 24th day of month she will have 5. Answer is D #### D QUESTION:A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay? options: A)270 B)360 C)276 D)271 E)272 SOLUTION:12*8 :16*9 = 18*6 8: 12: 9 12/29 * 870 = 360 Answer: B #### B QUESTION:Mario and Nina each have a bag of marbles, each of which contains 10 blue marbles, 10 red marbles, an 10 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble? options: A)3/4 B)2/9 C)1/4 D)1/8 E)1/16 SOLUTION:Mario and Nina each select one marble from their respective bags. Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble Probability that either Mario or Nina select a red marble = (10/30)*(10/30) + (10/30)*(10/30) = 2*(1/9) Probability that either Mario or Nina select a red marble = 2/9 Answer would be B. #### B QUESTION:If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K? options: A)30 B)4 C)5 D)66 E)All of these SOLUTION:The first term divisible by 3, so any term could be the third term. Answer =(E) #### E QUESTION:If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is? options: A)22 B)65 C)78 D)33 E)25 SOLUTION:Given that, cost price of 50 article is equal to selling price of 40 articles. Let cost price of one article = Rs. 1 Selling price of 40 articles = Rs. 50 But Cost price of 40 articles = Rs. 40 Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25% Answer:E #### E QUESTION:A family has two children. find the probability that both the children are girls given that at least one of them is a girl? options: A)1/3 B)1/5 C)1/7 D)1/9 E)2/3 SOLUTION:Let b stand for boy and g for girl. The sample space of the experiment is S = {(g, g), (g, b), (b, g), (b, b)} Let E and F denote the following events : E : ‘both the children are girls’ F : ‘at least one of the child is a girl’ Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)} Now E n F = {(g,g)} Thus P(F) = 3/4 and P (E n F )= 1/4 Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3 A) #### A QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually. options: A)812 B)712 C)412 D)512 E)612 SOLUTION:Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112. therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612. Answer is E. #### E QUESTION:Calculate the HCF of 64, 318, 250 options: A)6 B)5 C)4 D)3 E)2 SOLUTION:Explanation: Lets solve this question by factorization method. 64=2 x 2 x 2 x 2 x 2 x 2, 318=2 × 3 × 53, 250=2 × 5 × 5 × 5 So HCF will be minimum term present in all three, i.e. 2×32=18 Answer: Option E #### E QUESTION:Which number should replace both the asterisks in (* /18) x (*/162) = 1 ? options: A)27 B)36 C)54 D)72 E)90 SOLUTION:Let (y/18) x (y/162) = 1 y^2 = 18 x 162 = 18 x 18 x 9 y = (18 x 3) = 54 The answer is C. #### C QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day? options: A)Rs. 120 B)Rs. 150 C)Rs. 250 D)Rs. 400 E)None of these SOLUTION:Solution: Ratio of number of men, women and children, = (18/6): (10/5):(12/3) = 3:2:4 Total (Men +Women +Children) = 18 3X +2X +4X = 18 9X = 18 X = 2 Hence, number of women = 2X = 2*2 = 4 Share of all women = (10*4000)/40 = Rs. 1000 [18+10+12 =40] Thus, share of each woman = 1000/4 = Rs. 250. Answer: Option C #### C QUESTION:There are 36 students in a certain geometry class. If one third of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)9 B)12 C)18 D)24 E)27 SOLUTION:Total Students = 36 One third of the students are boys = 1/3*36 = 12 Three fourths of the boys are under six feet tall = 3/4*12 = 9 ... Therefore Number of boys in the class under six feet tall = 9 ... Answer A.... Alternatively... Number of boys in the class under six feet tall = 3/4 of 1/3 of Total Students = 3/4*1/3*36 = 9... Answer A #### A QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)288 B)2609 C)245 D)298 E)221 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer:C #### C QUESTION:The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability W that exactly two visitors will buy a pack of candy? options: A)0.343 B)0.147 C)0.189 D)0.063 E)0.027 SOLUTION:3C2 * (3/10)^2 * 7/10 = 3 * 9/100 * 7/10 = 189/1000 = 0.189=W Answer - C #### C QUESTION:If the integer w is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when w is rounded to the nearest ten. which of the following is a possible value of w? options: A)64 B)67 C)99 D)133 E)147 SOLUTION:We have to check options 1 by 1. 64 rounded to nearest hundred = 100 64 rounded to nearest ten = 60 now difference = 40 the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. therefore 40/60)*100 = 66 2/3 ==>this is the answer. 99 rounded to nearest ten = 100 133 rounded to nearest ten = 130 133 rounded to nearest hundred w= 100=A #### A QUESTION:The three competitors in a race have to be randomly chosen from a group of three men and three women. How many different such trios contain at least one woman? options: A)13 B)15 C)17 D)19 E)21 SOLUTION:The total number of ways to choose three runners 6C3 = 20 The number of trios with only males is 3C3 = 1 The number of trios which include at least one woman is 19. The answer is D. #### D QUESTION:What approximate value should come in place of question mark (?) in the following equation? 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ? options: A)230 B)225 C)232 D)220 E)240 SOLUTION:? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12 = 256.3 + 40.3 – 66.12 ≈ 232 Answer C #### C QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $500 per sq. metre. options: A)$10312.50 B)$13512.50 C)$16512.50 D)$14512.50 E)$18512.50 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $500 Hence, total cost =5.5×3.75×500= $10312.50 A #### A QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is: options: A)14 B)7 C)20 D)70 E)35 SOLUTION:Explanation : Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2. Number of Apples = 10x = 20. Answer : C #### C QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:18 C)18:22 D)18:39 E)18:39 SOLUTION:Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer:A #### A QUESTION:The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes? options: A)5! B)10!/(5!5!) C)10!/5! D)10! E)10!*5! SOLUTION:Total Soloists to choose from = 10 Soloist Required = 5 Question : How many different combinations R of soloists can appear in the liner notes? The language of the question clearly mentions that only the combinations need to be calculated i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question) Method-1: Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!) Method-2: No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6 Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter, Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!) Answer: Option B #### B QUESTION:Calculate the sum of first 89 natural numbers. options: A)2017 B)2647 C)2147 D)2045 E)4005 SOLUTION:Solution We know that(1+2+3+.....+89) = n(n+1)/2 Therefore (1+2+3+....+89) =(89×90 / 2) = 4005. Answer E #### E QUESTION:(x —1)(x + 3) > 0 (x +5)(x—4) < 0 Which of the following values of x satisfy both inequalities shown? I. -6 II. -4 III. 2 IV. 3 options: A)I and II only B)I and III only C)II and III only D)II and IV only E)II, III, and IV SOLUTION:(x - 1)(x + 3) > 0 --> x<-3 or x>1. (x + 5)(x - 4) < 0 --> -5<x<4. Among choices only -4 and 2 satisfy both inequalities. Answer: E. #### E QUESTION:The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is options: A)17.2 km B)7.2 km C)7.6 km D)17.6 km E)27.2 km SOLUTION:speed of a boat in still water = 15 km/hr Speed of the current = 3 km/hr Speed downstream = (15+3) = 18 km/hr Distance travelled downstream in 24 minutes=(24/60)×18=(2×18)/5 = 7.2 km Answer is B #### B QUESTION:There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible? options: A)435 B)367 C)361 D)297 E)261 SOLUTION:Explanation: Total number of persons = n = 30 Shakehands involve only 2 persons = r = 2 Number of shakehands = nCr = 30C2 30C2 = (30 * 29) /(2 * 1) = 435 nCr = (n!) / r! (n – r)! = 30! / 2! 28! = 435 ANSWER:A #### A QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men? options: A)15.5 B)15.4 C)15.25 D)15.3 E)15.6 SOLUTION:Total age of 20 men = 15.6 x 20 = 312 Now, total age of 25 men = 389. Total age of five men added later = 389 - 312 = 77. Hence, the total average of five men = 77/5 = 15.4 ANSWER:B #### B QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value W of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer W is 342. The correct answer is E. #### E QUESTION:Find the unit digit in the product 274*318*577*313 options: A)5 B)2 C)10 D)26 E)89 SOLUTION:Explanation: Required digit=Unit digit is in(4*8*7*3)=2 Answer B #### B QUESTION:An enterprising businessman earns an income of Re 5 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 10th day of business, he earns an income of: options: A)21 B)22 C)20 D)45 E)30 SOLUTION:2nd day he earns = 3(2 – 5) 3rd day he earns = 3(3 – 5) On 20th day he earns 3(20 -5) = 45 rupees ANSWER:D #### D QUESTION:The train travels at an average speed of 16km/h, to the top of the hill where the midpoint of the trip is. Going down hill, train travels at an average speed of 8km/h. Which of the following is the closest approximation of train's average speed, in kilometers per hour, for the round trip? options: A)9.6 B)10.6 C)4.3 D)2.5 E)5.3 SOLUTION:Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 16km/hour and 8 km/hour, using a multiple of both 16 and 8 would make the math easiest. Let's set the Distance up the hill at 64 km. So, going uphill, we have.... D = (R)(T) 64 = (16)(T) 64/16 = 4 = T 4 hours to go uphill Going downhill, we have.... D = (R)(T) 60 = (20)(T) 64/8 = 8 = T 8 hours to go downhill Total Distance = 120 km Total Time = 4+8 = 12 hours Average Speed = 128/12 = 10.6 km/hour B #### B QUESTION:The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is? options: A)38 B)27 C)75 D)28 E)21 SOLUTION:Explanation: The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75. Answer: C #### C QUESTION:If -1 < x < 0, which of the following must be true? I. x^4 < x^3 II. x^6 < 1 – x III. x^5 < x^2 options: A)I only B)II only C)III only D)II,III only E)I,II,III only SOLUTION:Answer : E #### E QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 7. options: A)18 B)20 C)17.5 D)30 E)32 SOLUTION:Solution Average = (7+14+21+28)/4) = 70 / 4 = 17.5. Answer C #### C QUESTION:If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? options: A)$28000 B)$15000 C)$12000 D)$10000 E)$9000 SOLUTION:Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($7,000*2)*2=$28,000 (after 9 years investment will become $7,000*2=$14,000 and in another 9 years it'll become $14,000*2=$28,000). Answer: A. #### A QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child? options: A)2 years B)5 years C)9 years D)4 years E)1 years SOLUTION:28 * 2 = 56 20 * 3 = 60 ----------- 4 years Answer:D #### D QUESTION:In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way? options: A)3 sec B)4 sec C)8 sec D)6 sec E)7 sec SOLUTION:T = 52/24 * 18/5 = 8 sec ANSWER:C #### C QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n? options: A)10 B)12 C)16 D)22 E)24 SOLUTION:The average of the numbers in set S is 10. If we increase the mean by 10%, the new mean is 11. Thus, on average, 5 numbers increase by 1. Therefore n = 11+5 = 16 The answer is C. #### C QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x options: A)1 B)2 C)4 D)5 E)6 SOLUTION:46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A #### A QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is options: A)91 B)910 C)61 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 671 and 610. ‹=› 61. Answer C #### C QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:A bat is bought for Rs.400 and sold at a gain of 30% find its selling price? options: A)s.460/- B)s.480/- C)s.500/- D)s.520/- E)s.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 130 % ------> 520 (130 * 4 = 520) Selling price = Rs.520/- Option 'D' #### D QUESTION:Three numbers are in the ratio 1:3:5 and their H.C.F is 5. The numbers are? options: A)5, 15, 35 B)5, 15, 30 C)5, 15, 25 D)5, 15, 40 E)5, 15, 20 SOLUTION:Let the required numbers be x, 3x and 5x. Then, their H.C.F = x. So, x = 5. The numbers are 5, 15, 25. Answer: C #### C QUESTION:The Snow Lovers Ski Team is comprised of 4 men and 8 women. If a team of 5 skiers is to be randomly selected to pack the skis into the bus, what is the probability that the team will have exactly 3 women? options: A)14/33 B)7/33 C)2/7 D)13/73 E)12/27 SOLUTION:Combination Probability Formula: nCr = n!/[r!(n-r)!] Total possible, select 5 people from 12 people = 12C5 = 12!/[5!(12 - 5)!] = 792. To have 3 women there must be 2 men, select 2 men from 4 = 4C2 = 6. And, select 3 women from 8 = 8C3 = 56. 3 women and 2 men = (6)(56) = 336 Probability = (number outcomes favorable)/(total number outcomes) = 336/792 = 14/33 Answer: A #### A QUESTION:The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle? options: A)1 : 96 B)1 : 48 C)1 : 84 D)1 : 68 E)None of these SOLUTION:Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96. ANSWER:A #### A QUESTION:What percent of 7.2 kg is 18 gms ? options: A)25 B)66 C)288 D)19 E)17 SOLUTION:Explanation: Required percentage = (18/7200 * 100)% = 1/4% = 0.25% Answer: A) .25% #### A QUESTION:In a room there are 11 people. Each person shook hands with every other person. How many hand shakes were there? options: A)52 B)53 C)54 D)55 E)56 SOLUTION:11C2 = 55 The answer is D. #### D <<<Examples ends QUESTION:In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is: options: A)2 B)4 C)7 D)12 E)15 SOLUTION:Sol. Speed in still water = 1/2 (9+5) kmph = 7 kmph. Answer C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The password for a computer account has to consist of exactly eight characters. Characters can be chosen from any of the following: letter of the alphabet, numerical digits from 0 to 9, a hyphen, or the exclamation mark. Upper-case letters (e.g., A) are considered different from lower-case letters (e.g., a), and characters can be repeated. Given these rules, how many different passwords are possible? options: A)2^9 B)2^14 C)2^18 D)2^40 E)2^48 SOLUTION:26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have; 26+26+10+1+1 = 64, or 2^6 possibilities per character of the password. Total number of possible combinations: (2^6)^8 = 2^48 ANSWER:E #### E QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5 and 6 such that the numbers are divisible by 9? options: A)1 B)2 C)4 D)6 E)8 SOLUTION:CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. =36, 45, 54, 63 --- 4 Cases Answer: option C #### C QUESTION:Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet? options: A)U B)Y C)O D)Y E)R SOLUTION:10th letter from your left is J 7th letter from your right is T The mid letter between J and T is O. Answer: Option 'C' #### C QUESTION:It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number X? options: A)a. 2^96 + 1 B)b. 2^16 - 1 C)c. 2^16 + 1 D)d. 7 * 2^33 E)e. 2^64 + 1 SOLUTION:a³ + b³ =(a+b)(a² -ab +b²) Now, let (2^32 + 1) be (a+b) a³ + b³ = (2^96 + 1) Now, as mentioned in formula above, a³ + b³ is always divisible by (a+b) So any factor of X=(a+b) is a factor of (a³ + b³) Henca A #### A QUESTION:19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)286 B)342 C)422 D)540 E)618 SOLUTION:2*19C2 = 2*171 = 342 The answer is B. #### B QUESTION:5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3294, how much was it in the beginning? options: A)2988 B)2776 C)4079 D)2871 E)881 SOLUTION:X * (95/100) * (85/100) = 3294 X = 4079 Answer:C #### C QUESTION:f, b, c, and d are positive integers. If the remainder is 9 when f is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d? options: A) 20 B) 19 C) 18 D) 16 E) 15 SOLUTION:When f is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6. b + d cannot be 15, hence E is the answer. #### E QUESTION:If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it? options: A)8 B)24 C)32 D)56 E)192 SOLUTION:let AABBCCDD is the group with same letter representing a sibling pair. total # ways to select 3 from 8 is 8C3=56 Qtn: committee of 3 NOT having siblings in it = Total (56) - committee of 3 with siblings in it committee of 3 with siblings = select 2As and one from rem. 6. This can be done in 4 ways as 4 different letters A,B,C and D = 4 * (2C2*6C1) = 24 Hence Answer = 56-24 = 32 ANS:C #### C QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision? options: A)2008 B)2004 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008. Answer: A. #### A QUESTION:In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3 4/3 = 22-2 / 13-x 52-4x = 66-6 x = -2 The answer is A. #### A QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:If n and y are positive integers and 450y = n^3, which of the following must be an integer? options: A)y/(3*2^2*5) B)y/(3^2*2*5) C)y/(3*2*5^2) D)y/(5^3*2^2) E)y/(5*3*2) SOLUTION:Solution: As y and n are both integers so y is of the form of 3*5*2*2*K where K= an integer. to make n as an integer and 450y to be a cube of a number. Now checking with the answers we get only 1 as K. So the answer is (1). #### A QUESTION:There are 1000000 people in city X, out of these 70% people having voting rights and out of those 55% voters votes candidate A and out of them 20% voters are senior citizens.Then find out the number of senior citizens who votes candidate A having voting rights? options: A)8300 B)14500 C)7700 D)13000 E)5900 SOLUTION:Total number of people having voting rights = 100000; out of those 70% voters votes candidate A = 70000; out of them 55% voters votes candidate A = 38500; out of them 20% voters are senior citizens = 7700 #### C QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? options: A)10 hours B)17 hours C)19 hours D)16 hours E)27 hours SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is? options: A)11 B)20 C)28 D)17 E)13 SOLUTION:Explanation: It is the same as a person with 20 years more age replaces an existing person of the group ( or village) Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village. Alternatively : ( n x 42 ) + 20 = ( n x 43 ) => n=20 Answer: B #### B QUESTION:A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 60 kmph. When and at what distance from Mumbai do the two trains meet? options: A)187 B)279 C)120 D)278 E)379 SOLUTION:When the second train leaves Mumbai the first train covers 40 * 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (60 -40) = 2 hours So, the two trains meet at 12 a.m. The two trains meet 2 * 60 = 120 km away from Mumbai. Answer:C #### C QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three? options: A)5 B)7 C)9 D)11 E)13 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 40 = 20 + 30 + 10 - (10) - 2x x = 5 So, answer will be A #### A QUESTION:Three houses of the same type were advertised to be let in a locality. four men made separate applications for a house. What is the probability that each of them applied for the same house. options: A)1/4 B)1/6 C)1/8 D)1/9 E)3/256 SOLUTION:Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 3 houses 1/3 Let us consider case where all 4 men choose House no 1 So for First men it will be 1/4,second men 1/4 , third men also 1/4 and fourth man 1/4 So probability of selecting house no 1 is 1/4*1/4*1/4*1/4= 1/256 And since there are 3 such house so probability that each men select the same house is 3*1/256 Ans is E #### E QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train. options: A)150 m B)145 m C)100 m D)135 m E)155 m SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 6 = 100 meter ANSWER: C #### C QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 * 11 * 7 = 154 ANSWER:B #### B QUESTION:What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58 ? options: A)1288 B)2797 C)3944 D)1299 E)1082 SOLUTION:Let the side of the square plot be 'a' ft. Given area of the plot (a x a) = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 x 58 = Rs. 3944. Answer: C #### C QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour. options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these SOLUTION:Explanation: We know Time = Distance/speed So total time taken = (120/60+160/80)=4hours Time taken for 280 Km = 280/4=70.km/hr Option A #### A QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:John throws a coin until a series of six consecutive heads or three consecutive tails appears. What is the probability that the game will end after the seventh throw? options: A)1/64 B)2/16 C)3/16 D)7/16 E)9/16 SOLUTION:Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are H-T-T-T-T-T ----> P = (1/2)^7= 1/128 T-H-H-H-H-H ----> P = (1/2)^7= 1/128 Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability. 1/128 + 1/128 = 2/128 = 1/64 Answer(A). #### A QUESTION:A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle? options: A)2.5π B)3π C)5π D)4π E)10π SOLUTION:If a rectangle is inscribed in a circle, then the diagonal of the rectangle = diameter of the circle. In this case, diagonal = (9 + 16)^(1/2) = 5 Hence the radius = 2.5 Circumference = 2πr = 2π*2.5 = 5π Correct Option: C #### C QUESTION:If ty > 0 and yz < 0, which of the following must be negative: options: A)tyz B)ty(z^2) C)t(y^2)z D)t(y^2)(z^2) E)(x^2)(y^2)(z^2) SOLUTION:ty > 0 means that ty is positive. yz < 0 means that yz is negative. t(y^2)z = (ty)(yz) = positive*negative = negative. Thus option C is always negative. #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 18 km/hr. What is the length of the platform? options: A)80 B)240 C)288 D)277 E)221 SOLUTION:Speed = 18 * 5/18 = 5 m/sec. Length of the train =5 * 20 = 100 m. Let the length of the platform be x m . Then, (x + 100)/36 = 5 => x = 80 m. Answer: A #### A QUESTION:15 + sqrt(- 6 + 8×5÷4) =? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:According to order of operations, inner brackets first where 8x5÷4 is first calculated since it has a multiplication and a division. 8x5÷4 = 40÷4 = 10 Hence 15 + sqrt(- 6 + 8×5÷4) = 15+ sqrt(- 6 + 10) = 15 + sqrt(4) = 15 + 16 = 31 correct answer A)31 #### A QUESTION:In the city of San Durango, 50 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 30 owned rabbits, and 20 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)8 D)5 E)12 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 50 = 20 + 30 + 30 - (20) - 2x x = 5 So, answer will be D #### D QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C QUESTION:Two trains of equal are running on parallel lines in the same direction at 48 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)60 m B)72 m C)80 m D)82 m E)84 m SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 48 - 36 = 12 km/hr. = 12 * 5/18 = 10/3 m/sec. 2x/36 = 10/3=> x = 60. ANSWER:A #### A QUESTION:Sebastian bought a meal at a restaurant and left a 15% tip. With the tip, he paid exactly $35.42. How much did the meal cost without the tip? options: A)$28.98 B)$29.91 C)$30.15 D)$30.60 E)$30.80 SOLUTION:The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip. Thus, 115% of this price equals $35.42: 1.15x = 35.42 Divide both sides by 1.15:=>x=35.42/1.15=30.80 correct answer E)$30.80 #### E QUESTION:#88 A necklace is made by stringing C individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then C could equal options: A)16 B)32 C)41 D)54 E)58 SOLUTION:You can just write out the pattern and count: RGWBYRGWBYRGWBY... But to save time a good test taker will just look for a pattern. Min # is 3, because W is the third one. Then every 5 beads another white comes, so it must be 3+5+5+5.. and so on... 3+5 = 8 3+5+5 = 13 3+5+5+5=18 3+5+5+5+5=23 So you see it ends in either 8 or 3. 58 IS THE NO. E #### E QUESTION:The average of first 20 natural numbers is? options: A)5.6 B)10.5 C)10.1 D)5.8 E)5.2 SOLUTION:Sum of 20 natural no. = 420/2 = 210 Average = 210/20 = 10.5 Answer:B #### B QUESTION:P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in --- days if all of them are working together. options: A)2 B)3 3⁄7 C)4 ¼ D)5 E)5 ¼ SOLUTION:Explanation : Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/6 Work done by R in 1 day = 1/12 Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24 => Working together, they will complete the work in 24/7 days = 3 3⁄7 days Answer : Option B #### B QUESTION:A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit? options: A)$10 B)$16 C)$20 D)$24 E)$25 SOLUTION:Let P be the original price paid by the retailer. 1.25*P = 100 P = 80 The profit is $20. The answer is C. #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)123 B)166 C)240 D)157 E)198 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: C #### C QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:?% of 360 = 126 options: A)277 B)35 C)64 D)72 E)None of these SOLUTION:?% of 360 = 126 or, ? = 126×100/360=35 Answer B #### B QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 4 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)4/9. C)6/11. D)3/5. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 4buckles = 5buckles + 4buckles = 9buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 9 = x*15 x = 9/15=3/5 Answer: D #### D QUESTION:7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ? options: A)502 B)503 C)504 D)505 E)506 SOLUTION:7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3. Now,we see 3,7,11,15....2015 are in AP tn=a+(n-1)d 2015=3+(n-1)4 2015=3+4n-4 4n=2016 n=504 ANSWER:C #### C QUESTION:A corporation ten times its annual bonus to 25 of its employees. What percent of the employees’ new bonus is the increase? options: A)25% B)44% C)38% D)9% E)90% SOLUTION:Let the annual bonus be X. A corporation triples its annual bonus. So new bonus = 10X. Increase = 10X-X =9X The increase is what percent of the employees’ new bonus = (9X/10X)*100 = 90% Hence E. #### E QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 21 months? options: A)18:11 B)18:15 C)21:11 D)18:121 E)18:112 SOLUTION:A invests Rs.8000 for 21 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*21 : (8000*4) + (4000*14) 168000 : 88000 A:B = 21:11.Answer:C #### C QUESTION:A natural number has exactly 10 divisors including 1 and itself.how many distint prime factors this natural number will have? options: A)37 B)29 C)27 D)99 E)11 SOLUTION:Answer:D #### D QUESTION:If a and b are the roots of the equation x2 - 9x + 20 = 0, find the value of a2 + b2 + ab? options: A)10 B)25 C)36 D)61 E)87 SOLUTION:Explanation: a2 + b2 + ab = a2 + b2 + 2ab - ab i.e., (a + b)2 - ab from x2 - 9x + 20 = 0, we have a + b = 9 and ab = 20. Hence the value of required expression (9)2 - 20 = 61. Answer D #### D QUESTION:Rahul went to a shop and bought things worth Rs. 45, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)A)19.7 B)B)19.9 C)C)20.9 D)D)21.9 E)E)39.7 SOLUTION:Total cost of the items he purchased = Rs.45 Given that out of this Rs.45, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (45−30/100−x)6/100 = 30/100 ⇒ 6(45 −0.3 −x) = 30 ⇒ (45 − 0.3 − x) = 5 ⇒ x = 45 − 0.3 − 5 = 39.7 E) #### E QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:2^2*3^3*2^2*3^6 = options: A)3^5*2^5 B)2^9*3^4 C)2^4*3^9 D)5^8 E)6^10 SOLUTION:2^2*3^3*2^2*3^6 = A) 3^5*2^5 B) 2^9*3^4 C) 2^4*3^9 D) 5^8 E) 6^10 If the base is same, powers are added so that follows C) 2^4*3^9. Hence the answer is C #### C QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these SOLUTION:Explanation: Volume of water displaced = (8 x 2 x 0.01) m3 = 0.16 m3. ∴ Mass of man = Volume of Water displaced x Density of water = (0.16 x 1000)kg = 160 kg. Answer: D #### D QUESTION:A car dealership has 40 cars on the lot, 15% of which are silver. If the dealership receives a new shipment of 80 cars, 30% of which are not silver, what percentage of total number of cars are silver? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:The number of silver cars is 0.15*40 + 0.3*80 = 30 The percentage of cars which are silver is 30/120 = 25% The answer is B. #### B QUESTION:If n + 14 is a positive odd integer, which of the following must be true about the sum of the next four integers? options: A)It is a multiple of 3 B)It is a multiple of 4 C)It is a multiple of 2 D)It is a multiple of 5 E)It is a prime number SOLUTION:n+14 is a positive odd integer. This means n will be an odd integer The next 4 integers would be: n + 14, n + 15, n + 16, n + 17 Sum = 4n + 62 This sum will always be even. Option C #### C QUESTION:Which of the following is not a prime number ? options: A)502 B)503 C)509 D)521 E)523 SOLUTION:Clearly, 502 is not a prime number. Answer : A #### A QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)40 B)41 C)48 D)67 E)45 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: Option C #### C QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11 SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify. As for your question, it is very simple and straightforward with number plug in. Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E QUESTION:Set A = {1, 2, 3, 4, 5, 6, q} Which of the following possible values for q would cause Set A to have the smallest standard deviation? options: A) 1 B) 2.5 C) 3 D) 3.5 E) 7 SOLUTION:I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice. Answer D. #### D QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)*28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y? options: A)7/9 B)14/9 C)7/18 D)11/13 E)It Cannot Be Determined SOLUTION:Ratio = 7k/9k = 7/9, 14/18, etc. v and y are increased by 4 --> (7k + 4)/(9k + 4) New ratio can be 11/13, 18/22, etc. Answer: E #### E QUESTION:A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? options: A)22 days B)4 days C)13 days D)6 days E)9 days SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12). B's 1 day's work =((1/4)-(1/12))=(1/6) Hence, B alone can complete the work in 6 days. Answer is D. #### D QUESTION:Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace? options: A)2/5525 B)3/5525 C)2/5525 D)2/5526 E)4/5525 SOLUTION:Let Q denote the event that the card drawn is queen and A be the event that the card drawn is an ace. Clearly, we have to find P (QQA) Now P(Q) = 4/52 Also, P (Q|Q) is the probability of second queen with the condition that one queen has already been drawn. Now there are three queen in (52 - 1) = 51 cards. Therefore P(Q|Q) = 3/51 P(A|QQ) is the probability of third drawn card to be an ace, with the condition that two queens have already been drawn. Now there are four aces in left 50 cards. Therefore P(A|QQ) = 4/50 By multiplication law of probability, we have P(QQA) = P(Q) P(Q|Q) P(A|QQ) = 4/52 × 3/51 × 4/50 = 2/5525. A) #### A QUESTION:Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there? options: A)20 toys B)30 toys C)40 toys D)60 toys E)50 toys SOLUTION:x : the total number of toys x/10 : the number of toys for first child x/10 + 12 : the number of toys for second child x/10 + 1 : the number of toys for the third child 2(x/10 + 1) : the number of toys for the fourth child x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x x = 30 toys : solve for x correct answer B #### B QUESTION:there are 15 cars and 16 trucks? which is greater15 or 16? options: A)15 B)14 C)12 D)17 E)16 SOLUTION:E #### E QUESTION:A boat goes 100 km downstream in 10 hours, and 80 km upstream in 20 hours. The speed of the stream is? options: A)4km/h B)3km/h C)2km/h D)(1/2) km/h E)E)None SOLUTION:100 --- 10 DS = 10 ? ---- 1 80 ---- 20 US = 4 ? ----- 1 S = (10 - 4)/2 = 3 kmph ANSWER:B #### B QUESTION:Janet has to pay back her bank loan over 10 months following the below sequence. $50, $55, $65, $80, $85, $95, $110, $115, $125, ? How much will she pay back on the tenth month? options: A)$155 B)$140 C)$135 D)$125 E)$130 SOLUTION:The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 10th Month is $140 Ans B #### B QUESTION:What least number must be subtracted from 427398 so that remaining number is divisible by 15 options: A)3 B)5 C)7 D)9 E)None of these SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Answer: Option A #### A QUESTION:Alex age after 13years will be 10 times his age 10years back. What is the present age of Alex? options: A)15 B)13 C)20 D)21 E)26 SOLUTION:Let Alex's present age be x Alex's age after 17 years = x+17 Alex's age 10 years back = x-10 x+17= 10(x-10) x = 13 Rajeev's present age = 13 years Answer is B #### B QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5 SOLUTION:We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10. # of different approximations are possible. Approach #1: 2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200); 2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107 Answer: C. Approach #2: 2*5=10 3*17=~50 (actually more than 50); 7*13=~100 (actually less than 100); 11*19=~200 (actually more than 200) 2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107. Answer: C. #### C QUESTION:A store reduced the price of all items in the store by 9% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? options: A)80.0 B)80.9 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 9% price becomes = 0.91 *100 = $ 91 after the final reduction of 10% price becomes = 0.9* 91 = $ 81.9 price of all items on second day is 81.9% of price on first day correct answer option E #### E QUESTION:Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is: options: A)0.20887 B)0.3887 C)0.33487 D)0.20833 E)0.38222 SOLUTION:Explanation: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x \therefore Cultivated land of village = 384000x \therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833 Answer: D #### D QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4? options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1 SOLUTION:Solving for y/x gives, 1/17 (C) #### C QUESTION:In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr? options: A)2.5 sec B)4.25 Sec C)5 sec D)12.5 sec E)None SOLUTION:Solution Speed = (144 x 5 /18) m/sec = 40 m / sec Time taken = (100 /40) sec = 2.5 sec. Answer A #### A QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:For a certain exam,a score of 86 was 5 standard deviations above mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam? options: A)50 B)55 C)48 D)42 E)49 SOLUTION:Mean+5SD=86 Mean+2.5SD=67 By solving above equations we get, SD (absolute value)=7.6 Mean=48 ANS. C #### C QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer: A #### A QUESTION:In a certain country, 60 percent of the population likes basketball, and 34 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf? options: A)20% B)33% C)40% D)57% E)67% SOLUTION:Correct Answer: (D). Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 34 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 34/60 = 57%, or choice D. #### D QUESTION:Boy sells a book for Rs. 540 he gets a loss of 10 %, To gain 10%, what should be the SP? options: A)430 B)450 C)550 D)590 E)660 SOLUTION:Cost price = 540/90 x 100 = 600 To gain 10% = 600 x 10/100 = 60 SP = CP + gain = 600 + 60 = 660 Answer :E #### E QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is options: A)153550 m^2 B)153600 m^2 C)153700 m^2 D)153800 m^2 E)153900 m^2 SOLUTION:Explanation: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m^2. Option B #### B QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) a < c - b (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 1800 options: A)30 B)70 C)210 D)300 E)180 SOLUTION:27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3. 100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10. Then we want to know what is the largest possible GCF of x and 2100. Well 1800 = 3 * 6 * 10 * 10 We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible. We know x has one factor of 3, but not two factors --- that takes the 3. We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking. 3*6*10 = 180 If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 1800. E #### E QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44 SOLUTION:A 11, 42 Let the age of Priya = x years Then, the age of her father = (x+ 31) years ATQ, (x+ 8) + (x+ 31 + 8) = 69 2x+ 47 = 69 2x= 69 – 47 = 22 x= 11 The age of Priya = 11 years The age of her father = 11 + 31 = 42 years #### A QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 20 years = (20 + 20) years =40 years. Answer : C #### C QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 10 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)20 litres E)8 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+10)=4/5 20x=4(3x+10) 8x=40 x=5 Quantity of alcohol = (4 x 5) litres = 20 litres. Answer is D. #### D QUESTION:When a certain number X is divided by 143, the remainder is 21. Which of the following numbers, if added to X, would result in a number divisible by 13? options: A)7 B)21 C)5 D)47 E)55 SOLUTION:Now X= 143q + 45 = 11*13*q + 21..so we have to make only 21 div by 13.. 21 + 5 = 26 divisible by 13 , add 5 ans C #### C QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:How many possible integer values are there for x if |4x - 3| < 6 ? options: A)One B)Two C)Three D)Four E)Five SOLUTION:Solution: |4x-3| < 6 let 4x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left (the less than sign represents that the a must be within boundaries ) (3-6)----------3----------(3+6) now, we have -3<a<9 but a =4x ==> -3<4x<9 dividing all values by +4 we have -0.75 <x < 2.24 Now question says Integer values (not rational ) therefore we have 0,1,2 ANSWER:C #### C QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C QUESTION:For which of the following values of s is (40+s)/s an integer? options: A)3 B)4 C)9 D)11 E)40 SOLUTION:This problem has to be solved by checking the options (40 + s)/s For this entity to be an integer, 50 + s should be divisible by s Option A: 43/3 - Not an Integer Option B:44/4 - Not an Integer Option C: 49/9 - Not an integer Option D: 51/11 - Not an integer Option E - 80/40- Integer Correct Option: E #### E QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ? options: A)3700 B)3890 C)88798 D)2789 E)2891 SOLUTION:Explanation: Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700. Answer: A) 3700 #### A QUESTION:The product Z of two prime numbers is between 10 and 30 . If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24, then what is Z? options: A)21 B)15 C)14 D)10 E)6 SOLUTION:The smallest possible product is 21 which is 3*7. All other products are too big. The answer is A. #### A QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)26% C)42% D)27% E)22% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer: A #### A QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean m. 72 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.6 years and the standard deviation is 2.6 years, what percent of the distribution has more than 10.2 years as a shelf’s average life? options: A)17% B)16% C)15% D)14% E)13% SOLUTION:Average = 7.6 SD = 2.6 7.6 - 2.6 < 72% of distribution < 7.6 + 2.6 5.0 < 72% of distribution < 10.2 28% is outside this range. Given: Distribution is symmetric. So 14% of distribution is less than 5.0 and the other 14% of distribution is greater than 10.2. Answer: D #### D QUESTION:Find the odd man out. 12, 24, 36, 48, 61, 72, 84 options: A)15 B)25 C)61 D)90 E)115 SOLUTION:Explanation : All except 61 are multiples of 7 Answer : Option C #### C QUESTION:Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid? options: A)D + 40 B)D + H – 1 C)D + 2H D)6.93H E)1.21D SOLUTION:before Discount price was: 1.4D+1.5H After Discount: 1.4D +1.5H-.42D-.45H substitute D=6H final value: 6.93H Ans Is D #### D QUESTION:David obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)None of these SOLUTION:Solution Average = (76+65+82+67+85 / 5) =(375 / 5) = 75. Answer D #### D QUESTION:If (x + 1)^2 = 144, which of the following could be the value of 2x? options: A)–26 B)–13 C)–10 D)12 E)-21 SOLUTION:You can also get to the answer by backsolving using answer choices Starting with choice B = -13 (x + 1)^2 = 144 (-13 + 1)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -13 will result in 144 in the equation so x must be -11, Then 2x = 2 * -13 = -26 Answer: A #### A QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour ⇒ x/7+x/5=1 ⇒5x+7x=35 ⇒12x=35 ⇒x=2.9 km Answer: Option C #### C QUESTION:The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number? options: A)72 B)83 C)45 D)53 E)64 SOLUTION:Sum of all the 13 numbers = 13 * 58 = 754 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 754 = 72. Answer:A #### A QUESTION:Karthikeyan arranged a party to celebrate his birth day.20 of his close friends were invited. One friend left before the cake was cut due to an urgent phone call.The big cake was drawing the attention of the party visitors. This cake is to be divided among friends and of course Karthikeyan will get his share. A man eats 3 pieces, a woman eats two pieces and a child eats half a piece of cake. Including Karthikeyan count the number of men,women and children in the party. There are 20 pieces of cake in all. options: A)6 women, 2 men and 12 children B)7 women, 1 men and 12 children C)5 women, 1 men and 14 children D)4 women, 2 men and 14 children E)None of these SOLUTION:Let the number of men be m, number of women be w and number of children be c Total number of pieces = Pieces ate by men + Pieces ate by women + Pieces ate by children There are 20 total pieces. Also a man eats 3 pieces, a woman eats 2 and children half. Therefore above equation becomes. 20 = 3m + 2w + 1/2c In the above equation, you have to substitute the values given in options to find which one satisfies the equation. Option c with m = 1, c = 14 and w = 5 perfectly satisfies the equation as follows 20 = 3(1) + 2(5) + (1/2)(14) 20 = 20 i,e our equation is satisfied perfectly by option c ANSWER:C #### C QUESTION:Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $12.00 each, what was Company C’s gross profit? options: A) $2,250 B) $2,500 C) $4,100 D) $3,250 E) $4,500 SOLUTION:Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900 Revenue : 500 * 12 = $6000 Profit: 6000 - 1900 = $ 4100 Option C is correct #### C QUESTION:If the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers? options: A)4:9 B)4:3 C)3:7 D)2:5 E)1:6 SOLUTION:The ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9. The ratio of apples to bananas to cucumbers is 4 to 3 to 9. The answer is A. #### A QUESTION:A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days? options: A)3.75 days B)3.99 days C)2.67 days D)2.98 days E)2.44 days SOLUTION:1/4 + 1/8 = 3/8 8/3 = 2.67 days Answer: C #### C QUESTION:A cab driver 5 days income was $250, $400, $750, $400 , $500. Then his average income is? options: A)$440 B)$450 C)$460 D)$470 E)$480 SOLUTION:avg = sum of observations/number of observations avg income=(250+400+750+400+500)/5 = 460 Answer is C #### C QUESTION:Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 50 years. The age of E is? options: A)50 B)47 C)48 D)49 E)46 SOLUTION:Solution 5 years ago average age of A,B,C,D = 45 years => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years => Total present age of A, B, C, D = 180 + 5x4 = 200 years If E's present age is x years = 200+x/5= 50 x=50 years. Answer A #### A QUESTION:A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers? options: A)330 B)650 C)729 D)800 E)890 SOLUTION:Choose 4 starters from a team of 11 players. Order is not important. \inline {\color{Black} 11C_{4}}= 330 A #### A QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l * l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 52 years now, the son's age five years back was? options: A)16 years B)14 years C)18 years D)21 years E)15 years SOLUTION:Let the son's present age be x years. Then, (52 - x) = x 2x = 52 => x = 26 Son's age 5 years back = (26 - 5) = 21 years. Answer: D #### D QUESTION:The train travels at an average speed of 16km/h, to the top of the hill where the midpoint of the trip is. Going down hill, train travels at an average speed of 8km/h. Which of the following is the closest approximation of train's average speed, in kilometers per hour, for the round trip? options: A)9.6 B)10.6 C)4.3 D)2.5 E)5.3 SOLUTION:Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 16km/hour and 8 km/hour, using a multiple of both 16 and 8 would make the math easiest. Let's set the Distance up the hill at 64 km. So, going uphill, we have.... D = (R)(T) 64 = (16)(T) 64/16 = 4 = T 4 hours to go uphill Going downhill, we have.... D = (R)(T) 60 = (20)(T) 64/8 = 8 = T 8 hours to go downhill Total Distance = 120 km Total Time = 4+8 = 12 hours Average Speed = 128/12 = 10.6 km/hour B #### B QUESTION:If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days? options: A)47.6 kg B)52.6 kg C)59.6 kg D)56.6 kg E)57.6 kg SOLUTION:(3 * 5)/48 = (9 * 2)/ x x = 57.6 kg ANSWER:E #### E QUESTION:If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle. options: A)127 cm^2 B)125 cm^2 C)120 cm^2 D)102 cm^2 E)None of them SOLUTION:Let length = x and breadth = y. Then, 2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289. Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120 Area = xy = 120 cm^2 Answer is C. #### C QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)227 B)177 C)120 D)288 E)271 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m.Answer:C #### C QUESTION:[1/(1.2.3)] + [1/(2.3.4)] + [1/(3.4.5)] + [1/(4.5.6)] is equal to options: A)7 / 30 B)11 / 30 C)13 / 30 D)17 / 30 E)None SOLUTION:Answer Given Exp. = [(4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3)] / [(2 x 3 x 4 x 5 x 6)] = 168 / (24 x 30) = 7 / 30 Correct Option: A #### A QUESTION:If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is options: A)1/2 B)1 C)2 D)4 E)8 SOLUTION:Given: 5/w + 5/x = 5/ywx=y Find: (w+x)/2 = ? 5(1/w + 1/x) = 5(1/y) - divide both sides by 5 (1/w + 1/x) = 1/y (x+w)/wx = 1/wx - sub'd in y=wx x+w - 1 = 0 x+w = 1 Therefore (w+x)/2 = 1/2 Ans: A #### A QUESTION:The rate of Interest on a sum of money is 11% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is options: A)1,000 B)2,000 C)2,100 D)2,250 E)2,540 SOLUTION:Explanation: I1 = (P x 3 x 11)/100 = P/3 I2 = (P x 4 x 4)/100 = 4P/25 I3 = (P x 1 x 5)/100 = P/20 P/3 + 4P/25 + P/20 = 540 27P/50 = 540 P = 1000 Answer: Option A #### A QUESTION:Some of the 50% solution of acid was removed and this was replaced with an equal amount of 14% solution of acid. As a result, a 23% solution of acid was obtained. What fraction of the original solution was replaced? options: A)1/2 B)1/3 C)2/3 D)3/4 E)4/5 SOLUTION:Let x be the fraction of the original solution that was replaced. 0.5*(1-x)+0.14(x)=0.23 0.36x=0.27 x=3/4 The answer is D. #### D QUESTION:A and B started a business with their capitals Rs. 3,00,000 and 18,00,000 respectively. Annual profit will be distributed between them in the ratio options: A)2:5 B)2:3 C)1:3 D)1:6 E)1:9 SOLUTION:3,00,000:18,00,000 Ans. 1:6 ANSWER:D #### D QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder. The dividend is options: A)74 B)78 C)86 D)92 E)106 SOLUTION:Divisor = (6 * 3) + 7 = 25 5 * Quotient = 25 Quotient = 5. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 5) + 6 = 106. E) #### E QUESTION:The population of a town is 45000; 5/9th of them are males and the rest females 40% of the males are married. What is the percentage of married females? options: A)56% B)50% C)57% D)10% E)80% SOLUTION:Male = 45,000* 5/9 = 25,000 Female = 45,000* 4/9 = 20,000 Married Male = 25,000* 40/100 = 10,000 Married Female = 10,000 20,000 ------------ 10,000 100 ------------- ? => 50% Answer: B #### B QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)88% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,11 = 11/100 x= 80*11/100 x= 8.8 8.8/10 = 0.88 = 88%, Answer C #### C QUESTION:What is the minimum value of |x-4| + |x+8| + |x-5| ? options: A)-13 B)13 C)5 D)7 E)8 SOLUTION:A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative. |x-4| >= 0 --> Minimum occurs at x = 4 |x+8| >= 0 --> Minimum occurs at x = -8 |x-5| >= 0 --> Minimum occurs at x = 5 x = -8 --> Result = 12 + 0 + 13 = 25. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9. x = 4 --> Result = 0 + 12 + 1 = 13 x = 5 --> Result = 1 + 13 + 0 = 14 x = 8 --> Result = 4 + 16 + 3 = 23 So minimum value of the expression occurs at x = 4 and the resultant value = 13 Answer: B #### B QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 20% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? options: A)40% B)45% C)55% D)60% E)64% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 80% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5*(4/5) of the original price, which nets to 0.64 of the original price, or 64%. E #### E QUESTION:A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: options: A)4 mph B)2.5 mph C)3 mph D)2 mph E)None of these SOLUTION:Explanation : Speed of the boat in still water = 10 mph Let speed of the stream be x mph Then, speed downstream = (10+x) mph speed upstream = (10-x) mph Time taken to travel 36 miles upstream - Time taken to travel 36 miles downstream = 90/60 hours =>36/(10−x) − 36/(10+x) = 3/2 =>12/(10−x) − 12/(10+x) = 1/2 =>24(10 + x) − 24(10 − x) = (10 + x)(10 − x) =>240 + 24x − 240 + 24x = (100−x2) =>48x = 100 − x2 =>x2 + 48x − 100 =0 =>(x+50)(x−2)=0 => x = -50 or 2. Answer : Option D #### D QUESTION:Find the odd man out 32, 34, 42, 46, 58, 59, 60, 66 options: A)31 B)41 C)67 D)59 E)61 SOLUTION:as 59 is only odd number. ANSWER:D #### D <<<Examples ends QUESTION:The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : options: A)144 m2 B)140 m2 C)108 m2 D)158 m2 E)None of these SOLUTION:Area of the outer rectangle = 23 × 16 = 368 m2 Area of the inner rectangle = 19 × 12 = 228 m2 Required area = (368 – 228) = 140 m2 Answer B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d? options: A) 5/6*d B) 7/3*d C) 10/3*d D) 7/2*d E) 9/2*d SOLUTION:Favid has d books; Jeff has d/3 books; Paula has 2d books; Total = d+d/3+2d=10d/3. Answer: C. #### C QUESTION:Insert the missing number 100,91,....,76,70 options: A)82 B)83 C)84 D)81 E)80 SOLUTION:Missing number: 83 Answer: B #### B QUESTION:How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol? options: A) 7/2 B) 5 C) 20/3 D) 8 E) 300/17 SOLUTION:20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents. If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters. According to the statement; 20+x = 32% of (100+x) OR 20+x=(100+x)8/25 500+25x=800+8x 17x=300 x=300/17 Ans:E #### E QUESTION:A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. options: A)40 B)50 C)62 D)45 E)56 SOLUTION:Let the average after 11th inning = x Then, average after 10th inning = x-5 10(x-5)+100 = 11x x = 100-50 = 50 Answer is B #### B QUESTION:From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x) options: A)10 B)14 C)15 D)16 E)30 SOLUTION:Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations E #### E QUESTION:Of the 25 cupcakes in the bakery, 20 percent are chocolate. How many vanilla cupcakes must be sold in order to bring the number of chocolate cupcakes up to 50 percent of the cupcakes in the bakery? options: A)1 B)5 C)10 D)15 E)20 SOLUTION:Now, there are 5 chocolate cupcakes (20% of 25) and 25-5=20 vanilla cupcakes at the bakery. We need there to be 5 chocolate and 5 vanilla cupcakes, in this case there will be 50% chocolate and 50% vanilla. Therefore 20-5=15 vanilla cupcakes must be sold. Answer: D. #### D QUESTION:For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? options: A)(-3)^2 B)2 C)3 D)4 E)5 SOLUTION:Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4 Step 2, For each number: subtract the Mean and square the result = (1-4)^2=(-3)^2 (2-4)^2=(-2)^2 (3-4)^2 =(-1)^2 (4-4)^2=(.0)^2 (5-4)^2=(1)^2 Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options. Hence A #### A QUESTION:If 6 (A's capital) = 8 (B's capital) = 8 (C's capital). Then the ratio of their capitals is? options: A)4:15:16 B)4:15:68 C)4:3:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 8 C A:B:C = 1/6:1/8:1/8 = 4:3:3 Answer: C #### C QUESTION:Find the odd man out. 14,35,49,60,70 options: A)14 B)35 C)49 D)60 E)70 SOLUTION:All except 60 are multiples of 7 Answer is D #### D QUESTION:Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit options: A)Rs. 8510 B)Rs. 8620 C)Rs. 8730 D)Rs. 8820 E)None of these SOLUTION:Explanation: =>(8000×(1+5/100)2) =>8000×21/20×21/20 =>8820 Option D #### D QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have? options: A)10 B)16 C)8 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1080 180n - 360 = 1080 180n = 1440 n = 1440/180 = 8 ANSWER:C #### C QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils? options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44 SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p. Selling at a loss: 90 - 90p = 40p --> p = 9/13. (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44. Answer: E. #### E QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n? options: A)10 B)12 C)16 D)22 E)24 SOLUTION:The average of the numbers in set S is 10. If we increase the mean by 10%, the new mean is 11. Thus, on average, 5 numbers increase by 1. Therefore n = 11+5 = 16 The answer is C. #### C QUESTION:In a 500 m race, the ratio of speeds of two runners P and Q is 3:5. P has a start of 200 m then the distance between P and Q at the finish of the race is: options: A)Both reach at the same time B)P wins by 100 m C)Q wins by 50 m D)Q wins by 100 m E)None of these SOLUTION:Explanation : When P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5. According to question P has already covered 200 m when Q is starting at starting point and Q needs to cove 300 m more mean while P covers this 300 m when Q can cover 500 m. So, both P and Q will reach the finishing point at the same time. Thus, Both reach at the same time. Answer : A #### A QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)12 B)18 C)22 D)24 E)none of these SOLUTION:Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x 27 * x = 36 * 18 x = (36 * 18)/27 x = 24. Answer is D. #### D QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 300*1 = revenue (eq -1) if he reduced his price by 20% then , 240*(customer) = 125/100*revenue customer = 1.25*300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:The area of a triangle is with base 3m and height 4m? options: A)4 m2 B)6 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 3 * 4 = 6 m2 Answer: B #### B QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/100*6000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day A on which the buses leave at the same time. options: A)A=Tuesday B)Wednesday C)Thursday D)Sunday E)A=The busses will never leave at the same time SOLUTION:The answer is E. I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide. Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E #### E QUESTION:The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is? options: A)10 years B)11 years C)12 years D)13 years E)14 years SOLUTION:Total age of 3 boys = 24*3 =72 ratio of their ages = 1:2:3 Age of the youngest = 72*1/6 = 12 years Answer is C #### C QUESTION:A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %? options: A)62 2/3% B)64 2/3% C)66 2/3% D)66 5/3% E)68 2/3% SOLUTION:Gain=40 lemons Total 100 lemons CP 100-40=60 (40/60)*100 =66 2/3% Ans C #### C QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:In how many ways can the letters of the word CAVERN be arranged in a row so that the vowels appear in alphabetic order? options: A)360 B)720 C)620 D)180 E)36 SOLUTION:Two letters can be arranged in 2! ways. only one combination EIU is required. 6 letters can be arranged in 6! ways. thus 6!/ 2! * 1 = 360. A #### A QUESTION:A train 250 m long is running at a speed of 58 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)18 sec E)15 sec SOLUTION:Answer : D. Speed of the train relative to man = (58 - 8) kmph = (50* 5/18) m/sec = (125/9)m/sec Time taken by the train to cross the man = Time taken by It to cover 250 m at 125/9 m / sec = 250 *9/ 125 sec = 18sec #### D QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss? options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents SOLUTION:50 % profit on $ 1 = $ 50/100 × 1 = $ 0.50× 1 = $ 0.50 Similarly, 40 % loss on $ 1 = $ 40/100 × 1 = $ 0.40× 1 = $ 0.40 Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40 So profit by amount $0.40. Answer is E. #### E QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speed∗Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)7 D)82 E)43 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many straight lines can be formed by joining them ? options: A)124 B)144 C)134 D)142 E)143 SOLUTION:The number of straight lines formed joining the 18 points, taking 2 at a time = 18C2=153. Number of straight lines formed by joining the 5 points, taking 2 at a time =5C2=10. But 5 collinear point, when joined pairwise give only one line. Required number of straight lines =153-10+1 =144. Answer :B #### B QUESTION:The lowest number which should be added to 8247 so that the sum is exactly divisible by 5, 6, 7, 8 and 9 is: options: A)1833 B)1853 C)1733 D)1233 E)1832 SOLUTION:L.C.M. of 5, 6, 7, 8 and 9 = 2520. On dividing 8247 by 2520, the remainder is 687. Number to be added = (2520 - 687) = 1833. Answer: Option 'A' #### A QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:How many of the positive factors of 19 are not factors of 29? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 19 - 1, 19 factors of 29- 1, 29 Comparing both, we have three factors of 19 which are not factors of 29- 19, The answer is B #### B QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 13*0 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:There are 136 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June? options: A)15 B)11 C)12 D)13 E)14 SOLUTION:IMO 15 Take each answer choice and substract it from 136 and the divided this with 11. A #### A QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is options: A)0.092 B)0.92 C)9.2 D)92 E)920 SOLUTION:F(69.28 × 0.004)/0.03 1. 0.004 = 4 × 10^(-3) 2. 0.03 = 3 × 10^(-2) 3. (a × b)/c = a × (b/c) 4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1) Therefore, (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33 Now, 7 × 2 = 14 7 × 1 = 7 or better: 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence, 6.9 <6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition.C #### C QUESTION:Fathers age is 5 times his son’s age. 4 years back the father was 9 times older than son.Find the fathers’ present age. options: A)40 years B)33 years C)22 years D)33 years E)44 years SOLUTION:Ans. 40 years #### A QUESTION:A boy has eight trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)80 ways B)86 ways C)88 ways D)108 ways E)89 ways SOLUTION:The boy can select one trouser in eight ways. The boy can select one shirt in 10 ways. The number of ways in which he can select one trouser and one shirt is 8 * 10 = 80 ways. Answer:A #### A QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:The average salary/head of allthe workers in a workshop is Rs.750, if the average salary/head of 5 technician is Rs.900 and the average salary/head of the rest is Rs.700, the total no. of workers in the work-shop is ? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:Let the total number of workers be y. So sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y -5 workers. 5 x 900 + 700(y -5) = 750 y ⇒ 4500 + 700y - 3500 = 750y ⇒ 50y = 1000 ∴ y = 20 So total number of workers = 20 B #### B QUESTION:If 4x = 8^y, which of the following expresses x in terms of y? options: A)2^(y-2) B)2^(y-1) C)2^(3y-2) D)2^(2y-3) E)2^y SOLUTION:By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: C #### C QUESTION:At what time between 4 & 5 will the hands of a watch point in opposite directions? options: A)50 min past 4 B)42 5/11 min past 4 C)43 min past 4 D)40 min past 4 E)50 4/11 min past 4 SOLUTION:At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30min. spaces apart. Minute hand will have to gain 5 min. spaces. 55min spaces are gained in 60 min. 5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min. Required time = 54 6/11 min. past 4. Answer is E #### E QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer? options: A)55 B)25 C)85 D)45 E)35 SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer. Therefore 0+1+3+4+5+6+7+9=35 Answer is E #### E QUESTION:If xy > 0, which of the following must be negative? options: A)-x/-y B)x/y C)-x/y D)2xy E)x+y SOLUTION:- / + = - Answer : C #### C QUESTION:x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days? options: A)x2/y2 units B)y3/x2 units C)x3/y2 units D)y2/x2 units E)None SOLUTION:Explanation: Let amount of work completed by y men working y hours per in y days = w units More men, more work(direct proportion) More hours, more work(direct proportion) More days, more work(direct proportion) Hence we can write as (men)x:y (hours)x:y (days)x:y }::x:w ⇒x^3w=y^3x ⇒w=y^3x/x^3 =y^3/x^2 Answer: Option B #### B QUESTION:A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? options: A)3:3 B)3:4 C)3:8 D)3:1 E)3:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by A and B = 6000 : 8000 => 3:4.Answer: B #### B QUESTION:A cube of edge 7 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to: options: A)1:25 B)1:49 C)1:52 D)1:522 E)None SOLUTION:Sol. Required ratio = 6 * 1 * 1 / 6 * 7 * 7 = 1/49 = 1:49. Answer B #### B QUESTION:1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10 what is....? options: A)7 B)8 C)9 D)6 E)10 SOLUTION:Equation 28 + 8 + 92 = 10 can be derived from twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10 Similarly for equation, 1 + 9 + 8 One (o) + nine (n) + eight (e) => one (1) correct answer is E)10 #### E QUESTION:How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example options: A)100 B)610 C)729 D)900 E)1000 SOLUTION:The hundred-thousand's digit won't be zero or else it's no longer a 6 digit integer (you could form a palindromic number with five digits though). The subesquent two digits, ten-thousand's and thousand's digit, can be 10 different numbers each, zero - nine. Thus, 9∗10∗10∗1∗1∗1=9009∗10∗10∗1∗1∗1=900 Answer D #### D QUESTION:A reduction of 30% in the price of apples would enable a man to obtain 54 more for Rs.30, what is reduced price per dozen? options: A)1 B)2 C)6 D)7 E)10 SOLUTION:B 30*(30/100) = 9 --- 54 ? --- 12 => Rs.2 #### B QUESTION:What is the value of √36% ? options: A)10% B)20% C)30% D)60% E)40% SOLUTION:Explanation: br>√16% =√36/√100 =6/10 =60/100=60% correct answer is D)60% #### D QUESTION:Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? options: A)3 B)9 C)5 D)6 E)7 SOLUTION:Suppose Anoop joined after 3 months. Then, 20000 * 12 = 80000 * (12 – x) => x = 9. ANSWER:B #### B QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:The timing of a college is from 12 p.m to 5.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. options: A)56 minutes B)45 minutes C)30 minutes D)48 minutes E)44 minutes SOLUTION:Explanation: Total time a student spends in college = 5 hours 00 minutes = 300 minutes As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes Hence, the duration of each lecture is = (300 – 20)/5 = 56 minutes ANSWER A #### A QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long? options: A)48 B)99 C)266 D)28 E)17 SOLUTION:Explanation: If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48. Answer: A) 48 #### A QUESTION:We run a business that rents out canoes and kayaks. A canoe rental costs $11 per day, and a kayak rental costs $16 dollars per day. One day, our business rents out 4 canoes for every 3 kayaks and receives a total of $460 in revenue. How many more canoes than kayaks were rented out? options: A)8 B)7 C)6 D)5 E)4 SOLUTION:Let x be the number of canoes. Then 3x/4 is the number of kayaks. 11x+(3x/4)*16=460 11x+12x=460 23x=460 x=20 (canoes) 3x/4=15 (kayaks) There were 20-15 = 5 more canoes rented out. The answer is D. #### D QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 110/100 × 110/100 = 12100 C #### C QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)20 SOLUTION:In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3. 5! = 120 has 1 trailing zeros. 10! will have 2 trailing zeros. 15! will have 3 trailing zeros. 20! will have 5 trailing zeros. Answer: E. #### E QUESTION:If both 5^2 and 3^3 are factors of n x (2^5) x (12^2) x (7^3) x (10), what is the smallest possible positive value of n? options: A)15 B)45 C)75 D)125 E)150 SOLUTION:(2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and one appearance of 5 (in the 10). Thus n must include at least 3 * 5 = 15 The answer is A. #### A QUESTION:there are two cubes with ratio between volume is 125:64. then what is the value of length of each cube? options: A)25:16 B)16:25 C)4:5 D)5:4 E)150:96 SOLUTION:given 6a12:a22=150:96 then a12:a22=25:16 a1:a2=5:4 so the answer is D #### D QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P? options: A)0.54 B)0.77 C)0.82 D)0.97 E)1.62 SOLUTION:This is a fairly straightforward question that can be solved quickly by just applying the options We are provided with Mean, m= 0 and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2*PD or m - 2*PD So, if these elements lie within 2 and 3 PDs of mean, m=0 we can find which one of these values of PD satisfies each value within Q Only PD = 0.77 does Answer : B #### B QUESTION:A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet? options: A)267 B)2667 C)200 D)269 E)265 SOLUTION:When the second train leaves Mumbai the first train covers 40 * 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (50 -40) = 4 hours So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai. Answer:C #### C QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/7 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x? options: A)x/3 B)5x/2 C)2x/3 D)3x/2 E)2x SOLUTION:x/(x+y) = 2/7 7x = 2x+2y 5x = 2y y = 5x/2 Answer B #### B QUESTION:If a is a number such that –2 ≤ a ≤ 2, which of the following has the largest possible absolute value? options: A)3a – 1 B)x^2 + 1 C)3 – x D)x – 3 E)x^2 – x SOLUTION:Ans is A .. leads to the max value of 7 for a = -2 #### A QUESTION:In a box of 9 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)2/9 B)3/10 C)4/11 D)5/12 E)6/13 SOLUTION:# defective pens = 3 # good pens = 6 Probability of the 1st pen being good = 6/9 Probability of the 2nd pen being good = 5/8 Total probability = 6/9 * 5/8 = 5/12 The answer is D. #### D QUESTION:If 4a = 16b and 8b = 13c, Find a:b:c? options: A)52:13:8 B)13:7:52 C)7:13:52 D)7:13:54 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (8b = 13c ==> b/c = 13/8) ==> a:b = 16:4 and b:c = 13:8 a:b:c = 52:13:8 Answer: Option A #### A QUESTION:Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? options: A)A)7 B)B)6 C)C)8 D)D)9 E)E)4.74 SOLUTION:1/5 + 1/15 - 1/x = 1/18 x = 4.74 Answer:E #### E QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)20 B)15 C)25 D)18 E)12 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 6 = 26 => x = 5 Deepak's age = 3x = 15 years. ANSWER B #### B QUESTION:On a map, 3.5 inches represent 35 miles. How many miles approximately is the distance if you measured 127 centimeters assuming that 1-inch is 2.54 centimeters? options: A)515 B)500 C)525 D)530 E)535 SOLUTION:1 inch = 2.54 cm 3.5 inch = 2.54 * 3.5 cm 8.89 cm = 35 miles 127 cms = 35/8.89*127= 500 miles Answer : B #### B QUESTION:A person buys an article at $500. At what price should he sell the article so as to make a profit of 20%? options: A)560 B)449 C)600 D)740 E)460 SOLUTION:C 600 Cost price = $500 profit = 20% of 500 = $100 Selling price = Cost price + Profit = 500 + 100 = 600 #### C QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:8, the price of the cheapest item is? options: A)2379 B)2889 C)5625 D)9000 E)28311 SOLUTION:Let their prices be 3x, 5x and 7x. Then, 2x + 6x + 8x = (15000 * 3) or x = 2812.5. Cost of cheapest item = 2x = Rs. 5625. Answer: C #### C QUESTION:The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria options: A)10 B)12 C)14 D)16 E)18 SOLUTION:The question basically asks how many minutes it takes for a population to increase by factor 50(50,000 / 1,000 = 50). Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes: 2^x >= 50, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^6 = 64, i.e. the population has to double 6 times. Since it takes the population 2 minutes to double once it takes 6*2 minutes = 12 minutes to double nine times. Thus, solution B = 12 is correct. #### B QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1 SOLUTION:Explanation: Let the cost of the brand be Rs. X per kg. C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x) S.P of 5 kg = Rs. (5 * 177) = Rs. 885 [885 - (400 + 3x)]/(400 + 3x) * 100 = 18 24250 - 150x = 3600 + 27x 177x = 20650 => x = 116 2/3 So, cost of the other brand = Rs. 116.66. Answer: D #### D QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:in how many possible ways you can write 3240 as product of 3 positive integers a, b, c . options: A)450 B)420 C)350 D)320 E)300 SOLUTION:3240 => 2^3 * 3^4 * 5^1 a => 2^x1 * 3^y1 * 5^z1 b => 2^x2 * 3^y2 * 5^z2 c => 2^x3 * 3^y3 * 5^z3 a * b * c = 3240 x1 + x2 + x3 = 3 => 5C2 y1 + y2 + y3 = 4 => 6C2 z1 + z2 + z3 = 1 => 3C2 5C2 * 6C2 * 3C2 = 10 * 15 * 3 = 450 ANSWER:A #### A QUESTION:A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? options: A)1/3 B)2by3 C)2/5 D)3/5 E)4/5 SOLUTION:Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol. Let x ml be the amount removed ---> total alcohol left = 4-0.4x New quantity of whiskey added = x ml out of which 0.19 is the alcohol. Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml. Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3. Hence, B is the correct answer. #### B QUESTION:The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class? options: A)1:2 B)3:4 C)3:5 D)2:3 E)None of these SOLUTION:let x = number of girls y = number of boys sum of girls ages / x = 15.4 sum of boys ages / y = 16.4 The sum of the girls' ages is 15.4x, and boys' sum is 16.4y (sum of girls ages + sum of boys ages) / (x+y)= 15.8 (15.4x + 16.4y) / (x+y) = 15.8 15.4x + 16.4y = 15.8(x+y) 15.4x + 16.4y = 15.8x + 15.8y 0.6y = 0.4x 0.6y/x = 0.4 y/x = 0.4/0.6 y/x = 2/3 which is the ratio of boys to girls ANSWER:D #### D QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:2*6=12.Answer is B. #### B QUESTION:Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride? options: A)28 B)30 C)32 D)34 E)36 SOLUTION:The cost of Annie's ride was 2.5+5+(0.25*14) = $11 Let x be the distance of Mike's ride. The cost of Mike's ride is 2.5+(0.25*x) = 11 0.25*x = 8.5 x = 34 miles The answer is D. #### D QUESTION:The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy? options: A)7 B)9 C)11 D)13 E)14 SOLUTION:Explanation: 3x + 5x + 7x = 45 x =3 3x = 9 B) #### B QUESTION:Given two fair dice, what is the probability G that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. G=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:In an examination 60% failed in Math and 40% failed in French. If 10% failed in both. What % of students passed in both. options: A)25% B)15% C)20% D)30% E)10% SOLUTION:Passed in Math = 100 - 60 = 40% Passed in French = 100 - 40 = 60% Students who passed Math or French = 100 -10 = 90% Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-90 =10% ANSWER:E #### E QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)120 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (9 - 8) = 1 km/hr. Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m. .'. Distance between the criminal and policeman = (265 - 50) m = 215 m. Answer : E #### E QUESTION:A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? options: A)65 sec B)89 sec C)100 sec D)150 sec E)160 sec SOLUTION:Explanation: Speed =240/24 m/sec = 10 m/sec Required time =(240+650 /10)sec=89sec ANSWER IS B #### B QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)Rs.500 B)Rs.1000 C)Rs. 3630 D)Rs.2500 E)Rs.6000 SOLUTION:Explanation: 6300:4200:10500 3:2:5 3/10 * 12100 =Rs. 3630 ANSWER:C #### C QUESTION:What percent of 60 is 90? options: A)133 1⁄3 B)150 C)60 D)33 1⁄3 E)25 SOLUTION:% of 60 is 90? = 90/60 = 3/2 = 150% Thus B is the correct answer. #### B QUESTION:jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all? options: A)5 B)10 C)15 D)20 E)14 SOLUTION:10+5=15. Answer is C #### C QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long? options: A)76 sec B)89 sec C)87 sec D)15 sec E)16 sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 650)/10 = 89 sec. Answer:B #### B QUESTION:Tough and Tricky questions: Ratios 1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5 SOLUTION:let total no. of students be 30 students left on a field trip = 1/5(30) =6 thus 24 students left behind 1/3(24)=8 students did not want to go. thus 16 students want to go on the trip 1/2(16)=8 were able to join the other students on the field trip. thus total number of students that went on a field trip =6+8 =14 thus required fraction = 14/30 =7/15 C #### C QUESTION:Calculate the largest 3 digit number which is exactly divisible by 89? options: A)911 B)969 C)979 D)977 E)971 SOLUTION:Largest 4 digit number is 999 After doing 999 ÷ 89 we get remainder 20 Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 C #### C QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Tuesday, what was the expected day when both the brothers were to return home and when did Rohit Return? options: A)Wednesday, Sunday B)Thursday, Monday C)Friday, Tuesday D)Monday, Friday E)none SOLUTION:Rajat returned on Tuesday -i.e. 3 days earlier so actual day to return home is Friday. Rohit returned after days so Tuesday. ANSWER:C #### C QUESTION:Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand? options: A)22 B)16 C)27 D)187 E)11 SOLUTION:Let the present ages of Anand and Bala be 'a' and 'b' respectively. a - 10 = 1/3 (b - 10) --- (1) b = a + 12 Substituting b = a + 12 in first equation, a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2 => 2a = 32 => a = 16. Answer:B #### B QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:If A= {2, 4, 6}, B= {1, 2, 5, 7}, and C= {2, 3, 4, 6}. Find A-(B U C) options: A){1 , 2} B){2 ,3 ,5 } C){ } D){5 } E)None of these SOLUTION:Explanation : A= {2, 4, 6}, B= {1, 2, 5, 7}, C = {2, 3, 4, 6} Now,(B U C) = {1, 2, 5, 7} U {2, 3, 4, 6} = {1,2,3,4,5,6,7} A-(B U C) = {2, 4, 6} - {1,2,3,4,5,6,7} = { } Hence (C) is correct answer. Answer : C #### C QUESTION:A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work? options: A)4 days B)2 days C)6 days D)8 days E)9 days SOLUTION:C 6 days 4/10 + 9/x = 1 => x = 15 1/10 + 1/15 = 1/6 => 6 days #### C QUESTION:Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is: options: A)Rs. 4800 B)Rs. 5000 C)Rs. 5400 D)Rs. 5600 E)Rs. 6600 SOLUTION:let investment is x... den remaining investment is (9800-x) x*9/75= (9800-x)*10/80 x=4800 9800-x=5000 ANSWER:B #### B QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)*(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)*(r+4)/(y+r+6) D)(y+3)/(y+r+7)*(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following T is a possible value for x + y? I. 18 II. 19 III. 20 options: A)I only B)II only C)T=III only D)II and III only E)None SOLUTION:TIP FOR SUCH QUESTIONS: Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7 i.e. Min Value of x = 8 AND i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11 i.e. Min Value of y = 12 i.e. Minimum Value of x+y = 8+12 = 20 Hence III only can be True Answer: Option C #### C QUESTION:Jerry, an electrician, worked 5 months out of the year. What percent of the year did he work? (round answer to the nearest hundredth) What percent 12 is 5? 12 months = 1 year options: A)58.33% B)68.33% C)78.33% D)88.33% E)41.66% SOLUTION:1. Multiply the opposites 5 x 100 = 500 100=5/12 Divide by the remaining number 41.66% (rounded to hundredth) correct answer E #### E QUESTION:If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true? I. xa= y II. y = 1 III. a and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2). I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2). Answer: A. #### A QUESTION:If a certain sample of data has a mean of 22.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean? options: A)12.0 B)13.5 C)14.5 D)23.5 E)26.5 SOLUTION:The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is C. #### C QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually. options: A)812 B)712 C)412 D)512 E)612 SOLUTION:Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112. therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612. Answer is E. #### E QUESTION:A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? options: A)42 B)70 C)140 D)165 E)225 SOLUTION:1 of 5 will be chosen for the math 2 of 10 will be chosen for the computer None of the 3 chosen people can be in more than one departments. We can choose any of the 5 candidates for the math dep., which gives as 5 selections. We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /2!*8!= (9*10) / 2 = 90 / 2 = 45. We are multiplying our individual selections: 5*45 = 225 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans E #### E QUESTION:In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have? options: A)180 B)45 C)60 D)90 E)135 SOLUTION:We can start with the known quantity and then go on to find the others. Shiny igneous ricks are 40. These are (2/3) of total igneous rocks. (2/3)*Total igneous rocks = 40 Total igneous rocks = 40 * (3/2) = 60 Total sedimentary rocks = 2*Total igneous rocks = 2*60 = 120 Total number of rocks = 60 + 120 = 180 Answer (A) #### A QUESTION:If a·b·c·d=270, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a? options: A)7 B)10 C)11 D)13 E)15 SOLUTION:prime factorize : 270 = 2*3*5*9 Hence a = 2 and d = 9 . Hence answer is 9 - 2 = 7 Answer A #### A QUESTION:The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840.At what rate of interest the same amount of interest can be received on the same sum after 5 years ? options: A)6% B)8% C)9% D)10% E)None SOLUTION:Solution S.I. = Rs. 840,R =5%,T= 8 Years. Principal = Rs.(800x840/5x8)= Rs. 2100. Now,P = Rs. 2100,S.I. = Rs. 840, T = 5 years. ∴ Rate =(100x840/2100x5) = 8%. Answer B #### B QUESTION:A will states that the estate would be divided among six sons with the remainder donated to charity. One stipulation in the will is that no one among the sons can receive an amount within 12% of another's amount. If one of the beneficiaries received $30,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the six sons? options: A)$4096 B)$14043 C)$7892 D)$17736 E)$15336 SOLUTION:1st - 30,000. 2nd - 0.88*30,000 = 26,400 3rd - 0.88*26,400 = 23,232 4th - 0.88*23,232 = 20,444.16 5th - 0.88*20,444.16 = ~17,990.86 6th - 0.88*17,990.86 = ~15,831.96 Range = 30,000 - 15,831 = 14,168 Answer: B. #### B QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)70 m B)60 m C)80 m D)90 m E)100 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 51st term in the sequence? options: A)9 B)8 C)7 D)6 E)4 SOLUTION:Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below 02,07,22,67, 202, 607, 1822, 5467... Observe the last two digits of the sequence which have the cyclicity of4and the last two digits repeat in the order {02, 07, 22, 67} Also 51st Term =6*8 +3 i.e. 51th Terms will have same Last two digits as 3rd term of the sequence = 22 i.e. Sum of lat two digits of 35th Term = 2+2 = 4 E #### E QUESTION:A store reduced the price of all items in the store by 12% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? options: A)80.0 B)79.2 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 12% price becomes = 0.88 *100 = $ 88 after the final reduction of 10% price becomes = 0.9* 88 = $ 79.2 price of all items on second day is 79.2% of price on first day correct answer option B #### B QUESTION:In g is a positive integer smaller than 200 and (14g)/60 is an integer, then g has how many different positive prime factors? options: A)2 B)3 C)5 D)6 E)8 SOLUTION:7g/30 tells us that g is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3. Answer: B #### B QUESTION:In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner? options: A)$9 x 10^4 B)$9.90 x 10^6 C)$1.00 x 10^7 D)$1.05 x 10^7 E)$9.90 x 10^7 SOLUTION:The max product of any two balls can be 9 * 10 = 9900 = 9 * 10 If we multiply it by $1000 the max amount will be 9 * 10^4. A #### A QUESTION:If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station. options: A)10 km B)8 km C)6km D)4km E)7 km SOLUTION:Sol. Let the required distance be x km Difference in the time taken at two speeds=1 min =1/2 hr Hence x/5-x/6=1/5<=>6x-5x=6 x=6 Hence, the required distance is 6 km Option C #### C QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 . Number of pages typed by Kumar in 1 hour = 40/5 = 8. Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 . Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours = 8 hours 15 minutes. ANSWER : E #### E QUESTION:What is the greatest positive integer x such that 5^x is a factor of 125^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:125^10 = (5^3)^10 = 5^30 ANSWER:E #### E QUESTION:John bought 9.25m of cloth for $397.75. Find the cost price per metre. options: A)46 B)47 C)58 D)56 E)43 SOLUTION:Cloth bought by John = 9.25 m Cost of 9.25 m = $397.75 Cost per metre = 397.75 ÷ 9.25 The cost of the cloth per metre = $ 43 Answers: E #### E QUESTION:A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 10% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax? Choices options: A)$22.68 B)$23.94 C)$24 D)$25.20 E)$30 SOLUTION:A. #### A QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)3630 B)3637 C)3630 D)3631 E)3635 SOLUTION:6300:4200:10500 3:2:5 3/10 * 12100 = 3630 Answer: A #### A QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years. The age of the 15th student is options: A)9 years B)11 years C)17 years D)21 years E)25 years SOLUTION:Solution Age of the 15th student =[15x15-(14x8+16x6)] = (225 - 208) = 17 years. Answer C #### C <<<Examples ends QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:250/15 = 16 (plus remainder) so there are 16 multiples of 15 250/14 = 17 (plus remainder) so there are 17 multiples of 14 We need to subtract 1 because 15*14 is a multiple of both so it was counted twice. The total is 16+17-1 = 32 The answer is C. #### C QUESTION:An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is: options: A)2/91 B)1/22 C)3/22 D)2/77 E)None of these SOLUTION:Explanation : Let S be the sample space. Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455 Let E = event of getting all the 3 questions from simple mathematics section. n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10 P(E) = n(E)/n(S) = 10/455 = 2/91 . Answer : A #### A QUESTION:y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b? options: A)-512 B)-257 C)-256 D)-513 E)128 SOLUTION:As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation. For the quadratic equation is in the form of ax^2+bx+c=0, The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b 512 can be expressed as product of two numbers in the following ways: 1 * 512 2 * 256 4 * 128 8 * 64 16 *32 The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513. The least value possible for b is therefore -513. D #### D QUESTION:0.9*0.007= ­­­­­­­­­­_________ options: A)0.063 B)0.0063 C)0.63 D)0.00063 E)63 SOLUTION:9*7=63 Sum of decimal places= 4 So, 0.9*0.007= 0.0063 ANSWER:B #### B QUESTION:What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-79)*(50-80)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 5 minutes? options: A)36 B)54 C)108 D)270 E)324 SOLUTION:ONE Veggiematik machine can chop 36 carrots in 4 minutes So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes In other words, ONE Veggiematik machine can chop 54 carrots in5minutes So,SIXVeggiematik machines can chop (5)(54) carrots in5minutes In other words, SIX Veggiematik machines can chop 270 carrots in5minutes Answer D #### D QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 4 candidates are there to fill the 4 positions? options: A)420 B)770 C)840 D)165 E)315 SOLUTION:1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer None of the 4 chosen people can be in more than one departments. We can choose any of the 7 candidates for the math dep., which gives as 7 selections. We can choose 3 of the 10 candidates for the computer dep., which gives us 3 selections and 7 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /3!*7!= 120 We are multiplying our individual selections: 7*120 = 840 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans C #### C QUESTION:Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)? options: A) 22 hours B) 30 hours C) 44 hours D) 60 hours E) It cannot be determined from the information above. SOLUTION:Say the rates of machines A, B and C are a, b, and c, respectively. Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4; Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11. Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours. Answer: C. #### C QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture? options: A)1 : 9 B)1 by 5 C)1 : 7 D)1 : 3 E)1 : 1 SOLUTION:Selling price of the mixture = 70 and profit = 20% Cost price of the mixture = 70×100120=70×5670×100120=70×56 By applying alligation rule: So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5 Answer:B #### B QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)210m B)240m C)963m D)874m E)578m SOLUTION:Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B)240m #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)11 B)18 C)99 D)77 E)51 SOLUTION:A:B = 2:3 B:C = 2:5 A:B:C = 4:6:15 6/25 * 75 = 18 Answer: B #### B QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be? options: A)15 m, 12 m B)15 m, 11 m C)15 m, 20 m D)15 m, 10 m E)15 m, 11 m SOLUTION:lb = 150 2(l + b) = 50 => l + b = 25 l – b = 5 l = 15 b = 10 D #### D QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C *100 =50% Answer A #### A QUESTION:A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? options: A)3:3 B)3:4 C)3:8 D)3:1 E)3:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by A and B = 6000 : 8000 => 3:4.Answer: B #### B QUESTION:When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8? options: A)3 B)4 C)5 D)6 E)2 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 24) 3n = 3(6) =18, which leaves a remainder of 2 when divided by 8. Answer E #### E QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick? options: A)5 B)8 C)24 D)15 E)20 SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min Nick's rate - 10 laps per hour --> 10/60 laps/min lets set equations: 20/60*t=4 (since Maria had to run 4 laps before Nick would start) 10/60*t=0 (Hick has just started and hasn't run any lap yet) (20/60-10/60)*t=4-0 (since Nick was chasing Maria) t=24 min needed Maria to run 4 laps Answer : C #### C QUESTION:If the price of a certain bond on May 1st was 1/2 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? options: A)50% B)75% C)120% D)133 1/3% E)160% SOLUTION:The price on June 1st = 12 (assume); The price on May 1st = 1/2*12 = 6; The price on July 1st = 6*1.5 = 9. The average price of the bond on May 1st and July 1st = (6+9)/2 = 7.5. The price of the bond on June 1st (12) is 8/5 times (160%) the average price of the bond on May 1st and July 1st. Answer: E. #### E QUESTION:A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture? options: A)1 kgs B)3 kgs C)5 kgs D)6 kgs E)None of these SOLUTION:Explanation : If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg. We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg. Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C. Step 1: Find out the ratio Qa:Qc using alligation rule. Qa/Qc=(30−25)/(25−20)=1/1. Step 2: Find out the ratio Qb:Qc using alligation rule. Qb/Qc=30−25/(25−24)=5/1. Step 3: Qc is found by adding the value of Qc in step 1 and step 2 =1+1=2. Therefore, the required ratio =1:5:2. If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture. Answer : C #### C QUESTION:Insert the missing number 100,91,....,76,70 options: A)82 B)83 C)84 D)81 E)80 SOLUTION:Missing number: 83 Answer: B #### B QUESTION:A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month? options: A)6/25 B)5/16 C)4/9 D)3/7 E)2/5 SOLUTION:Let x be the fraction of her take-home pay that the worker saved. Let P be the monthly pay. 12xP = 8(1-x)P 12xP = 8P - 8xP 20xP = 8P x = 2/5 The answer is E. #### E QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm SOLUTION:In one hour, the first train travels 60 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train at 10:00 am. The answer is B. #### B QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. #### C QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:2*6=12.Answer is B. #### B QUESTION:A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 5 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.03N + 8,000 SOLUTION:I will go with option E According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 8000 votes from independent voters and 5 percent from registered voters (i.e 0.05 * 0.6 * N = 0.03N). Hence total votes = 8000 + 0.03N ....option E #### E QUESTION:Find the number of different prime factors of 6440 options: A)4 B)2 C)3 D)5 E)6 SOLUTION:Explanation: L.C.M of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2, 5,7,23 Number of different prime factors is 4. Answer: Option A #### A QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=u ii. u is not equal to v iii. s > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true. Answer: D. #### D QUESTION:Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race? options: A)450 m B)680 m C)700 m D)900 m E)1000 m SOLUTION:Explanation: When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race ANSWER C #### C QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (5*27) - (4*25) = 135-100 = 35 Answer: Option A #### A QUESTION:A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is? options: A)72 kmph B)88 kmph C)54 kmph D)18 kmph E)19 kmph SOLUTION:S = 120/6 * 18/5 = 72 kmph Answer: A #### A QUESTION:Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days. options: A)11 B)12 C)13 D)15 E)16 SOLUTION:Work done by Kamal in 1 day = 1/20 Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16 => Suresh can complete the work in 16 days Answer is E. #### E QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 70, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 70 ⇒ 1.75x = 70 ⇒ x = 40 coins Answer C #### C QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:What is the difference between the place value of 2 in the numeral 7229? options: A)150 B)160 C)180 D)190 E)200 SOLUTION:Option 'C' 200 - 20 = 180 #### C QUESTION:Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions: The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow. The paint will be namedBrun Xif the paint contains 3 jars of brown paint. The paint will be namedJaune Xif the paint contains at least 2 jars of yellow. The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow. What is the probability W that the new color will be one of theJaunecolors? options: A)5/42 B)37/42 C)1/21 D)4/9 E)5/9 SOLUTION:I get B. Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40 Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34 Total combinations = 9 choose 3 = 84 Probability of Jaune W= (40 + 34)/84 = 37/42 #### B QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 13 km/hr downstream and 10 km/hr upstream. options: A)3 kmph B)9 kmph C)4 kmph D)8 kmph E)6 kmph SOLUTION:Speed in still water = (13 + 5)1/2 kmph = 9 kmph. answer :B #### B QUESTION:Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car options: A)960 km B)950 m C)906 km D)906 m E)950 m SOLUTION:60(x + 1) = 64x X = 15 60 * 16 = 960 km ANSWER A #### A QUESTION:P is three times as old as Q. In 10 years, P will be twice as old as Q. How old was P three years ago? options: A)27 B)30 C)33 D)36 E)39 SOLUTION:P = 3Q so Q = P/3 P+10 = 2(Q+10) = 2(P/3+10) P/3 = 10 P = 30 Three years ago, P was 27. The answer is A. #### A QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent? options: A)200 B)100 C)276 D)280 E)279 SOLUTION:Profit on first article = 10% of 1000 = 100. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: B #### B QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A QUESTION:Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next? options: A)7 B)10 C)14 D)15 E)16 SOLUTION:Explanation: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on. Answer: Option D #### D QUESTION:Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary? options: A)RS.3500 B)Rs.1500 C)Rs.4500 D)Rs.2500 E)Nill SOLUTION:Answer: Option D Let's anil's salary be Rs. 100. Money spent on Rent = 40% of 100 = Rs. 40. Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18. Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40 anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60 for 33.6 ---> 100 ; 840 ---> ? Required salary = 840/33.6 * 100 = Rs. 2500 #### D QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)22.4% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/53000 * 100 = 22.4% Answer: B #### B QUESTION:How many odd integers X between 200 and 600 are there such that their tens digit is even? options: A)20 B)25 C)100 D)150 E)200 SOLUTION:The hundreds digit can take 4 values: 2, 3, 4 and 5; The tens digit can take 5 values: 0, 2, 4, 6 and 8; The units digit can take 5 values: 1, 3, 5, 7 and 9; Total X: 4*5*5=100. Answer: C. #### C QUESTION:Pavan travelled for 15 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4. So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes. If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1. The number of 10 pound boxes remains the same so we still have 4 of them. To get a ratio of 1:1, the number of 20-pound boxes must be 4. We need to remove 12 of the 20-pound boxes. The answer is B. #### B QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9} options: A)20 B)40 C)80 D)140 E)60 SOLUTION:Explanation: The given digits are 1, 2, 3, 5, 7, 9 A number is even when its units digit is even. Of the given digits, two is the only even digit. Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways. Number of even numbers = ⁵P₃ = 60. Answer:E #### E QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years options: A)27 B)24 C)40 D)32 E)35 SOLUTION:sameer and anand be 5x years and 4x years respectively (5x+3)/(4x+3)=11/9 9(5x+3)= 11(4x+3), 45x+27=44x+33 45x-44x=33-27 x=6, therefore anand's present age : 4x=24 years correct answer(B) #### B QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:There are 6 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set? options: A)15 B)30 C)69 D)78 E)90 SOLUTION:We can select from 0 to 6 pens and from 0 to 9 books. Thus the total possible ways to select objects is 7*10 = 70 We must subtract 1 for the case with 0 pens and 0 books. The answer is C. #### C QUESTION:Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution? options: A)62.0 B)65.25 C)68.75 D)70.15 E)72.35 SOLUTION:SOL: Lets assume that 46L of sol1 was mixed with 10L of sol2. Alcohol in Sol1: 46*3/4 = 34.5L Alcohol in Sol2: 10*2/5 = 4L Total Alcohol in the mixed solution of 56L = 34.5 + 4 = 38.5L Alcohol concentration in the new sol: (38.5/56)*100 = 68.75% ANSWER:C #### C QUESTION:Sagar was riding bike towards north,turned left road 1 km turnes towrds left &road 2km found himself 1km west of starting how far did he road north? options: A)2km in north. B)2km in south. C)2km in east. D)2km in west. E)4km in north. SOLUTION:He travelled total distance of 3km. From which he travelled 1km in west. Hence in all he travelled total 2km in north. ANSWER:A #### A QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 * 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:The sale price sarees listed for Rs.390 after successive discount is 15% and 25% is? options: A)298 B)237 C)248 D)876 E)291 SOLUTION:390*(85/100)*(75/100) = 248 Answer: C #### C QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing? options: A)191 B)400 C)737 D)840 E)1,560 SOLUTION:Let weight of side of beef before processing = x (60/100)*x = 240 => x = (240 * 100)/60 = 400 Answer B #### B QUESTION:A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work? options: A)30 days B)20 days C)25 days D)35 days E)45 days SOLUTION:Work done by A in 10 days = 10/80 = 1/8 Remaining work = (1 - (1/8)) = 7/8 Now, work will be done by B in 42 days. Whole work will be done by B in (42 x 8/7) = 48 days Therefore, A’s one day’s work = 1/80 B’s one day’s work = 1/48 (A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30 Hence, both will finish the work in 30 days. ANSWER:A #### A QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is: options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 20 : 8 :: 12 : x => 8 x 20 x x = 10 x 8 x 12 => x = 10 x 8 x 12 / (8 x 20) => x = 6 Answer : C #### C QUESTION:What is the remainder when 103 * 505 * 607 is divided by 9 options: A)6 B)18 C)2 D)4 E)7 SOLUTION:103/9==> Remainder=4 505/9==> Remainder=1 607/9==> Remainder=4 =4*4*1=16/9==> Remainder=7 Answer: E #### E QUESTION:If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)7/3 E)9/7 SOLUTION:70 Workers = 3 hours then, 1 Worker = 3*70 Hours 30 Workers = (3*70) /(30) = 7 ANSWER:C #### C QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double? options: A)1/3 B)1/6 C)1/12 D)1/24 E)1/36 SOLUTION:ways you can get double - 6...as each dice showing any number from 1 to 6... total ways = 6∗6=36.6∗6=36.. P=6/36=1/6 ANSWER: B #### B QUESTION:A driver goes on a trip of 50 kilometers, the first 25 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour. What is the average speed of the entire trip in kilometers per hour? options: A)35 B)36 C)40 D)42 E)45 SOLUTION:The time for the first part of the trip was 25/60 = 5/12 hours. The time for the second part of the trip was 25/30 = 5/6 hours. The total time for the trip was 5/12 + 5/6 = 15/12 = 5/4 hours. The average speed for the trip was 50 / (5/4) = 40 kph The answer is C. #### C QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table? options: A)7297 B)2977 C)2871 D)6925 E)2981 SOLUTION:Explanation: CP = SP * (100/(100 + profit%)) = 8587(100/124) = Rs. 6925. Answer: D #### D QUESTION:A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ? options: A)220 metre B)230 metre C)250 metre D)260 metre E)270 metre SOLUTION:Distance covered in 26 seconds = 26×72×5/18=520 meter Length of the train = 520-250=270 meter ANSWER: E #### E QUESTION:What is the units digit of (12^3)(15^4)(31^7)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8. The units digit of 15^4 is the units digit of 5^4 which is 5. The units digit of 31^7 is the units digit of 1^7 which is 1. The units digit of 8*5*1 is 0. The answer is A. #### A QUESTION:A numberais squared and then multiplied by negative 3. The result of this operation Q is equal to three times the sum of three timesaand two. What is one possible value ofa? options: A)-3 B)-2 C)1 D)2 E)3 SOLUTION:Q=-3*a^2=3(3a+2) a= -2 or -1 a=-2=B #### B QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:6C1*5C2 = 6*10 = 60 The answer is C. #### C QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is options: A)91 B)910 C)61 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 671 and 610. ‹=› 61. Answer C #### C QUESTION:The average height of 60 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ? options: A)287 cm B)150.8 cm C)276 cm D)287 cm E)297 cm SOLUTION:Total height = 150 * 60 = 9000 cm. New average = [9000 - 5 * 146 + 5 * 156 ] / 60 = 150.8 cm. Answer:B #### B QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:What is the sum of odd integers from 35 to 55, inclusive? options: A)495 B)1,500 C)1,240 D)1,120 E)1,100 SOLUTION:Number of odd integers = (55-35)/2 + 1 = 20/2 + 1 = 11 Sum of odd integers = (35+55)/2 * 11 = 495 Answer A #### A QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:If the integer N = 139,k50 where k is the hundreds digit, N can NEVER be divisible by which of the following? options: A)2 B)3 C)4 D)6 E)9 SOLUTION:It is divisible by 2 irrespective of k value as unit digit's value is even(0). It can be divisible by 3 for k values 2,5,8 as sum will be divisible by 3 It can be divisible by 6 if divisible by 2 and 3. It can be divisible by 9 for k value 2 as sum will be divisible by 9. Therefore answer is 4 as number is divisible if last two digits are divisible.In this case 50(No) Hence answer C #### C QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/6 Part filled by B in 1 hour = 1/18 Part filled by C in 1 hour = 1/36 Part filled by (A+B+C) in 1 hour = 1/6+1/18+1/36=9/36 So all pipes will fill the tank in 4 hours. Option C #### C QUESTION:If 80% of 90 is greater than 70% of a number by 30, what is the number? options: A)70 B)60 C)10 D)75 E)85 SOLUTION:Explanation: 80/100 * 90 - 70/100 * x = 30 72 - 70/100 * x = 30 72 - 30 = 70/100 *x 42 = 70/100 * x 42 * 100 / 70 = x 60 = x Answer: Option B #### B QUESTION:The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary? options: A)2888 B)1266 C)1000 D)2779 E)2661 SOLUTION:X * (110/100) * (95/100) = 1045 X * (11/10) * (1/100) = 11 X = 1000 Answer: C #### C QUESTION:Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own? options: A)6 B)7 C)8 D)12 E)14 SOLUTION:Lets suppose Anne and Bruce take A and B hrs working separately So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours) After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 3 hours) Solving these 2 equations we can find B as 12 ANSWER:D #### D QUESTION:A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:Calculate the distance covered by 350 revolutions of a wheel of radius 25.3 cm. options: A)558.6 m B)556.6 m C)516.6 m D)156.6 m E)256.6 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 350 resolutions. =350 * 2 * 22/7 * 25.3 = 55660 cm = 556.6 m ANSWER:B #### B QUESTION:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts? options: A)6 B)14 C)19 D)20 E)81 SOLUTION:< 6 hours sleep>= 6 hours sleepTOTAL Tired75-- Not Tired-0.7*X? TOTAL80X100 Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5; TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14; Interns who areNot Tired S= 5 + 14 = 19. Answer: C. #### C QUESTION:List R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list? options: A)12 B)16 C)20 D)24 E)28 SOLUTION:The middle number is 40. Let the smallest number be x. Then the largest number is 2x+20. To make x as small as possible, let's make the remaining numbers as large as possible. So the second largest = the largest = 2x+20. The second smallest should be equal to the median. The numbers are x, 40, 40, 2x+20, 2x+20. x + 40 + 40 + 2x + 20 + 2x + 20 = 5*40 = 200 5x = 80 x = 16 The answer is B. #### B QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700 P1’s income = Rs 5*700 = Rs.3500 ANSWER:D #### D QUESTION:If two numbers are in the ratio 4:5. If 10 is added to both of the numbers then the ratio becomes 5:6 then find the smallest number? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Explanation: 4:5 4x + 10 : 5x + 10 = 5 : 6 6[4x + 10] = 5[5x + 10] 24x + 60 = 25x + 50 25x - 24x = 60 - 50 x = 10 Then smallest number is =4 4x = 40 Answer: Option D #### D QUESTION:Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:P makes x sprockets per hour. Then Q makes 1.1x sprockets per hour. 880/x = 880/1.1x + 10 1.1(880) = 880 + 11x 11x = 88 x = 8 The answer is D. #### D QUESTION:In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same) options: A)1:2 B)3:5 C)1:1 D)3:7 E)2:4 SOLUTION:C 1:1 This is a very simple probability question in a software interview. This question might be a little old to be ever asked again but it is a good warm up. Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method. Number of girls = 0*(Probability of 0 girls) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + … Number of girls = 0*(C*1/2) + 1*(C*1/2*1/2) + 2*(C*1/2*1/2*1/2) + … Number of girls = 0 + C/4 + 2*C/8 + 3*C/16 + … Number of girls = C (using mathematical formulas; it becomes apparent if you just sum up the first 4-5 terms) The proportion of boys to girls is 1 : 1. #### C QUESTION:62467 × 9998 = ? options: A)624545037 B)627745452 C)624545077 D)624545066 E)625454211 SOLUTION:D 624545066 62467 × 9998 = 62467 × (10000 - 2) = 62467 × 10000 - 62467 × 2 = 624670000 - 124934 = 624545066 #### D QUESTION:If a function f is defined by f(x)= (1-x)/x for all non zero numbers x. If f(a) = 1 and f(a/b) = 3 then b= ? options: A)3 B)1/3 C)2 D)1/2 E)-2 SOLUTION:Given that f(x)= (1-x)/x and f(a) = 1, then f(a) =(1-a)/a=1 ===> a=1/2, then backsolve using the answer choices: f(a/b) = f(1/2b) = 3 A) 3 ===> f(1/2*3) = f(1/6) = 5 B) 1/3 ===> f((1/2)/(1/3)) = f(3/2) = (-1/2)/(3/2) = -1/3 C) 2 ===> f(1/2*2) = f(1/4) =3 WINS D) 1/2 ===> f((1/2)/(1/2)) = f(1) = 0 E) -2 ===> f((1/2)/-2) = f(-1/4) = (5/4)/(-1/4) = -5 Answer: C #### C QUESTION:How many multiples of 2 are less than 2400, and also multiples of 8? options: A)104 B)208 C)300 D)832 E)833 SOLUTION:The LCM of 2 and 8 is 8. Divide 2400/8 = 300.xxx. So C is your answer. #### C QUESTION:The greatest number of four digits which is divisible by 12, 20, 36 and 60 is: options: A)9000 B)9900 C)9500 D)9800 E)9700 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 12, 20, 36 and 60 is 180. On dividing 9999 by 180, the remainder is 99. Required number (9999 - 99) = 9900. Answer: Option B #### B QUESTION:5020−(502÷100.4)=? options: A)15 B)20 C)5015 D)25 E)35 SOLUTION:Explanation: =5020−(502/1004×10) =5020−5=5015 Option C #### C QUESTION:Three types of tea the a,b,c costs Rs. 95/kg,100/kg and70/kg respectively.How many kgs of each should be blended to produce 100 kg of mixture worth Rs.90/kg, given that the quantities of band c are equal options: A)70,15,15 B)50,25,25 C)60,20,20 D)40,30,30 E)20,30,30 SOLUTION:given quantities of b and c are equal . therefore instead of considering them as a different quantities take average of both and consider it as a single entity . so the cost of the mixture "D" (equal quantities of "B" and "C") is 170/2=85rs/kg now the tea contains only "A" of 95 rs/per and "D" of 85 rs/kg. it is clearly seen that "A" is 5 more and "D" is 5 less than the required cost per kg . therefore 50/50 will go well . A=50kg and D=50kg. (D= B&C in equal ratio). therefore B&C=25kg each . (A:B:C)=(50,25,25) ANSWER:B #### B QUESTION:In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 2/3 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight options: A)1/6 B)1/8 C)1/4 D)3/4 E)7/8 SOLUTION:Good question. So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved). we're told that 2/3 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/3 are yellow. We're also told there is an equal probability of straight or curved, 1/2. We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ). So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 1/3 * 1/2 = 1/6, or A. #### A QUESTION:The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 3 years? options: A)5100 B)4096 C)5200 D)5400 E)5500 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 8000 × 80/100 × 80/100 x 80/100= 4096 Answer : B #### B QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? options: A)45 B)33 1/3 C)27 D)16 2/3 E)15 SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x: 1.5/x = 1/20 x = 30 Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution. Answer is A. #### A QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 130 pounds? options: A)8 B)14 C)12 D)9 E)none of the above SOLUTION:Ans is B: 39 pounds --> 6 days 130 pounds --> x days x = 130*6/39 = 20 the animal has already consumed food in 6 days so the the number of days for it's total consumption be 130 pounds is 20-6 = 14 #### B QUESTION:What is the remainder when 3990990900032 is divided by 32 ? options: A)0 B)8 C)4 D)2 E)3 SOLUTION:Though i was unaware of the divisibility test for 32 but i guessed the pattern!! divisibility rule for 4- last two digits must be divisible by 4 divisibility rule for 8- last three digits must be divisible by 8 similarly, divisibility rule for 32 - last five digits must be divisible by 32 Hence, Ans A #### A QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)100 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer C, 50 cans #### C QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44 SOLUTION:A 11, 42 Let the age of Priya = x years Then, the age of her father = (x+ 31) years ATQ, (x+ 8) + (x+ 31 + 8) = 69 2x+ 47 = 69 2x= 69 – 47 = 22 x= 11 The age of Priya = 11 years The age of her father = 11 + 31 = 42 years #### A QUESTION:A total of 22 men and 30 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women? options: A) 31 B) 31.5 C) 32.8 D) 32.5 E) 33 SOLUTION:Let Aw = average age of women Average = (Number of men X average age of men + Number of women X average age of women)/total number of people 35 * 52 = 22 * 38 + 30 * Aw =>1820 = 836 + 30 Aw => 30 Aw = 984 =>Aw = 32.8 Answer C #### C QUESTION:A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 180 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year? options: A)2989 B)2765 C)6000 D)2989 E)9772 SOLUTION:Total production of salt by the company in that year = 5000 + 5180 + 5360 + .... + 6980 = 72060. Average monthly production of salt for that year = 72060/12 = 6005. Answer:C #### C QUESTION:Magnabulk Corp sells boxes holding i magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate? options: A)100bi/m B)bi/(100m) C)100bi/m D)m/(bi) E)bi/m SOLUTION:We're given some facts to work with: 1) Magnabulk Corp sells boxes holding I magnets each. 2) The boxes are shipped in crates, each holding B boxes. 3) Magnabulk charges M DOLLARS for each crate We're asked for the price charged per magnet, in CENTS.... IF.... I = 2 B = 3 M = 12 (2 magnets per crate)(3 crates) = 6 magnets $12 for 6 magnets = $2 per magnet = 200 cents per magnet So we're looking for an answer that equals 200 when I=2, B=3 and M=12. There's only one answer that matches... Answer is C #### C QUESTION:In a party attended by 13 persons, each clinch their glass with every other. How many glass clinches? options: A)51 B)52 C)78 D)54 E)55 SOLUTION:Total no. of person = 11 Total no. of glass clinches = n(n-1)/2 =13*12/2 = 78 ANSWER:C #### C QUESTION:The average of first five multiples of 3 is? options: A)2 B)9 C)8 D)6 E)3 SOLUTION:Average = 3(1 + 2 + 3 + 4 + 5)/5 = 45/5 = 9. Answer:B #### B QUESTION:A is twice as good a workman as B and together they complete a work in 12 days. In how many days A alone can do the work? options: A)32 B)33 C)34 D)35 E)36 SOLUTION:A’s one day’s work : B’s one day’s work= 2:1 (A+B)’s one day’s work= 1/12 B’s one day’s work= 1/12 *1/3 = 1/36 B alone can do the work in 36 days ANSWER:E #### E QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142 options: A)23 B)25 C)46 D)49 E)50 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 30 + 16 = 46 . #### C QUESTION:In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N? options: A)(N-M) B)MN/(M + N) C)(NM) D)(N-M)/(M+N) E)NONE OF THESE SOLUTION:The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N). Answer: B #### B QUESTION:There are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? . options: A)75 Kg B)80 Kg C)85 Kg. D)90 Kg E)92 Kg SOLUTION:New average weight= 110+60/2= 85 kgs Since avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85 C is the answer #### C QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:Mohan has 8 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 16 shoes, what is the probability that she will select 2 shoes of the same color? options: A)2/5 B)1/15 C)1/9 D)1/10 E)1/25 SOLUTION:Can be tackled in this way as well: Probability of selecting any 1 out of 16 shoes = 16/16 = 1 Probability of selecting the next shoe (out of 16 available) having the same color = 1/16 (as after selecting the 1st one, there is only 1 another shoe left with the same color). Thus the total probability = 1*1/15=1/15. B is the correct answer. #### B QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 3*1*2=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:The average age 12 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)24 years B)21 years C)18 years D)29 years E)30 years SOLUTION:12 * 2 = 24 years Answer:A #### A QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 5 years ago? options: A)152460 B)214560 C)138214 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^5 Answer is C #### C QUESTION:In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term? options: A) 192 B) 154 C) 134 D) 174 E) 120 SOLUTION:1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times) 6 + (3 x 63) = 3 + 189 = 192 Answer A #### A QUESTION:Max scored 6 marks more than what he did in the previous examination in which he scored 30. Maria scored 30 marks more than she did in the previous examination in which she scored 60. Who showed less improvement? options: A)58% B)50% C)80% D)20% E)55% SOLUTION:Max percentage improvement in the first exam = (6/30 × 100) % = (600/30) % = 20 % Maria percentage improvement in the first exam = (30/60 × 100) % = (3000/60) % = 50 % Hence, 20 % < 50 % Therefore, Max showed less improvement. Answer:B #### B QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 600. What is their H.C.F.? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 600 x = 10 The numbers are (3 x 10), (4 x 10) and (5 x 10). The H.C.F. is 10. The answer is A. #### A QUESTION:In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is : options: A)35 B)38 C)40 D)42 E)44 SOLUTION:Explanation: Let the number of correct answers be X. Number of incorrect answers = (60 – X). 4x – (60 – x) = 140 => 5x = 200 => x = 40 Answer: C #### C <<<Examples ends QUESTION:judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 6th position from either end of the row. Can you find out how many girls are practicing together? options: A)4 B)9 C)11 D)6 E)8 SOLUTION:As judith is 6th from either end of the row, it means that 5 girls are on one of her sides and 5 are present on the other. 5 + 5 + 1(judith herself) = 11. Hence, 11 girls are practicing the dance together. correct answer is C)11 #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:A family has two children. find the probability that both the children are girls given that at least one of them is a girl? options: A)1/3 B)1/5 C)1/7 D)1/9 E)2/3 SOLUTION:Let b stand for boy and g for girl. The sample space of the experiment is S = {(g, g), (g, b), (b, g), (b, b)} Let E and F denote the following events : E : ‘both the children are girls’ F : ‘at least one of the child is a girl’ Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)} Now E n F = {(g,g)} Thus P(F) = 3/4 and P (E n F )= 1/4 Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3 A) #### A QUESTION:If a sum of money at simple interest doubles in 6 years, it will become 4 times in options: A)15years B)16years C)11years D)18years E)12years SOLUTION:Explanation: let sum =x . s.i.=x rate =(100*x)/(x*6)=50/3% now ,sum =x, s.i= 3x, rate =50/3% time =(100*3x)/(x*50/3) = 18 years Answer: D #### D QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:In what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way? options: A)3 B)5.4 C)4.3 D)6.5 E)7 SOLUTION:T = 75/50 * 18/5 = 5.4 sec Answer:B #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done? options: A)2880 B)2778 C)2682 D)8222 E)6282 SOLUTION:Explanation: There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways. Further, in each category (subject), books are to be arranged in different order, we get, Required number of ways: 3! * [2! * 2! * 5!] = 2880 ANSWER: A #### A QUESTION:In a group of 70 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there? options: A)1140 B)1160 C)1180 D)1200 E)1040 SOLUTION:Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12. Number of sweets 80 children got = 70 * 12 = 840. Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20. Number of sweets 10 youngsters got = 10 * 20 = 200. Total number of sweets = 840 + 200 = 1040. E) #### E QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C *100 =50% Answer A #### A QUESTION:When a 192 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ? options: A)52 B)68 C)62 D)67 E)69 SOLUTION:Answer No. of pieces = Total length / Length of each piece = 192/3.2 = 60 Option: D #### D QUESTION:While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%) options: A)4.09 B)4.0 C)4.04 D)4.02 E)4.01 SOLUTION:Explanation: Given Error = 2% while measuring the side of a square. If the correct value of the side of square is 100, the measured value: => 100 + 2% *100 = 100+2=102 The area of square with edge 100 = side*side => 100*100 => 10000 The area of square with side 102 = 102*102= 10404 Error in area calculation = 10404-1000 = 404 % error= (404/10000)*100 = 4.04% ANSWER: C #### C QUESTION:A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ? options: A)11:10:15 B)20:17:23 C)19:19:18 D)5:4:9 E)None of these SOLUTION:Explanation: A:B:CA:B:C =(25 lakhs××1)+(35 lakhs××2) :(35 lakhs××2+25 lakhs××1) :(30 lakhs××3) = 95 lakhs : 95 lakhs : 90 lakhs =19:19:18=19:19:18. ANSWER IS C #### C QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 4 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)4/9. C)6/11. D)3/5. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 4buckles = 5buckles + 4buckles = 9buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 9 = x*15 x = 9/15=3/5 Answer: D #### D QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was? options: A)23777 B)35000 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100) (9x + 1100000 - 11x)/100 = 29000/3 = 9700 (9x + 1100000 - 11x) = 970000 x = 65000 Sum invested at 9% = Rs. 65000 Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000. Answer: B #### B QUESTION:In a two-digit number, the digit in the unit’s place is four times the digit in ten’s place and sum of the digits is equal to 10. What is the number? options: A)14 B)41 C)41 D)None of these E)Cannot be determined SOLUTION:Solution Let the ten's digits be x. Then, unit's digit = 4x. ∴ x + 4x = 10 ⇔ 5x = 10 ⇔ x = 2. So, ten's digit = 2, unit's digit = 8. Hence, the required number is 28. Answer D #### D QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)14355 B)15432 C)17576 D)18543 E)16878 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x? options: A)7 B)8 C)9 D)6 E)5 SOLUTION:(3+11+7+9+15+13+8+19+17+21+14+x)/12 =12 ⇒(137+x)/12=12 ⇒137+x=144 ⇒x=144−137=7 Answer is A. #### A QUESTION:A fruit seller sells mangoes at the rate of Rs.16 per kg and thereby loses 12%. At what price per kg, he should have sold them to make a profit of 20%? options: A)Rs.21.81 B)Rs.12 C)Rs.12.25 D)Rs.12.31 E)None SOLUTION:Solution 88 : 16 = 120 : x x= (16×120/88) = Rs.21.81 Hence, S.p per Kg = Rs.21.81 Answer A #### A QUESTION:What is 35% of 4/13 of 585? options: A)52 B)63 C)74 D)85 E)96 SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate. The number 585 is between 540 and 630, so (1/9)*585 will be about 65. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently. The closest answer is 63, so this is the answer to choose. The answer is B. #### B QUESTION:(a/2)/(b/c) In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression? options: A)8/2 B)2/4 C)1/8 D)2/4 E)4/6 SOLUTION:(a/2)/(b/c) = (a*c)/2b The expression will have the largest value when numerator (a*c) is the largest. = (2*4)/2*1 =8/2 Answer A #### A QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is? options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease SOLUTION:100 * 100 = 10000 80 * 115 = 9200 ----------- 10000-----------800 100-----------? => 8% decrease Answer: B #### B QUESTION:The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now? options: A)10.5 B)12.5 C)13.5 D)11.5 E)11 SOLUTION:1000*15 = 1200*x x = 12.5 ANSWER B #### B QUESTION:Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo? options: A)9 B)11 C)24 D)48 E)54 SOLUTION:Terry can pick one lunch salad bar....we can choose lettuce 2c1 , tomatoes - 3c1 and olives - 4c1... Two types of soups , if he picks one then 2c1 ways. Terry decided to have the combo : Soup + salad...Hmmm... Using the above information, we get ( 2c1 * 2c1* 3c1 * 4c1 ) = 48.. ANS option D is correct answer.. #### D QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:Find the odd man out. 187, 264, 386, 473, 682, 781 options: A)386 B)187 C)781 D)682 E)564 SOLUTION:Explanation : In all numbers except 386, the middle digit is the sum of other two digits. Answer : Option A #### A QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60? options: A)2.82 B)7.82 C)5.82 D)12.82 E)8.82 SOLUTION:In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65 In 85 points B give 15 since 80-65=15 In 50 points B gives=50*15/85=8.82 ANSWER:E #### E QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? options: A)1227 B)2088 C)26788 D)8112 E)1871 SOLUTION:A = 7500(26/25)2 = 8112 Answer: D #### D QUESTION:Mr Katial buys a house for Rs 1,00,000 and rents it. He puts 12.5% of each month’s rent aside for upkeep and repairs, pays Rs 325 per year as taxes and realizes 5.5% annually on his investment . Find the monthly rent? options: A)Rs 634.76 B)Rs 554.76 C)Rs 654.76 D)Rs 664.76 E)none of these SOLUTION:Let the monthly rent be Rs X. We have, 5.5% of 100000 = 12 (X - 12.5% of X) - 325 5500/12 = X - (X/8) - 325/12 5500/12 + 325/12 = 7/8 x X X = 5825/12 x 8/7 Rs 554.76 per month ANSWER:B #### B QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men? options: A)15.5 B)15.4 C)15.25 D)15.3 E)15.6 SOLUTION:Total age of 20 men = 15.6 x 20 = 312 Now, total age of 25 men = 389. Total age of five men added later = 389 - 312 = 77. Hence, the total average of five men = 77/5 = 15.4 ANSWER:B #### B QUESTION:Diana picked a number of pears, each of which she sold, canned, or poached. If she canned 60 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 115 pears, then how many pears did she sell? options: A)41 B)44 C)47 D)50 E)53 SOLUTION:Let x be the amount of pears that she sold. Then she poached 0.5x. Then she canned 1.6*0.5x=0.8x. The total amount of pears is x+0.5x+0.8x=2.3x The fraction of pears that she sold is 1/2.3=10/23. The number of pears she sold is (10/23)*115=50. The answer is D. #### D QUESTION:Set R has a mean of 12 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){15, 16} B){3, 4} C){6, 7} D){5, 6} E){11, 13} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 12,the values (11,13) are closer than others. Hence Answer : E #### E QUESTION:The least number which when increased by 4 each divisible by each one of 22, 32, 36 and 54 is : options: A)427 B)859 C)860 D)4320 E)None of these SOLUTION:Solution Required number = (L.C.M. of 24, 32, 36, 54) - 4 = 864 - 4 = 860. Answer C #### C QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.2 x = 3.2 Alternate solution: Try to backsolve. Initial volume = 3.2 After one hour --> (1/4)3.2 = 0.8 After two hours --> (1/4)0.8 = 0.2 Answer: B #### B QUESTION:Find out the next word in the series below... FAG, GAF, HAI, IAH, ...? options: A)GAK B)JAK C)HGF D)JAH E)KHG SOLUTION:In first FAG it was reodering the first and last letters and these are the continuous alphabets ANSWER:B #### B QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? options: A)4% B)8% C)4.2% D)4.8% E)5% SOLUTION:Let's say there is a TOTAL of100students at this college. 60 percent of the total number of students are freshmen. # of freshmen = 60% of 100 =60 40 percent of the fresh-men are enrolled in the school of liberal arts... Number of liberal arts freshmen = 40% of 60 =24 ...and, of these, 20 percent are psychology majors... Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8 What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? 4.8/100= 4.8% Answer:D #### D QUESTION:A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:13 C)23:12 D)11:9 E)11:10 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only. A : B 8000*18 : (8000*8) + (4000*10) 144000 : 104000 A:B = 18:13 ANSWER:B #### B QUESTION:Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.9 hour B)2.1 hour C)4.7 hour D)2.4 hour E)3.2 hour SOLUTION:Part filled by pipe A in 1 hour =1/8 Part filled by pipe B in 1 hour =1/4 Part filled by pipe C in 1 hour =1/24 Part filled by pipes A,B,C together in 1 hour=1/8+1/4+1/24=10/24 i.e, pipes A,B,C together can fill the tank in = 24/10 hr =2.4 hour. ANSWER:D #### D QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? options: A)21 B)36 C)39 D)60 E)65 SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96. Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room. Therefore there are 3/8*96=36 people in the room under the age of 21. Answer: B. #### B QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B QUESTION:Jerry, an electrician, worked 5 months out of the year. What percent of the year did he work? (round answer to the nearest hundredth) What percent 12 is 5? 12 months = 1 year options: A)58.33% B)68.33% C)78.33% D)88.33% E)41.66% SOLUTION:1. Multiply the opposites 5 x 100 = 500 100=5/12 Divide by the remaining number 41.66% (rounded to hundredth) correct answer E #### E QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)Rs.4082.67 B)Rs.4082.99 C)Rs.4082.29 D)Rs.4082.40 E)Rs.4082.12 SOLUTION:Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs.4082.40 Answer:D #### D QUESTION:If 18 is 15 percent of 25 percent of a certain number, what is the number? options: A)9 B)36 C)480 D)81 E)400 SOLUTION:Let the certain number be x. => (15/100)*(25/100)*x = 18; => x=480; Ans is (C). #### C QUESTION:Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/8 gallon of paint. How many statues can she paint? options: A)7 B)20 C)28 D)14 E)19 SOLUTION:number of statues=all the paint÷amount used per statue =7/8 ÷ 1/8 =7/8*8/1 =7/1 =7 Answer is A. #### A QUESTION:A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box? options: A)5 m B)6 m C)4 m D)7 m E)8 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:Mr. Sane invested a total amount of 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was 3,620, what was the amount invested in scheme B? options: A)8,000 B)8,600 C)8,150 D)Data inadequate E)None of these SOLUTION:% interest on total amount per annum = 3620×100/16500×2=362/33% Now, use Alligation method. Hence, ratio of amount invested in schemes A and B = (12 - 362⁄33) : (362⁄33 - 10) = 17 : 16 Hence, amount invested in B = 16×16500/(17+16)=8000 Answer A #### A QUESTION:The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : options: A)Rs. 113.5 B)Rs. 119.7 C)Rs. 124.75 D)Rs. 130.75 E)Rs. 134.45 SOLUTION:For an income of Rs.756, investment = Rs.9000 For an income of Rs., investment = = Rs.125 For a Rs.100 stock, investment = Rs.125. Market value of Rs. 100 stock = = Rs. 124.75 C #### C QUESTION:A shopkeeper sold an article at $100 with 30% profit. Then find its cost price? options: A)$120 B)$100 C)$91 D)$77 E)$69 SOLUTION:cost price = selling price *100/(100+profit) C.P. = 100*100/130 = $77(approximately) Answer is D #### D QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm SOLUTION:In one hour, the first train travels 60 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train at 10:00 am. The answer is B. #### B QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)18% B)22% C)12% D)92% E)14% SOLUTION:Original price = 100 CP = 80 S = 80*(140/100) = 112 100 - 112 = 12% Answer: C #### C QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 162 => x= 9 Answer: B #### B QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is options: A)16 B)24 C)48 D)96 E)78 SOLUTION:Solution Required number = (2×4×6) = 48. Answer C #### C QUESTION:A box contains 8 pairs of shoes (16 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/19 D)1/10 E)1/15 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 16, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/15(as after taking one at random there are 15 shoes left and only one is the pair of the first one)=1/15 Answer: E. #### E QUESTION:A sum of money is sufficient to pay B's wages for 12 days and C's wages for 24 days. The same money is sufficient to pay the wages of both for? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Let the total money be $x B's 1day work = $ x/12 C's 1day work = $ x/24 A+B 1day work = $ x/8 Money is sufficient to pay the wages of both for 8days Answer is C #### C QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/9 B)5/12 C)1/36 D)7/12 E)4/9 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 ANSWER:B #### B QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice? options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7 SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2*(1/2)^2 = 2/4 =0.5. The answer is, therefore, (A). #### A QUESTION:A girl has 10 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts? options: A)A)100 B)B)102 C)C)108 D)D)110 E)E)120 SOLUTION:The girl can select one jeans in 10 ways. The girl can select one shirt in 12 ways. The number of ways in which he can select one jeans and one shirt is 10 * 12 = 120 ways. E #### E QUESTION:How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)22 B)54 C)99 D)77 E)12 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 900 * 3/50 = 54 sec. Answer: B #### B QUESTION:If circles x and y have the same area and circle x has a circumference of 14π, half of the radius of circle y is: options: A)16 B)8 C)4 D)3.5 E)1 SOLUTION:x be radius of circle x y be radius of circle y given: pi*x^2 = pi*y^2 also, 2*pi*x = 14*pi x =7 thus y =7 y/2 = 3.5 Ans: D #### D QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea? options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None SOLUTION:Solution: 1st Method: Let the original price of tea be Rs. x/kg. After reduction the price becomes = x -10% of x = 9x/10 per kg. Now, (22500/(9x/10))-22500/x = 25 Or, 22500[10/9x- 1/x] = 25 Or, 25*9x = 22500; Or, x = (22500/2589) = Rs. 100. Hence, new price = 90 per kg. Thought process Method: Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg. After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg. So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea. Answer: Option C #### C QUESTION:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold? options: A) 11 B) 13 C) 15 D) 17 E) 19 SOLUTION:(x+5)*150 +x*85=2160 =>x=6 total lens=6+(6+5)= 17 Answer D #### D QUESTION:A person was going through train from Bombay to Pune. After every five minutes he finds a train coming from opposite direction. Velocity of trains are equal of either direction. If the person reached Pune in one hour then how many trains he saw in the journey ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:11 ANSWER:C #### C QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is? options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5 SOLUTION:3:1 Answer:B #### B QUESTION:10 books are placed at random in a shelf. The probability that a pair of books will always be together is - options: A)1/5 B)1/3 C)1/4 D)118/2 E)21/4 SOLUTION:10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Answer: C #### C QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ? options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours SOLUTION:Explanation: We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as Work done for 1 hour without leak = 1/3 Work done with leak = 3 1/2=7/2 Work done with leak in 1 hr=2/7 Work done by leak in 1 hr=1/3=2/7=1/21 So tank will be empty by the leak in 21 hours. ANSWER IS D #### D QUESTION:When a merchant imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $94.50, what was the total value of the item? options: A)$2,350 B)$2,850 C)$3,250 D)$3,400 E)$3,750 SOLUTION:Let x be the value in excess of $1,000. 0.07x = 94.5 x = $1,350 The total value was $1,350 + $1,000 = $2,350. The answer is A. #### A QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? options: A)58 B)70 C)63 D)65 E)72 SOLUTION:1/2bh=1/2(2a+1)(2a+6) Now 4a-2=2a+6 2a=8 . a=4 Therefore, A(0,0); B(0,14); C(9,14) 1/2*9*14=63 Answer: C #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)615 m B)240 m C)168 m D)197 m E)691 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m Answer: B #### B QUESTION:A train 120 m long passed a pole in 20 sec. How long will it take to pass a platform 780 m long? options: A)150 B)170 C)160 D)100 E)120 SOLUTION:Speed = 120/20 = 6 m/sec. Required time = (120 + 780)/6 = 150 sec. Answer: Option A #### A QUESTION:In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are finance majors? options: A)3 B)5 C)8 D)11 E)17 SOLUTION:pqrs = 1365 = 3* 5 *7 * 13 Since 1< p < q < r < s, the number of students who are finance majors is q = 5. The answer is B. #### B QUESTION:A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? options: A)450. B)412. C)432. D)502. E)522. SOLUTION:Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30 Only option A satisfies the condition, and hence is the answer #### A QUESTION:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 100 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters? options: A)250 B)300 C)350 D)400 E)500 SOLUTION:Nice problem. +1. First timetogetherthey run half of the circumference. Second timetogetherthey run full circumference. First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters. Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 100 meters, thus the circumference is 200 + 100 = 300 meters. Answer: B. #### B QUESTION:The measure of the side of a square is quadrupled. If x represents the perimeter of the original square, what is the value of the new perimeter? options: A)3x B)4x C)9x D)12x E)27x SOLUTION:Original perimeter = x Hence original side = x/4 New side = 4x/4 New perimeter = 4*4x/4 = 4x Correct Option: B #### B QUESTION:By selling 8 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 10%? options: A)6.54 B)9.45 C)7.34 D)6.67 E)5.09 SOLUTION:90% --- 8 110% --- ? 90/110 * 8 = 6.54 Answer: A #### A QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: 1) 80% of the team consists of spinners. 2) The opening batsmen were spinners. options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow. D #### D QUESTION:A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/7 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x? options: A)x/3 B)5x/2 C)2x/3 D)3x/2 E)2x SOLUTION:x/(x+y) = 2/7 7x = 2x+2y 5x = 2y y = 5x/2 Answer B #### B QUESTION:In 100 litres mixture milk and water are in the ratio 3:2. After adding how many liters of water its ratio will become 3:4 options: A)48 B)50 C)62 D)78 E)100 SOLUTION:Milk quantity = 3/5 * 60 = 36 water quantity = 100-36 = 64 new ratio of M:W = 36:64+x = 3:4 192+3x = 144 x = 48 Answer is A #### A QUESTION:There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle. options: A)18 B)99 C)12 D)07 E)11 SOLUTION:Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm. a2 = 784 = (4)(196) = (22).(142) a = (2)(14) = 28 a = 2l, l = a/2 = 14 l = (7/3)s Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm. Answer: C #### C QUESTION:Find the value of y from the given equation. 9^y = 3^12, what is y? options: A)3 B)5 C)7 D)8 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:If a number p is prime, and 2p+4 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:1/6 = 0.1666666... (a repeating pattern one digit long) A #### A QUESTION:In a group of 25, 13 can speak Latin, 15 can speak French, and 6 don't speak either. How many of these speak both Latin and French? options: A)9 B)10 C)11 D)12 E)8 SOLUTION:let no.of persons who speeks booth latin and french = x so, no.of persons who speeks only latin = 13-x no.of persons who speeks only french= 15-x no.of persons who speeks dont speek any lag = 6 therefore (13-x)+(15-x)+x+6=25 34-x=25 x=9 ANSWER:A #### A QUESTION:If 60 percent of the members of a certain organization are women and 6/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization. options: A)II B)III C)I, II D)I E)II, III SOLUTION:6/10 (60%) of the members are women and 6/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 6/10*80 = 48 women; 80 - 48= 32 men; 6/8*32 = 24 married men; 32 - 24 = 8 unmarried men. So, option I,II is true. Answer: C #### C QUESTION:The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy? options: A)7 B)9 C)11 D)13 E)14 SOLUTION:Explanation: 3x + 5x + 7x = 45 x =3 3x = 9 B) #### B QUESTION:If the sides of a triangle are 26 cm, 24 cm and 20 cm, what is its area? options: A)120 B)772 C)288 D)266 E)240 SOLUTION:The triangle with sides 26 cm, 24 cm and 20 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 20 = 240 cm2 Answer: E #### E QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? options: A)17% B)18% C)30% D)17% E)12% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 123.50 Let the marked price be Rs. x. Then, 95/100 x = 123.50 x = 12350/95 = Rs. 130 Now, S.P. = Rs. 130, C.P. = Rs. 100 Profit % = 30%. Answer: C #### C QUESTION:A person borrows Rs.5000 for 2 years at 5% p.a. simple interest. He immediately lends it to another person at 61⁄4% p.a for 2 years. Find his gain in the transaction per year. options: A)62.5 B)150 C)225 D)112.5 E)212.5 SOLUTION:Explanation : The person borrows Rs. 5000 for 2 years at 5% p.a. simple interest Simple interest that he needs to pay = PRT/100=5000×5×2/100=500 He also lends it at 6 1⁄4% p.a for 2 years Simple interest that he gets = PRT/100=5000×25/4×2/100=625 His overall gain in 2 years = Rs.625 - Rs.500 = Rs.125 His overall gain in 1 year = 125/2 = Rs.62.5 Answer : Option A #### A QUESTION:The second of two numbers is two less than three times the first. Find the numbers if there sum is 74. options: A)7-19 B)8-20 C)10-16 D)15-9 E)19-55 SOLUTION:We are looking for two numbers. #1 - x #2 - 3x – 2 The sum is 74. #1 + #2 = 74 Substituting x + 3x – 2 = 74 4x – 2 =74 4x = 76 x = 19 The first number is 19, the second number is two less than three times 19 or 55. correct answer E #### E QUESTION:Cereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight? options: A)2:5 B)1:3 C)2:7 D)3:4 E)1:5 SOLUTION:2% is 2%-points below 4% and 11% is 7%-points above 4%. The ratio of A:B should be 2:7. The answer is C. #### C QUESTION:On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ? options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation: Formula: (Divisor*Quotient) + Remainder = Dividend. Soln: (56*Q)+29 = D -------(1) D%8 = R -------------(2) From equation(2), ((56*Q)+29)%8 = R. => Assume Q = 1. => (56+29)%8 = R. => 85%8 = R => 5 = R. Answer B #### B QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:If x and y are different integers, both divisible by 11, then which is not necessarily true? options: A)x^2 + y^2 is divisible by 11 B)x - y is divisible by 11 C)xy is divisible by 11 D)x + y is divisible by 11 E)x + y is divisible by 22 SOLUTION:Let x = 11k and let y = 11j. Then x+y = 11(k+j) and k+j could be even or odd. Thus 11(k+j) is not necessarily divisible by 22. The answer is E. #### E QUESTION:A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)235 m B)245 m C)247 m D)249 m E)252 m SOLUTION:length of the bridge = x meter Total distance covered = 130+x meter total time taken = 30s speed = Total distance covered /total time taken = (130+x)/30 m/s = 45 × (10/36) = (130+x)/30 = 45 × 10 × 30 /36 = 130+x = 45 × 10 × 10 / 12 = 130+x = 15 × 10 × 10 / 4 = 130+x = 15 × 25 = 130+x = 375 = x = 375-130 =245 #### B QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is: options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these SOLUTION:Explanation: Let A, B, C represent their respective weights. Then, we have: A + B + C = (45 x 3) = 135 …. (i) A + B = (40 x 2) = 80 …. (ii) B + C = (45 x 2) = 90 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv) Subtracting (i) from (iv), we get : B = 35. B’s weight = 35 kg. Answer: D #### D QUESTION:How many numbers from 10 to 1000 are exactly divisible by 9? options: A)100 B)10 C)11 D)12 E)14 SOLUTION:10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100 Answer : A #### A QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 8p have. p = 3 --> 8p = 24--> 24 has 6 even divisors: 2, 4, 6, 8, 12, 24. Answer: D. #### D QUESTION:A wildlife preserve is being planned for 6,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population? options: A) 340 B) 330 C) 670 D) 310 E) 300 SOLUTION:Number of rhinos = 6000 Watering area = 10,000 acres Number of rhino to increase by 10 percent ,then number of rhino = 6600 Grazing area for a rhino = 100 Total grazing area for 6600 rhinos= 6600 * 100 = 6,60,000 Total area required for the wildlife preserve = 6,60,000 + 10,000 = 6,70,000 = 670 * 1000 Answer C #### C QUESTION:One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader? options: A)120 % B)140 % C)162/3 % D)20 % E)None SOLUTION:Sol. CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain. Answer D #### D QUESTION:The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area? options: A)288 B)240 C)267 D)299 E)162 SOLUTION:4a = 68 => a = 17 172 – 82 = 152 1/2 * 16 * 30 = 240 Answer:B #### B QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies options: A)200 B)300 C)400 D)500 E)600 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 * 5C2) = 200 ANSWER A #### A QUESTION:Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/10 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now? options: A)$110 B)$152.3 C)$180 D)$220 E)$260 SOLUTION:Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition. A-E = 1/10*(A+E) ==> 9A = 11E ------------ (1) Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E 1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2) Substituting (1) in (2): 11E/9*11 = 220+12E or (121/9-12) E = 220 or 13/9 E =220 E = 220*9/13 =152.3 B #### B QUESTION:What will be in unit's place digit of 3 to the power 34. options: A)1 B)6 C)3 D)0 E)9 SOLUTION:as the unit place digit of 3 to the power of 1 is 3, to the power of 2 is 9.to the power of 3 is 7 ,to the power of 4 is 1 and it'll be repeated again in the same order.... so the unit place digit of 3 to the power of 34 is 9.. ANSWER:E #### E QUESTION:A boat moves upstream at the rate of 1 km in 25 minutes and down stream 1 km in 12 minutes. Then the speed of the current is : options: A)1 kmph B)2 kmph C)3 kmph D)1.3 kmph E)3.5 kmph SOLUTION:Rate upstream = (1/25 *60) = 2.4 kmph Rate dowm stream = 1/12 * 60 = 5 kmph Rate of the current = ½ (5-2.4) = 1.3 kmph ANSWER:D #### D QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. options: A)600 B)500 C)575 D)655 E)675 SOLUTION:Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. So answer is E. #### E QUESTION:The ratio of cats to dogs to birds to fish is 3:4:5:6. There are no other types of animals in the pet store. which of the following cannot be the total number of animals in the store? options: A)36 B)54 C)72 D)90 E)101 SOLUTION:The parts add up to 3 + 4 + 5 + 6 = 18, so we know that any possible number of total answers must be a multiple of 18. All five answer choices are multiples of 18: (A) 36 = 18*2 (B) 54 = 18*3 (C) 72 = 18*4 (D) 90 = 18*5 (E) 101 = not a multiple of 18 ans is E #### E QUESTION:Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol. What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol? options: A)32 B)21 C)27 D)None of these E)18 SOLUTION:Explanation: Let t be the time after Kajol starts, when she meets Ajay, then \inline t=\frac{300}{(x+y)} This should be less than 2.5 or (x+y)>120 Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72 This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol. Answer: D #### D QUESTION:A 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar? options: A)6%. B)7.5%. C)9.2%. D)10.5%. E)14%. SOLUTION:Denominator: 340+10+3.2+6.8=360 Numerator: 340(1-.80-.06)+3.2 340(0.14)+3.2 47.6+3.2 50.8 Ratio: 50.8/360=0.14 Answer: E #### E QUESTION:In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number? options: A)26 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=3x Therefore x + 3x = 8 ‹=›4x = 8 ‹=›x= 2. So, ten's digit = 2, unit's digit = 6. Hence, the required number is 26. Answer A #### A QUESTION:A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is? options: A)1250m B)1750m C)950m D)1000m E)1300m SOLUTION:Speed = 15*5/18 = 15/18 m/sec Distance covered in 35 minutes = 15/18 *35 *60 = 1750 m Answer is B #### B QUESTION:The population of a town is 8100. It decreases annually at the rate of 10% p.a. What was its population 2 years ago? options: A)9000 B)8000 C)8500 D)9500 E)10000 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 8100 × 100/90 × 100/90 = 10000 E) #### E QUESTION:log3 N+log5 N what is 3 digit number N that will be whole number options: A)629 B)729 C)829 D)125 E)727 SOLUTION:No of values N can take is 1 5^3=125 ANSWER:D #### D QUESTION:A and B are two partially filled buckets of water. If 6 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 6 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)66/5 B)13 C)17 D)21 E)23 SOLUTION:Let Bucket A be A and Bucket B be B Scenario 1 A-6 = 1/3 (B+6) ----> 3A-18 =B+6 Scenario 2 B-6 = 1/2 (A+6) -----> 2B-12 = A+6 From Scenario 1, B = 3A-24 Substitute B with this information in Stmt 2 2 (3A-24) -12 = A+6 ------> 6A -48-12 = A+6 ------> 6A- A = 60+6 ---> 5A= 66 A= 66/5, Answer choice A #### A QUESTION:The LCM of two numbers is 2310 and HCF is 26. If one of the numbers is 210. Then what is the other number ? options: A)715 B)825 C)286 D)582 E)465 SOLUTION:First number * Second Number = LCM * HCF Other number = 2310 * 26 / 210 = 11*26 = 286 ANSWER :C #### C QUESTION:What is x if x + 5y = 24 and y = 2? options: A)1 B)3 C)5 D)7 E)14 SOLUTION:Substitute y by 2 in x + 5y = 24 x + 5(2) = 24 x + 10 = 24 If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence x = 14 correct answer E #### E QUESTION:Three different containers contain 496 litres, 403 litres and 713 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ? options: A)29 litres B)31 litres C)35 litres D)19 litres E)26 litres SOLUTION:M1 = 496 litres M2 = 403 litres M3 = 713 litres Required measurement = H.C.F. of M1,M2,M3 = 31 litres Answer is B #### B QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 6*6 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:The distance light travels in one year is approximately 5,890,000,000,000 miles. The distance light travels in 100 years is options: A)A) 587 × 108 miles B)B) 587 × 1010 miles C)C) 587 × 10-10 miles D)D) 589 × 1012 miles E)E) 587 × 10-12 miles SOLUTION:The distance of the light travels in 100 years is: 5,890,000,000,000 × 100 miles. = 589,000,000,000,000 miles. = 589 × 1012 miles. The answer is (D) #### D QUESTION:The daytime telephone rate between two cities is 50 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 60 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is: options: A) 0.4(0.60) + 35c B) 0.4(0.50 + 0.32c) C) 0.4(0.60 + 9c) D) 0.6(0.60 + 32c) E) 0.6(0.60 + 0.35c) SOLUTION:For first three minutes = 50 cents Remaining minutes = 35 -3 = 32 charge for 32 minutes = 32c total cost (if the call was made in daytime) = 0.50 + 32c 60% chargereducedon night calls => 40% charge =>0.4(0.50 + 32c) Hence, Answer is B #### B QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)15 C)20 D)22 E)23 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15 Answer: Option B #### B QUESTION:The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range: options: A)30 < x < 36 B)30 < x < 37 C)31 < x < 37 D)31 < x < 38 E)32 < x < 38 SOLUTION:f(n) = number of perfect squares less than n 1,4,9,16,25,36 f(25) = 4 f(26)=f(27)=...=f(35)=f(36) = 5 f(37) = 6 g(n) = number of prime numbers less than n 2,3,5,7,11,13,17,19,23,29,31,37 g(31)=10 g(32)=g(33)=...=g(36)=g(37) = 11 g(38)=12 f(x)+g(x)=16 implies that f(x)=5 and g(x)=11. So, x = 32,33,34,35,or36. Answer C, 31 < x < 37. #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)16 B)18 C)24 D)22 E)26 SOLUTION:C 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### C QUESTION:City A to city B, Andrew drove for 1hr at 46 mph and for 3 hours at 60 mph. What was the average speed for the whole trip? options: A)56.5 B)57.5 C)61 D)61.5 E)62.5 SOLUTION:The total distance is 1×46+3×60=226 And the total time is 4 hours. Hence, Average Speed=(Total Distance/Total Time) =226/4=56.5 A #### A QUESTION:In the faculty of Reverse-Engineering, 240 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total? options: A)515. B)545. C)661. D)644. E)666. SOLUTION:Answer is C :661 Solution : Total number of students studying both are 423 + 240 - 134 = 529 (Subtracting the 134 since they were included in the both the other numbers already). So 80% of total is 529, so 100% is approx. 661. #### C <<<Examples ends QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? options: A)240 B)65 C)110 D)130 E)200 SOLUTION:Adult + Children = 200 Let, Children = y then, Adult = y+20 i.e. y+(y+20) = 200 i.e. y = 900 i.e. Adult = 90+20 = 110 Adults include only Men and Women i.e. Men + Women = 110 Let women, W = x then Men, M = x+20 i.e. x+(x+20) = 2x+20 = 110 i.e. x = 45 i.e. Men, M = 45+20 = 65 Answer: Option B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the product of the integers from 1 to n is divisible by 378, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:378 = 2 x 3 x 3 x 3 x 7 N must include at least 3, 2*3, and 3*3. The answer is C. #### C QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction? options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively. d = 2n - 1 (n + 1)/(d + 1) = 4/5 5n + 5 = 4d + 4 5n + 5 = 4(2n - 1) + 4 => n = 5/3 d = 2n - 1 => d = 3/7 Hence the fraction is : 5/7 ANSWER:B #### B QUESTION:The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is : options: A)1520 m2 B)2420 m2 C)2480 m2 D)2520 m2 E)None of these SOLUTION:Solution We have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103. Solving the two equations, we get, l = 63 and b = 40. ∴ Area = (l × b) = (63 × 40) m2 = 2520 m2. Answer D #### D QUESTION:0.40 represents what percent of 0.008? options: A)0.05% B)0.5% C)5% D)500% E)5000% SOLUTION:One more method 0.40 represents what percent of 0.008? Adjusting the decimal 400 represents what percent of 8? Divide by 8 50 represents what percent of 1? Answer = 50*100 = 5000% = E #### E QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth? options: A)80 B)28 C)90 D)26 E)11 SOLUTION:Explanation: SP of 1m of cloth = 8925/85 = Rs. 105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 105 - Rs. 25 = Rs. 80. Answer: A #### A QUESTION:The average of the marks of 30 students in a class is 45. If the marks of each student are doubled, find the new average? options: A)85 B)77 C)33 D)90 E)75 SOLUTION:Sum of the marks for the 30 students = 30 * 45 = 1350. The marks of each student are doubled, the sum also will be doubled. The new sum = 1350 * 2 = 2700. So, the new average = 2700/30 = 90. Answer:D #### D QUESTION:2/5 of the fish in an aquarium is red and 1/4 of the fish is brown. 1/4of the red fish and 1/5 of the brown fish is male. If the rest of the fish in the aquarium is female, what is the probability that a fish randomly picked from the aquarium is male? options: A)3/20 B)7/30 C)5/16 D)1/3 E)2/5 SOLUTION:Straight method.... 1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20 ANSWER:A #### A QUESTION:We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy? options: A)A)36 B)B)90 C)C)40 D)D)42 E)E)44 SOLUTION:Let B be the number of blue hats and let G be the number of green hats. B+G=85. B=85-G. 6B+7G=600. 6(85-G)+7G=600. 510-6G+7G=600. G=600-510=90. The answer is B. #### B QUESTION:If the number 653ab is divisible by 90, then (a + b) = ? options: A)2 B)3 C)4 D)6 E)8 SOLUTION:90 = 10 x 9 Clearly, 653ab is divisible by 10, so b = 0 Now, 653a0 is divisible by 9. So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4. Hence, (a + b) = (4 + 0) = 4. ANSWER:C #### C QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm SOLUTION:Explanation: Required Length = H.C.F of 700 cm, 385 cm and 1295 c = 35 cm. Answer: C #### C QUESTION:Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo? options: A)9 B)11 C)24 D)48 E)54 SOLUTION:Terry can pick one lunch salad bar....we can choose lettuce 2c1 , tomatoes - 3c1 and olives - 4c1... Two types of soups , if he picks one then 2c1 ways. Terry decided to have the combo : Soup + salad...Hmmm... Using the above information, we get ( 2c1 * 2c1* 3c1 * 4c1 ) = 48.. ANS option D is correct answer.. #### D QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce options: A)100 B)65 C)25 D)11 E)18 SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. So if machine X produces 100 widgets, then machine Y produces 120 widgets. Ratio of 120/100 = 6/5. This is their speed of work (Y:X). i.e. speed of their work (X:Y) = 5/6 Now, time is inversely proportional to speed. Hence the ratio of the time spent (X:Y)= 6/5 Let us assume that they spend 6x and 5x hours. Given that 6x-5x = 10 So, x = 10. Hence 6x = 6*10 = 60 hours. Hence X takes 120 hours to produce 1080 widgets. So, in 1 hour, it can produce (1 * 1080)/60 = 18 Hence option (E). #### E QUESTION:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster? options: A)30 B)44 C)42 D)46 E)50 SOLUTION:Total # of students 20+28+18-(9+7+10)+4=44. Answer: B. #### B QUESTION:At what rate of annual simple interest,a certain sum will amount to four times in 15 year? options: A)15% B)17.5% C)20% D)25% E)35% SOLUTION:r=? t=15 yrs SI=p*r*t/100 Amount = SI+p = 4p (p*r*15/100)+p = 4p p(15r/100 + 1) = 4p 15r + 100 = 400 15r = 300 r = 20% ANSWER:C #### C QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)6 SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours Answer: option E #### E QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1500 B)2000 C)3000 D)3500 E)2500 SOLUTION:Profit as x since 5% and 95% of x will be divided b/w A and B ration 3:2 =>profit 95x/100 * 3/5 given that A's share is Rs 855 => 95x/100 * 3/5 = 855 hence x = 1500 ANSWER A #### A QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3 SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1055 B)1050 C)1057 D)1060 E)1070 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055. A #### A QUESTION:A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper? options: A)140 B)388 C)238 D)119 E)112 SOLUTION:when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 14*10 = 140 sq cmV Answer: A #### A QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)24 B)66 C)55 D)88 E)61 SOLUTION:(15*18)/12 = 24 Answer:A #### A QUESTION:Ayesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)6 B)40 C)50 D)10 E)20 SOLUTION:Mother's age when Ayesha's brother was born = 42 years. Father's age when Ayesha's brother was born = (58 + 4) years = 62 years. Required difference = (62 - 42) years = 20 years. Answer:E #### E QUESTION:In a bowl, the number of marbles gets doubled after every minute. If the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled. options: A)1 hour and 59 minutes B)2 hour and 59 minutes C)4 hour and 59 minutes D)4 hour and 59 minutes E)5 hour and 59 minutes SOLUTION:Solution: The correct way to solve this question is go backwards. If the number of marble gets doubled every minute and after two hours, it is filled completely, one minute ago it would be half. So, it will take 1 hour and 59 minutes for it to be filled half. Answer A #### A QUESTION:A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)3 B)7.5 C)2.25 D)1.5 E)4 SOLUTION:M = 9 S = x DS = 9 + x US = 9 - x 9 + x = (9 - x)2 9 + x = 18 -2x 3x = 9 x = 3 ANSWER:A #### A QUESTION:Find the median of the data 25, 37, 47, 18, 19, 26, 36. options: A)22 B)23 C)24 D)25 E)26 SOLUTION:Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47 Here, the number of observations is odd, i.e., 7. Therefore, median = (n + 1/2)th observation. = (7 + 1/2)th observation. = (8/2)th observation = 4th observation. 4th observation is 26. Therefore, median of the data is 26. ANSWER :E #### E QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)4096 D)1024 E)1536 SOLUTION:0.4*2^10=0.4*1024=409.6 The answer is C. #### C QUESTION:there is four light.all light glow in blue,white,yellow and red. all glow together and take different color.every time each light change its color in given four of the color.but at same time no two light have same color then tell how many design will form? options: A)20 B)24 C)18 D)16 E)22 SOLUTION:it is so simple,it is just permutation of 4 item. 4P4=4!=24 answer B #### B QUESTION:Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%? options: A)30000 B)40000 C)50000 D)60000 E)70000 SOLUTION:let first parrt is x and second part is y then x+y=50000----------eq1 total profit=profit on x +profit on y 7000=(x*10*1)/100 + (y*20*1)/100 70000=x+2y-----------------------------------eq2 70000=50000+y so y=20000 then x =50000-20000=30000 first part =30000 ANSWER:A #### A QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:What is 2/5 of 5/9 of 1/2? options: A)1/4 B)1/9 C)9/16 D)5/8 E)16/9 SOLUTION:2/5 * 5/9 * 1/2= 1/9 Answer: B #### B QUESTION:calendar=52097083 november=538=8651 march=2*308 blue=7154 december=? options: A)9535&153 B)9585&153 C)9525&153 D)9525&*53 E)9525&*54 SOLUTION:from above in formation d=9 e=5 c=2 e=5 m=3 b=1 e=5 r=8 95253158( Order doesnot matter i guess!) another thing is &=8 for mathcing above ans ANSWER:C #### C QUESTION:The ratio of Laxmi's age to the age of her mother is 3:11. The difference of their ages is 24 years. The ratio of their ages after 3 years will be? options: A)1 : 9 B)1 : 3 C)1 : 2 D)1 : 1 E)3 : 3 SOLUTION:Suppose age of Laxmi is x years. The difference of their ages \inline \therefore Ratio of their ages after 3 years = = = 12 : 36 = 1 : 3 Answer:B #### B QUESTION:3,8,18,38,78,__ options: A)158 B)156 C)154 D)150 E)148 SOLUTION:8=3*2+2 18=8*2+2 38=18*2+2 78=38*2+2 158=78*2+2 ANSWER:A #### A QUESTION:The ratio of two quantities is 1 to 2. If each of the quantities is increased by 15, what is the ratio of these 2 new quantities? options: A)5:6 B)25:27 C)15:16 D)20:21 E)It cannot be determined from the information given SOLUTION:The ratio cannot be straight way added any quantity... 1:2means 1X:2X... So when you add a quantity, it becomes 1x + 15 : 2x +15.. So value of x is must.. Ans E #### E QUESTION:There are 8 balls in a bucket, 4 balls are blue and 4 balls are red. If two ball chosen randomly , how many chances there are at least one blue ball will present? options: A)21 B)25 C)16 D)22 E)20 SOLUTION:Two ball will be chosen. At least 1 blue ball Total ways = 8C2 = 28 Total without any blue ball = 4C2 = 6 Hence ways in which at least one blue will be present = 28 - 6 = 22 Correct option: D #### D QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:Evaluate 25% of 450 + 45% of 250 options: A)225 B)242 C)252 D)262 E)272 SOLUTION:Explanation: = (25/100) * 450 + (45/100) * 250 = 225 Option A #### A QUESTION:Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 13 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip? options: A)48 B)42.5 C)44 D)50 E)52.5 SOLUTION:Total Time taken by jerry = (8/40)*60 Minutes + 13 Minutes + (20/60)*60 Minutes = 35 Minutes Average Speed = Total Distance / Total Time = (8+20) miles / (35/60)Hours = 28*60 / 35 = 48 Miles per hour Answer: option A #### A QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line? options: A)30sec B)45sec C)36sec D)29sec E)52sec SOLUTION:Speed of the train = 50*5/18 = 250/18 m/sec Distance moved in passing the standing man = 500m Required time taken = 500/(250/18) = 500*18/250 = 36sec Answer is C #### C QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856 SOLUTION:(900*3*3)/100 = 81 920 + 81 = 1001 ANSWER:B #### B QUESTION:The average of a couple was 26Yrs when they were married 6Yrs ago.The avg age of the couple and a child, who was born during the interval, is 22Yrs now. How old is the child now ? options: A)2 Yrs B)4 Yrs C)3 Yrs D)1 Yrs E)None of these SOLUTION:(a+b-6-6)/2=26; a+b=64; a+b+c/3=22; solving both c=2 ANSWER:A #### A QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)*(100%-19%) = 1.07*.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D QUESTION:If 9^y = 3^12, what is y? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Also note here the relevance of 'K must be less than 400'. 21K is 180n (a multiple of 180). 180n = 2^2 * 3^2 * 5 * n = 3*7*K n must have a 7 at least. K must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60. So K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 60*7 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 60*2 or 60*3*2 or 60*5 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has. Answer (C) #### C QUESTION:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? options: A)88 B)90 C)96 D)98 E)102 SOLUTION:2 multiples-choice questions can be answered in = 4 x 4 = 16 ways 3 true-false questions can be answered in = 2x2x2 = 8 ways But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways Total ways to answer the quiz = 16 x 6 = 96 Answer C #### C QUESTION:A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15? options: A)3 B)4 C)5 D)8 E)9 SOLUTION:Explanation: 50 + 25 = 75/15 = 5 (Remainder) C #### C QUESTION:A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn? options: A) 188 B) 258 C) 376 D) 470 E) 517 SOLUTION:consider 5x acres of land used for bean consider 2x acres of land used for wheat consider 4x acres of land used for corn Total given is 1034 acres 11x =1034 x = 94 land used for corn Y= 4 * 94 = 376 correct option - C #### C QUESTION:Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: options: A)4 B)6 C)5 D)7 E)9 SOLUTION:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4 Answer: Option A #### A QUESTION:I. j; k; m; n; p II. j - 10; m; m; m; p + 15 III. j + 2; k + 1; m; n - 1; p - 2 If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation D to least standard deviation in which of the following? options: A) I, III, II B) II, I, III C) II, III, I D) III, I, II E) III, II, I SOLUTION:Range of 1st Set = (p-j) Range of 2nd Set = P+15 - j +10 = (p-j) +25 Range of 3rd Set = P -2 - j - 2 = (p-j) - 4 R2 > R1 > R3 ==> SD2 > SD1 > SD3 Since,D= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B #### B QUESTION:A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A options: A)26.2 km B)25.7 km C)23.2 km D)26.67 km E)None of these SOLUTION:Explanation: Distance travelled by each of them is to be made equal. => Distance travelled walking = Distance covered cycling. Let after 4 hours of walking, A walk for x hours more before B catches up with him. => Distance = Speed * Time (4+x)4 = 10x x = 8/3 Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67 ANSWER: D #### D QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142 options: A)23 B)25 C)46 D)49 E)50 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 30 + 16 = 46 . #### C QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)22 B)88 C)27 D)20 E)98 SOLUTION:Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D #### D QUESTION:If x is less than y by 25% then y exceed x by: options: A)33.33% B)25% C)75% D)66.66% E)None of these SOLUTION:Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%) => 25(100-25)*100 =33.33% ANSWER:A #### A QUESTION:Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related) options: A)100 B)200 C)300 D)90 E)80 SOLUTION:Well, the pattern looked REALLY familiar to me, like it's a binary progression. And it is...but with a twist. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence). BUT, if you convert 8 to base 8, you get 10. And if you convert 32 to base 8, you get 40. Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8. If this is true, then you next number would be: 2^7 = 128 That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A #### A QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies options: A)231 B)150 C)200 D)450 E)451 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 * 5C2) = 200 Ans: C #### C QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these SOLUTION:Reqd ratio 4 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100 = 4 × 140 : 7 × 150 : 8 × 175 = 8 : 15 : 20 Answer C #### C QUESTION:66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)120 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m. Answer A #### A QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 10 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 10 years = (20 + 10) years =30 years. Answer : A #### A QUESTION:Worker A takes 12 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? options: A)40 days B)40/9 days C)39/9 days D)30/9 days E)20/3 days SOLUTION:A's one hour work = 1/12. B's one hour work = 1/15. (A+B)'s one hour work = 1/12+1/15 = 9/60 = 3/20. Both A & B can finish the work in 20/3 days E #### E QUESTION:What is the Compound Interest on Rs.7000 at 8.5% p.a. compounded half-yearly for 5 years. options: A)3616.5 B)3613.5 C)3313.5 D)3616.5 E)3113.5 SOLUTION:Compound interest : A = P(1 + r/n)nt A = 10,613.50 C.I. >> 10,613.50 - 7000 >> Rs. 3613.5 Answer:B #### B QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)190 C)109 D)278 E)211 SOLUTION:Explanation: 624/6 = 104 kmph Answer:C #### C QUESTION:An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ? options: A)175 seconds B)195 seconds C)155 seconds D)115 seconds E)115 seconds SOLUTION:Explanation: Let the time required by x seconds. Then, More cloth means More time (Direct Proportion) So, 0.128 : 1 :: 25 : x => x = {\color{Blue} \frac{25\times 1}{0.128}} => x = 195.31 So time will be approx 195 seconds Answer: B #### B QUESTION:The ratio of flour to water to sugar in a recipe is 11:8:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 4 cups of water, how much sugar is required? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:The ratio of flour to water is 22:8=11:4. The ratio of flour to sugar is 5.5:1=11:2. The new ratio of flour to water to sugar is 11:4:2 If we need 4 cups of water, then we need 2 cups of sugar. The answer is D. #### D QUESTION:The ratio between the length and the breadth of a rectangular park is 1 : 4. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)102400 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 1x metres and breadth = 4x metres. Then, 2(1x + 4x) = 1600 or x =160. Length = 160 m and Breadth = 640 m. Area = (160 x 640) m2 = 102400 m E #### E QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)1687 B)1478 C)1480 D)14000 E)1500 SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 Answer: D #### D QUESTION:The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 6 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A? options: A)45 B)65 C)75 D)78 E)90 SOLUTION:A + B + C = 3 *84 = 252 A + B + C + D = 4 * 80 = 320 ---- (i) So, D = 68& E = 68 + 6 = 74 B + C + D +E = 79 * 4 = 316 --- (ii) From Eq. (i) & (ii) A-E = 320 – 316 = 4 A = E +4 = 74 + 4 = 78 D #### D QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball? options: A)12 cm B)16 cm C)18 cm D)20 cm E)none of the these SOLUTION:similar triangle properties.. 2/r+6 = 6/r-6 giving r = 12. Answer: A #### A QUESTION:852.68 − 4.0 + 108.98 = ? − 2132.54 options: A)6078.58 B)6078.08 C)6258.58 D)6088.58 E)None SOLUTION:Option 'B' #### B QUESTION:Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age? options: A)1 B)2 C)4 D)5 E)6 SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years. (4x + 8) = 5 (x + 8) 2 8x + 16 = 5x + 40 3x = 24 x = 8. Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2. B #### B QUESTION:The 7th grade French and Spanish classes each have 26 students in them, and there are nine students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes? options: A)26 B)28 C)30 D)32 E)34 SOLUTION:French class + Spanish class = 52 students. Nine students are in both classes so they were counted twice. The number of students taking just one class is 52 - 2(9) = 34. The answer is E. #### E QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? options: A)15% B)25% C)35% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(300) / 1000 = 15% The answer is A. #### A QUESTION:x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days? options: A)x2/y2 units B)y3/x2 units C)x3/y2 units D)y2/x2 units E)None SOLUTION:Explanation: Let amount of work completed by y men working y hours per in y days = w units More men, more work(direct proportion) More hours, more work(direct proportion) More days, more work(direct proportion) Hence we can write as (men)x:y (hours)x:y (days)x:y }::x:w ⇒x^3w=y^3x ⇒w=y^3x/x^3 =y^3/x^2 Answer: Option B #### B QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)80 km/hr B)81 km/hr C)85 km/hr D)84 km/hr E)83 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y-4.5)(10/36) ---(1) x/8.5 = (y-5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y-4.5)/ (y-5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4 .1y = 8.5×5.4 - 8.4×4.5 => .1y = 45.9-37.8 = 8.1 => y = 81 km/hr Answer is B. #### B QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area? options: A)11 + √5 B)11 + √6 C)11 + 4√7 D)11 + √65 E)11 + 3√17 SOLUTION:We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16) = √65 The perimeter is 11 + √65 The answer is D. #### D QUESTION:Two mechanics were working on your car. One can complete the given job in 5 hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)4/3 C)14/5 D)10/3 E)17/5 SOLUTION:Rate(1)=1/5 Rate(2)=1/8 Combined = 13/40 Work done in 2 days=13/20 Work left = 7/20 Rate * Time = Work left 1/8 * Time = 7/20 Time=14/5 C #### C QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:The present age of a father is 3 years more than three times the age of his son. Five years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father. options: A)33 B)38 C)27 D)40 E)48 SOLUTION:if the present age be x years. father's will be (3x+3)years.. so, (3x+3+5)=2(x+3)+10 or, x=8 so the fathers present age =(3x+3)=(3*8+3)years =27 years.. ANSWER : OPTION C #### C QUESTION:A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers? options: A)700; 1100 B)1072; 528 C)1000; 800 D)1200; 800 E)None of the above SOLUTION:The method given above is the one given in the book. However the method I used was (1*x*5)/100 + (1600-x)*6/100 = 1600*5.67/100 Simplifying we get x= 528 B #### B QUESTION:The price of stock decreased by 5% last year and rose by 10% this year. What is the net percentage change in the price of the stock? options: A)0.2% B)0.8% C)1.2% D)1.6% E)4.5% SOLUTION:(100% - 5%) * (100% + 10%) = 0.95 * 1.10 =1.045 = 104.5%. The net percentage change in the price of the stock is (+) 4.5% The answer is E #### E QUESTION:If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x? options: A)308 B)154 C)70 D)44 E)21 SOLUTION:If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that. LCM of 2,7,11= 154 Hence x must be divisible by 154 Hence B #### B QUESTION:A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 160 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start? options: A)5.0 B)5.5 C)6.0 D)6.5 E)7.0 SOLUTION:In 2 hours, A travels 60 km. B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts. So A and B both travel a distance of 240 km. C needs 1.5 hours to travel 240 km, so C leaves 6.5 hours after A. The answer is D. #### D QUESTION:Three years ago, the average age of M and N was 18 years. With P joining them, the average age becomes 22 years, How old is P now? options: A)24 years B)27 years C)28 years D)30 years E)40 years SOLUTION:Explanation : Present age of (M + N) = (18 x 2 + 3 x 2) years = 42 years. Present age of (M + N + P) = (22 x 3) years = 66 years. P's age = (66 - 42) years = 24 years. Answer : A #### A QUESTION:Mario and Nina each have a bag of marbles, each of which contains 10 blue marbles, 10 red marbles, an 10 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble? options: A)3/4 B)2/9 C)1/4 D)1/8 E)1/16 SOLUTION:Mario and Nina each select one marble from their respective bags. Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble Probability that either Mario or Nina select a red marble = (10/30)*(10/30) + (10/30)*(10/30) = 2*(1/9) Probability that either Mario or Nina select a red marble = 2/9 Answer would be B. #### B QUESTION:A does half as much work as B in three- fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it? options: A)30 days B)35 days C)40 days D)45 days E)50 days SOLUTION:Explanation: Let ‘x’ be the number of days taken by B alone to finish the whole work Then, A alone will finish the whole work in 3x/4 × 2 days = 3x/2 days. Then, working together, 3x/2 × x/3x/2 + x = 18 days 3x × x/5x = 18 3x/5 = 18 Therefore, the number of days taken by B = x = 18 × 5/3 = 30 days. Answer: Option A #### A QUESTION:John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend? options: A)$2,125 B)$1,320 C)$2,000 D)$1,580 E)$2,000.75 SOLUTION:Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125. #### A QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A. options: A)256 B)388 C)379 D)277 E)122 SOLUTION:Explanation: (3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 672 = 256 Answer: A #### A QUESTION:Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected. options: A)2/35 B)2/3 C)7/35 D)1/7 E)7/5 SOLUTION:Let A be the event that Ram is selected and B is the event that Ravi is selected. P(A) = 5/7 P(B) = 1/5 Let C be the event that both are selected. P(C) = P(A) x P(B) as A and B are independent events: = 5/7 x 1/5 = 1/7 ANSWER:D #### D QUESTION:In a sequence, each term is obtained by adding 8 to the preceding one. If the sum of the first 30 terms is equal to 210, what is the result of the addition of the first 50 terms? options: A)8400 B)8575 C)8650 D)8680 E)8700 SOLUTION:a is first term and d = 8 since the preceding number is always greater than the previous one.. Now 30th term is a+29(2). Sum of n terms is n/2(first term + last term)and here we have to get sum of 30 terms , we get 30/2 ( a + a+58) = 210 ( given sum of 30 terms is 210) => 15(2a+58) = 210 => 2a+58 = 14 => a = -22 Now to get sum of first 50 terms , we need to get 50th term value i.e. -22+49(8) = 370. Sum of first 50 terms = 50/2( -22 + 370) = 8700. Hence option E is correct answer.. #### E QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate? options: A)100 B)50 C)Cannot be determined D)105 E)25 SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position. Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:What is the tens digit of 36^12? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:36^10 = 6^24 (6^2)=6*6 = 36 (6^3)= 36*6 = .16 (6^4)= .16*6 = ..96 (6^5) = ..96*6 = ..76 (6^6) = ..76*6 = ...56 (6^7) = ....56*6 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9 #### E QUESTION:A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)17% B)25% C)69% D)31% E)19% SOLUTION:Let the price be 100. The price becomes 130 after a 30% markup. Now a discount of 10% on 130. Profit=117-100 17% answer A #### A QUESTION:Two trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ? options: A)10.7 Seconds B)10.8 Seconds C)10.9 Seconds D)11.8 Seconds E)None of these SOLUTION:Explanation: Relative Speed = 60+40 = 100 Kmph = 100*(5/18) = 250/9 m/sec Distance to be covered = 140 + 160 = 300 metres Time = Distance/Speed Time=300∗9/250=54/5=10.8 seconds Option B #### B QUESTION:In what ratio should a variety of oil costing Rs. 9 per ltr be mixed with another variety of oil costing Rs. 17.25 per ltr to obtain a mixture costing Rs. 11.75 per ltr? options: A)4 : 1 B)1 : 3 C)3 : 1 D)1 : 2 E)2 : 1 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (17.25 - 11.75) / (11.75 - 9) = 22/11=2/1 ANSWER:E #### E QUESTION:If A lends Rs.4000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? options: A)112.5 B)122.5 C)132.5 D)114.5 E)180 SOLUTION:(4000*1.5*3)/100 => 180 ANSWER:E #### E QUESTION:Find the odd man out 864, 420, 200, 96, 40, 16, 6 options: A)420 B)200 C)96 D)40 E)6 SOLUTION:6x2+4=16 16x2+8=40 40x2+12=92 92x2+16=200.. and so on. ANSWER:C #### C QUESTION:A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively. options: A)200, 360,162 B)200, 460,160 C)200, 360,160 D)200, 360,138 E)200, 360,129 SOLUTION:Explanation: let ratio be x. Hence no. of coins be 5x ,9x , 4x respectively Now given total amount = Rs.206 => (.50)(5x) + (.25)(9x) + (.10)(4x) = 206 we get x = 40 => No. of 50p coins = 200 => No. of 25p coins = 360 => No. of 10p coins = 160 Answer: C) #### C QUESTION:Seven years ago the average age of a family of 2 members was 25 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child? options: A)7 years B)5 years C)3 years D)8 years E)10 years SOLUTION:Explanation: Average of the family of two numbers 7 years ago = 25 = (25+ 7) * 2 = 64 years Average age of the family of three members at present = 23 years = 23 * 3 = 69 YEARS Age of child = 69 - 64 = 5 years Answer: Option B #### B QUESTION:There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted? options: A)6 B)7 C)8 D)2 E)9 SOLUTION:Let xx be the number of roses. Then the number of birches is 24−x24−x, and the number of boys is 3×(24−x)3×(24−x). If each girl planted 3 roses, there are x3x3 girls in the class. We know that there are 24 students in the class. Therefore x3+3(24−x)=24x3+3(24−x)=24 x+9(24−x)=3⋅24x+9(24−x)=3⋅24 x+216−9x=72x+216−9x=72 216−72=8x216−72=8x 1448=x1448=x x=18x=18 So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches. Answer:A #### A QUESTION:A train 225 m long passes a man, running at 10km/hr in the same direction in which the train is going, in10 seconds. The speed of the train is: options: A)81 B)90 C)91 D)85 E)96 SOLUTION:Speed of the train relative to man =225/10 m/sec =45/2m/sec. =45/2x18/5km/hr = 81 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 10 = 81 =91km/hr. Answer:C #### C QUESTION:An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? options: A)$480 B)$489.60 C)$634.64 D)$800.32 E)$240 SOLUTION:1.04*1.04*6000 = $6489.60 The answer is B. #### B QUESTION:A no. x when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)1 B)4 C)9 D)11 E)13 SOLUTION:221 + 43 = 264/17 = 9 (Remainder) C #### C QUESTION:The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is options: A)0.4869 B)0.5904 C)0.6234 D)0.5834 E)0.2952 SOLUTION:P(winning prize atleast on one ticket) = 1 - P("Losing on all tickets") = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2) = (1.64)(0.36) = 0.5904 ANSWER:B #### B QUESTION:A meal cost $ 32.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-39 E)36-37 SOLUTION:10%(32.5) = 3.25 15%(32.5) =4.875 total amount could have been 32.5+3.25 and 32.5+4.875 => could have been between 35.75 and 37.375 => approximately between 36 and 37 Answer is E. #### E QUESTION:Which of the following is NOT a prime number? options: A)21 B)31 C)41 D)11 E)51 SOLUTION:Ans is A A prime number has itself and 1 as the only factors. e.g. 2, 3, 7, 11, 19. Factors of 21 = {1 , 3 , 7 , 21} => 21 is not a prime number #### A QUESTION:Find the value of x which satisfies the relation Log10 3+log10 (4x+1)=log10 (x+1)+1 options: A)2.5 B)3.5 C)3.2 D)6.8 E)9.8 SOLUTION:[log10a + log10b = log10 ab] and also 1 can be written as log10 10, so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)), this can be solved to get 12x+3=10x+10, that gives x=7/2=3.5 ANSWER:B #### B QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? options: A)230 B)783 C)291 D)112 E)221 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer:A #### A QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage? options: A)80% B)50% C)75% D)40% E)53% SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 175 (35 * 5) Profit percentage = (175 - 100)/100 * 100 = 75% Answer: C #### C QUESTION:How many cubes of 5cm edge can be cut out of a cube of 20cm edge options: A)36 B)64 C)216 D)484 E)None of these SOLUTION:Explanation: number of cubes=(20 x 20 x 20) / (5 x 5 x 5) = 64 Answer: B #### B QUESTION:If A(k)=(k+1)^k, and k=1, what is the value of A(A(A(k-1)))? options: A)0 B)2 C)1 D)6 E)9 SOLUTION:A(A(A(0)))=A(A(0))=A(0)=1. Thus, the answer is C. #### C QUESTION:If x is an even integer and y = 5x + 1, which of the following CANNOT be a divisor of y? options: A)11 B)31 C)21 D)41 E)30 SOLUTION:x takes even values as 2,4,6,8., y=5x+1 x is an even term so 5x must be an even term when it adds with 1 so it must be a odd integer 30 didn't follows this condition ans is E #### E QUESTION:What will come in place of the x in the following Number series? 75, 225, x, 2025, 6075 options: A)675 B)752 C)300 D)400 E)1200 SOLUTION:(A) 25 x 3 = 75, 75 x 3 = 225 , 225 x 3 = 675, 1675 x 4 = 2025. #### A QUESTION:A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there? options: A)15 B)30 C)28 D)24 E)32 SOLUTION:number of workers = 10* (25-10)/10 = 15 Answer is A #### A QUESTION:A man can row his boat with the stream at 16 km/h and against the stream in 12 km/h. The man's rate is? options: A)8 kmph B)9 kmph C)2 kmph D)4 kmph E)1 kmph SOLUTION:DS = 16 US = 14 S = ? S = (16 - 2)/2 = 2 kmph Answer:C #### C QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? options: A)1 mins B)3 mins C)8 mins D)6 mins E)4 mins SOLUTION:D = 25 * 60 + 1500 = 3000 m T = 3000/60 * 18/5 = 180 sec = 3 mins Answer: B #### B QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:If p is a natural number and p! ends with w trailing zeros, then the number of zeros that (5p)! ends with will be options: A)a) (p+w) trailing zeros B)b) (5p+y) trailing zeros C)c) (5p+5y) trailing zeros D)d) (p+5y) trailing zeros E)e) none of them above SOLUTION:Let p = 1. p! = 1! = 1, which means w= 0 (5p)! = 5! = 120, trailing zeros = 1 1 = 1 + 0 = p + w Answer (A). #### A QUESTION:If 0.5% of A =85 paise, then the value of A is ? options: A)Rs. 170 B)Rs. 17 C)Rs. 1.70 D)Rs. 4.25 E)None SOLUTION:Answer ∵ 0.5/100 of A = 85/100 ∴ A = Rs. (85 / 0.5) = Rs. 170 Correct Option: A #### A QUESTION:Two dice are rolled. The probability of getting a sum of at least 9 is options: A)13/36 B)5/18 C)35/36 D)11/36 E)15/36 SOLUTION:Sum of 9 = {(3,6) (6,3)} = 2ways. Sum of 10 = {(5,5) (6,4) (4,6) (5,5)} = 4 ways. Sum of 11 = {(6,5) (5,6)} = 2 ways. Sum of 12 = {(6,6) (6,6)} = 2 ways. Therefore, Favourable cases = 10 Total cases = 6 x 6 = 36. Therefore, Probability = 10/36 = 5/18. ANSWER:B #### B QUESTION:18 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. options: A)190 B)153 C)210 D)220 E)230 SOLUTION:1st person will shake hand with 17 people 2nd person will shake hand with 16 people 3rd person will shake hand with 15 people ...... total no. of handshakes = 17+...+3+2+1 = 17*(17+1)/2 = 153 or, if there are n persons then no. of shakehands = nC2 = 18C2 = 153 ANSWER:B #### B QUESTION:A company pays 12.5% dividend to its investors. If an investor buys Rs.40 shares and gets 25% on investment, at what price did the investor buy the shares? options: A)20 B)66 C)18 D)19 E)01 SOLUTION:Explanation: Dividend on 1 share = (12.5 * 40)/100 = Rs.5 Rs.25 is income on an investment of Rs.100 Rs.5 is income on an investment of Rs. (5 * 100)/25 = Rs.20 ANSWER: A #### A QUESTION:The average score of a cricketer for five matches is 45 runs. If the average for first three matches is 30, then average for last two matches is options: A)33.25 B)32.25 C)67.5 D)60.5 E)45.5 SOLUTION:Explanation: =(45×5)−(30×3)/2 =(225 −90)4=67.5 Answer: Option C #### C QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 3*1*2=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:A hall 36m long and 15m broad is to be paved with stones, each measuring 8dm by 5 dm. The number of stones required is: options: A)180 B)1800 C)18 D)18000 E)1350 SOLUTION:Area of the hall= 3600*1500 Area of each stone= (80*50) Therefore, number of stones= (3600*1500/ 80*50)= 1350 ANSWER:E #### E <<<Examples ends QUESTION:How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length? options: A)12.9 sec B)12.1 sec C)24.2 sec D)16.8 sec E)14.9 sec SOLUTION:Speed = 36 * 5/18 = 10 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/10 = 24.2 sec. Answer: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4*side = 4* (3p/5) = 12p/5 Answer is C. #### C QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 5*60/60 = 5*1/1 = 5 New time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1600. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)70.00% B)86.98% C)76.99% D)45% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1600 = Rs. 17600 and SP = Rs. 31150 Profit(%) = (31150 - 17600)/17600* 100 = 76.99% ANSWER:C #### C QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:What is the Compound Interest on Rs.7000 at 8.5% p.a. compounded half-yearly for 5 years. options: A)3616.5 B)3613.5 C)3313.5 D)3616.5 E)3113.5 SOLUTION:Compound interest : A = P(1 + r/n)nt A = 10,613.50 C.I. >> 10,613.50 - 7000 >> Rs. 3613.5 Answer:B #### B QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have? options: A)5 B)12 C)19 D)36 E)50 SOLUTION:A+P+G= 39*3 A=3G P=2.5G 3G+2.5G+G= 39*3 G=39*3/6.5= 18 A= 6*3=54 Difference = 36 'D' is the answer #### D QUESTION:Each of the integers from 1 to 18 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even options: A)19 B)12 C)11 D)10 E)3 SOLUTION:Out of the 18 integers: 9 are odd and 9 are even. If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case: 1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first 2. 10th number will be the first even number So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even. So, answer will be 10. (D) #### D QUESTION:Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age? options: A)56 years B)72 years C)56 years D)66 years E)76 years SOLUTION:Let the age before 10 years =x. Then, 115x/100=x+10 ⇒115x=100x+1000 ⇒x=1000/15=66 Present age =x+10=66+10=76 ANSWER:E #### E QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area? options: A)120 cm2 B)187 cm2 C)178 cm2 D)189 cm2 E)176 cm2 SOLUTION:The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 10 = 120 cm2 Answer: A #### A QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.4 B)3.9 C)4.1 D)4.2 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:A car travels from P to Q at a constant speed. If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance. It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two cities options: A)100 km B)120 km C)150 km D)180 km E)None of these SOLUTION:Explanation : Let the distance between two cities = D, D = x*t (x = usual speed and t is the actual time) D = (X + 20)*(T -2) and D = (X +30)*(T – 2.5) Solve the above equation, u will get T = 5 and X = 30, so distance = 30*5 = 150 km Answer – C #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5 and 6 such that the numbers are divisible by 9? options: A)1 B)2 C)4 D)6 E)8 SOLUTION:CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. =36, 45, 54, 63 --- 4 Cases Answer: option C #### C QUESTION:If x^2 + 1/x^2 = 9, what is the value of x^4 + 1/x^4 ? options: A)10 B)72 C)79 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 9 andSQUAREboth sides: (x² + 1/x²)²= 81 So, (x² + 1/x²)(x² + 1/x²) = 81 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 81 Simplify: x⁴ + 1/x⁴ = 79 Answer: C #### C QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:Set A contains all the even numbers between 8 and 50 inclusive. Set B contains all the even numbers between 108 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? options: A)2200 B)2550 C)5050 D)6275 E)11325 SOLUTION:Set A contains 8, 10, 12... 50 Set B contains 108 , 110 , 112 ... 150 Number of terms in each set = 22 Difference between corresponding terms in set A and B = 100 Difference between Sum of set B and set A = 100*22 = 2200 Answer A #### A QUESTION:If HARD is coded as 1357 and SOFT is coded as 2468 what will 21448 stand for? options: A)SHOOR B)SHOOA C)SHOOT D)SHEOT E)SWOOT SOLUTION:HARD = 1357 => 1=H, 3=A , 5=R , 7=D SOFT = 2468 => 2=S, 4=O , 6=F , 8=T so, 21448 = SHOOT ANSWER:C #### C QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)5 sec D)12.5 sec E)12 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. ANSWER:A #### A QUESTION:Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions? options: A)54 B)432 C)864 D)2,916 E)148,824 SOLUTION:We have the rectangle with dimensions 9*4 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis. Choose the (x,y) coordinates for vertex A: 9C1*4C1; Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A); Choose the y coordinate for vertex B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A). 9C1*4C1*8C1*3C1=864. Answer: C. #### C QUESTION:On January 1, 2010, Dolly invests 30% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 40% in Antarctic smallcaps. In 2010, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 20% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dolly has the same total amount of retirement savings as he did two years before, then x is between options: A)10 and 20 B)20 and 30 C)30 and 40 D)40 and 50 E)50 and 60 SOLUTION:Pick a smart number for the total retirement savings Dolly starts with—say, $10,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.) Here are the starting values: L = $3000 M = $3000 S = $4000 Apply the first year’s changes, so that you have these numbers on 1/1/2012: Newer L = $3000 + 10% = $3300 Newer M = $3000 + 20% = $3600 Newer S = $4000 + 15% = $4600 Now apply the second year’s changes to L and M: Newest L = $3300– 20% = $3300– $660 = $2640 Newest M = $3600– 10% = $3600– $360 = $3240 Add these to get $5880. So the newest S must be $10,000 (the target final total of Dolly’s retirement savings) minus $5880, $4120 The dollar change in S from 1/1/12 to 1/1/13 is $4600 – $480 = $4120. So the question is this: what percent change does $480 represent, from a starting point of $4600? Since $4600 is a nasty divisor, switch to benchmarks: 10% of $4600 = $460. So 20% is just double that, or $920. And so on. From this $480 lies between $460 and $920 The correct answer is A. #### A QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:(128.5 x 32) + (13.8 x 30) = ? x 25 options: A)524.48 B)556.02 C)574.36 D)181.04 E)595.46 SOLUTION:Explanation : ? = (128.5 x 32) + (13.8 x 30)/25 = 4112 + 414/25 = 181.04 Answer : Option D #### D QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x*4x=900 x^2= 225 x= 15 Length= 4*15= 60 difference= 60-15= 45 E is the answer #### E QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21 Ans: B #### B QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles. SOLUTION:Solution: 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 Answer C #### C QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:A person can swim in still water at 20 km/h. If the speed of water 12 km/h, how many hours will the man take to swim back against the current for 40km? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:M = 20 S = 12 US = 20 - 12 = 8 D = 40 T = 40/8 = 5 Answer:C #### C QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:The total cost of 100 paper plates and 200 paper cups is $7.50 At the same rates what is the total cost of 20 of the plates and 40 of the cups? options: A)$.90 B)$1.00 C)$1.20 D)$1.50 E)$1.60 SOLUTION:U dont need to go through all this What u have with u is 100 P + 200 C = $7.50 Just divide the equation by 5 and you will get what u are looking for 20P + 40 C = $1.50 Therefore OA is D #### D QUESTION:If x is divisible by 2 and 7, which of the following must divide evenly into x? I. 60 II. 32 III. 14 options: A)I,II only B)I,III only C)I only D)III only E)II only SOLUTION:If x is divisible by 2,7 means it will be = or > 14, 28,42 etc... That are not divisible by 60, 32. So, the answer is D #### D QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 seconds. What is the length of the fast train? options: A)23 m B)23 (2/9)m C)38 (8/9)m D)29 m E)28 m SOLUTION:Relative speed = (40 - 20) km/hr = (20 x(5/18))m/sec = (50/9)m/sec. Therefore Length of faster train = ((50/9) x 7) m = (350/9)m = 38 (8/9) m. C #### C QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? options: A)8 B)6 C)4 D)10 E)12 SOLUTION:Together they make 5/4 w widgets in 3 days. So they make w widgets in 3*4/5 = 12/5 days. 1/(t+2) + 1/t = 5/12 Now, calculating this is really cumbersome so try to plug in options to get to the answer. If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4. 1/6 + 1/4 = 5/12 It works so t = 4. Answer : A #### A QUESTION:Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21 options: A)1 B)-1 C)2 D)-2 E)3 SOLUTION:B -1 19x + 19y + 17 = -19x + 19y - 21 38x = -38 => x = -1 #### B QUESTION:Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? options: A)5/5 B)5/9 C)3/4 D)5/7 E)5/2 SOLUTION:In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27 The probability = 27/36 = 3/4. Answer: C #### C QUESTION:The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994? options: A)5N B)7N C)10N D)15N E)20N SOLUTION:In 1992, the company's assets were N. In 1993, the company's assets were N + 4N = 5N. In 1994, the company's assets were 5N + 5N = 10N. The answer is C. #### C QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration C of the acid in the mixture? options: A)1/2 B)1/3 C)1/4 D)1/6 E)1/5 SOLUTION:Do not need any computation 30%-----------21%---------12% if volume of both sol. were equal the concentration C would be 21%=1/5, but 12% is more than 3 times only possibility is 1/6 D #### D QUESTION:A man has some hens and cows. If the number of heads be 44 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)18 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x*2+y*4=140 heads: x*1+y*1=44 implies, 2x+4y=140 and x+y=44 solving these two equations, we get x=18 and y=26 Therefore, hens are 26. ANSWER:C #### C QUESTION:Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance. What is the distance traveled by each tyre? options: A)75000 B)80000 C)90000 D)67800 E)50000 SOLUTION:B 80,000. The distance traveled by each tyre: 4/5 * 1, 00, 000km = 80,000 km. #### B QUESTION:The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is? options: A)6 kmph B)7 kmph C)9 kmph D)4 kmph E)2 kmph SOLUTION:S = 1 M = x DS = x + 1 US = x - 1 35/(x + 1) + 35/(x - 1) = 12 x = 6 Answer: A #### A QUESTION:Concentrated pineapple juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated pineapple juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum? options: A)288 B)266 C)120 D)277 E)6123 SOLUTION:Let the present worth be Rs. x. Then, S.I. = (132 - x) (x * 5 * 2) / 100 = (132 - x) 10x = 13200 - 100x 110x = 13200 => x = 120. Answer: C #### C QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760 SOLUTION:After one year: 1.2 * $2500 After two years: (1.2)^2 * $2500 After three years: (1.2)^3 * $2500 = $4320 The answer is D. #### D QUESTION:A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? options: A)1 B)6 C)7 D)9 E)3 SOLUTION:Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 * 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 = 6 sec. Answer: B #### B QUESTION:If |x + 132| = 32 what is the sum of all the values of x. options: A)-264 B)200 C)-64 D)0 E)-328 SOLUTION:There will be two cases x+132 = 32 and x+132 = -32 Solve for x => x=32-132=> x=-100 or x= -32 - 132 => x= -164 The sum of both values will be -164 + -100 = -264 Answer is A #### A QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1⁄7 hours B)6 2⁄7 hours C)8 2⁄7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 × 2 = 16 km Distance covered in next two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 – 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. ∴ Time taken = 4⁄12 = 1⁄3 hour. Total time= 6 + 1⁄3 = 6 1⁄3 hour Answer E #### E QUESTION:66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)120 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m. Answer A #### A QUESTION:The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot? options: A)14 M B)20 M C)18 M D)12 M E)15 M SOLUTION:LB = 460 M2 LET BREATH = B L = B * (100 + 15)/100 = 115B/100 FROM THESE 115B/100 * B = 460 B2 = 46000/115 = 400 B = ROOT OF 400 = 20 M ANSWER B #### B QUESTION:Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is options: A)Rs.1550 B)Rs.1650 C)Rs.1750 D)Rs.2000 E)None SOLUTION:Solution C.I. =Rs[4000x(1+10/100)²-4000] Rs.(4000x11/10x11/10-4000) = Rs.940. Sum =Rs. [420x100 /3x8] = Rs.1750. Answer C #### C QUESTION:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture? options: A)2 B)2 1/2 C)3 D)3 1/2 E)4 SOLUTION:Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. B #### B QUESTION:Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2. options: A)29 B)27 C)28 D)24 E)21 SOLUTION:(4)^11x (7)^5 x (11)^2 = (2 x 2)^11 x (7)^5 x (11)^2 = 2^11 x 2^11 x7^5x 11^2 = 2^22 x 7^5 x11^2 Total number of prime factors = (22 + 5 + 2) = 29. Answer is A. #### A QUESTION:How many diagonals does a 62-sided convex polygon have? options: A)1829 B)2356 C)3458 D)3843 E)4820 SOLUTION:A 62-sided convex polygon has 62 vertices. If we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal. If each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658 However, we must recognize that we have counted every diagonal twice. To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829. The answer is A. #### A QUESTION:If n=3*4*p where p is a prime number greater than 3,how many different positive non-prime divisors does n have, excluding 1 and n? options: A)Six B)Seven C)Eight D)Nine E)Ten SOLUTION:n=3∗2^2∗p Number of divisors = 2 * 3 * 2 = 12 The 12 divisors includes 1, n, 3, 2 and p Number of different non prime divisors excluding 1 and n = 12 - 5 = 7 Answer: B #### B QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is options: A)3 months B)4 months C)6 months D)8 months E)10 months SOLUTION:Solution S.I on Rs. 1600 = T.D on Rs. 1680. Rs.1600 is the P.W of Rs.1680. Rs.80 is S.I on Rs.1600 at 15%. Time = (100x80 / 600x15) = 1/3 year = 4 months. Answer B #### B QUESTION:In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 39 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake? options: A)36 B)2^4*3 C)24 D)38 E)47 SOLUTION:Working backward from the day it's covered: day 39: fully covered day 38: half covered So 38 days ANSWER:D #### D QUESTION:The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000 SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=4500pi r=15 so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx) E #### E QUESTION:Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = options: A)18 B)15 C)-13 D)-21 E)-24 SOLUTION:f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = f(4) = 0= 16+4b+c--- Taking 16 to the other side -> 4b+c= -16 f(-3) = 0= 9-3b+c --- taking -3b+c to the other side -> 3b-c=9 When we add these 2 equations, we get 7b= -7---> b= -1 And while substituting b= -1 we get c= -12. b+c= -13--- Answer C #### C QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes? a. b. c. d. e. options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5) SOLUTION:no of different stocks for 4-letter code = 26^4 no of different stocks for 4-letter code = 26^5 total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4) ANS:C #### C QUESTION:A car covers a distance of 624 km in 3 hours. Find its speed? options: A)104 kmph B)194 kmph C)208 kmph D)174 kmph E)101 kmph SOLUTION:624/3 =208 kmph Answer:C #### C QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:8.008/1.001 options: A)0.008 B)8 C)0.8 D)80 E)800 SOLUTION:Answer is 8, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 8008/1001= 8 Answer B #### B QUESTION:Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ? options: A)Rs.17 B)Rs.18 C)Rs.12 D)Rs.11 E)Rs.10 SOLUTION:Average price per book = (1150 + 920) / (65 + 50) = 2070 / 115 = Rs.18 Answer:B #### B QUESTION:Find the number which is nearest to 3105 and is exactly divisible by 21 options: A)1208 B)3108 C)241 D)217 E)3147 SOLUTION:On dividing 3105 by 21, we get 18 as remainder. Number to be added to 3105 = (21 - 18) - 3. Hence, required number = 3105 + 3 = 3108. ANSWER B 3108 #### B QUESTION:Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 25-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs? options: A)60 B)70 C)80 D)100 E)45 SOLUTION:let x be the number of 25 ounce cans. Therefore (x+30) is the number of 15 ounce cans. Total volume is same, therefore 25x=15(x+30) 10x=450 x=45 Ans - E #### E QUESTION:there are 15 cars and 16 trucks? which is greater15 or 16? options: A)15 B)14 C)12 D)17 E)16 SOLUTION:E #### E QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day? options: A)2880. B)4860. C)5780 D)4320 E)6380. SOLUTION:Normal Day = 600 kw/h Stormy Day = 600*1.2=720 kw/h 3 windmills for 2 hours on stormy day 720*3*2=4320 Answer: D #### D QUESTION:If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+r + 11r × 6pr--1=B #### B QUESTION:How many ways could two people sit at a table with four seats in which two of the four seats will remain empty? options: A)60 B)12 C)112 D)118 E)120 SOLUTION:ways in which 2 seats out 4 can be selected = 4C2 ways in which 2 people can be arranged in 2 seats = 2! Total ways of arrangement = 4C2*2! =4*3 =12 Ans = B #### B QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)Rs.81.60 B)Rs.160 C)Rs.172 D)Rs.727 E)Rs.728 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer:A #### A QUESTION:If x = 1- 3t and y = 2t - 3, then for what value of t does x = y? options: A) 5/2 B) 3/2 C) 2/3 D) 4/5 E) 0 SOLUTION:We are given x = 1 – 3t and y = 2t – 3, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 3t for x and 2t – 3 for y in the equation x = y. This gives us: 1 – 3t = 2t – 3 4 = 5t 4/5 = t The answer is D. #### D QUESTION:In how many ways can five boys and three girls sit in a row such that all boys sit together? options: A)A)2888 B)B)2885 C)C)2880 D)D)2876 E)E)2224 SOLUTION:Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways. Required number of arrangements = 4! * 5! = 24 * 120 = 2880. Answer:C #### C QUESTION:A train cross a 450 m bridge in 42 s and another bridge 650 m length in 50 s what is approximate speed of train in km/h? options: A)90 Km /hr. B)25 Km /hr. C)30 Km /hr. D)20 Km /hr. E)None of these SOLUTION:Explanation: Let the length of the train be L. Then, => (450 + L)/42 = (650+L)/50. => L= 600 m. Now, speed = (450+600)/42 or (650+600)/50 = 25 m/s i.e. 25*(18/5) = 90 Km /hr. ANSWER IS A #### A QUESTION:The 40 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees? options: A)4 B)6 C)8 D)9 E)10 SOLUTION:The formula is Total = A+B+C - sum of exactly two + 2*all three + neither 21+18+19-x-2*5=40 solving for x you get 8 Answer C #### C QUESTION:How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 30% iodine solution? options: A)30.5 B)49 C)100 D)105 E)140 SOLUTION:Solution 1: Assume the iodine solution to be mixed = x lts. Iodine = 0.4x lts, Water = 0.6x lts. Solution 2: 35 liters of a 20% iodine solution Iodine = 7 lts, Water = 28 lts. Total iodine = 0.4x + 7 Total water = 0.6x + 28 The resultant is a 35% idoine solution. Hence (0.4x + 7) / (x + 35) = 30/100 40x + 700 = 30x + 1050 10x = 305 x = 30.5 lts Correct Option: A #### A QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION:By the how much is two-fifth of 300 greater than three -fifths of 125? options: A)15 B)3 C)5 D)45 E)None of these SOLUTION:Reqd no. = 2⁄5 × 300 - 3⁄5 × 125 = 120 - 75 = 45 Answer D #### D QUESTION:How many diagonals does a polygon with 23 sides have, if one of its vertices does not connect to any diagonal? options: A)201 B)159 C)179 D)189 E)209 SOLUTION:If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals n= 23-1 then 22*(22-3)/2 = 209 Correct Option:E #### E QUESTION:I have a three digit number in my mind. In that number, the tens digit is seven more than the ones digit and the hundreds digit is six less than the tens digit. What is the number? options: A)281 B)239 C)254 D)276 E)277 SOLUTION:A 281 #### A QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)Rs.64.18 B)Rs.64.67 C)Rs.64.08 D)Rs.64.10 E)Rs.64.22 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:In a bag, there are two 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum? options: A)60 B)50 C)42 D)84 E)61 SOLUTION:As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited: 1) The minimum number on any given die is 1 2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each. With 4 dice, we could end up with any SUM between: 4 (if we rolled 1s on all 4 dice) to 64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice). Thus, there are only 61 possible sums. E #### E QUESTION:Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive? options: A)20% B)17% C)4.0% D)3.3% E)2.8% SOLUTION:20/6 =3.33 Answer : D #### D QUESTION:What is the sum of the local values of the digits 2, 3, 4, 5 in the number 2345? options: A)2345 B)4500 C)5000 D)6000 E)7000 SOLUTION:2000 + 300 + 40 + 5 = 2345 ANSWER A #### A QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)9:4 C)5:6 D)5:0 E)2:4 SOLUTION:Explanation: 45 * 5/18 = 10 25:20 => 5:4 Answer: Option A #### A QUESTION:Of the 100 athletes at a soccer club, 40 play defense and 62 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between options: A)10 to 20 B)10 to 40 C)22 to 40 D)30 to 70 E)40 to 70 SOLUTION:First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E. {Total} = {defense} + {midfield} - {both} + {neither} 100 = 40 + 62 - {both} + {neither} {both} = {neither} + 2. Since the least value of {neither} is given to be 20, then the least value of {both} is 20+2=22.Eliminate A and B. Answer: C. #### C QUESTION:If x^2 + 1/x^2 = 3,what is the value of x^4 + 1/x^4 ? options: A)7 B)12 C)14 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 3 andSQUAREboth sides: (x² + 1/x²)²= 9 So, (x² + 1/x²)(x² + 1/x²) = 9 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 9 Simplify: x⁴ + 1/x⁴ = 7 Answer: A #### A QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 75 and n is not prime, what is the greatest possible value of f(n)? options: A)72 B)69 C)65 D)60 E)58 SOLUTION:Since we need the largest value of f (n), we will start with the largest option. Option A: 2*2*2*2*2*2 = . This is not a product of distinct prime numbers. Hence incorrect Option B: 69 = 3*23. This is a product of distinct prime numbers. Rest all the options are smaller that 69. Correct Option: B #### B QUESTION:What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent? options: A)6200 B)3000 C)3000 D)2000 E)1000 SOLUTION:P - 2336 = (P*10*5)/100 P = 6200 Answer: A #### A QUESTION:In a certain country, 60 percent of the population likes basketball, and 34 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf? options: A)20% B)33% C)40% D)57% E)67% SOLUTION:Correct Answer: (D). Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 34 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 34/60 = 57%, or choice D. #### D QUESTION:A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule? options: A)18 B)81 C)56 D)72 E)24 SOLUTION:IMO 'E' is the answer. Matches will be in multiples of 5x+4. The answer that satisfies this condition is E #### E QUESTION:The age of teacher is the same as the digit in the student's age, but in reverse order. In five years teacher will be twice as old as student will be then. what is the difference in their current age ? options: A)18 B)12 C)25 D)13 E)7 SOLUTION:Teacher's age= 10x+y so student's age= 10y+x.. after 5 years , 10x+y+5=2*(10y+x+5).... so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is A..18 #### A QUESTION:If (x-13)(x-3) < 0, which of the following must be true? options: A)x^2 + 5x + 6 < 0 B)x^2 + 5x + 6 > 0 C)5 - x < 0 D)x - 5 < 0 E)13 - x > 0 SOLUTION:(x-13)(x-3)<0 can be written as (13-x)(x-3)>0 So,to inequality hold true multiple of (13-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<13 Answer Choice E matched which says 13-x>0 or x<13,which must be true (I started to look from E to A for making easy decision first) Correct Answer E #### E QUESTION:A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in? options: A)0.35 days B)0.45 days C)0.55 days D)0.25 days E)0.2 days SOLUTION:B = 1/4 – 1/20 =0.2 days ANSWER:E #### E QUESTION:In how many ways the letters in the word MANAGEMENT can be arranged such that A’s does not come together. options: A)181440 B)191440 C)171440 D)182440 E)185440 SOLUTION:Methods to arrange all the letters leaving A = 8*7*6*5*4*3*2*1/(2*1)*(2*1)*(2*1)= 5040 Now between these 8 letters , there are 9 places so methods to place A and A in these positions = 9*8/2*1 = 36 thus total methods are 5040*36 = 181440 ANSWER:A #### A QUESTION:In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ? options: A)100 B)72 C)110 D)135 E)145 SOLUTION:Explanation : Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x. .'. 60% of x = 36 +5/6 *36 =>60/100 * x = 66 =>x = 110 Answer : C #### C QUESTION:The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 16000, then find the annual income of A? options: A)Rs. 537600 B)Rs. 180000 C)Rs. 201600 D)Rs. 504000 E)None of these SOLUTION:B's monthly income = 16000 * 112/100 = Rs. 17920 B's monthly income = 2 parts ----> Rs. 17920 A's monthly income = 5 parts = 5/2 * 17920 = Rs. 44800 A's annual income = Rs. 44800 * 12 = Rs. 537600 ANSWER:A #### A QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs. 7500 B)Rs. 9000 C)Rs. 9500 D)Rs. 10,000 E)None of these SOLUTION:Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs. 7500. ANSWER IS A #### A QUESTION:A grocery store bought some apples at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples? options: A)1:7 B)1:5 C)1:4 D)1:2 E)2:5 SOLUTION:To avoid fractions, assume there were 45 apples. So the store bought them for 45/5 = 9 dollars. To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these. 45 split in the ratio 1:4 gives 9 and 36. 9 apples split into 3 apples each will give $3. 36 apples split into 6 apples each will give $6. They add up to $9 so we have hit the right answer. Answer (C) #### C QUESTION:Bob finishes the first half of an exam in one-thirds the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam? options: A)20 B)24 C)27 D)30 E)40 SOLUTION:Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/3's the time of the second half (3/3's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 1:5 and the second half is 3:5). With each fifth of an hour being 15 minutes (60/4), the first half of the exam would have taken 30 minutes. Correct answer is D. #### D QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? options: A)32 Yrs B)36 Yrs C)40 Yrs D)48 Yrs E)None SOLUTION:Explanation: Let the mother's present age be x years. Then, the person's present age = (2/5)*x years. ((2/5)*x)+8 = (1/2)(x+8) 2(2x + 40) = 5(x + 8) x = 40. Answer: C #### C QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exact 8 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)6 B)7 C)8 D)4 E)2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 4No. of days when B works = 4 → 4x + 4y = 1 When B starts: No. of days when A works = 5No. of days when B works = 3 → 5x + 3y = 1 Solving the above two equations for xy x = 1/8 y = 1/8 → Total work done by AB in a day = 1/8 + 1/8 = 1/4 → No. of days to complete the work when both work together = 4 Answer: D #### D QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph. SOLUTION:DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A #### A QUESTION:During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 300 percent. Which of the following is the percent change in the stock's value during those two years? options: A)60 percent decrease B)20 percent decrease C)20 percent increase D)60 percent increase E)140 percent increase SOLUTION:Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-80/100)=100*0.2=20 and in 2002 its value would be 20*(1+300/100)=80. Hence during those two years the value of the stock decreased from 100 to 80, so by 20%. Answer: B. #### B QUESTION:The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is options: A)64 sq.m B)70 sq.m C)78 sq.m D)84 sq.m E)None SOLUTION:Solution Perimeter of the rhombus = 56 m Each side of the rhombus = 56 / 4 m = 14 m. Height of the rhombus = 5 m Area = (14 x 5) m² = 70 m² Answer B #### B QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/4 meter, and then if the cable were cut at each mark, how many different size length of cable would result? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:In this particular example length (10 meter) is just extraneous information. The location of the marks for 1/3 meter would be 4/12, 8/12, 12/12, etc... The location of the marks for 1/4 meter would be 3/12, 6/12, 9/12, 12/12, etc... The distances between marks are 3/12, 1/12, and 2/12. The answer is C. #### C QUESTION:If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^3 have? options: A)7 B)5 C)6 D)8 E)9 SOLUTION:take the example of 4... it has 3 positive divisors (1,2,4) Now, take the example of 64... it has only 7 divisors.. so A is the ans #### A QUESTION:Amy has two decks of 54 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack? options: A)1/6 B)1/8 C)1/9 D)1/10 E)1/12 SOLUTION:Your solution is correct answer should be 1/12. E #### E QUESTION:How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336 options: A)4 B)3 C)6 D)8 E)9 SOLUTION:Explanation : Here 3, 4 and 11 are pairwise co-prime numbers. 132 = 3 × 4 × 11 . Also 3,4 and 11 are factors of 132. Hence if a number is divisible by 3, 4 and 11, the number will be divisible by their product 132 also. If a number is not divisible by 3 or 4 or 11, it is not divisible by 132 You must learn Divisibility Rules to say whether a given number is divisible by another number without actually performing the division. further. 264 is divisible by 3, 4 and 11 => 264 is divisible by 132 396 is divisible by 3, 4 and 11 => 396 is divisible by 132 462 is divisible by 3 and 11, but not divisible by 4 => 462 is not divisible by 132 792 is divisible by 3, 4 and 11 => 792 is divisible by 132 968 is divisible by 4 and 11, but not divisible by 3 => 968 is not divisible by 132 2178 is divisible by 3 and 11, but not divisible by 4 => 2178 is not divisible by 132 5184 is divisible by 3 and 4, but not divisible by 11 => 5184 is not divisible by 132 6336 is divisible by 3, 4 and 11 => 6336 is divisible by 132 Hence, only 264, 396 ,792 and 6336 are divisible by 132. So the answer is 4. Answer : Option A #### A QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. options: A)32 B)15 C)18 D)20 E)25 SOLUTION:Relative speed = (420/18)m/s = (420/18)*(18/5) = 84 kmph speed of goods train = 84-64 = 20 kmph Answer is D #### D QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c − a? options: A)25 B)70 C)90 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=160 --2 subtracting 1 from 2 we have c-a=70; ANSWER:B #### B QUESTION:2+2^2+2^+......+2^9=? options: A)2044 B)1022 C)1056 D)1065 E)None of them SOLUTION:This is a G.P. in which a=2, r=2^2/2=2 and n=9 S^n=a(r^n -1)/(r-1) =2x(2^9-1)/(2-1) =2x(512-1)=2x511 =1022 Answer is B #### B QUESTION:If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is options: A)5 km/hr B)4 km/hr C)2 km/hr D)1 km/hr E)None of these SOLUTION:Explanation: Rate upstream = (15/3) kmph Rate downstream (21/3) kmph = 7 kmph. Speed of stream (1/2)(7 - 5)kmph = 1 kmph Answer: D #### D QUESTION:The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is: options: A)60 kg B)59 kg C)62 kg D)63 kg E)61 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (75 x 3) = 225 …. (i) A + B = (88 x 2) = 176 …. (ii) B + C = (72 x 2) = 144 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 288 …. (iv) Subtracting (i) from (iv), we get : B = 63. B’s weight = 63 kg. Answer D #### D QUESTION:A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work? options: A)6 B)5 C)5.5 D)7 E)8 SOLUTION:B's 10 day's work = ( 1 x 10 ) = 2 . 15 3 Remaining work = ( 1 - 2 ) = 1 . 3 3 Now, 1 work is done by A in 1 day. 18 Therefore 1 work is done by A in ( 18 x 1 ) = 6 days. #### A QUESTION:A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour? options: A)(a) 60/11 B)(b) 5 C)(c) 26/5 D)(d) 27/5 E)(e) 28/5 SOLUTION:from the uphill we can find out the distance = 5*2 = 10 average speed = total distance/total time = 20/ (2+ (10/6)) = 60/11 Answer is A. #### A QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member? options: A)13.5 B)14 C)15 D)12.5 E)None SOLUTION:Solution: At present the total age of the family = 5*20 =100. The total age of the family at the time of the birth of the youngest member, =[100−10−(10*4)]=50. Therefore, average age of the family at the time of birth of the youngest member, = 50/4 = 12.5. Answer: Option D #### D QUESTION:You need to climb 10 stairs. At each support, you can walk one stair or you can jump two stairs. In what number alternative ways you'll climb ten stairs? options: A)99 B)79 C)55 D)89 E)66 SOLUTION:D #### D QUESTION:A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M): m------M---------------W w In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 3*15/60 =15/20 miles and the man walks the distance mM, which is 3*9/60 = 9/20 mile. The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes. Answer B. #### B QUESTION:Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent? options: A)16% B)17% C)18% D)58% E)23% SOLUTION:Total CP = Rs. 36000 + Rs. 15000 = Rs. 51000 and SP = Rs. 62900 Profit(%) = (62900 - 51000)/51000 * 100 = 23% Answer: E #### E QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44 SOLUTION:A 11, 42 Let the age of Priya = x years Then, the age of her father = (x+ 31) years ATQ, (x+ 8) + (x+ 31 + 8) = 69 2x+ 47 = 69 2x= 69 – 47 = 22 x= 11 The age of Priya = 11 years The age of her father = 11 + 31 = 42 years #### A QUESTION:A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system correct answer D #### D QUESTION:Concentrated grapes juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated grapes juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:Concentrated grapes juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A <<<Examples ends QUESTION:What number should replace the question mark? 11, 15, 16, 12, 21, 9, ---? options: A)21 B)29 C)28 D)27 E)26 SOLUTION:Answer: E 11, 15, 16, 12, 21, 9, ---? There are two alternate sequences: +5 and -3. #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$72.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 60.50 = (20/100)*60.50 = $12.1 Total spent 60.50 + 12.1 = $72.6 correct answer B #### B QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 1 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)2/5. C)6/11. D)5/9. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 6 = x*15 x = 6/15=2/5 Answer: B #### B QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area Q of the triangle in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA Q= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:If x and y are positive integers, find which of the following CANNOT be the greatest common divisor of 25x and 20y? options: A)5 B)5(x-y) C)20x D)20y E)35x SOLUTION:We are looking for a choice that CANNOT be the greatest common divisor of 25x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer. lets check a. 5 25x/5 = 5x and 20y/5 = 4y both are integers so eliminate b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 25x and 20y ... or 25x/20x = 5/4 which is not a integer. so answer is C. #### C QUESTION:power windows: 60% anti-lock brakes: 25% CD player: 45% The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? options: A)25 B)8 C)11 D)3 E)0 SOLUTION:Answer: B Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for. If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation: 45=15+22+x x=8, choice B. #### B QUESTION:A 25% stock yielding 20% is quoted at: options: A)s. 83.33 B)s. 110 C)s. 112 D)s. 125 E)s. 140 SOLUTION:Income of Rs 20 on investment of Rs 100 Income of Rs 25 on investment of ? = (25*100)/20=125 ANSWER:D #### D QUESTION:To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. options: A)530 B)675 C)330 D)987 E)854 SOLUTION:Let x e the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is: options: A)233 B)37 C)25 D)27 E)11 SOLUTION:Explanation: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x Gain = (5x - 4x) = Rs. x Gain % = (x * 100)/ 4x = 25%. Answer: C #### C QUESTION:Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy? options: A)4 B)10 C)7 D)8 E)12 SOLUTION:Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence X + Y = 20 If X is the number of cards at $0.25, then the X cards cost 0.25 X If Y is the number of cards at $0.15, then the Y cards cost 0.15 Y The total cost of the X cards and the the Y cards is known to be $4.2 and also given by 0.25 X + 0.15 Y = 4.2 We now need to solve the system of equations X + Y = 20 0.25 X + 0.15 Y = 4.2 The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve 0.25 X + 0.15 (20 - X) = 4.2 X(0.25 - 0.15) + 3 = 4.2 0.1 X = 1.2 X = 12 and Y = 20 - 12 = 8 correct answer D #### D QUESTION:A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ? options: A)Rs.8600 B)Rs.8620 C)Rs.8820 D)Rs. 8840 E)Rs. 8940 SOLUTION:Amount = 8000 *1+(5/100)2 = 8000 *21/20 * 21/20 = Rs.8820 ANSWER:C #### C QUESTION:For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6? options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4. SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6 = 6*0 + 2*7.2 + 8 - 6.6 = 0 +14.4 +1.4 15.8 Answer B #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs. 51.25 B)Rs. 51.22 C)Rs. 51.219 D)Rs. 51.18 E)Rs. 51.11 SOLUTION:Explanation: Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer:A #### A QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x*4x=900 x^2= 225 x= 15 Length= 4*15= 60 difference= 60-15= 45 E is the answer #### E QUESTION:If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is? options: A)250 m B)112 m C)117 m D)125 m E)123 m SOLUTION:A A = 180 * 5/18 * 5 = 250 m #### A QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done? options: A)6^6 ways B)8^9 ways C)7^8 ways D)8^7 ways E)8^6 ways SOLUTION:6 people can be prized with distinct prizes in 6^6 ways ANSWER:A #### A QUESTION:I have a three digit number in my mind. In that number, the tens digit is seven more than the ones digit and the hundreds digit is six less than the tens digit. What is the number? options: A)281 B)239 C)254 D)276 E)277 SOLUTION:A 281 #### A QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:A university cafeteria offers 1 flavors of pizza - pepperoni. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ? options: A)4 B)8 C)12 D)1 E)32 SOLUTION:1 flavours * 1 choices = 1C1*1C1 = 1*1=1=D #### D QUESTION:At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ? options: A)Rs.7.50 per kg B)Rs.8.20 per kg C)Rs.8.85 per kg D)Rs.9 per kg. E)None SOLUTION:Explanation: Total C.P of 200 kg of sugar = Rs.(80×6.75+120×8)=Rs.1500 C.P of 1 kg = Rs.[1500/200]=Rs.7.50 Gain required = 20% S.P of 1 kg = (120% of Rs.7.50) = Rs.[120/100×7.50]=Rs.9 per kg. Correct Option : D #### D QUESTION:40, 45, 50, 50, 60, 75, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:Two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)28 B)266 C)990 D)20 E)22 SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 160 + 280 = 440 m. The time required = d/s = 440/20 = 22 sec. Answer: E #### E QUESTION:Which of the following is a prime number ? options: A)27 B)45 C)97 D)98 E)100 SOLUTION:Clearly, 97 is a prime number. #### C QUESTION:A train is 485 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length options: A)20 seconds B)30 seconds C)40 seconds D)50 seconds E)None of these SOLUTION:Explanation: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 485+140 = 625 meter Time = Distance/speed =625∗2/25=50seconds Option D #### D QUESTION:Find the value of x which satisfies the relation Log10 3+log10 (4x+1)=log10 (x+1)+1 options: A)2.5 B)3.5 C)3.2 D)6.8 E)9.8 SOLUTION:[log10a + log10b = log10 ab] and also 1 can be written as log10 10, so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)), this can be solved to get 12x+3=10x+10, that gives x=7/2=3.5 ANSWER:B #### B QUESTION:Length of a rectangular plot is 28 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)54 m B)64 m C)74 m D)84 m E)94 m SOLUTION:Let breadth = x metres. Then, length = (x + 28) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 28) + x] = 200 2x + 28 = 100 2x = 72 x = 36. Hence, length = x + 28 = 64 m B #### B QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 * 17/100 = 119 The answer is B. #### B QUESTION:Out of 470 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ? options: A)80 B)150 C)100 D)180 E)220 SOLUTION:n(A)=325,n(B)=175,n(AuB)=470-50=420. Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80. Answer is A #### A QUESTION:Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:150 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? options: A)1~10 B)10~20 C)20~30 D)45~55 E)55~65 SOLUTION:150 = 2*3*5^2 There are factors in each range except for 55~65 The answer is E. #### E QUESTION:Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ? options: A)2 B)5 C)1 D)9 E)4 SOLUTION:4-3=1. Answer is C #### C QUESTION:12,31,68,129,220,? options: A)129 B)220 C)387 D)347 E)520 SOLUTION:2*2*2 + 4 = 12 3*3*3 +4 = 31 4*4*4 + 4 = 68 5*5*5 + 4 = 129 6*6*6 + 4 = 220 7 *7 *7 + 4 = 347 ANSWER : D #### D QUESTION:Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) options: A)27 B)30 C)33 D)36 E)39 SOLUTION:33/4 ÷ 4 = 33/16 pounds in each container 33/16 pounds * 16 ounces / pound = 33 ounces in each container The answer is C. #### C QUESTION:What is the shortest distance between points (-2, 1) and (2,-2)? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The shortest distance between any two points is a line. Points are written in the (x,y) format, where x is the x-coordinate and y is the y-coordinate. Calculate the difference between the x and y values of each coordinate. Difference between y values = 1 - (-2) = 1 + 2 = 3 Difference between x values = (-2) - 2 = -4 If you start at (2, -2) and travel over -4 units (i.e., travel to the left) and then travel straight up 3 units, you will end up at (-2, 1). This sketches out a right triangle, where the hypotenuse is the length of the shortest distance between the two points (i.e., a straight line between the two points). Use the Pythagorean Theorem with a = -4 and b = 3 to solve for this distance between the two points. a2+ b2 = c2 (-4)2+ 32 = c2 Solve for c 16 + 9 = c2 25 = c2 c = 5 (Negative 5 cannot be a solution to a length so it is discarded) Answer is E #### E QUESTION:An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 40% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount? options: A)91.23% B)95.56% C)97.86% D)101.45% E)103.68% SOLUTION:0.6*1.2^3 = 1.0368 The answer is E. #### E QUESTION:P is three times as old as Q. In 11 years, P will be twice as old as Q. How old was P three years ago? options: A)21 B)24 C)27 D)30 E)33 SOLUTION:P = 3Q so Q = P/3 P+11 = 2(Q+11) = 2(P/3+11) P/3 = 11 P = 33 Three years ago, P was 30. The answer is D. #### D QUESTION:The ratio 25:50 expressed as percent equals to options: A)50 % B)85 % C)25 % D)75 % E)None of above SOLUTION:Explanation: Actually it means 25 is what percent of 50, which can be calculated as, (25/50)*100 = 25 * 2 = 50 Answer: Option A #### A QUESTION:The G.C.D. of 1.08, 0.33 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.33 and 0.90. H.C.F. of 108, 33 and 90 is 3, H.C.F. of given numbers = 0.03. Answer A #### A QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base * Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)196 E)200 SOLUTION:185 Answer is B #### B QUESTION:A shopping mall give 40% sale on T-shirts and increase 25% price of pants. The cost price of pants and T-shirts are 1500 and 400 respectively. Overall they makes a? options: A)200 B)250 C)300 D)215 E)180 SOLUTION:Let the SP of the pants and T-shirts be Rs. p and Rs. t respectively. p = 1500(1 + 25/100) = 1500 + 375 t = 400(1 - 40/100) = 400 - 160 Total SP - Total CP = p + t - (1500 + 400) = 375 - 160 = Rs. 215 As this is positive, an overall profit of Rs. 500 was made. Answer: D #### D QUESTION:A two digit number reversed and multiplied by 4 is 3 more than the original digit. what is the digit? options: A)61 B)62 C)63 D)64 E)66 SOLUTION:If no is xy , then 10x+y = 4*(10y+x)-3= 40y +4x-3 6x-39y +3 =0 2x-13y +1 =0 13 y =2x+1 when y=1, x=6 so number is 61. ANSWER:A #### A QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:The perimeter of one face of a cube is 48 cm. Its volume will be: options: A)125cm3 B)400cm3 C)250cm3 D)625cm3 E)None of these SOLUTION:Explanation: Edge of cude = 48/4 = 12 cm Volume = a*a*a = 12*12*12 = 1728 cm cube Option E #### E QUESTION:Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48 SOLUTION:Diameter of tube= 5 inches Height of wooden tube= 15 inches Two tubes can stand in 31 inches height Two tubes can fit in 11 inches length Two tubes can fit in 10 inches width So, one box can hold 8 tubes Three boxes can hold= 8*3= 24 tubes A is the answer #### A QUESTION:If 0.75: x :: 5:9, then x is equal to: options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *9) X=6.75/5 = 1.35 Answer: D #### D QUESTION:In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum? options: A)1 1/4 B)1 1/6 C)1 1/0 D)1 1/5 E)1 5/1 SOLUTION:Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10% Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.Answer: A #### A QUESTION:33 1/3% OF 330? options: A)80 B)90 C)110 D)120 E)130 SOLUTION:33 1/3 % = 1/3 1/3 × 330 = 110 C) #### C QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time. options: A)10 hours B)12 hours C)14 hours D)16 hours E)None of these SOLUTION:Explanation : speed of the boat = 6 km/hr Speed downstream = (6+2) = 8 km/hr Speed upstream = (6-2) = 4 km/hr Distance travelled downstream = Distance travelled upstream = 32 km Total time taken = Time taken downstream + Time taken upstream = (32/8) + (32/4) = (32/8) + (64/8) = (96/8) = 12 hr. Answer : Option B #### B QUESTION:The sum of the two numbers is 11 and their product is 24. What is the sum of the reciprocals of these numbers ? options: A)11/24 B)11/25 C)13 D)13/15 E)None SOLUTION:Let the numbers be x x and y y Then x + y = 11 x y = 24 x+y=11xy=24 Hence, x + y x y = 11 24 x+yxy=1124 ⇒ 1 y + 1 x = 11 24 Answer is A #### A QUESTION:Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min. options: A)8 min B)3 min C)21 min D)23 min E)24 min SOLUTION:3/4 tank is filled by A in 18 mins. then balance 1/4 tank is filled by B in 32*1/4 = 8 mins. ANSWER:A #### A QUESTION:E = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set E and one integer from set B. What is the probability that the sum of the two integers will equal 9 ? options: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33 SOLUTION:The total number of pairs E,B possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2. Answer: B. #### B QUESTION:There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate? options: A)776 B)864 C)299 D)257 E)125 SOLUTION:W = 60% L = 40% 60% - 40% = 20% 20% -------- 288 60% -------- ? => 864 Answer:B #### B QUESTION:The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000 SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=4500pi r=15 so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx) E #### E QUESTION:Find the sum of all odd number upto 250. options: A)15345 B)15645 C)15625 D)15342 E)15683 SOLUTION:Explanation: Number of odd numbers upto 250 = n/2 = 250/2 = 125 Sum of first 125 odd numbers = (125)2 = 15625 Answer: Option C #### C QUESTION:The average of four positive integers is 67. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers? options: A)72 B)78 C)80 D)82 E)84 SOLUTION:Let the four integers be A, B, C and D where A > B > C > D. (A + B + C + D)/4 = 67 => A + B + C + D = 268 ---> (1) A = 93, D = 39 and B - C = 28 (1) => B + C = 268 - (A + D) = 268 - 132 = 136. B + B -28 = 136 B = (136 + 28)/2 = 82 ANSWER:D #### D QUESTION:If n is an integer and 5^n > 4,000,000, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:When you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8 2 to the ^ 8 = 256 so its 256 x 5^6 that means 5^6 x 5^x must be greater 5^x > 256 5^1=5 5^2=25 5^3= 125 5^4= 625 - > so x must be at least 4 5^(6+4)= 5^10 ANSWER:D #### D QUESTION:A retailer buys 80 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)115 C)112 D)118 E)120 SOLUTION:let the market price of each pen be $1 then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20 profit %=((43.20*100)/36) %=120% Answer E)120 #### E QUESTION:It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold Calculate the break even point if the price he charges for 1 hotdog is $1.50 options: A)140 B)150 C)160 D)170 E)180 SOLUTION:Let x be the number of hotdogs sold Let C be the cost of buying and selling x hotdogs Let R be the revenue made for selling x hotdogs R = selling price of 1 hotdog × number of hotdogs sold R = 1.50x C = fixed cost + variable cost variable cost = fee charged for 1 hotdog × number of hotdogs sold variable cost = 1x C = 75 + 1x R = C 1.50x = 75 + 1x 1.50x - 1x = 75 + 1x - 1x 0.5x = 75 x = 150 since 0.5 × 150 = 75 The break even point is to sell 150 hotdogs. Answer B #### B QUESTION:There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season? options: A)A)55% B)B)60% C)C)80% D)D)72% E)E)70% SOLUTION:There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 30% chance that Federer will not play at all in the whole season We can also infer that there is 70% chance that Federer will play. Answer E #### E QUESTION:Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n. What is the value of 30~ ? options: A)1 B)0 C)2 D)8 E)31 SOLUTION:n~ = (n-1)! so 30~ = (30-1)! = 29! when 29!/30 we have 16*2 inside 29! hence 30 gets cancelled and we get remainder as 0 B #### B QUESTION:What is the difference between the local value of 3 and 9 in the number 23974? options: A)430 B)377 C)288 D)277 E)210 SOLUTION:Explanation: 300 – 90 = 210 Answer: E #### E QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=u ii. u is not equal to v iii. s > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true. Answer: D. #### D QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought? options: A)20 B)18 C)24 D)26 E)28 SOLUTION:Smallest gumballs = (19-16) + (19-14) +19= 27 Largest gumballs = (25-16) + (25-14) +25= 45 Difference = 45 - 27 = 18 B #### B QUESTION:Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 4,700 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip? options: A)14.0 B)13.0 C)12.0 D)11.0 E)10.0 SOLUTION:Solution:H stopped 700 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs. this means she reached there at 11:00. speed difference between them is 800-500=300 ft/hr so by the time H stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11:00 means 12:00 is the answer. C #### C QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 30 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam. options: A)15 B)30 C)35 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 90(x - 5) 80x - (5 * 30) = 90(x - 5) 300 = 10x => x = 30 ANSWER:B #### B QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be? options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999. 366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday Answer: A #### A QUESTION:If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^3 have? options: A)7 B)5 C)6 D)8 E)9 SOLUTION:take the example of 4... it has 3 positive divisors (1,2,4) Now, take the example of 64... it has only 7 divisors.. so A is the ans #### A QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)69 E)71 SOLUTION:1/2 * d (12 + 8) = 690 d = 69 Answer: D #### D QUESTION:In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r? options: A)-4/3 B)1/4 C)-4 D)3/4 E)4/3 SOLUTION:The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x. Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3. Answer: A. #### A QUESTION:Simplify: 244 x 301 options: A)73144 B)73143 C)73200 D)72956 E)73444 SOLUTION:244 x 301 = 244 x (300 + 1) = 73200 + 244 =73444 Answer is E #### E QUESTION:50% of a number is added to 120, the result is the same number. Find the number? options: A)240 B)288 C)1687 D)997 E)121 SOLUTION:(50/100) * X + 120 = X X = 240 Answer:A #### A QUESTION:If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a eight-percent vinegar solution, what was the concentration of the original solution? options: A)9.3% B)17.3% C)26.67% D)35.5% E)41.3% SOLUTION:Let X be the quantity of non-vinegar in the strong vinegar solution Thus vinegar quantity will be 12 - X When 50 ounces of water were added the percentage of vinegar becomes 8%, thus (12 - X)/62 = 8/100 From this equation X = 7.04 Answer (12-7.04)/12 = 41.3% ANSWER:E #### E QUESTION:How many different subsets of the set {0, 1, 2, 3, 4, 5,6,} do not contain 0? options: A)A.66 B)B.57 C)C.31 D)D.32 E)E.58 SOLUTION:Number of subset Since we have 6 digits other than 0, we can take any numbers from the set of 6 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations. 6c1+6c2+6c3+6c4+6c5+6c6=57 And one set is the NULL set having no elements in it so 57+1=58. ANSWER E. #### E QUESTION:If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1, then what is the value of abc/def ? options: A) 27/4 B) 27/8 C) 3/4 D) 3/2 E) 1/4 SOLUTION:Say a = 2. Then: a/b = 1/3 --> b = 6; b/c = 2 --> c = 3; c/d = 1/2 --> d = 6; d/e = 3 --> e = 2; e/f = 1 --> f = 2. abc/def = (2*6*3)/(6*2*2) = 3/2. Answer: D. #### D QUESTION:A worker earns $20 on the first day and spends $15 on the second day. The worker earns $20 on the third day and spends $15 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $100? options: A)30 B)33 C)35 D)38 E)40 SOLUTION:Every two days, the net total is $5. After 32 days, the worker will have $80. On day 33, the worker will receive $20 for a net total of $100. The answer is B. #### B QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.9 - 19 x 15) kg = 13 kg. Correct Option: D #### D QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles? options: A)4329 B)2799 C)4312 D)2799 E)2712 SOLUTION:Let the radii of the smaller and the larger circles be s m and l m respectively. 2∏s = 264 and 2∏l = 352 s = 264/2∏ and l = 352/2∏ Difference between the areas = ∏l2 - ∏s2 = ∏{1762/∏2 - 1322/∏2} = 1762/∏ - 1322/∏ = (176 - 132)(176 + 132)/∏ = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m Answer: C #### C QUESTION:Two numbers A and B are such that the sum of 5% of A and 3% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B. options: A)2 : 1 B)1 : 2 C)7 : 3 D)1 : 1 E)3 : 2 SOLUTION:Explanation: 5% of A + 3% of B = 2/3(6% of A + 8% of B) 5A/100 + 3B/100 = 2/3(6A/100+8B/100) ⇒5A + 3B = 2/3(6A + 8B) ⇒15A + 9B = 12A + 16B ⇒ 3A = 7B ⇒ AB = 7/3 ⇒ A:B=7:3 Answer: Option C #### C QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:The average age of a husband, wife and their child 12 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is? options: A)19.01 years B)5.25 years C)16 years D)15 years E)4.75 years SOLUTION:Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years. Required average = 57/12 = 4.75 years. Answer:E #### E QUESTION:A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)24 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x*2+y*4=140 heads: x*1+y*1=48 implies, 2x+4y=140 and x+y=48 solving these two equations, we get x=26 and y=22 Therefore, hens are 26. ANSWER:D #### D QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 The total amount of Fuel paid by the company during the given period is approximately what percent of the total amount of salary paid during this period? options: A)A)0.5% B)B)1% C)C)1.25% D)D)3% E)E)4% SOLUTION:Required percentage = (288 + 342 + 324 + 336 + 420) = [ 17 x 100 ] % 1710 ~= 1%. Answer : B #### B QUESTION:If December 3rd, 1999 is a Friday, what day is January 8th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 36 days from Dec. 3rd 1999 to Jan. 8th 2000. 36/7 has a remainder of 1. Jan. 8th is: Friday + 1 day = Saturday The answer is D. #### D QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.2 x = 3.2 Alternate solution: Try to backsolve. Initial volume = 3.2 After one hour --> (1/4)3.2 = 0.8 After two hours --> (1/4)0.8 = 0.2 Answer: B #### B QUESTION:A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following? options: A)1/6 B)1/9 C)1/18 D)1/24 E)1/36 SOLUTION:There are 6*6 = 36 possibilities. Bob has 2 chances so the probability is 2/36 = 1/18. The answer is C. #### C QUESTION:Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is: options: A)18 B)19 C)20 D)21 E)22 SOLUTION:Explanation: Let first number be x. So,2nd no. = 4x & 3rd no.=8x. So,x+4x+8x=78 × 3 = 234. 13x = 234 x = 234/13 Hence,smallest Number x=18. Answer: A #### A QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (750 ~ 1020)/1020 = 26% Loss A #### A QUESTION:If 1 = 3 2 = 6 3 = 9 4 = 12 5 = 15 Then 9 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)3 D)4 E)5 SOLUTION:C 3 As stated 3=9 => 9=3 Answer is C #### C QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible? options: A)270 B)252 C)272 D)292 E)285 SOLUTION:number of astronauts with previous experience = 7 Remaining =9 we need to pick exactly one from the first group and 2 from the second group (7C1)*(9C2) =7*36= 252 Answer : B #### B QUESTION:A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 5500. What is the share of B ? options: A)1000 B)800 C)1400 D)1200 E)None of them SOLUTION:Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x A’s capital = Rs. (3 x (2/3).x) = Rs. 2x. Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3. Hence, B's share = Rs. ( 5500 x (2/11))= Rs. 1000. Answer is A #### A QUESTION:A boat can move upstream at 30 kmph and downstream at 15 kmph, then the speed of the current is? options: A)5 B)7.5 C)32.5 D)9.2 E)5.8 SOLUTION:US = 30 DS = 15 M = (30 - 15)/2 = 7.5 Answer: B #### B QUESTION:A batsman scored 210 runs which included 3 boundaries and 8 sixes. What % of his total score did he make by running between the wickets options: A)40% B)50% C)65% D)71.4% E)75% SOLUTION:Number of runs made by running = 210 - (3 x 4 + 8 x 6) = 210 - (60) = 150 Now, we need to calculate 60 is what percent of 120. => 150/210 * 100 = 71.4 % D #### D QUESTION:If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years? options: A)(1+k/100)^n B)(1+k)^n C)(1+kn/100) D)(1+k/100)^4n E)(1+kn) SOLUTION:Amount after 7n years will be = x ( 1 + k/100)^4n Amount after 3n years will be = x ( 1 + k/100)^3n So, required ratio will be - { x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n Hence answer will be a. (1+k/100)^4n D #### D QUESTION:Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:Total price of 5 packet milk=5*20=100 Total price of 3 packet milk=3*12=36 Total price of 2 packet returned milk=100-36=64 Average price of 2 packet milk=64/2=32 Correct option Answer:C #### C QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)200 B)300 C)500 D)600 E)700 SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: Option C #### C QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2 = 62 m2. answer :D #### D QUESTION:Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 6 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 6 questions did Zachary answer correctly? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:i got two equations: 3x-2y=25 x+y=6 3x-2(6-x)=25 3x-12+2x=25 5x=37 x=7.4 or between 7 and 8. (ANS B) #### B QUESTION:How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 30% iodine solution? options: A)30.5 B)49 C)100 D)105 E)140 SOLUTION:Solution 1: Assume the iodine solution to be mixed = x lts. Iodine = 0.4x lts, Water = 0.6x lts. Solution 2: 35 liters of a 20% iodine solution Iodine = 7 lts, Water = 28 lts. Total iodine = 0.4x + 7 Total water = 0.6x + 28 The resultant is a 35% idoine solution. Hence (0.4x + 7) / (x + 35) = 30/100 40x + 700 = 30x + 1050 10x = 305 x = 30.5 lts Correct Option: A #### A QUESTION:Seller selling an apple for Rs.18, a Seller loses 1/6th of what it costs him. The CP of the apple is? options: A)10 B)12 C)19 D)18 E)20 SOLUTION:SP=18Loss=CP19Loss=CP−SP=CP−18⇒CP19=CP−18⇒18 CP19=18⇒CP19=1⇒CP=19 C #### C QUESTION:Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose? options: A)1.25% B)2.1% C)2.25% D)2.65% E)3% SOLUTION:Generally in such cases, there is always loss. So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss. Loss% = Common loss and gain% 2 = x 2 10 10 Therefore, here common loss and gain % = 15% Hence, Loss% = 15 2 = 2.25% C #### C QUESTION:If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ? options: A)7.2 kg. B)10.8 kg. C)12.4 kg. D)18.0 kg E)None SOLUTION:Answer ∵Weight of 13 m long rod = 23.4 kg ∴ Weight of 1 m long rod = 23.4 / 13 kg ∴ Weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg Option: B #### B QUESTION:The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 144 metres, what is its area? options: A)1320 sq.metres B)1260 sq.metres C)1280 sq.metres D)1380 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 144 ⇒ x = 6 Area = 7 × 6 × 5 × 6 = 1260 sq.m. Answer B #### B QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 5 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 5 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 8 a.m. Answer: C #### C QUESTION:A batsman had a certain average of runs for 16 innings. In the 17th innings, he made a score of 87 runs thereby increasing his average by 3. What is his average after 17 innings? options: A)39 B)88 C)266 D)278 E)221 SOLUTION:Explanation: Assume his initial average = xx His total runs after 16 innings = 16xx After scoring 87 runs his average got increased by 3 to xx + 3 So his total runs after 17 innings = 17 × (xx+3) But it was given that the difference in the total scores after 16 innings and 17 innings = 87 Therefore 17×(x+3)−16x=87⇒x=3617×(x+3)−16x=87⇒x=36 His new average = 36 + 3 = 39 Answer:A #### A QUESTION:For prime numbers x and y, x^3*y^5=z^4. How many positive factors does positive integer z have? options: A)One B)Two C)Three D)Four E)Five SOLUTION:Solution: given x^3*y^5=z^4; here if x and y are two different prime numbers then z = x^3/4 * y^5/4 in this case z can not be and integer. now to make z = (x^3*y^5)^1/4 an integer it is required to have x=y then equation will become z=x^2 or z=y^2 hence total positive factors will be 3. ANSWER:C #### C QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)50 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer E, 50 cans #### E QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast? options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2 SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes. Answer: C. #### C QUESTION:A furniture dealer purchased a desk for $100 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? options: A)40% B)45% C)50% D)55% E)60% SOLUTION:Anyway, in this question, there is no discount but the mark up is given as 40% of the selling price. So it is not 40% of $100 but instead, 40% of Selling price which is obtained by adding mark up to $100. So if selling price is S, 100 + 40% of S = S or 100 = 0.6S therefore S = 100/0.6 = S = Profit = 100/0.6- 100 which is calculated on cost price in % terms. So 40/100 * 100 = 40% is profit. A #### A QUESTION:Based on this year's costs, an orchard grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to decrease 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be: options: A)100% less than N B)200% less than N C)Equal to N D)100% greater than N E)200% greater than N SOLUTION:Correct answer is (D). This year, the price of a tree is price1=P/N. If this price decreases by 50% it becomes Price2=P/N*0.5 Then with P dollars, you can grow P/Price2 trees i.e. P/(P/N*0.5) i.e. N/0.5 i.e. 2*N Which is 100% greater than N. #### D QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be: options: A)5:2 B)7:3 C)9:2 D)13:4 E)3:4 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 ANSWER:B #### B QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow? options: A)4/8 B)9/2 C)7/6 D)9 E)2/21 SOLUTION:Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³Câ‚‚/¹⁵Câ‚‚ = (3 * 2)/(15 * 14) = 1/35 Probability that both are yellow = ²Câ‚‚/¹⁵Câ‚‚ = (2 * 1)/(15 * 14) = 1/105 Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵Câ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35 Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 * 35) = 2/21 Answer: E #### E QUESTION:the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? options: A)20 B)55/4 C)25 D)14 E)13 SOLUTION:After passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles/hour. In those 5 mins the cyclist travels a distance of 5/4 miles. In those 5 mins the hiker travels a distance of 1/3 miles. So the hiker still has to cover 11/12 miles to meet the waiting cyclist. The hiker will need 55/4 mins to cover the remaining 11/12 miles. So the answer is B. #### B QUESTION:Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him? options: A)2000 B)3000 C)4000 D)1000 E)5000 SOLUTION:Let the money he took for shopping be m. Money he spent = 30 % of m = 30/100 × m = 3/10 m Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10 But money left with him = $ 2100 Therefore 7m/10 = $ 2100 m = $ 2100× 10/7 m = $ 21000/7 m = $ 3000 Therefore, the money he took for shopping is $ 3000. Answer:B #### B QUESTION:In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 272 runs? options: A)6.25 B)6.22 C)6.29 D)6.39 E)6.0 SOLUTION:Required run rate = [272 - (3.2 * 10)]/40 = 240/40 = 6.00 Answer: E #### E QUESTION:There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 36, then find the smaller number? options: A)25 B)66 C)77 D)60 E)44 SOLUTION:Let the two positive numbers be 5x and 8x respectively. 8x - 5x = 36 3x = 36 => x = 12 => Smaller number = 5x = 60. Answer: D #### D QUESTION:One out of every 600 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment? options: A)60,000 B)5,000 C)10,000 D)50,000 E)52,000 SOLUTION:20 broken glasses indicates that 10*10= 100 defected bulbs are present. 100 defected bulbs indicates that 100*600= 60,000 light bulbs are present. A is the answer #### A QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:There is a group of persons each of whom can completea piece of work in 16 days, when they are working individually. On the 1st day 1 person works, on the second day another person joins him, on the third day one more person joins them & this process continues till the work is completed. How many days are needed to complete the work? options: A)5 1⁄2 days B)5 1⁄3 days C)5 1⁄6 days D)6 1⁄6 days E)7 1⁄6 days SOLUTION:Work completed in 1st day = 1/16 Work completed in 2nd day = (1/16) + (1/16) = 2/16 Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16 … An easy way to attack such problems is from the choices. You can see the choices are very close to each other. So just see one by one. For instance, The first choice given in 3 1⁄4 The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16 The work done in 4 days = (1+2+3+4)/16 = 10/16 The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it? The work done in 6 days = (1+2+3+4+5+6)/16 > 1 Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days. (Just for your reference, work done in 5 days = 15/16. Pending work in 6th day = 1 – 15/16 = 1/16. In 6th day, 6 people are working and work done = 6/16. To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days. Hence total time required = 5 + 1/6 = 5 1⁄6 days C #### C QUESTION:If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is options: A)not an even B)an even C)a perfect square D)an odd E)a prime SOLUTION:x^2 - 2x + 2y + 3 = 2x^2 - 3x + y + 1 y = x^2 - x - 2 y = (x-2)(x+1) (Note that one factor is even and one factor is odd.) Then y must be even. The answer is B. #### B QUESTION:How many words can be formed by using all letters of the word ‘DESK’ ? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The word contains 4 different letters. The number of permutations is 4! = 24 The answer is C. #### C <<<Examples ends QUESTION:There are 22 students in a class. In how many different ways can a committee of 3 students be formed? options: A)1180 B)1320 C)1540 D)1760 E)1920 SOLUTION:22C3 = 22*21*20 / 6 = 1540 The answer is C. #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 43 kmph. For how many minutes does the bus stop per hour? options: A)70 min B)16 min C)20 min D)8.4 min E)40 min SOLUTION:D 8.4 min Due to stoppages, it covers 7 km less. Time taken to cover 9 km = (7/50 x 60) min = 8.4 min #### D QUESTION:If X is to be chosen at random from the integers between 1 to 6, inclusive, and Y is to be chosen at random from the integers between 7 and 11, inclusive, what is the probability that X + Y will be even? options: A)1/2 B)2/3 C)3/4 D)4/5 E)5/6 SOLUTION:X+Y will be even if X and Y are both even or both odd. P(X and Y are both even) = 3/6*2/5 = 1/5 P(X and Y are both odd) = 3/6*3/5 = 3/10 P(X+Y is even) = 1/5 + 3/10 = 1/2 The answer is A. #### A QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate? options: A)Cannot be determined B)43 C)3 D)6 E)10 SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position. Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40 Answer:A #### A QUESTION:X is an even number and Y is a positive odd number. Which of the following expressions cannot be even? options: A)(XY)^Y B)X^3Y^3 C)X^3 D)XY E)Y^2 SOLUTION:If x is even, let x = 0 and see what happens. A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE) B. 0³Y³ = 0 (EVEN - ELIMINATE) C. 0³ = 0 (EVEN - ELIMINATE) D. (0)Y = 0 (EVEN - ELIMINATE) E. Y² Answer:E #### E QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:400 students took a mock exam in Delhi, 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination? options: A)50 B)100 C)120 D)140 E)180 SOLUTION:60%*x+80%*(400-x)=65%*400 Ans=100 ANSWER:B #### B QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y? options: A)15.5 sec B)8.4 sec C)33.6 sec D)31.11 sec E)16.8 sec SOLUTION:Z--------------------------------------|----------------------------Y Car A(20mps)------------------------->P<---------------Car B(15mps) Let 2 cars meet each other at point P in t seconds. Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t. From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further. so, 15t/20 = 10 So t=40/3 sec and total distance = (35*40)/3 Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx. Answer D #### D QUESTION:A 140 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? options: A)35 B)20 C)47 D)36 E)40 SOLUTION:1: 2/5 = 5: 2 2/7 * 140 =40 Answer:E #### E QUESTION:From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 7, what is the probability that the 2 numbers included the number 5? options: A)1/5 B)2/5 C)3/10 D)3/5 E)1/3 SOLUTION:We know that the sum of two numbers picked was 7. So, there could be the following cases: (1, 6); (6, 1); (2, 5); (5, 2); (3, 4); (4, 3); Total of 6 cases out of which 2 have 5, thus the probability is 2/6=1/3. Ans E #### E QUESTION:When asked what the time is,a person answered that the amount of time left is 4/8 of the time already completed.what is the time. options: A)2 PM B)9 PM C)4 PM D)8 PM E)6 PM SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=4/8x⇒x=20 Time is 4 PM Answer:C #### C QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent? options: A)200 B)100 C)276 D)280 E)279 SOLUTION:Profit on first article = 10% of 1000 = 100. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: B #### B QUESTION:Seven people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: options: A)7/8 B)1/8 C)1/3 D)1/6 E)1/9 SOLUTION:Original share of 1 person =1/7 New share of 1 person =1/6 Increase =1/6 - 1/7 =1/42 Required fraction = (1/42)/(1/7)=1/6 Answer is D. #### D QUESTION:log(a(a(a)^1/4)^1/4)^1/4 here base is a. options: A)0 B)21/64 C)1 D)22/63 E)23/65 SOLUTION:log(a(a(a^1/4)^1/4)^1/4 => log(a(a^1+1/4)^1/4)^1/4 => log(a(a^5/4)^1/4)^1/4 =>log(a(a^5/16)^1/4 =>log(a^1+5/16)^1/4 =>log(a^21/16)^1/4 =>log(a^21/64) =>21/64 log(a) =>21/64 ANSWER:B #### B QUESTION:A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? options: A)10 B)15 C)21 D)36 E)42 SOLUTION:Since the order in which we select the socks does not matter, we can use combinations. We can select 2 socks from 5 socks in 5C2 ways. 5C2 = 10 Answer : A #### A QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10 SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others C #### C QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 3 specific shirts with 2 specific pants? options: A)66 B)51 C)36 D)70 E)56 SOLUTION:Total no of combinations available is= 8 shirts X 9 pants = 72 Eliminate the 3shirts X 2 pants combo = 6 which gives.......>> 72-6=66 ANSWER: A #### A QUESTION:In a class of 50 students, 20 play SNOOKER, 15 play Cricket and 11 play Football. 7 play both SNOOKER and Cricket, 4 play Cricket and Football and 5 play SNOOKER and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports? options: A)10 B)12 C)34 D)45 E)566 SOLUTION:Notice that7 play both SNOOKER and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and SNOOKER/Football. [color=#ffff00]{Total}={SNOOKER}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more check ADVANCED OVERLAPPING SETS PROBLEMS [/color] 50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2; Those who play ONLY SNOOKER and Cricket are 7-2=5; Those who play ONLY Cricket and Football are 4-2=2; Those who play ONLY SNOOKER and Football are 5-2=3; Hence, 5+2+3=10 students play exactly two of these sports. Answer: A. #### A QUESTION:A train 280 m long, running with a speed of 63 km/hr will pass a tree in? options: A)18 sec B)16 sec C)19 sec D)11 sec E)12 sec SOLUTION:: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec Answer: B #### B QUESTION:Which 2 digit number has its digits reversed when you double it and take 1? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:reverse it and you get 73 which is 2*37-1. ANSWER:E #### E QUESTION:f a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:The probability that A speaks truth is 15/23 and that of B speaking truth is 17/29. What is the probability that they agree in stating the same fact? options: A)182/395 B)129/289 C)197/353 D)479/667 E)None of these SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 15/23 * 17/29 + 14/23 * 16/29 = 255/667 + 224/667 = 479/667 ANSWER:D #### D QUESTION:Find value of x (11^2 + 12^2 + 13^2 + ... + 20^2) = x options: A)1200 B)1340 C)1234 D)1203 E)2485 SOLUTION:(11^2 + 12^2 + 13^2 + ... + 20^2) = (1^2 + 2^2 + 3^2 + ... + 20^2) - (1^2 + 2^2 + 3^2 + ... + 10^2) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = (2870 - 385) = 2485 E #### E QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5? options: A)3 B)16 C)75 D)24 E)26 SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens. 2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers). 3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers. 4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left! 6) Answer choice E. #### E QUESTION:The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles? options: A)20° B)70° C)60° D)120° E)140° SOLUTION:If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence 3x + 6x = 90 9x = 90 x = 10 Measures of the two acute angles are 3x = 3 × 10 = 30° 6x = 6 × 10 = 60° C #### C QUESTION:A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300m B)278m C)350m D)228m E)282m SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 36 = 50/3 3(x + 300) = 1800 è x = 300m. Answer:A #### A QUESTION:If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ? options: A)4x + 6y B)x + y + 4 C)4x - 9y D)9x + 4y E)x + y - 4 SOLUTION:By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11. (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11; (x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11; (9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11; (4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11. correct answer C #### C QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)100 B)102 C)104 D)108 E)90 SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 10 = 90 ways. E #### E QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)12.6 kmph B)17.5 kmph C)12.8 kmph D)12.5 kmph E)14.5 kmph SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 5: 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony? options: A)A)1:5 B)B)1:1 C)C)1:8 D)D)1:9 E)E)1:3 SOLUTION:Number of men in the colony = 5/7 * 70 = 50. Number of women in the colony = 2/7 * 70 = 20. Number educated women in the colony = 1/5 * 30 = 6. Number of uneducated women in the colony = 4/5 * 50 = 24. Number of educated persons in the colony = 8 /35 * 70 = 16. As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 50 - 10 = 40. Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4. Answer:A #### A QUESTION:Half of 2 percent written as decimal is options: A)5 B)0.01 C)0.05 D)0.005 E)None of these SOLUTION:Explanation: It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01 Answer: Option B #### B QUESTION:What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad? options: A)814 B)266 C)287 D)999 E)661 SOLUTION:Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = Required number of tiles = = 814 Answer: A) 814 #### A QUESTION:What is the smallest positive integer that can be multiplied by 605 to make it a perfect square? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:605 is multiplied by 5 gives 3025 Its a square root of 55 Answer is 5 -Option C #### C QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick? options: A)5 B)8 C)24 D)15 E)20 SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min Nick's rate - 10 laps per hour --> 10/60 laps/min lets set equations: 20/60*t=4 (since Maria had to run 4 laps before Nick would start) 10/60*t=0 (Hick has just started and hasn't run any lap yet) (20/60-10/60)*t=4-0 (since Nick was chasing Maria) t=24 min needed Maria to run 4 laps Answer : C #### C QUESTION:For which of the following values of s is (40+s)/s an integer? options: A)3 B)4 C)9 D)11 E)40 SOLUTION:This problem has to be solved by checking the options (40 + s)/s For this entity to be an integer, 50 + s should be divisible by s Option A: 43/3 - Not an Integer Option B:44/4 - Not an Integer Option C: 49/9 - Not an integer Option D: 51/11 - Not an integer Option E - 80/40- Integer Correct Option: E #### E QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero? options: A)472392 B)648421 C)720756 D)729951 E)810364 SOLUTION:All six digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 9 ways. And, fourth digit can be filled in 9 ways. And, fifth digit can be filled in 9 ways. And, sixth digit can be filled in 8 ways. Total ways = 9*9*9*9*9*8 = 472392 Hence option (A). #### A QUESTION:A car traveled 75% of the way from town A to town B at an average speed of 60 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ? options: A)10 B)20 C)25 D)30 E)37.5 SOLUTION:Total distance = 100 miles (easier to work with %) 75% of the distance = 75 miles 25% of the distance = 25 miles 1st part of the trip → 75/60 = 1.25 2nd part of the trip → 25/S = t Total trip → (75+25)/40 = 1.25 + t » 100/40 = 1.25 + t » 2.5 = 1.25 + t » t = 1.25 Back to 2nd part of the trip formula: 25/S = 1.25 » S = 20 Ans B #### B QUESTION:In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a four or a one on either die, that player wins. What is the probability that a player wins after playing the game once? options: A)1/3 B)4/9 C)5/9 D)2/3 E)3/4 SOLUTION:We're looking for the number of outcomes that include AT LEAST a 1 or a 4. #getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6 #getting a one in 2nd die {(2,1), ...(5,1),(6,1) } = 4 [exclude 1,1 and 4,1] since it will be counted twice #getting a three in 1st die {(3,1), (3,2), ...(3,6) }= 6 #getting a three in 1st die {(2,4), (3,4), ...(6,4) } = 4 [exclude 1,4 and 4,4] since it will be counted twice Total possibities = 20 Probability of rolling at least a 1 or a 4 on two dice: 20/36 = 5/9 C #### C QUESTION:A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 18 = 6 + 12 - {Both} + 0; {Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: A. #### A QUESTION:The Snow Lovers Ski Team is comprised of 4 men and 8 women. If a team of 5 skiers is to be randomly selected to pack the skis into the bus, what is the probability that the team will have exactly 3 women? options: A)14/33 B)7/33 C)2/7 D)13/73 E)12/27 SOLUTION:Combination Probability Formula: nCr = n!/[r!(n-r)!] Total possible, select 5 people from 12 people = 12C5 = 12!/[5!(12 - 5)!] = 792. To have 3 women there must be 2 men, select 2 men from 4 = 4C2 = 6. And, select 3 women from 8 = 8C3 = 56. 3 women and 2 men = (6)(56) = 336 Probability = (number outcomes favorable)/(total number outcomes) = 336/792 = 14/33 Answer: A #### A QUESTION:Three coworkers P , W , R meet for Dinner. P had 5 sandwiches, W had 3 and R had none. Both PW share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PW, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split. options: A)a) 5$ B)b) 3 $ C)c) 7 $ D)d) 4 $ E)e) 5.5 $ SOLUTION:we got total 8 sandwiches ....we are dividing equally in 3 people. per person: 8/3 initially p:8 W:3 r:0 now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches. now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r ok we have 8 dollars for 8/3 sandwich therefore for 7/3 sandwich we will get 7 dollars. hence p should get 7 dollars. hence C #### C QUESTION:Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years. options: A)306.05 B)306.00 C)306.04 D)306.05 E)306.01 SOLUTION:A = 5000(51/50)3 = 5306.04 5000 ----------- 306.04 Answer: A #### A QUESTION:Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x – 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.3600, what will be the difference between Q and R's share? options: A)2788 B)4500 C)7282 D)2782 E)2729 SOLUTION:4 --- 3600 5 --- ? => 4500 Answer:B #### B QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)3 sec C)8.9 sec D)6.9 sec E)2.9 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 120/40 = 3 sec. Answer: B #### B QUESTION:What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each? options: A)$3.36 B)$6.85 C)$8.46 D)$10.08 E)$12.46 SOLUTION:Answer = E 2 * 2.49 + 4 * 1.87 = 2 (2.50 - 0.01) + 4 (2.00 - 0.13) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46 #### E QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B QUESTION:Two trains of length 200 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)22 sec B)77 sec C)76 sec D)20 sec E)24 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 200 + 280 = 480 m. The time required = d/s = 480/20 = 24 sec. Answer:E #### E QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)76 m B)178 m C)225 m D)187 m E)176 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x)= 750 => x = 225 m. Answer: C #### C QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:1) Draw a simple cube 2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes. 3) Remember that the OUTSIDE of the cube is the part that's painted.... The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. J=4 + 4 + 4 = 12. Answer A #### A QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(6200*5*3)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:If 15% of 40 is greater than 25% of a number by 2, the number is options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Explanation: 15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16 Option B #### B QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)Rs.486 B)Rs.455 C)Rs.487 D)Rs.480 E)Rs.489 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480 Answer: D #### D QUESTION:The price of 2 sarees and 4 shirts is 16000. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall one have to pay? options: A)2,400 B)4,800 C)1,200 D)Cannot be determined E)None of these SOLUTION:Let the price of one saree and one shirt be x and y respectively. Then, 2x + 4y = 1600 or, x + 2y = 800 ... (i) Also, x + 6y = 1600 ... (ii) Solving equations (i) and (ii), we get 4y = 800 or,y = 200 ∴ cost of 12 shirts = 12 × 200 = 2400 Answer A #### A QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? options: A)52% B)64% C)72% D)76% E)80% SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A QUESTION:x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days? options: A)x2/y2 units B)y3/x2 units C)x3/y2 units D)y2/x2 units E)None SOLUTION:Explanation: Let amount of work completed by y men working y hours per in y days = w units More men, more work(direct proportion) More hours, more work(direct proportion) More days, more work(direct proportion) Hence we can write as (men)x:y (hours)x:y (days)x:y }::x:w ⇒x^3w=y^3x ⇒w=y^3x/x^3 =y^3/x^2 Answer: Option B #### B QUESTION:Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood? options: A)a) 90 B)b) 100 C)c) 110 D)d) 130 E)e) 140 SOLUTION:C. 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3rd piece (sorted in increasing length) length = 140 (median) for sum of first 2 wood length to become max, last two should be least. let 4th, 5th wood also have length 140 each. total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220/2 = 110 Answer C #### C QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.2 x = 3.2 Alternate solution: Try to backsolve. Initial volume = 3.2 After one hour --> (1/4)3.2 = 0.8 After two hours --> (1/4)0.8 = 0.2 Answer: B #### B QUESTION:There are different 15 circles. What is the number of the greatest possible points with which the circles intersect? options: A)390 B)100 C)110 D)180 E)210 SOLUTION:Maximum points of intersection between n different circles = n*(n - 1) = 15*14 = 210 Answer: E #### E QUESTION:In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 10 is options: A)8 B)625 C)16 D)20 E)24 SOLUTION:I've never seen such kind of question in GMAT before. OK there can be 4 cases: |x+y| + |x-y| = 10 A. x+y+x-y = 10 --> x=5 B. x+y-x+y = 10 --> y=5 C. -x-y +x-y= 10 --> y=-5 D. -x-y-x+y=10 --> x=-5 The area bounded by 4 graphs x=5, x=-5, y=5, y=-5 will be square with the side of 4 so the area will be25*25=625 Answer: B #### B QUESTION:If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? options: A)100 B)10 C)0.01 D)0.0001 E)0.0001 SOLUTION:Given that 100 microns = 1 decimeter =10,000 angstroms So, 1 micron = 10,000/100 =100 Answer : A #### A QUESTION:If a and b are positive integers and x = 4^a and y = 5^b, which of the following is a possible units digit of xy? options: A)0 B)4 C)5 D)7 E)8 SOLUTION:The units digit of 4^a is either 4 or 6. The units digit of 5^b is 5. 4*5 = 20 and 6*5 = 30. The units digit of xy is 0. The answer is A. #### A QUESTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. options: A)6 B)6.5 C)7 D)7.5 E)5 SOLUTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total) Hour miles/hour Total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 It takes a total of nine hours to cover the 210 mile distance. ANSWER: A 6 #### A QUESTION:What is the greatest positive integer T such that 3^T is a factor of 9^10? options: A)5 B)T=9 C)T=10 D)T=20 E)30 SOLUTION:What is the greatest positive integer T such that 3^T is a factor of 9^10? 9^10 = (3^2)^10 = 3^20 D. 20 #### D QUESTION:In an examination, 25% of total students failed in Hindi, 50% failed in English and 25% in both. The percentage of these who passed in both the subjects is : options: A)23 B)37 C)28 D)40 E)50 SOLUTION:Explanation: Formula n(a∪b) = n(a) + n(b) − n(a∩b) Fail in Hindi or English = 25 + 50 – 25 = 50 Therefore students who passed = 100 – 50 = 50. Answer: E #### E QUESTION:Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought? options: A)20 B)18 C)24 D)26 E)28 SOLUTION:Smallest gumballs = (19-16) + (19-14) +19= 27 Largest gumballs = (25-16) + (25-14) +25= 45 Difference = 45 - 27 = 18 B #### B QUESTION:On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1? options: A) 8 B) 12 C) 24 D) 32 E) 36 SOLUTION:Jan 1 = C Feb 1 = C - 3 March 1 = C - 6 April 1 = C - 9 May 1 = C - 12 June 1 = C - 15 July 1 = C - 18 Aug 1 = C - 21 Sept 1 = C - 24 Difference between stock on September 1 than were in stock on January 1 will be - C - ( C - 24 )= 24 Hence answer will be (C) #### C QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)1 B)7 C)3 D)8 E)5 SOLUTION:40*(40/100) = 16 --- 64 ? --- 12 => Rs.3 Answer: D #### D QUESTION:A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 30%. Their gross income from sales for one month increases by what percent? options: A)9% B)11% C)13% D)15% E)17% SOLUTION:Let P be the original price and let x be the number of items sold originally. The original income is P*x. After the changes, the income is 0.9P*1.3x = 1.17*(P*x), an increase of 17%. The answer is E. #### E QUESTION:What is the units digit of 3333^(333)*3333^(222)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits. Here's another way to organize the information. We're given [(2222)^333][(3333)^222] We can 'combine' some of the pieces and rewrite this product as.... ([(2222)(3333)]^222) [(2222)^111] (2222)(3333) = a big number that ends in a 6 Taking a number that ends in a 6 and raising it to a power creates a nice pattern: 6^1 = 6 6^2 = 36 6^3 = 216 Etc. Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6. 2^111 requires us to figure out thecycleof the units digit... 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....). 111 = 27 sets of 4 with a remainder of 3.... This means that 2^111 = a big number that ends in an 8 So we have to multiply a big number that ends in a 6 and a big number that ends in an 8. (6)(8) = 48, so the final product will be a gigantic number that ends in an 6. Final Answer: D #### D QUESTION:Evaluate 35 / .07 options: A)400 B)500 C)505 D)None of these E)506 SOLUTION:Explanation: 35/.07 = 3500/7 = 500 Option B #### B QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall? options: A)120 B)350 C)1470 D)2,520 E)5,040 SOLUTION:Number of ways to choose 2 colors among 7 - 7c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 7c2 * 2* 7c4 = 1470 C #### C QUESTION:The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? options: A)2197 B)1267 C)1750 D)2267 E)1262 SOLUTION:Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000] = (4000 * 11/10 * 11/10 - 4000) = Rs. 840. Sum = (420 * 100)/(3 * 8) = Rs. 1750 Answer:C #### C QUESTION:A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? options: A)29% B)17% C)44% D)46% E)21% SOLUTION:g% = 10 + 10 + (10*10)/100 = 21% Answer: E #### E QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7 SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144. Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520. P = favorable/total = 2520/144 = 35/2. Answer: B. #### B QUESTION:A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 980gm. for a kg.His gain is …%. options: A)2.04% B)5.36% C)4.26% D)6.26% E)7.26% SOLUTION:His percentage gain is 100*20/980 as he is gaining 20 units for his purchase of 980 units. so 2.04%..ANSWER:A #### A QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)Monday SOLUTION:Explanation: Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer: Option C #### C QUESTION:A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route? options: A)12km B)15km C)18km D)24km E)Data Inadequate SOLUTION:time=distance/speed so, let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so, (x/4+y/3)+(y/6+x/4)=6 x+y=12 km. ANSWER:A #### A QUESTION:Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? options: A)2,145 B)6,435 C)12,100 D)2420 E)25,740 SOLUTION:Since we are given atleast one symmetric letter in the three letter word we can take the following cases 1. All two 2. One symmetry and other two non 4. All the two letters can be arranged in 2 ways ( 11c2+ 11c1 * 15c2) *2 ( 11*10/ 2 + 11 * 15 * 14 / 2 ) * 2 2420 IMO option D is the correct answer.. OA please...will correct if I missed anything..D #### D QUESTION:Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point? options: A)20sec B)15sec C)30sec D)24sec E)1min SOLUTION:They meet every 360/7+8 = 24sec Answer is D #### D QUESTION:Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: options: A)7/8 B)1/8 C)1/3 D)1/5 E)1/9 SOLUTION:Original share of 1 person =1/6 New share of 1 person =1/5 Increase =1/5 - 1/6 =1/30 Required fraction = (1/30)/(1/6)=1/5 Answer is D. #### D QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5 B)6 C)7 D)1 E)2 SOLUTION:160 = (180*4*R)/100 R = 5% Answer: A #### A QUESTION:There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ? options: A)120ways B)220ways C)420ways D)720ways E)520ways SOLUTION:By kept 3boys together(1) and arranging 4 girls with them 5! = 5*4*3*2*1 = 120ways. (i.e., 4+1 =5) Possible arrangements of 3 boys in following ways 3! = 3*2*1 = 6ways Now, arrange all with the boys together 120*6 = 720ways ANSWER:D #### D QUESTION:Find the value of a from (15)^2 x 8^3 ÷ 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 ÷ 256 = a = 225 x 512 ÷ 256 = 450 E #### E QUESTION:In "Clash Royal" App Game, Warrior "The Bomber" is a very good defensive options. It can be purchased from the card shop. The cost of the bomber is quite interesting. The Cost of 1st bomber is: 2 The Cost of 2nd bomber is: 4 The Cost of 3rd bomber is: 6 The Cost of 4th bomber is: 8 The Cost of 5th bomber is: 10 i.e to buy 5 bombers you need 2+4+6+8+10 = 30 coins. How many bombers can you buy using 1000 coins ? ? options: A)61 B)62 C)63 D)64 E)65 SOLUTION:Solution 62 The Cost of 1st bomber is: 2 i.e Total coins spend: 2 The Cost of 2nd bomber is: 4 i.e Total coins spend: 6 The Cost of 3rd bomber is: 6 i.e Total coins spend: 12 The Cost of 4th bomber is: 8 i.e Total coins spend: 20 The Cost of 5th bomber is: 10 i.e Total coins spend: 30 The Cost of 6th bomber is: 12 i.e Total coins spend: 42 The Cost of 7th bomber is: 14 i.e Total coins spend: 56 The Cost of 8th bomber is: 16 i.e Total coins spend: 72 The Cost of 9th bomber is: 18 i.e Total coins spend: 90 The Cost of 10th bomber is: 20 i.e Total coins spend: 110 The Cost of 11th bomber is: 22 i.e Total coins spend: 132 The Cost of 12th bomber is: 24 i.e Total coins spend: 156 The Cost of 13th bomber is: 26 i.e Total coins spend: 182 The Cost of 14th bomber is: 28 i.e Total coins spend: 210 The Cost of 15th bomber is: 30 i.e Total coins spend: 240 The Cost of 16th bomber is: 32 i.e Total coins spend: 272 The Cost of 17th bomber is: 34 i.e Total coins spend: 306 The Cost of 18th bomber is: 36 i.e Total coins spend: 342 The Cost of 19th bomber is: 38 i.e Total coins spend: 380 The Cost of 20th bomber is: 40 i.e Total coins spend: 420 The Cost of 21st bomber is: 42 i.e Total coins spend: 462 The Cost of 22nd bomber is: 44 i.e Total coins spend: 506 The Cost of 23rd bomber is: 46 i.e Total coins spend: 552 The Cost of 24th bomber is: 48 i.e Total coins spend: 600 The Cost of 25th bomber is: 50 i.e Total coins spend: 650 The Cost of 26th bomber is: 52 i.e Total coins spend: 702 The Cost of 27th bomber is: 54 i.e Total coins spend: 756 The Cost of 28th bomber is: 56 i.e Total coins spend: 812 The Cost of 29th bomber is: 58 i.e Total coins spend: 870 The Cost of 30th bomber is: 60 i.e Total coins spend: 930 The Cost of 31st bomber is: 62 i.e Total coins spend: 992 Answer B #### B QUESTION:If a/b = 6/5, Then (5a + 4b) / (5a - 4b) = ? options: A)4 B)7 C)5 D)3 E)6 SOLUTION:Answer Dividing numerator as well as denominator by b, we get Given Exp. = (5a + 4b) / (5a - 4b) = (5a/b + 4) / (5a/b - 4) Since a/b = 6/5 this implies that =[(5*6)/5 +4]/[(5*6)/5 -4)] = (6 + 4) / (6 - 4) = 5 Option: C #### C QUESTION:The fourth proportional to 14, 22 and 28 is? options: A)21 B)66 C)88 D)99 E)44 SOLUTION:(22*28)/14 = 44 Answer: E #### E QUESTION:10 books are placed at random in a shelf. The probability that a pair of books will always be together is - options: A)1/5 B)1/3 C)1/4 D)118/2 E)21/4 SOLUTION:10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Answer: C #### C QUESTION:A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number? options: A)297 B)187 C)278 D)200 E)267 SOLUTION:25 + 25 = 50 25% ------ 50 100% ----- ? => 200 Answer:D #### D QUESTION:What is value of (P + Q)/(P - Q) if P/Q = 7 ? options: A)1/3 B)2/3 C)4/3 D)5/3 E)None of these SOLUTION:Explanation: (P + Q)/(P - Q) = (P/Q+1)/(P/Q - 1) = (7 +1)/(7 - 1) = 4/3. Answer: C #### C QUESTION:If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average R (arithmetic mean) annual increase in the index over this period? options: A) (x + 100)/18 B) x/18 C) (100 − x)/18 D) (x − 100)/18 E) 100x/18 SOLUTION:CPI in end of 1967 = 100 CPI in end of 1985 = x Number of years = 18 Average annual increase in CPI R= (x-100)/18 Answer D #### D QUESTION:By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be: options: A)Rs. 2,600 B)Rs. 2,700 C)Rs. 2,800 D)Rs. 3000 E)NOne SOLUTION:Solution: Let Cost Price was X. X + 14% of X = 2850 X + 14X/100 = 2850 X + 0.14X = 2850 1.14X = 2850 X = 2500. So, Cost Price = Rs. 2500. Now, Selling Price When profit remains at 8%, = 2500 + 8% of 2500 = Rs. 2700. Short-Cut CP of bicycle = 100/114*2850 = Rs. 2500; SP for a profit of 8% = 108/100*2500 = Rs. 2700. Answer: Option B #### B QUESTION:How many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number? options: A)4 B)10 C)11 D)12 E)15 SOLUTION:The Question basically asks how many positive odd integers less than 100 are odd multiples of 5 So we have 5,15,25,35,45,55,65,75,85,95 =10 Ans B #### B QUESTION:A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15? options: A)3 B)4 C)5 D)8 E)9 SOLUTION:Explanation: 50 + 25 = 75/15 = 5 (Remainder) C #### C QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)$37.5 B)$40 C)$50 D)$48 E)$52 SOLUTION:Dividend on 1 share = $(10/100*50) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(100*2/25*5)=40 Thus, cost of 1 share =$40 option B #### B QUESTION:A man sells two articles for Rs.3600 each and he gains 40% on the first and loses 40% on the next. Find his total gain or loss? options: A)16% loss B)400 C)4000 D)324 E)8% LOSS SOLUTION:(40*40)/100 = 16%loss ANSWER:A #### A QUESTION:Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 4 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)18 D)12 E)6 SOLUTION:21-12 < no of hrs < 21-6 9< no of hrs < 17. D #### D QUESTION:Tom can hit a target 3 times in 6 shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4shots. What is the probability that at least 2 shots hit the target ? options: A)1/2 B)2/5 C)2/3 D)3/7 E)3/11 SOLUTION:Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by Karan hits tha target and Raja not hit the target. or Karan does not hit the target and Raja hits the target. or. Karan hits the target and Raja hits the target = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6 = 24/36 = 2/3 C #### C QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680? options: A)1500 B)2777 C)2889 D)27670 E)2771 SOLUTION:1680 = P [1 + (5*12/5)/100] P= 1500.Answer:A #### A QUESTION:If f(a)=5b, what is the value of (f(a)-f(6b)) ? options: A)32b B)25b C)6a-6b D)3a+2b E)52a SOLUTION:f(a)=5b f(6b) = 30b (f(6b)-f(a)) = 30b-5b = 25b Answer is B #### B QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is? options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) M + O = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv) Subtracting (ii) from (iv), we get M = 4000. M's monthly income = Rs. 4000 C #### C QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)20, 35, 48 E)None of these SOLUTION:Let the present ages are 4x, 7x, 9x. => (4x-8) + (7x-8) + (9x-8) = 56 => 20x = 80 => x = 4 So their present ages are: 16,28,36 ANSWER:B #### B QUESTION:P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last? options: A)5 days B)10 days C)14 days D)22 days E)26 days SOLUTION:Explanation : Work done by P in 1 day = 1/10 Work done by Q in 1 day = 1/6 Work done by P in 2 days = 2 × (1/10) = 1/5 Remaining work = 1 – 1/5 = 4/5 Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15 Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3 Total days = 2 + 3 = 5 Answer : Option A #### A QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)23% B)56% C)70% D)35% E)20% SOLUTION:C C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420 Profit = 420 - 125 = Rs. 295 Required percentage = 295/420 * 100 = 1475/21 = 70% #### C QUESTION:A train 120 m long running at 60 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)213 B)298 C)350 D)726 E)267 SOLUTION:D = 60 * 5/18 = 20 = 333 – 120 = 213 Answer: A #### A QUESTION:A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? options: A)66 2/3 % B)33 7/3 % C)33 1/3 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer: A #### A QUESTION:If d<0, which of the following represents a positive number? options: A)d|d| B)|d|d C)|d|/d D)-d|d| E)d/ |d| SOLUTION:Answer : D #### D QUESTION:A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work? options: A)5 days B)21 days C)15 days D)25 days E)30 days SOLUTION:Explanation: WC = 2:1 2x + x = 1/14 => x = 1/42 2x = 1/21 A can do the work in 21 days. Answer: B #### B QUESTION:An employer has 4 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection? options: A)a) 1,490 B)b) 132 C)c) 120 D)d) 60 E)e) 23 SOLUTION:4C3 * 4C2 = 24. Answer C. #### C QUESTION:The average (arithmetic mean) of four numbers is 5x + 3. If one of the numbers is 2x, what is the average of the other three numbers? options: A)x + 1 B)3x + 3 C)4x + 1 D)5x + 3 E)6x + 4 SOLUTION:The sum of all four numbers is 4 * (5x + 3) = 20x + 12. If one of the numbers is 2x, the sum of the other 3 numbers is 18x+12. The average of the remaining three numbers is (18x+12)/3 = 6x+4. The answer is E. #### E QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)? options: A)0 B)20 C)75 D)5 E)10 SOLUTION:Explanation : Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0 Answer : A #### A QUESTION:Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? options: A)129 B)128 C)189 D)187 E)112 SOLUTION:CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135 SP = CP[(100 + profit%)/100] = 135 * [(100 + 40)/100] = Rs. 189. Answer: C #### C QUESTION:A man's age is 125% of what it was 10 years ago, but 83 X 1/3% of what it will be after 10years. What is his present age? options: A)20 B)60 C)50 D)70 E)80 SOLUTION:C 50 Let the age before 10 years =x Then, 125x/100=x+10 ⇒125x=100x+1000 ⇒x=1000/25=40 Present age =x+10=40+10=50 #### C QUESTION:If a book is sold at 5% profit instead of 5% loss, it would have brought Rs 13 more. Find out the cost price of the book options: A)75 B)72 C)130 D)70 E)80 SOLUTION:Let C.P. of the book be Rs. ’X’ Given, 1.05 X - 0.95X = 13 => 0.1 X = 13 = 13/0.1 = Rs 130 ANSWER:C #### C QUESTION:If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars? options: A)3⁄20 B)11⁄60 C)9⁄40 D)1⁄5 E)2⁄15 SOLUTION:Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car. Half of them are men, and the other half are women, more precisely 60. It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total. Answer E #### E QUESTION:TOM traveled the entire 60 miles trip. If he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour? options: A)20mph B)24mph C)30mph D)40mph E)42mph SOLUTION:avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (12+48) / ((12/24)+(48/48)) = 60*2/3 = 40mph D #### D QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)26% C)42% D)27% E)22% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer: A #### A <<<Examples ends QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? options: A)165 B)161 C)162 D)163 E)164 SOLUTION:To minimize one quantity maximize other. 164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165. Answer: A. #### A QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)7508 C)7528 D)7527 E)7232 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 Answer:A #### A QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:In how many ways letters of the word LEADER be arranged? options: A)5 B)78 C)69 D)58 E)120 SOLUTION:LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways E #### E QUESTION:The sum of first nine prime numbers is? options: A)12 B)100 C)24 D)28 E)30 SOLUTION:Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23) = 100. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. B #### B QUESTION:David obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? options: A)75 B)27.6 C)66.6 D)16.5 E)11 SOLUTION:Explanation: Average = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6. Answer:C #### C QUESTION:If 13 = 13w/(1-w) ,then (4w)2 = options: A)1/4 B)1/2 C)1 D)2 E)4 SOLUTION:13-13w=13w 26w=13 w=1/2 4w=2 4w*2=2*2=4 ANSWER:E #### E QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 66900. What is his profit percent? options: A)22 B)77 C)18 D)21.6 E)88 SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 66900 Profit(%) = (66900 - 55000)/55000 * 100 = 21.6% Answer: D #### D QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer:A #### A QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60 total S=84 outcomes D #### D QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? A. 30 km/hr B. 45 km/hr options: A)11 B)78 C)60 D)28 E)81 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.Answer: C #### C QUESTION:If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5+a^6)? options: A)-14 B)-4 C)-1 D)4 E)14 SOLUTION:if a = -1, then putting values in equation = -[ (-1)^2 + (-1)^3 + (-1^4) + (-1^5)+(-1^6) ] = -[ 1 - 1 + 1 - 1 + 1] = -1 Answer = C = -1 #### C QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)10 m B)16 m C)245 m D)19 m E)235 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: E #### E QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle? I. 4 II. 12 III. 24 options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only SOLUTION:Answer = A. I, II, and III With dimensions of only 2 sides given (for a triangle), this becomes an open ended question Any area is possible out of the three #### A QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)20% B)30% C)40% D)50% E)60% SOLUTION:(SP of 33m)-(CP of 33m)=Gain=SP of 11m SP of 22m = CP of 33m Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33. Gain%=[(11/22)*100]%=50% ANSWER D #### D QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => |x-2| < 6. Hence, answer is D #### D QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? options: A)45 B)33 1/3 C)27 D)16 2/3 E)15 SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x: 1.5/x = 1/20 x = 30 Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution. Answer is A. #### A QUESTION:If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks. options: A)120 MILES B)130 MILES C)140 MILES D)150 MILES E)160 MILES SOLUTION:LET ORIGINAL SPEED BE V AND TIME TAKEN BE T... AS DISTANCE BETWEEN TWO POINTS IS CONSTANT, 30*(T-1)=20*(T+1)=V*T HENCE, V=24MILE/HR T=5 HRS DISTANCE BETWEEN TWO POINTS IS 120 MILES ANSWER:A #### A QUESTION:Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 6 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 6 questions did Zachary answer correctly? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:i got two equations: 3x-2y=25 x+y=6 3x-2(6-x)=25 3x-12+2x=25 5x=37 x=7.4 or between 7 and 8. (ANS B) #### B QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result? options: A)600 B)480 C)538 D)650 E)560 SOLUTION:23th result = sum of 45results - sum of 44 results 10*45-16*22+20*22 = 450-352+440 = 538 Answer is C #### C QUESTION:Find the number of solutions for 3x+4y=60, if x and y are positive integers options: A)1 B)2 C)3 D)4 E)5 SOLUTION:3x+4y=60 =>x=(60-4y)/3 as x and y are positive integers, put y=1,2,3,... & find x y=3,x=16 y=6,x=12 y=9,x=8 y=12,x=4 (x,y)=(4,12),(8,9),(12,6),(16,3) only 4 solution ANSWER:D #### D QUESTION:A man buys s cycle for $100 and sells it at a loss of 10%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 90% of the $100 = 90/100 * 100 = $90 Answer is E #### E QUESTION:Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b? options: A)5 B)6 C)11 D)16 E)19 SOLUTION:The number of possible permutation without 2 in the first digit is 4X4X3X2X1=96 ways. The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways. 18c1/96c1 = 18/96= 3/16= > a+b=19. ANSWER:E #### E QUESTION:A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)22 B)20 C)88 D)71 E)10 SOLUTION:x ------- 12 (x + 10) ---- 6 x * 12 = (x + 10)6 x = 10 \Answer: E #### E QUESTION:What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58 ? options: A)1288 B)2797 C)3944 D)1299 E)1082 SOLUTION:Let the side of the square plot be 'a' ft. Given area of the plot (a x a) = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 x 58 = Rs. 3944. Answer: C #### C QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score? options: A)662 B)672 C)654 D)642 E)721 SOLUTION:8 * 83 = 664 – 10 = 654 ANSWER:C #### C QUESTION:The present ratio of students to teachers at a certain school is 35 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:We are given that the ratio of students to teacher is 35 to 1. We can rewrite this using variable multipliers. students : teachers = 35x : x We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation: Students/Teachers  25/1 = (35x + 50)/(x + 5) If we cross multiply we have: 25(x + 5) = 35x + 50 25x + 125 = 35x + 50 7.5 = x x~8 Since x is the present number of teachers, currently there are 8 teachers. Answer B. #### B QUESTION:2, 4, 6, 8, 10, ? options: A)10 B)14 C)16 D)12 E)24 SOLUTION:The sequence is a series of even numbers, 2, 4, 6, 8, 10, 12.... Answer : D. #### D QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is: options: A)400 B)500 C)600 D)800 E)1000 SOLUTION:Let the sum be $. P. (P(1+10/100)^2-P)=525 P((11/10)^2-1)=2500 SUM = 2500 So SI = 500 ANSWER B #### B QUESTION:A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train. options: A)15 kmph B)36 kmph C)21 kmph D)17 kmph E)19 kmph SOLUTION:Let the speed of the goods train be x kmph. Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours 10x = 4 x 90 or x =36. So, speed of goods train = 36kmph. Ans: B #### B QUESTION:A group of 11 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase? options: A) E/(12 - n) B) (12 - n)/E C) E/[12(12-n)] D) nE / [11(11-n)] E) (12-n)E/(12n) SOLUTION:total cost =E no of people willing to participate initially =11 initial cost for each =E/11 when n people decided not to participate Cost for each =E/11-n D #### D QUESTION:The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)8:9 B)B)3:5 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 6x and 8x years respectively. Then, 8x - 6x = 4 => x =2 Required ratio = (6x + 4) : (7x + 4) 16 : 18 = 8:9 ANSWER:A #### A QUESTION:At what time between 4 & 5 will the hands of a watch point in opposite directions? options: A)50 min past 4 B)42 5/11 min past 4 C)43 min past 4 D)40 min past 4 E)50 4/11 min past 4 SOLUTION:At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30min. spaces apart. Minute hand will have to gain 5 min. spaces. 55min spaces are gained in 60 min. 5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min. Required time = 54 6/11 min. past 4. Answer is E #### E QUESTION:A thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 15km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ? options: A)A)1km B)B)300m C)C)650m D)D)750m E)E)800m SOLUTION:Relative speed of the policeman = 20-15 = 5 km/hr time taken by policeman to cover 100m = (100/1000)*(1/5) = 1/50 hr In 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m Answer is B #### B QUESTION:A certain basketball team that has played 2/3 of its games has a record of 18 wins and 2 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games? options: A) 7 B) 6 C) 5 D) 4 E) 3 SOLUTION:18 wins, 2 losses - total 20 games played. The team has played 2/3rd of all games so total number of games = 30 3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 2 games so it can lose another 5 at most. Answer (C) #### C QUESTION:A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? options: A)35 hours B)25 hours C)20 hours D)Cannot be determined E)None of these SOLUTION:Suppose the efficiencies of pipes C, B and A are 4K, 2K and K. Since, the tank is filled in 5 hours by the three pipes having combined efficiency equal to 7K, the time required to fill the tank by A alone = 7K×5 /K=35hours Answer A #### A QUESTION:In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000 SOLUTION:total vote = N vote cast by independent voters = 0.4 N vote cast by registered voters = 0.6 N vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N Answer choice E #### E QUESTION:Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters Look at this series: D12, H16, __, P24, T28, ... What number should fill the blank? options: A)H16 B)I17 C)J18 D)K19 E)L20 SOLUTION:E L20 In this series, the letters progress by 4, and the numbers increase by 4. #### E QUESTION:Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt? options: A)25/33 B)31/44 C)41/55 D)53/66 E)65/77 SOLUTION:Total possible ways to choose 4 students out of 12 = 12C4 = 495 The number of ways to choose 4 students with no green shirts = 9C4 = 126 P(no green shirts) = 126/495 = 14/55 P(at least 1 green shirt) = 1 - 14/55 = 41/55 The answer is C. #### C QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame? options: A)12 B)20 C)30 D)40 E)50 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so Area of frame = (1/2) * a^2 Area of Frame + Painting = a^2 + (1/2)*a^2 = (3/2)*a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2 so, b * sqrt2 = 6 so, b = 3 * sqrt2 b^2 = 18 we know that b^2 = (3/2)*a^2 so, a^2 = (2/3)*b^2 = (2/3)*18 = 12 And area of painting = a^2 = 12 So, answer will be A. #### A QUESTION:A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.45 B)8.45 C)7.45 D)3.45 E)1.45 SOLUTION:Explanation: 40*(46/100) = 18.4 --- 64 ? --- 12 => Rs.3.45 Answer: D #### D QUESTION:A baker filled with a measuring cup with 1/3 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with? options: A)1/8 cup B)3/8 cup C)11/24 cup D)1/2 cup E)7/8 cup SOLUTION:1/3 is the original water in cup .half in batter.So left is 1/6 out which 1/8 is spilled out.So again left with 1/24. so 50% more than what he started was = 1/3+1/2*(1/3)=1/2 Amount of water needed to add = 1/2 - 1/24=11/24 C #### C QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900 Vehicles inspected within 3 hours = 60*3/9 = 19 P = 19/900 Ans:D #### D QUESTION:A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple? options: A)1/5 B)2/7 C)2/9 D)3/5 E)4/11 SOLUTION:The total number of ways to choose 2 apples is 7C2 = 21 The number of ways that include the spoiled apple is 6C1 = 6 P(the spoiled apple is included) = 6/21 = 2/7 The answer is B. #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)12 B)72 C)48 D)99 E)11 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.75 + 1.25 = 3 km = 3000 m. Required time = 3000 * 3/125 = 72 sec. Answer: B #### B QUESTION:A man invests Rs. 5,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? options: A)Rs. 1200 B)Rs. 1300 C)Rs. 2500 D)Rs. 2000 E)None of these SOLUTION:Explanation : Interest on Rs.5000 at 5% per annum = ( 5000 × 5 × 1) / 100 = Rs. 250 Let his additional investment at 8% = x Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25. To earn 6% per annum for the total, interest = (5000 + x) × 6 × 1/100. => 250 + 2x/25 = (5000 + x) × 6 × 1/100. => 25000 + 8x = (5000 + x) × 6. => 25000 + 8x = 30000 + 6x. => 2x=5000. => x=2500. Answer : C #### C QUESTION:There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is options: A)10 B)15 C)16 D)13 E)18 SOLUTION:Explanation: abcbcd=3851001=>ad=513 abcbcd=3851001=>ad=513 So d = 13 D #### D QUESTION:A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the president? options: A) 1/720 B) 1/5 C) 1/10 D) 1/9 E) 1/6 SOLUTION:This question is much easier than it appears. Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the president is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the president is 1/10+1/10=2/10. Answer: B #### B QUESTION:How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length? options: A)12.9 sec B)12.1 sec C)24.2 sec D)16.8 sec E)14.9 sec SOLUTION:Speed = 36 * 5/18 = 10 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/10 = 24.2 sec. Answer: C #### C QUESTION:hat should come in place of question mark (?) in the following equation ? 197 × ? + 16(2) = 2620 options: A)22 B)12 C)14 D)16 E)None of these SOLUTION:? = 2620−256 /197=12 Answer B #### B QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 75 and n is not prime, what is the greatest possible value of f(n)? options: A)72 B)69 C)65 D)60 E)58 SOLUTION:Since we need the largest value of f (n), we will start with the largest option. Option A: 2*2*2*2*2*2 = . This is not a product of distinct prime numbers. Hence incorrect Option B: 69 = 3*23. This is a product of distinct prime numbers. Rest all the options are smaller that 69. Correct Option: B #### B QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:A person was going through train from Bombay to Pune. After every five minutes he finds a train coming from opposite direction. Velocity of trains are equal of either direction. If the person reached Pune in one hour then how many trains he saw in the journey ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:11 ANSWER:C #### C QUESTION:John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam four years ago? options: A)2 B)4 C)6 D)8 E)16 SOLUTION:j= 3s after 6 years j +6 = 2(s+6) j= 2s+6 2s +6 = 3s s= 6 four years ago s= 6-4= 2 A is the answer #### A QUESTION:One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ? options: A)Rs. 130,000 B)Rs. 150,000 C)Rs. 160,000 D)Rs. 140,000 E)None SOLUTION:EXPLANATION Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then, 1/3x=1/2(350000-x) => x/3 + x/2 = 175000 => 5x/6 = 175000 => x= 175000 x 6 /5= 210000 Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000 Answer D #### D QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time? options: A)70 min B)94 min C)110 min D)112 min E)120 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) And now we have 4 robots So Total = (1) + (2) = 70 minutes Answer - A #### A QUESTION:A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in : options: A)13 1/3 days B)16 days C)15 days D)20 days E)30 days SOLUTION:C alone can finish the work in 80 days. (A + B)can do it in 20 days (A + B)s 1 days wok = 1/20. As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2. A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30 (A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/80) = 1/16 All the three together will finish it in 16 days. ANSWER:B #### B QUESTION:In the exam the average was found to be p mark. After deducting typographical error the average marks of 94 student reduced from 84 to 64 . Due to this the average came down by 18.8 marks. What was the number of students who took the exam? options: A)100 B)120 C)110 D)130 E)160 SOLUTION:Explanation : Number of student = (84-64) * 94/18.8 = 100 Answer : A #### A QUESTION:A man can row upstream at 15 kmph and down strem 30 kmph. He takes 9 hours to row from lower point A to upper point B and back to A. What is the total distance traveled by him in 9 hours? He must return back to base point A in remaining time. options: A)80 B)120 C)140 D)180 E)200 SOLUTION:Upward distance traveled per hour - 15 km, distance traveled after 6 hours = 90 km. He remained with 3 hours travel downward, i.e. distance traveled in remaining 3 hours downward = 90 km so total distance traveled from A to B and Back to point A = 90 km upward + 90 km downhill = 180 km (Answer : D) #### D QUESTION:Two trains of length 120 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other? options: A)100/7 sec B)80/7 sec C)57/7 sec D)120/7 sec E)104/7 sec SOLUTION:Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps. The time required = d/s = (120 + 100 + 300)/35 = 520/35 = 104/7 sec. ANSWER:E #### E QUESTION:There are 9 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played? options: A)24 B)25 C)28 D)32 E)36 SOLUTION:9C2 = 36 The answer is E #### E QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed: options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(27 x 16)/3= 144. Birds killed by A =(5x/24) =(5/24*144)= 30. Answer is C. #### C QUESTION:Louie takes out a three-month loan of $2000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month? options: A)A)333 B)B)383 C)C)402 D)D)433 E)E)804 SOLUTION:Here's the calculation for that case, assume monthly payment is X. After 1st month: (2000)(1.1)-X = 2200-X After 2nd month: (2200-X)(1.1)-X = 2420-2.21X After 3rd month: (2420-2.21X)(1.1)-X = 2662-3.31X Now, the amount after the last payment in 3rd month must bring the total to 0. Hence: 2662-3.31X = 0 X = 2662/3.31 = 804 Answer E #### E QUESTION:If the height of a cone is increased by 100% then its volume is increased by? options: A)200% B)300% C)100% D)500% E)350% SOLUTION:Height of=>100% so increased by 100% ANSWER C #### C QUESTION:In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:6C3 = 6!/(3! . 3!) = (6 × 5 × 4)/(3 × 2) = 5 × 4 = 20 B) #### B QUESTION:If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available. options: A)35 7/8 B)36 C)21 3/7 D)34 5/7 E)34 6/7 SOLUTION:Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts. If we use 8 tons of cement, then we'll get 5/7*30 = 21 3/7 tons of mixture. Answer: C. #### C QUESTION:If the probability W of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period? options: A)8/125 B)2/25 C)5/16 D)8/25 E)3/4 SOLUTION:5C3 (1/2)^3(1/2)^2 = (5 * 4 * 3!)/2!3! * 1/32 W= 5/16 Answer - C #### C QUESTION:A man has Rs.680 in the denominations of two-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)160 B)40 C)680 D)120 E)180 SOLUTION:Let number of notes of each denomination be x. Then 2x + 5x + 10x = 680 17x = 680 x = 40 Hence, total number of notes = 3x = 120. Answer is D #### D QUESTION:Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings? options: A)1/2 B)1/4 C)1/6 D)1/8 E)1/16 SOLUTION:Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible). Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8. Answer: D. #### D QUESTION:In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater? options: A)600 B)640 C)680 D)720 E)760 SOLUTION:The number of seats in the theater is 15 + (15+2) + ...+ (15+38)= 20(15) + 2(1+2+...+19)= 20(15) + 2(19)(20)/2= 20(15+19) = 20(34) = 680 The answer is C. #### C QUESTION:A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)6 ½ sec B)6 ½ sec C)9 ½ sec D)8 sec E)7 ½ sec SOLUTION:D 8 sec D = 160 S = 72 * 5/18 = 20 mps T = 160/20 = 8 sec #### D QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? options: A)289 B)132 C)279 D)277 E)278 SOLUTION:2 * 22/7 * 14 = 88 88 * 1 1/2 = Rs.132 Answer: B #### B QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly? options: A)4 B)6 C)10 D)12 E)24 SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5∗150=90 2nd Question : four fifths of the remainder answered the second question correctly so 4/5∗(150−90)=4/5∗60=48 total students who answered at least one Q correct =90+48=138 so students who answered BOTH incorrectly = 150−138=12 ANSWER:D #### D QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:A certain fraction has the same ratio to 1/18, as 2/5 does to 7/9. What is this certain fraction? options: A)1/20 B)1/25 C)1/30 D)1/35 E)1/40 SOLUTION:x / (1/18) = (2/5) / (7/9) x = 2*9*1 / 18*5*7 = 1/35 The answer is D. #### D QUESTION:A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)28 sec B)16 sec C)36 sec D)18 sec E)17 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 240 + 120 = 360 m. Time taken = 360/10 = 36 sec. Answer:C #### C QUESTION:Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets. options: A)4 B)6 C)8 D)10 E)24 SOLUTION:I am getting 12. E. Hope havent done any calculation errors.. approach.. let y=no. of days taken by Y to do w widgets. Then X will take y+2 days. 1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day) Solving, we have y = 4 =>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets. Answer : E #### E QUESTION:A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 30% while buying and by 10% while selling. What is his percentage profit? options: A)10.22% B)20.22% C)21.22% D)30% E)Can't be calculated SOLUTION:The owner buys 100kg but actually gets 130kg; The owner sells 100kg but actually gives 90kg; Profit: (130-90)/90*100=30% Answer: D. #### D QUESTION:Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour? options: A)a) 66.67-x B)b) 40-x C)c) 80-2x D)d) 120-x E)e) 40-x/2 SOLUTION:Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same. Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of: R = (100 mi)/(1.5) = 66.67 mph That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars. One of the speeds is x, and let's call the other y. We want y. x + y = 66.67 y = 66.67 - x Answer =(A) #### A QUESTION:Calculate the percentage increase in the area of a square if each of its sides is increased by 15%? options: A)32.25% B)39.25% C)36.25% D)35.25% E)31.25% SOLUTION:Assume original length = 100m by 50m original area = 100*50= 5000 15% increase on each side l = 100 + 15 = 115 w = 50 + 7.5 = 57.5 new area = 115*57.5= 6612.5 increase in area = 6612.5 - 5000 = 1612.5 %increase =21% Answer A #### A QUESTION:A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday SOLUTION:This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B #### B QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2000 B)2879 C)2700 D)2797 E)2761 SOLUTION:(10*10)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer:A #### A QUESTION:Each of 435 bags contains at least one of the following three items: coconut, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only coconut and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item? options: A)256 B)260 C)316 D)320 E)350 SOLUTION:Fill the diagram step by step: coconut, almonds, and peanuts.PNGAlso given that there are total of 435 bags and 210 bags contain almonds. From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320. Answer: D. #### D QUESTION:If two numbers are in the ratio 4:5. If 10 is added to both of the numbers then the ratio becomes 5:6 then find the smallest number? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Explanation: 4:5 4x + 10 : 5x + 10 = 5 : 6 6[4x + 10] = 5[5x + 10] 24x + 60 = 25x + 50 25x - 24x = 60 - 50 x = 10 Then smallest number is =4 4x = 40 Answer: Option D #### D QUESTION:The inverse ratio of 4: 2: 1 is? options: A)2:4:8 B)2:3:9 C)2:3:2 D)2:3:6 E)2:3:1 SOLUTION:1/4: 1/2: 1/1 = 2:4:8 Answer:A #### A QUESTION:A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take? options: A)80 B)288 C)4^4 D)576 E)288^2 SOLUTION:The condition that TWO boys or TWO girls cannot be together means they should be alternate.. Total five means 3 of one and 2 of other.. 1) choose 3 girls and arrange them... 4C3*3! = 4!= 24 2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C2*2!= 12 Total ways = 24*12 = 288.. 2) same as above.. 2 girls and 3 boys.. 288 Total 288*2=576 ANS:D #### D QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer? options: A)55 B)25 C)85 D)45 E)35 SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer. Therefore 0+1+3+4+5+6+7+9=35 Answer is E #### E QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is? options: A)150 m B)778 m C)200 m D)276 m E)971 m SOLUTION:2(l + 150) = 600 => l = 150 m Answer:A #### A QUESTION:The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be options: A)12 years B)20 years C)25 years D)28 years E)None SOLUTION:Solution Let the present ages of son and father be x and (60 - x) years respectively. Then, (60 - x) - 6 = 5(x - 6) = 54 - x = 5x - 30 ‹=›6x = 84 ‹=›x= 14. ∴Son's age after 6 years = (x + 6) = 20 years. Answer B #### B QUESTION:A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo? options: A)10 B)12 C)15 D)20 E)30 SOLUTION:Two students can be selected from 6 in 6C2 =15 ways. Therefore, the teacher goes to the zoo 15 times. Option C is answer #### C QUESTION:What is the next number of the following sequence 2, 12, 4, 24, 8, 48, (...) options: A)10 B)12 C)16 D)20 E)22 SOLUTION:The series is 2*6=12 12/3=4 4*6=24 24/3=8 8*6=48 48/3=16 ANSWER: C #### C QUESTION:If c is 20% of a and 10% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 200% SOLUTION:Answer = E 20a/100 = 10b/100 b = 20a/10 = 200a/100 = 200% #### E QUESTION:A number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is: options: A)1220 B)1250 C)2030 D)22030 E)1350 SOLUTION:Required number = (555+445)*2*110+30 = 220000+30 = 220030. ANSWER:D #### D QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time? options: A)9 B)8 C)10 D)8.5 E)21 SOLUTION:63/3=21 Answer : E #### E QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job? options: A)6 B)13 1⁄2 C)17 D)Data inadequate E)None of these SOLUTION:12 M × 18 = 12 W × 18 × 3/1 \ w = 1/3 M 10M + 8W = 10M + 8 × 1/3M = 12 2/3 M \12 2/3 men can complete the same work in 12×18/12 2/3=17days Answer C #### C QUESTION:If Mason is now twice as old as Gunther was 5 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now? options: A)3G+14 B)3G+8 C)3G+15 D)3G+10 E)3G+9 SOLUTION:G is Gunther's current age. Let Mason's current age be M. given M = 2(G-5). four years from now Mason's age will be = 2(G-5) + 10 = 2G four years from now Gunther's age will be = G+10 Sum of ages of Mason and Gunther's after 4 years = 2G+G+10 = 3G+10 Ans : D #### D QUESTION:In how many years will a sum of money double itself at 10% per annum? options: A)2 years 4 months B)4 years 2 months C)8 years 4 months D)10 years 8 months E)None SOLUTION:Sol. Let sum = x. Then, S.I. = x ∴ Time = [100 * S.I. / P*R] = [100 * x / x * 12] years = 8 1/3 years = 8 years 4 months. Answer C #### C QUESTION:If m and n are positive integers, and m=2n and k=9m, then - options: A)k is a factor of m. B)2m is a factor of k. C)3m is a factor of k/2. D)m/2 is a factor of k. E)k is a factor of m/2. SOLUTION:m=2n --> m is even. k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k. Answer: D. #### D QUESTION:A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle? options: A)19 cm2 B)30 cm2 C)17 cm2 D)18 cm2 E)12 cm2 SOLUTION:The circumference of the circle is equal to the permeter of the rectangle. Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5 => x = 1 Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2 Answer:B #### B QUESTION:At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 4 receives how many more dollars per hour than an employee with a salary grade of 1? options: A)$0.75 B)$1.00 C)$1.25 D)$1.50 E)$1.75 SOLUTION:Salary grade of 4 is p(4)=9.50+0.25(4–1)=9.50+0.25*3; Salary grade of 1 is p(1)=9.50 + 0.25(1–1)=9.50; p(4)-p(1)=9.50+0.25*4-9.50=0.75. Answer: A. #### A QUESTION:A division of a company consists of six men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/11 D)5/12 E)7/15 SOLUTION:Total number of ways to select 2 members = 11C2 = 55 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/55 = 2/11 The answer is C. #### C QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet? options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location. In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same. Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle. Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate. The correct answer is (E). #### E QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer: B #### B QUESTION:If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 5 days. If he works at reduced efficiency, he can work without break and finish that same job in 5 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency? options: A)5/2 B)4/1 C)9/5 D)4/5 E)2/5 SOLUTION:We're told that there are 2 ways for Dale to complete a job: 1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 5 days. 2) Reduced Efficiency: 5 straight days with no days off. Working at Full Efficiency creates the following pattern: 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2= 5 days Totals: 4 days on, 1 days off Reduced Efficiency means that Dale will do 6 days of work in 5 days, thus those Reduceddaysare 4/1 of Full Efficiency. Answer : B #### B QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $8,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$61,500 B)$54,000 C)$21,000 D)$ 5,400 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 8200 less between 3 people(x-(8200*3))/3 Set both eq. equal to each other. 61,500 Answer A) #### A QUESTION:A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. options: A)15/7 B)4/17 C)7/18 D)19/6 E)7/15 SOLUTION:Let S be the sample space Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45 Let E=event of getting both balls of same colour Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4) =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21 P(E)=n(E)/n(S)=21/45=7/15 Option E #### E QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam. options: A)15 B)25 C)30 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 92(x - 5) 80x - (5 * 20) = 92(x - 5) 360 = 12x => x = 30 ANSWER:C #### C QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is? options: A)12 B)14 C)15 D)19 E)10 SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank. 1/x + 1/(x - 5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x- 15)(x - 3) = 0 => x = 15. Answer:C #### C QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 162 => x= 9 Answer: B #### B QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS: options: A)15 B)16 C)18 D)25 E)NONE OF THESE SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4 SUPPOSE TANYA TAKES X DAYS TO DO THE WORK; 5:4::20:X, X=(4x20/5), X=16 DAYS. CORRECT OPTION: B #### B QUESTION:A will states that the estate would be divided among six sons with the remainder donated to charity. One stipulation in the will is that no one among the sons can receive an amount within 12% of another's amount. If one of the beneficiaries received $30,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the six sons? options: A)$4096 B)$14043 C)$7892 D)$17736 E)$15336 SOLUTION:1st - 30,000. 2nd - 0.88*30,000 = 26,400 3rd - 0.88*26,400 = 23,232 4th - 0.88*23,232 = 20,444.16 5th - 0.88*20,444.16 = ~17,990.86 6th - 0.88*17,990.86 = ~15,831.96 Range = 30,000 - 15,831 = 14,168 Answer: B. #### B QUESTION:Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest? options: A)65% p.a B)88% p.a C)20% p.a D)66% p.a E)44% p.a SOLUTION:Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year. Rate of interest = (100 * 240) / (100 * 1) = 20% p.a Answer: C #### C QUESTION:The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 360 m, its area is? options: A)180 B)882 C)277 D)261 E)281 SOLUTION:5x + 12x + 13x = 360 => x = 12 a = 60, b = 144, c = 156 S = (60 + 144 + 156)/2 = 180 Answer: A #### A QUESTION:The total of the ages of Amar, Akbar and Anthony is 30 years. What was the total of their ages three years ago ? options: A)20 years B)28 years C)71 years D)21 years E)31 years SOLUTION:Explanation: Required sum = (30 - 3 x 3) years = (30 - 9) years = 21 years. Answer: Option D #### D QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:20, 19, 17, ?, 10, 5 options: A)14 B)15 C)13 D)18 E)17 SOLUTION:A 14 The Pattern is - 1, - 2, -3, ... #### A QUESTION:Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number? options: A)9 B)12 C)14 D)16 E)18 SOLUTION:Explanation: We have, 2/3 * 2/5 * 3/4 * X = 36 X = 180 Now, 4/5 * X ===> 4/5 * 180 = 144 √144 = 12 ANSWER: B #### B <<<Examples ends QUESTION:In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)32% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 38 are employed males,hence 26% are employed females. (employed females)/(total employed people)=26/64=40% Answer: D. #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 244 passengers. Find the no of passengers in the beginning? options: A)292 B)180 C)276 D)144 E)168 SOLUTION:Let no of passengers in the beginning be X After first station no passengers=(X-X/3)+280=2X/3 +280 After second station no passengers =1/2(2X/3+280)+12 1/2(2X/3+280)+12=244 2X/3+280=2*232 = 464 - 280 = 184 2X/3=184 X=276. So the answer is option C) 276. #### C QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers? options: A)1 B)5 C)7 D)8 E)9 SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6 y = mx + b => 12 2/3 = -22*5/6 + b => b = 31 y = -5x/6 + 31 Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point. A #### A QUESTION:3^b + 3^b + 3^b = options: A)7^b B)7^(b + 1) C)7^(7b) D)3^(b + 1) E)49^B SOLUTION:Easy one. 3*3^b = 3^(b+1) Ans. D #### D QUESTION:In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term? options: A) 192 B) 154 C) 134 D) 174 E) 120 SOLUTION:1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times) 6 + (3 x 63) = 3 + 189 = 192 Answer A #### A QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)45 E)55 SOLUTION:there are 9 books less(75-66) which represents 20% of the loaned books (100-80) So total loaned out books = 45 Answer D #### D QUESTION:1/2+[(2/3*3/8)+4]-7/16= options: A)29/16 B)19/16 C)69/16 D)9/13 E)0 SOLUTION:1/2+[(2/3*3/8)+4]-7/16= 1/2+[(1/4)+4]-7/16= 1/2+[17/4]-7/16= 8/16 + 68/16 - 7/16 = 69/16 C #### C QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:A password for a computer uses three digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero? options: A)1/32 B)1/16 C)1/8 D)2/5 E)1/2 SOLUTION:To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 = 1,000 possible combinations. Prime numbers constitute 2, 3 In addition to zero, this is 3 total possibility for each digit. So the number of satisfactory variants is 3× 3 × 3 . So the probability is 1/2 × 1/2 × 1/2 = 1/8. The right answer is choice (C). #### C QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in options: A)6 days B)2 days C)3 days D)5 days E)4 days SOLUTION:That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. C #### C QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.25000? options: A)8275 B)1879 C)2779 D)2672 E)2782 SOLUTION:A = 25000(11/10)^3 = 33275 = 25000 ---------- 8275 Answer: A #### A QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 15 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder? options: A) $204 B) $216 C) $220 D) $230 E) $240 SOLUTION:Wholesale cost of video recorder = 200 $ Video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 15 Emlpoyee paid = .85 * 240 = 204 $ Answer A #### A QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree. From the diagram, (36−x)2=x2+122(36−x)2=x2+122 ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144 ⇒72x=1296−144⇒72x=1296−144 ⇒x=16 Answer:A #### A QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:There are three foam generators in the factory, each of the first two can generate 8 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)146. D)154. E)115 SOLUTION:Let the foam generators capacity be - A = 8 lit/hr B = 8 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 34 lit ( 8 + 8 + 18 ) ; since in 1 and 1/2 hr they will generate 34 + 17 => 51 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 8 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 52 litres {2 (8+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 8 => 12 litres So, total foam generated will be 115 Litres ( 51 + 52 + 12 ) ; hence answer will be (E) #### E QUESTION:In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are finance majors? options: A)3 B)5 C)8 D)11 E)17 SOLUTION:pqrs = 1365 = 3* 5 *7 * 13 Since 1< p < q < r < s, the number of students who are finance majors is q = 5. The answer is B. #### B QUESTION:The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000? options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796. SOLUTION:30,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively. Only option B fulfills the condition and hence is the answer #### B QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.18000? options: A)6620 B)2888 C)2776 D)2997 E)5958 SOLUTION:A = 18000(11/10)^3 = 23958 = 18000 ---------- 5958 Answer: E #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ? options: A)24 B)17 C)18 D)9 E)11 SOLUTION:Explanation: Less Men, means more Days {Indirect Proportion} Let the number of days be x then, 72 : 36 :: 18 : x x = 9 Answer: D) 9 days #### D QUESTION:A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)120 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (9 - 8) = 1 km/hr. Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m. .'. Distance between the criminal and policeman = (265 - 50) m = 215 m. Answer : E #### E QUESTION:How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once? options: A)21 B)42 C)120 D)600 E)200 SOLUTION:Vowel: E O Consonants: V R M N T First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel) Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant) Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter Second letter can be filled in 5 Ways Third letter can be filled in 4 Ways So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200 Answer E #### E QUESTION:There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? options: A)941,1009 B)991,1001 C)991,1009 D)791,1009 E)931,1009 SOLUTION:999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a2-b2=(a+b)(a-b) =(1000+9)*(1000-9) = (1009)*(991) Given that number of cats is less than number if mice. So number of cats is 991 and number of mice were 1009 Answer C #### C QUESTION:A is twice as good a workman as B and together they complete a work in 12 days. In how many days A alone can do the work? options: A)32 B)33 C)34 D)35 E)36 SOLUTION:A’s one day’s work : B’s one day’s work= 2:1 (A+B)’s one day’s work= 1/12 B’s one day’s work= 1/12 *1/3 = 1/36 B alone can do the work in 36 days ANSWER:E #### E QUESTION:A committee of 3 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee? options: A)1/28 B)3/28 C)1/14 D)4/28 E)3/14 SOLUTION:3/8*4/7*1/6*3! = 3/14. We are multiplying by 3! because we can choose secretary, economist, and accountant is several way: SEA, SAE, ESA, EAS, ASE, AES. Answer: E. #### E QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 9 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)30/13 hours E)60/29 hours SOLUTION:Speed downstream = 20 + 9 = 29 kmph. Time required to cover 60 km downstream = d/s = 60/29 = 60/29 hours. Answer: E #### E QUESTION:A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit W on this shipment? options: A)a) $100 B)b) $115 C)c) $125 D)d) $130 E)e) $135 SOLUTION:I recommend one should use fractions to solve this one rather than converting it into decimals Sol: 1500 heads -> $600 1 head -> $600/1500 1 head -> $(2/5) 25% more of (2/5) -> 125/100 * 2/5 = $(1/2) He sold 2/3*1500 = 1000 heads for $(1/2) per head Total revenue by selling 1000 heads = 1000 * 1/2 = $500 Heads left: 500 Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20) Total revenue by selling 500 heads = 9/20 * 500 = 225 Total revenue after selling 1500 cabbage heads - 225+500 = $725 Money spent on the purchase: $600 Profit W= 725-600 = $125 Ans:C #### C QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean? I. 14.5 II. 15.3 III. 9.5 options: A)I only B)I and II only C)II only D)III only E)I and III only SOLUTION:Mean = 12 SD = 1.3 2 SD above mean = 12+2*1.3 = 14.6 2 SD below mean = 12-2*1.3 = 9.4 14.5 and 9.5 lies in the range of 2SD from mean Answer: Option C #### C QUESTION:What is the next number of the following sequence 7, 0, 1, 8, 5, 12, 9, 26, 3, 2, 23, ? options: A)28 B)29 C)30 D)31 E)32 SOLUTION:7,0,1,8,5,12,9,26,3,2,23,X (7,0,1,8),(5,12,9,26),(3,2,23,X) 7+0+1=8 5+12+9=26 3+2+23=X => X=28 ANSWER:A #### A QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.3 x = 4.8 Alternate solution: Try to backsolve. Initial volume = 4.8 After one hour --> (1/4)4.8 = 1.2 After two hours --> (1/4)1.2 = 0.3 Answer: C #### C QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/9 B)5/12 C)1/36 D)7/12 E)4/9 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 ANSWER:B #### B QUESTION:A student is ranked 13th from right and 8th from left.how many are there? options: A)18 B)19 C)20 D)21 E)22 SOLUTION:13th from right means = x + 12 8th from left means = 7 + x Total = 12+7+1 = 20 ANSWER:C #### C QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble? options: A)134 B)167 C)125 D)113 E)111 SOLUTION:C lb : reverse the calculations: So 48.75 ÷ 0.75 = 65, 65 ÷ 0.8 = 81.25 and 81.25 ÷ 0.65 = 125. #### C QUESTION:A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 kmph B)7.5 kmph C)8 kmph D)9 kmph E)4 kmph SOLUTION:US = 20 DS = 35 M = (35 - 20)/2 = 7.5 Answer:B #### B QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)7 cm B)6 cm C)4 cm D)3 cm E)9 cm SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer: E #### E QUESTION:A single discount equivalent to the discount series of 10%, 10% and 5% is? options: A)23.05 B)31.95 C)21.65 D)23.45 E)23.15 SOLUTION:100*(90/100)*(90/100)*(95/100) = 76.95 100 - 76.95 = 23.05 Answer: A #### A QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)8 B)10 C)12 D)14 E)15 SOLUTION:Number of ways in which one can travel from P to R =3×4=12 Answer: Option C #### C QUESTION:A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)36 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=288/32=9 m/s Distance covered by B in 4 seconds = Speed × time =9×4=36 metre i.e., A beat B by 36 metre Answer is E #### E QUESTION:A train 120 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)443 m B)354 m C)450 m D)380 m E)250 m SOLUTION:D 350 D = 72 * 5/18 = 25 = 500 – 120 = 380 #### D QUESTION:X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 8. What is the value of Z? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2. X + 3Y + 3Z = 5Y + 8 Z+2+3Z+3+3Z = 5Z+5+8 2Z = 8 Z = 4 The answer is C. #### C QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second? options: A)1234 B)1567 C)1349 D)1456 E)1356 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have? options: A)27 B)32 C)43 D)54 E)77 SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys 49 - 5 = 44 for Tom and Bob If distributed equally, each one will have 44 / 2 = 22 toys Bob has 5 more toys than Tom, so Bob has 22 + 5 = 27 toys correct answer A #### A QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B #### B QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 7*1+1 (7*1+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:In the faculty of Reverse-Engineering, 100 second year students study numeric methods, 100 second year students study automatic control of airborne vehicles and 25 second year students study them both. How many students are there in the faculty if the second year students are approximately 50% of the total? options: A)340 B)335 C)370 D)360 E)350 SOLUTION:Total number of students studying both are 100 + 100 - 25 = 175 (Subtracting the 25 since they were included in the both the other numbers already). So 50% of total is 175, so 100% is 350 Answer is E #### E QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/95 B)33/91 C)33/94 D)33/16 E)33/17 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:B #### B QUESTION:A shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal? options: A)18% B)20% C)17% D)18% E)None of these SOLUTION:Explanation: Let the CP of the article = Rs.100. Then labeled price = Rs.130. SP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117. Gain = Rs.117 – Rs.100 = Rs.17 Therefore, gain/profit percent = 17%. Answer: Option C #### C QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)165 B)771 C)245 D)177 E)121 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer: C #### C QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.) options: A)4 B)5 C)6 D)12 E)24 SOLUTION:Let's start with 4 minimum number of colors So single color code we can make 4 nos. Now if we need to make 2 color combination out of 4 we can do so in 4!/2!*2! or 4*3/2 or 6 So total we can make 4+6=10 color combinations but we have 12 boxes So let's look at 5 we get 5 single color codes and out 5 color choices, we can choose 2 in 5!/2!*3! ways or 10 ways. So total we can have 5+10=15 color combinations. So, minimum number we need will be 5 Ans is B....... #### B QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 2x+ 2y > 2z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 2x+ 2y > 2z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B #### B QUESTION:Two trains 200m and 250m long run at the speed of 72kmph and 18kmph in opposite directions in parallel tracks. The time which they take to cross each other is? options: A)5.6sec B)8.9sec C)10.8sec D)12.6sec E)18 sec SOLUTION:Relative speed = 72+18 = 90 kmph * 5/18 = 25 m/s Distance covered in crossing each other = 200+250 = 450m Required time = 450*1/25 = 18 sec Answer is E #### E QUESTION:What is the smallest positive integer x, such that 1944x is a perfect cube? options: A)4 B)3 C)8 D)12 E)18 SOLUTION:Take out the factors of 1944 that will come 2^3*3^3 *3^2. for perfect cube you need every no. raise to the power 3. for 1944 to be a perfect cube, need 1 3 that means =3 B is the answer. #### B QUESTION:A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:√(36)^2 options: A)6 B)14 C)36 D)21 E)None of these SOLUTION:explanation √(36)^2 =? or, ? = 36 Answer C #### C QUESTION:What is the smallest number which when increased by 3 is divisible by 27, 35, 25, & 21 ? options: A)4722 B)4725 C)4728 D)4731 E)4733 SOLUTION:Here smallest number means LCM Hence LCM of 27,35,25,21 = 3^3 x 5^2 x 7 = 4725 Therefore required number is 4725 - 3 =4722 Ans - A #### A QUESTION:Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 43 kmph. For how many minutes does the bus stop per hour? options: A)70 min B)16 min C)20 min D)8.4 min E)40 min SOLUTION:D 8.4 min Due to stoppages, it covers 7 km less. Time taken to cover 9 km = (7/50 x 60) min = 8.4 min #### D QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)2.5 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 + x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 Answer:E #### E QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is? options: A)25/42 B)25/46 C)25/41 D)25/49 E)25/23 SOLUTION:Total fruits = 9 Since there must be at least two apples, (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42. Answer:A #### A QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 10 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? options: A)17.14286 min B)62 min C)70.1346 min D)74 min E)76.1346 min SOLUTION:x=time for type B prolems 2x=time for type A problem total time=3hrs=180min 190x+10*2x=180 x=180/210 x=0.72 time taken for type A problem=10*2*0.857143=17.14286min ANSWER:A #### A QUESTION:The price of 357 mangoes is Rs. 1517.25 what will be the approximate price of 9 dozens of such mangoes ? options: A)Rs. 3000 B)Rs. 3500 C)Rs. 4000 D)Rs. 2500 E)None of these SOLUTION:Solution Let the required price be Rs. x. Then, More mangoes, More price ∴ 357 : (49 × 12) : : 1517.25 : x ⇔ 357 x = (49 × 12 × 1517.25) ⇔ x = 49x12x1517.25/357⇔ x = 2499. Hence, the approximate price is Rs. 2500 . Answer D #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)11% B)25% C)87% D)19% E)12% SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:The successive discounts 20% and 15% are equal to a single discount of? options: A)43% B)72% C)32% D)44% E)29% SOLUTION:C 32% Let the CP of an article be Rs. 100 Given that successive discounts are 20% and 15%. SP = 85% of 80% of 100 = (85/100)(80/100)(100) => SP = Rs. 68 Clearly, single discount is 32%. #### C QUESTION:Machine T can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? options: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33 SOLUTION:Let the following be true: T makes x in time t Then the following follows: N makes x in 4t/3 O makes x in 3/2(4t/3) = 2t M:N:O = 1:4/3:2=3:4:6 So N=4/(3+4+6)=4/13=C #### C QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ? options: A)118 B)290 C)119 D)139 E)132 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer:C #### C QUESTION:Rs.12320 were divided among W, X & Y in such a way that W had Rs.640 more than X and Y had Rs 480 more than X . How much was X’s share? options: A)Rs.4590 B)Rs.4610 C)Rs.4620 D)Rs.4630 E)Rs.4640 SOLUTION:Let X gets Rs x. Then We can say W gets Rs (x + 640 ) and Y gets Rs ( x + 560) . x + 640 + x + x + 1120 = 12320 3x = 10560 x = 3520 . C’s share = Rs ( 3520+1120 ) = Rs.4640 E #### E QUESTION:Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? . options: A)20 B)30 C)50 D)80 E)100 SOLUTION:150 employees 80 are full-time 100 have worked at company X for at least a year 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? 150-80=70 employees not full time 70-20= 50 employees not full time who worked over a year 100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year ANSWER:C #### C QUESTION:How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest? options: A)2.35 years B)4.25 years C)7 years D)1.25 years E)2 years SOLUTION:Explanation: Time = (100 x 60)/(400 x 12) years = 1.25 years. Answer: D #### D QUESTION:Find a a prime number the options below. options: A)78 B)80 C)81 D)82 E)83 SOLUTION:Clearly, 83 is a prime number. E #### E QUESTION:A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed? options: A)32 B)88 C)67 D)11 E)66 SOLUTION:One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10 Remaining work = 7/10 The number of days required for this initial work = 7 days. The total number of days required = 4 + 7 = 11 days. Answer:D #### D QUESTION:If n ≠ 0, which of the following must be greater than n? I. 2n II. 2 - n III. n^2 options: A)I only B)II only C)I and II only D)II and III only E)None SOLUTION:n ≠ 0 => n = negative or n = positive if n = negative: 2n < n (n = -1 then 2n = -2 => -2 < -1) n^2 > n (n =-1 then n^2 = 1 => n^2 > n) 2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n) but if n = positive: n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II 2 - n < n(n =2 then 2-2 = 0) => only III =>answer is E #### E QUESTION:A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? options: A)230 B)288 C)267 D)256 E)298 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer: A #### A QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 20 years = (20 + 20) years =40 years. Answer : C #### C QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)24 B)66 C)55 D)88 E)61 SOLUTION:(15*18)/12 = 24 Answer:A #### A QUESTION:5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3294, how much was it in the beginning? options: A)2988 B)2776 C)4079 D)2871 E)881 SOLUTION:X * (95/100) * (85/100) = 3294 X = 4079 Answer:C #### C QUESTION:By selling 20 pens for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%? options: A)8.76 B)10.76 C)8.76 D)9.76 E)5.76 SOLUTION:70% --- 20 130% --- ? 70/130 * 20 = 10.76 Answer: B #### B QUESTION:Four persons enter the lift of a six storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor options: A)625 B)1296 C)1540 D)1478 E)360 SOLUTION:Each person out of 4 has 5 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 5*5*5*5=5^4=625. Answer: A. #### A QUESTION:If the sum of a number and its square is 132, then what is the number? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Explanation: Let the number be x. Then, x2 + x = 132 => x2 + x - 132 = 0 => (x + 12)(x - 11) = 0 => x = 11 Answer: Option B #### B QUESTION:Convert 50miles into yards? options: A)25630 yards B)35200 yards C)88000 yards D)42560 yards E)41520 yards SOLUTION:1 mile = 1760 yards 50 miles = 50*1760 = 88000 yards Answer is C #### C QUESTION:If x and y are integers and x=50y + 49, which of the following must be odd? options: A)xy B)x + y C)x + 4y D)3x-1 E)3x+1 SOLUTION:x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd you don't know whether Y is even or odd, so you need to try. A: odd * even = even ; odd*odd= odd ->not true B: odd + odd = even ; odd+even = odd -> not true C: odd + 4*odd = odd ; odd + 2*even = odd -> TRUE, stop here. D&E -- EVEN Answer C #### C QUESTION:Which of the following will give a non-integer on taking cube root? options: A)–64 B)–1 C)8 D)9 E)27 SOLUTION:all except 9, square root of 9 is 3 which is an integer but cube root is not an integer so answer is D #### D QUESTION:A person travelled from his house to office at 45km/hr and office to house at 55km/hr. Then find the average speed? options: A)49km/hr B)49.5km/hr C)50km/hr D)50.5km/hr E)51km/hr SOLUTION:Average speed = (2*45*55)/(45+55) = 49.5km/hr Answer is B #### B QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:How many 4's are there in the following series which are preceded by 7, but are not preceded by 8? 3 4 5 7 4 3 7 4 8 5 4 3 7 4 9 8 4 7 2 7 4 1 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:count 1 - - - - - - 7 4 3 count 2------------748 count 3------------749 count 4------------741 ANSWER:D #### D QUESTION:The mean of 50 observations was 36. It was found later that an observation 43 was wrongly taken as 23. The corrected new mean is options: A)35.2 B)36.1 C)36.2 D)36.4 E)None SOLUTION:Solution Correct sum= (36x50+43-23) = 1820. ∴ Correct mean= 1820 / 50 = 36.4. Answer D #### D QUESTION:Two hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 400 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(200) / 400 = 25% The answer is B. #### B QUESTION:There are 3 classes having 20, 24 and 30 students respectively having average marks in an examination as 20,25 and 30 respectively. The three classes are represented by A, B and C and you have the following information about the three classes. a. In class A highest score is 22 and lowest score is 18 b. In class B highest score is 31 and lowest score is 23 c. In class C highest score is 33 and lowest score is 26. options: A)can't be determined in both cases B)definite decrease in both cases C)definite increase in both cases D)will remain constant in both cases E)will remain constant in both cases21 SOLUTION:Ans: B Explanation: Class A average is 20. And their range is 18 to 22 Class B average is 25. And their range is 23 to 31 Class A average is 30. And their range is 26 to 33 If 5 students transferred from A to B, A's average cannot be determined but B's average comes down as the highest score of A is less than lowest score of B. If 5 students transferred from B to C, C's average cannot be determined the B's range fo marks and C's range of marks are overlapping. Answer:A #### A QUESTION:Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day A on which the buses leave at the same time. options: A)A=Tuesday B)Wednesday C)Thursday D)Sunday E)A=The busses will never leave at the same time SOLUTION:The answer is E. I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide. Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E #### E QUESTION:X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13750 ? options: A)3200 B)4000 C)3250 D)3825 E)3985 SOLUTION:Ratio of investment, as investments is for different time. Investment x Number of units of time. Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8. X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16. Ratio of investments => X : Y : Z = 18 : 21 : 16. Investment Ratio = Profit sharing Ratio. Z = 13750 × 16/55 = Rs.4000. Share of Z in the profit is Rs.4000. Option B #### B QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is: options: A)14 B)7 C)20 D)70 E)35 SOLUTION:Explanation : Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2. Number of Apples = 10x = 20. Answer : C #### C QUESTION:If n is an integer and 5^n > 4,000,000, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:When you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8 2 to the ^ 8 = 256 so its 256 x 5^6 that means 5^6 x 5^x must be greater 5^x > 256 5^1=5 5^2=25 5^3= 125 5^4= 625 - > so x must be at least 4 5^(6+4)= 5^10 ANSWER:D #### D QUESTION:If the length of the sides of two cubes are in the ratio 2:1, what is the ratio of their total surface area? options: A)2:1 B)3:1 C)4:1 D)6:1 E)8:1 SOLUTION:Let x be the length of the small cube's side. The total surface area of the small cube is 6x^2. The total surface area of the large cube is 6(2x)^2=24x^2. The ratio of surface areas is 4:1. The answer is C. #### C QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank? options: A)50% B)40% C)33.5% D)37.5% E)None of these SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8 ∴ required% = 3A⁄ (8 × A) × 100 = 37.50% Answer D #### D QUESTION:In what time will a train 100 meters long cross an electric pole, if its speed is 126 km/hr options: A)8.5 seconds B)2.86 seconds C)3.5 seconds D)2.5 seconds E)2.6 seconds SOLUTION:First convert speed into m/sec Speed = 126*(5/18) = 35 m/sec Time = Distance/speed = 100/35 = 2.86 seconds Answer: B #### B QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet? options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m SOLUTION:D = 50 * 1 ½ = 75 km RS = 75 – 50 = 25 T = 75/25 = 3 h 3.30 + 3 h = 6.30 p.m. Answer: C #### C QUESTION:If two-third of a bucket is filled in one minute then the time taken to fill the bucket completely will be . options: A)90 seconds B)70 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 1 mint 1/3 filled in 1/2 mint thn 2/3+1/3=1 in mint 60 sec+30 sec=90 sec ANSWER:A #### A QUESTION:Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter? options: A)201 B)132 C)772 D)592 E)261 SOLUTION:2 * 22/7 * 16 = 100.5 100.5 * 2 = Rs.201 Answer: A #### A QUESTION:The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of options: A)20% B)19% C)18% D)11% E)10% SOLUTION:Say the original price of the TV was $p, then the final price would be (0.9p)∗0.9=0.81p. Therefore the original price was discounted by 19%. Answer: B. #### B QUESTION:In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg? options: A)16 : 30 B)30 : 14 C)16 : 31 D)31 : 15 E)15 : 31 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (31.50 - 23.75) / (23.75 - 20) = 31/15 ANSWER:D #### D QUESTION:Find the odd man out.10, 25, 45, 50, 66, 70, 80 options: A)45 B)50 C)66 D)70 E)80 SOLUTION:Each of the numbers except 66 is multiple of 5. ANSWER :C #### C QUESTION:What is the Compound Interest on Rs.7000 at 8.5% p.a. compounded half-yearly for 5 years. options: A)3616.5 B)3613.5 C)3313.5 D)3616.5 E)3113.5 SOLUTION:Compound interest : A = P(1 + r/n)nt A = 10,613.50 C.I. >> 10,613.50 - 7000 >> Rs. 3613.5 Answer:B #### B QUESTION:Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100) options: A)1/15 B)1/17 C)1/20 D)1/21 E)3/25 SOLUTION:Option 'C' (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100) 5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20 #### C QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:A disease has infected an ant colony that consists of "workers" and "soldiers": 30% of the soldiers and 14% of the "workers" were infected. If that colony is inhabited by 7000 ants, out of which 1700 are infected, how many "workers" inhabit the colony? options: A)1500 B)2500 C)2750 D)3000 E)3250 SOLUTION:From two question we get wo equations: (1) 0,3s + 0,14w = 1700 (2) s + w = 7000 From (2) we get w=7000-s In (1) 0,3s + 980-0,14s= 1700 0,16s=720 72000:16= 4500 =s In (2) 4500 + w = 7000 w= 2500 ANSWER:B #### B QUESTION:If f(a)=5b, what is the value of (f(a)-f(6b)) ? options: A)32b B)25b C)6a-6b D)3a+2b E)52a SOLUTION:f(a)=5b f(6b) = 30b (f(6b)-f(a)) = 30b-5b = 25b Answer is B #### B QUESTION:220% of a number X is 44. What is 44% of X. options: A)8.8 B)8.9 C)6.6 D)7.7 E)None SOLUTION:Solution: Given, 220% of X = 44 Or, X = 20. Thus, 44% of 20 = (44 *20) /100 = 8.8 Answer: Option A #### A QUESTION:A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in : options: A)13 1/3 days B)16 days C)15 days D)20 days E)30 days SOLUTION:C alone can finish the work in 80 days. (A + B)can do it in 20 days (A + B)s 1 days wok = 1/20. As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2. A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30 (A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/80) = 1/16 All the three together will finish it in 16 days. ANSWER:B #### B QUESTION:Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)3 hours B)6 hours C)4 hours D)8 hours E)10 hours SOLUTION:Number of pages typed by Ronald in one hour = 32/6 = 16/3 Number of pages typed by Elan in one hour = 40/5 = 8 Number of pages typed by both in one hour = ((16/3) + 8) = 40/3 Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours. ANSWER:D #### D QUESTION:If all the sides of a right triangle increase in length by 10%, then by what percentage does the area of the triangle increase? options: A)21% B)42% C)80% D)96% E)120% SOLUTION:Let B be the base and H be the height of the original triangle. The original area is (1/2)BH. The area of the expanded triangle is (1/2)(1.1B)(1.1H) = (1.1)(1.1)(1/2)BH = 1.21(1/2)BH The answer is A. #### A QUESTION:In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively? options: A)10,16 B)8,14 C)16,22 D)14,20 E)12, 18 SOLUTION:Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10. Given (x + 4) + (x + 10) = 30 => 2x + 14 = 30 => x = 8 The third number = x + 4 = 8 + 4 = 12. The sixth number = x + 10 = 8 + 10 = 18. Answer: E #### E QUESTION:In 16 minutes, the minute hand gains over the hour hand by options: A)16° B)80° C)88° D)96° E)None of these SOLUTION:In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minute, the minute hand gains 330° over the hour hand. ∴ In 16 minutes, the minute hand gains over the hour hand by 330°⁄60 × 16° = 88° Answer C #### C QUESTION:The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : options: A)Rs. 113.5 B)Rs. 119.7 C)Rs. 124.75 D)Rs. 130.75 E)Rs. 134.45 SOLUTION:For an income of Rs.756, investment = Rs.9000 For an income of Rs., investment = = Rs.125 For a Rs.100 stock, investment = Rs.125. Market value of Rs. 100 stock = = Rs. 124.75 C #### C QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? options: A)6 hrs 21 min B)6 hrs 71 min C)6 hrs 32 min D)6 hrs 27 min E)6 hrs 23 min SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs. Number of stoppages = 600/75 - 1 = 7 Total time of stoppages = 3 * 7 = 21 min Hence, total time taken = 6 hrs 21 min. Answer:A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)200 metres E)180 metres SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50 x 12/3 m = 200 m. ANSWER : OPTION D #### D QUESTION:f, b, c, and d are positive integers. If the remainder is 9 when f is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d? options: A) 20 B) 19 C) 18 D) 16 E) 15 SOLUTION:When f is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6. b + d cannot be 15, hence E is the answer. #### E QUESTION:How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3? options: A)14 B)13 C)12 D)11 E)10 SOLUTION:The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers. The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form. So, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number. We get a total of 19−5=1419−5=14 numbers. Answer A #### A QUESTION:Suppose there is a number 235 such that sum of first two digits is equal to the third digit. How many such 3 digits numbers are possible? options: A)42 B)43 C)44 D)45 E)46 SOLUTION:As we know that total digits are 0 ,1, 2, 3,4,5,6,7,8,9 if three digit no is xyz this means x+y=z must hold so we have to select two no out of 10 ans is 10 c 2=45 ANSWER:D #### D QUESTION:5% of (25% of $1600) is? options: A)$20 B)$30 C)$45 D)$15 E)$60 SOLUTION:5% of (25% of $1600) = 5/100 (25/100 * 1600) = $20 Answer is A #### A QUESTION:If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest? options: A)$ 4 B)$ 8 C)$ 12 D)$ 16 E)$ 432 SOLUTION:Solution Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.08/2)^2= 5408 Amount (SI) = P+PTR/100 = 5000+(5000*1*8/100)=5400 Difference = 5408-5400=8 $ ANSWER:B #### B QUESTION:A manufacturer of a certain product can expect that between 0.4 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units? options: A) Between $15,000 and $25,000 B) Between $30,000 and $50,000 C) Between $200,000 and $250,000 D) Between $150,000 and $250,000 E) Between $300,000 and $500,000 SOLUTION:Number of defective units is between = .4 % of 20000 and .5% of 20000 = 80 and 100 Retail Price per unit = 2500 $ Expected price of refund is between = 2500 x 80 and 2500 x 100 =2,00,000 and 2,50,000 dollars Answer C #### C QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 6:30:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 150 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)1200 B)1300 C)1500 D)1800 E)1900 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 6:30:90 Initial soap:alcohol = 6/30 =6:30 after doubled soap:alcohol =2* 6/30 = 12/30=12:30 Initial soap:water = 6/90=6:90 after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360 After soap: alcohol:water --> 12:30:360 given alcohol 150 cubic centimeter. ratio is 60:150:1800 (12:30:360) For 150 cubic centimeter of Alcohol ---1800 cu cm water is required. Answer-D #### D <<<Examples ends QUESTION:If two balls are randomly selected from a green urn containing 7 black and 7 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change? options: A)A.2/9 B)B.4/9 C)C.3/13 D)D.1/3 E)E.1/9 SOLUTION:To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white. Probability (first ball is white) = 7/14 Probability(second ball is white) = 6/13 Probability (both balls are white) = (7/14)*(6/13) = 3/13 Answer C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train running at the speed of 36 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)286 B)278 C)90 D)150 E)287 SOLUTION:Speed=(36 * 5/18) m/sec = (10) m/sec Length of the train = (Speed x Time) = (10 * 9) m = 90 m. Answer:C #### C QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)17 Kmph B)78 Kmph C)72 Kmph D)18 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer: C #### C QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:The average age of a husband, wife and their child 12 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is? options: A)19.01 years B)5.25 years C)16 years D)15 years E)4.75 years SOLUTION:Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years. Required average = 57/12 = 4.75 years. Answer:E #### E QUESTION:If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ? options: A)x-2 B)x-4 C)x+4 D)x-3 E)x-1 SOLUTION:Original Digits=xy i.e. Number=10x+y After reversing the digits: Digits=yx i.e. Number=10y+x 10y+x is 36 more than 10x+y 10x+y+36=10y+x 10x-x+36=10y-y 9x+36=9y x+4=y OR y=x+4 Answer : C #### C QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these SOLUTION:Solution Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr. Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+34 3x + 6 = x + 34 2x = 28 \inline \therefore x = 14 \inline \therefore Middle number = x + 2 = 14+2 = 16 D #### D QUESTION:Joshua is fifth from the bottom in a queue of 100 boys. What is the position of Joshua from the top of the queue? options: A)51 B)52 C)53 D)54 E)55 SOLUTION:Solution: 51 Explanation: The position of boys higher than Joshua in the queue is 100 - 50 = 50. Therefore, the position of Joshua from the top is 50 + 1 = 51. Answer A #### A QUESTION:In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3 4/3 = 22-2 / 13-x 52-4x = 66-6 x = -2 The answer is A. #### A QUESTION:P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}? options: A){6, 12} B){6, 15} C){21,28} D){9, 15} E){15, 24} SOLUTION:p/q= d=p/q+7 d= .75 q d= .6(q+7) we get d = 21 and q = 28. Answer = C. #### C QUESTION:30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years? options: A)15% B)20% C)80% D)70% E)90% SOLUTION:Explanation : Let number of men = 100. Then, 80 men are less than or equal to 50 years old i.e 20 men are greater than 50 years of age. Now, the number of men above 50 years who play football = 20% of 20 = 4. 20% of all men play football i.e total no. of men who play football = 20, out of which 4 men are above 50 years old. So, 20 - 4 = 16 men are less than or equal to 50 years old. Therefore, percentage of football players less than or equal to 50 years = (16/20) x 100 = 80% . Answer : C #### C QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:There are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)141 D)154. E)166. SOLUTION:Let the foam generators capacity be - A = 12 lit/hr B = 12 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate 42 + 21 => 63 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 12 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 60 litres {2 (12+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 12 => 18 litres So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C) #### C QUESTION:Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought? options: A)20 B)18 C)24 D)26 E)28 SOLUTION:Smallest gumballs = (19-16) + (19-14) +19= 27 Largest gumballs = (25-16) + (25-14) +25= 45 Difference = 45 - 27 = 18 B #### B QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)11 B)25 C)77 D)99 E)21 SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25%.Answer:B #### B QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:If x, y, and z are all factors of 35, which of the following must be true? options: A)The product xyz > 35 B)Either x = y, y = z, or x = z C)x – y – z = even D)The product xyz is odd E)yz/x is an integer SOLUTION:All the factors of 35 are odd numbers. The product of odd numbers is odd. The answer is D. #### D QUESTION:A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo? options: A)10 B)12 C)15 D)20 E)30 SOLUTION:Two students can be selected from 6 in 6C2 =15 ways. Therefore, the teacher goes to the zoo 15 times. Option C is answer #### C QUESTION:What is the remainder when 4^381 is divided by 5 ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:I also agree that the remainder is '4' (using the last digit of the powers of 7). Could we have the official answer please?E #### E QUESTION:Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest? options: A)12 to 1 B)6 to 1 C)5 to 1 D)20 to 7 E)1 to 5 SOLUTION:The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job; The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 3*7=21 The ratio thus is 60 to 21, or 20 to 7. Answer: D. #### D QUESTION:Six children — A, B, C, D, E and F— are going to sit in six chairs in a row. The children B & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children? options: A)240 B)720 C)1440 D)4320 E)4800 SOLUTION:for such questions , we can treat both as one then total person=5. these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways BF or FB.. so ans =5!*2=240 ans A #### A QUESTION:If x and y are positive integers, find which of the following CANNOT be the greatest common divisor of 25x and 20y? options: A)5 B)5(x-y) C)20x D)20y E)35x SOLUTION:We are looking for a choice that CANNOT be the greatest common divisor of 25x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer. lets check a. 5 25x/5 = 5x and 20y/5 = 4y both are integers so eliminate b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 25x and 20y ... or 25x/20x = 5/4 which is not a integer. so answer is C. #### C QUESTION:A and B together have $1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)$310 B)$395 C)$484 D)$512 E)$542 SOLUTION:4/15 A = 2/5 B A = 2/5 * 15/4 B A = 3/2 B A/B = 3/2 A:B = 3:2 B's share = 1210*2/5 = $484 Answer is C #### C QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? options: A)480 B)540 C)600 D)720 E)900 SOLUTION:4C2 x 3C3 x 5! = 720 The answer is D. #### D QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x * 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share? options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164 SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B #### B QUESTION:The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L? options: A)5 B)4 C)1/2 D)1/5 E)1/8 SOLUTION:If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5. The answer is D. #### D QUESTION:A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform? options: A)39.9 B)37.88 C)35 D)38.88 E)38.09 SOLUTION:Speed = [200 / 42] m/sec = 100/21 m/sec. Let the length of the platform be x meters. Then, x + 200 / 50 = 100/21 21(x + 200) = 5000 è x = 38.09 m. Answer: E #### E QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60 total S=84 outcomes D #### D QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)767 E)408 SOLUTION:1h ----- 2 ? ------ 60 12 h RS = 16 + 18 = 34 T = 12 D = 34 * 12 =408 Answer: E #### E QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 14 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)13 B)13.5 C)14 D)14.5 E)15 SOLUTION:Ans is E Given d_ab = 2*d_bc let d_ab = d and d_bc = x so d=2x for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time) #### E QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used? options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7 SOLUTION:Rate of machine R =1/50 Rate of machine S =1/20 since same no of machines used for R and S to do the same work in 5 hrs So collective rate needed to finish the work in 5 hrs= 1/5 Let the no of machine be x So, x/50 +x/20 =1/5 (2x+5x)/100=1/5 7x=20 x=20/7 So no of machine R is 20/7 Answer E #### E QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)247 m B)256 m C)245 m D)527 m E)725 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C #### C QUESTION:When an amount was distributed among 14 boys, each of them got $80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount? options: A)5050 B)5020 C)5040 D)5030 E)5075 SOLUTION:Let the total amount be Rs. X the, x/14 - x/18 = 80 ==> 2x/126 = 80 ==> x/63 = 63 x 80 = 5040. Hence the total amount is 5040. Answer C. #### C QUESTION:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 100 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters? options: A)250 B)300 C)350 D)400 E)500 SOLUTION:Nice problem. +1. First timetogetherthey run half of the circumference. Second timetogetherthey run full circumference. First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters. Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 100 meters, thus the circumference is 200 + 100 = 300 meters. Answer: B. #### B QUESTION:Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year? options: A)10% B)16% C)70% D)80% E)20% SOLUTION:Let the rate of interest during the second year be R%. Given, 4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544 R = 10% Answer:A #### A QUESTION:In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1? options: A)25 B)45 C)55 D)70 E)30 SOLUTION:Day 1&2 = 80; Only Day 1&2 (80-20) = 60, Day 2&3 = 70; Only Day 2&3 (70-20) = 50, Only Day 1 = 175 - (60+50+20) = 45 Answer:B #### B QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)4096 D)1024 E)1536 SOLUTION:0.4*2^10=0.4*1024=409.6 The answer is C. #### C QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%? options: A)3 B)8 C)9 D)6 E)4 SOLUTION:96% ---- 12 144% ---- ? 96/144 * 12 = 8 Answer: B #### B QUESTION:If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in: options: A)12 years B)18 years C)16 years D)14 years E)19 years SOLUTION:Explanation: The sum P becomes 3P in 4 years on compound interest 3P = P(1+R/100)4 ⇒ 3 = (1+R/100)4 Let the sum P becomes 81P in n years 81P = P(1+R/100)n ⇒ 81 = (1+R/100)n ⇒ (3)4 = (1+R/100)n ⇒ ((1+R/100)4)4 = (1+R/100)n ⇒ (1+R/100)16 = (1+R/100)n n=16 i.e, the sum will become 81 times in 16 years ANSWER IS C #### C QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 Then 6 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)3 D)4 E)5 SOLUTION:A 1 As stated 1=6 => 6=1 #### A QUESTION:On return from a business trip Mr. Chidambaram was to be picked up from the railway station by his coachman. Someone he managed a train connection earlier and thus arrived two hours too early. Immediately on arrived he rang up home for the coach and was told that it had just left in order to be exactly in time for the train by which he was scheduled to come. To save the time he started walking homeward at 3kmph. On the way he met the coachman who brought him home an hour before schedule. How far is the Mr. Chidambaram’s house from the railway station? options: A)22 B)18 C)99 D)27 E)11 SOLUTION:Very good questions. Appeared in Puzzles book of Ravi Nirula. Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am. But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance. So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km. We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km. Answer:B #### B QUESTION:A man wants to sell his scooter .There are two offers one at Rs12000 cash and other at a credit of Rs12880 to be paid after 8 months ,money being at 18% per annum which is better offer? options: A)Rs.12880 B)Rs.12000 C)Both are equally good D)None of the above E)Cannot be determined SOLUTION:Explanation: PW of Rs.12,880 due 8 months hence =Rs.[12880×100/100+(18×812)]=Rs.11500= Clearly 12000 in cash is a better offer. Answer: B #### B QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? options: A)45% B)48% C)57% D)59% E)61% SOLUTION:Total number of votes polled = (5136 + 7636 + 11628) = 24400 So, Required percentage = 11628/24400 * 100 = 48% B #### B QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs. 7500 B)Rs. 9000 C)Rs. 9500 D)Rs. 10,000 E)None of these SOLUTION:Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs. 7500. ANSWER IS A #### A QUESTION:The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is : options: A)15 cm B)25 cm C)35 cm D)42 cm E)62 cm SOLUTION:Solution Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C #### C QUESTION:70,76, 74,85,90,105,105,130,130,130 The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD. We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74. Answer: C. #### C QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:Sandy had $231 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? options: A)$270 B)$290 C)$310 D)$330 E)$350 SOLUTION:Let the money Sandy took for shopping be x. 0.7x = 231 x = 330 The answer is D. #### D QUESTION:what is the radius of a circle that has a circumference of 3.14 meters? options: A)0.5 mtr B)1.5 mtr C)2.3 mtr D)0.2 mtr E)1.2 mtr SOLUTION:circumference of a cirlce = 2nr, given circumference= 3.14 mtr. 2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (A) #### A QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.320 B)Rs.450 C)Rs.550 D)Rs.640 E)Rs.680 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)150 m B)200 m C)240 m D)400 m E)150 m SOLUTION:Answer: Option C Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. #### C QUESTION:A room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles. What will be the least number of square tiles required to cover the floor? options: A)176 B)124 C)224 D)186 E)190 SOLUTION:LENGTH = 5 M 44 CM = 544 CM BREADTH = 3 M 74 CM = 374 CM AREA = 544 * 374 HCF = 34 AREA OF SQUARE = 34 * 34 CM2 NO OF TILES REQ = 544* 374/34*34 = 16 * 11 =176 ANSWER A #### A QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A QUESTION:A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)11 sec C)88 sec D)33.33 sec E)10 sec SOLUTION:Speed = 54 * 5/18 = 15 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 1/15 = 33.33 sec Answer: D #### D QUESTION:The age of man is three times the sum of the ages of his two sons.Five years hence,his age will be double of the sum of the ages of his sons.The father's present age is : options: A)50 years B)46 years C)20 years D)45 years E)30 years SOLUTION:Let the sum of present ages of the two sons be x years. then father's present age =3x years. (3x+5)=2(x+10) 3x+5=2x+20 x=15. Hence, father's present age =45 years. Answer is D #### D QUESTION:Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. After how much time will the trains meet? options: A)20/8 sec B)20/4 sec C)5/2 sec D)22/7 sec E)60/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (54 + 90)*5/18 = 8*5 = 40 mps. The time required = d/s = 100/40 = 5/2 sec.Answer:C #### C QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest? options: A)Rs. 560 B)Rs. 560.75 C)Rs. 551.25 D)Rs. 550 E)Rs. 560 SOLUTION:Explanation: Present worth of Rs. x due T years hence is given by Present Worth (PW) = x/(1+R/100)T Let x be the annual payment Then, present worth of x due 1 year hence + present worth of x due 2 year hence = 1025 x(1 + 5/100)1 + x(1 + 5/100)2 = 1025 x/(21/20) + x/(21/20)2 = 1025 20x/21 + 400x/441 = 1025 820x/441 = 1025 x = (1025 × 441)/820 = (205 × 441)/164 = Rs. 551.25 Answer: Option C #### C QUESTION:Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. options: A)z=3x B)x=3z C)y=2x D)x=2y E)y=3x SOLUTION:Rovert Travelled for x,y and for z min. Total Time : x + y + z Which is equal to : 3y Equating both sides we get x+y+z = 3y => x+z =2y ........ Eqn 1 Looking out at options D Says x =2y Using it in Eqn 1 2y + z = 2y => Z = 0 mins, Which I guess is not possible. The Ans isD #### D QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? options: A)18 cm B)20 cm C)22 cm D)24 cm E)26 cm SOLUTION:2(l + b) = 5 b 1 2l + 2b = 5b 3b = 2l b = 2 l 3 Then, Area = 216 cm2 l x b = 216 l x 2 l = 216 3 l2 = 324 l = 18 cm. A) #### A QUESTION:curie bakes 5 cookies for 5 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:curie made 5*5 cookies = 25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends. 9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same. The nearest multiple of 2 is 8. 9-8=1 A is the correct answer #### A QUESTION:How many ONE letter words are formed using the letters of the word WALK? options: A)1 B)16 C)7 D)4 E)2 SOLUTION:The number of letters in the given word is 4. The number of ONE letter words that can be formed using these four letters is 4P1=4*1=4 Answer:D #### D QUESTION:Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -7 then by what factors will the Mean,Variance and Standard Deviation respectively change ? options: A)-7,-7,-7 B)-7,7,7 C)1,1,1 D)-7,49,7 E)7,7,49 SOLUTION:Mean: If all values are multiplied by -7 then their sum will also be multiplied by -7 so Mean will also get -7 Variance: Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values When we multiply all the values by -7 then the difference between the mean and the individual values also gets multiplied by -7 and the square of that difference becomes 49. So, the variance gets multiplied by a factor of 49 SD: Standard Deviation is the square root of variance so sqrt(49)=7. So SD gets multiplied by a factor of 7. So, answer will be D. #### D QUESTION:Find the odd man out 2, 5, 10, 17, 26, 37, 50, 64 options: A)50 B)26 C)64 D)27 E)17 SOLUTION:Difference is series of ODD numbers 2+3 = 5 5+5 =10 10+7=17 17+9=26 26+11=37 37+13=50 50+15=65 ANSWER:C #### C QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents. Answer: C. #### C QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members 51* 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 3/3% C)33 1/3% D)39 1/3% E)33 4/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is? options: A)35 B)50 C)88 D)66 E)22 SOLUTION:Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr. Answer:A #### A QUESTION:A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? options: A)5/6 km/hr B)25 km/hr C)79.2 km/hr D)15 km/hr E)38 km/hr SOLUTION:Explanation: Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr Answer:C #### C QUESTION:A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work. options: A)27 days B)54 days C)56 days D)68 days E)78 days SOLUTION:Explanation: As per question, A do twice the work as done by B. So A:B = 2:1 Also (A+B) one day work = 1/18 To get days in which B will finish the work, lets calculate work done by B in 1 day = =(1/18∗1/3)=1/54 [Please note we multiplied by 1/3 as per B share and total of ratio is 1/3] So B will finish the work in 54 days Option B #### B QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 6 years hence? options: A)22 B)77 C)70 D)98 E)72 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 6 years, their ages will be 46 and 26. Sum of their ages = 46 + 26 = 72. Answer: E #### E QUESTION:A river 7m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is? options: A)54996.5 B)32296.5 C)34996.5 D)34996.5 E)31255.5 SOLUTION:Rate of water flow-4kmph--4000/60--66.66 m/min depth of river--7m width of river--75m vol of water per min--66.66 *7*75---34996.5 Answer C #### C QUESTION:Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride? options: A)14 mph B)20 mph C)70/3 mph D)80/3 mph E)30 mph SOLUTION:Average speed for first two hours, S1 = 30 mph Distance travelled in these two hours, D1 = 60 miles Average speed for the entire 5 hour ride, S = 30 mph Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles. Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90 Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30 Hence, the correct answer is E #### E QUESTION:Some consecutive natural numbers, starting with 1, are written on the board. Now, one of the numbers was erased and the average of the remaining numbers is 800/39. Find the number which was erased. options: A)24 B)20 C)18 D)16 E)15 SOLUTION:Explanation: We know that average of n consecutive numbes average = n×(n+1)/2 /n =(n+1)/2 If the given n is sufficiently large, the average does not change much even though we exclude one or two numbers from it. So the approximate number of observations is almost double to the average (Remember: the average of consecutive numbers almost lies in the middle) The approximate average is 800/39 = Approx 20. So the initial numbers may be nearer to 40. In this question it is actually 40 as from the denominator of the new average 800/39. The initial numbers are 40. Sum of 40 consecutive numbers = 40×(40+1)/2=820 Sum of 39 numbers = average x number of observations = 800/39×39 = 800 So the number excluded = 820 - 800 = 20 Correct Option: B #### B QUESTION:8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work? options: A)5 days B)15 days C)28 days D)4 days E)7 days SOLUTION:Explanation: 1 man’s 1 day’s work = 1/8 × 12 = 1/96 10 men’s 1 day’s work = 1 × 10/96 = 5/48 1 woman’s 1 day’s work = 1/192 20 women’s 1 day’s work = 1/192 × 20 = 5/48 1 child’s 1 day’s work = 1/240 10 children’s 1 day’s work = 1/24 Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24 =1/4 The required No. of days = 4 days Answer: Option D #### D QUESTION:Two roads XY and YZ of 15 metres and 20 metres length respectively are perpendicular to each other. What is the distance between X & Z by the shortest route? options: A)35 metres B)30 metres C)24 metres D)25 metres E)None of these SOLUTION:XYZ is a right-angled triangle XZ =√15(2)+20(2)=√=625=25m Answer D #### D QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d? options: A)2 B)8 C)10 D)11 E)14 SOLUTION:1155 = 3 * 5 * 7 * 11 a = 11 d = 3 a - d = 8 Answer is B #### B QUESTION:A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit? options: A)39:40 B)39:45 C)39:40 D)39:41 E)39:42 SOLUTION:3: 4 A = 3/7*210 = 90 390: 400 39:40 Answer: A #### A QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these SOLUTION:Reqd ratio 4 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100 = 4 × 140 : 7 × 150 : 8 × 175 = 8 : 15 : 20 Answer C #### C QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:Two representatives must be selected from each of two groups of students. One group consists of four men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ? options: A)1/6 B)1/4 C)2/7 D)7/15 E)1/2 SOLUTION:Group 1: 4 Men and 1 Woman Group 2: 1 Men and 2 Woman Need: 2 Men and 2 women Case 1: 2 Men from Group 1 and 2 women from group 2 - 4C2*2C2 = 6 ways Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 4*1*1*2 = 8 ways Total Favorable cases = 6+8 = 14 Total Possible ways of selecting students 2 from each group = 5C2*3C2 = 10*3 = 30 Probability = 14/30 = 7/15 Answer : Option D #### D QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters? options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n SOLUTION:C is the answer. To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra. Given - tank was already 1/3 full. - When n ltr added, it became 5/9 So 1/3 + n = 5/9 n = 5/9 - 3/9 n = 2/9 capacity of the tank is full fraction . i.e. 1 i.e. 9/9 so the question is 9/9 is how much times n = 9/9 = 1 = xn so x = 9/2 and total = 9/2n #### C QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)22 B)30 C)99 D)77 E)62 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 500 * 3/50 = 30 sec. Answer:B #### B QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be? options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999. 366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday Answer: A #### A QUESTION:A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ? options: A)22 B)23 C)25 D)35 E)30 SOLUTION:Explanation: Clearly, we have : B-3 = E ...(i) B + 3 = D ...(ii) A+B = D + E+10 ...(iii) B = C + 2 ...(iv) A+B + C + D + E= 133 ...(v) From (i) and (ii), we have : 2 B = D + E ...(vi) From (iii) and (vi), we have : A = B + 10 ...(vii) Using (iv), (vi) and (vii) in (v), we get: (B + 10) + B + (B - 2) + 2B = 133 => 5B = 125=> B = 25. ANSWER IS C #### C QUESTION:John deposited $10,000 to open a new savings account that earned 2 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened? options: A)$10,100.25 B)$10,101.50 C)$10,200.75 D)$10,201.00 E)$10,400.35 SOLUTION:2 percent annual interest compounded quarterly --> 0.5% in 3 moths. For the first 3 moths interest was 0.5% of $10,000, so $50; For the next 3 moths interest was 0.5% of $10,000,plus0.25 earned on previous interest of $100, so $50+$0.25=$50.25; Total interest for 6 months was $50+$50.25=$100.25, hence balance after 6 months was $10,000+ $100.25=$10,100.25. Answer: A. #### A QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2360 TD = Rs. 360 PW = F - TD = 2360 - 360 = Rs. 2000 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2000 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2360 for unexpired time =360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B QUESTION:If the sum of 5 consecutive integers is y, which of the following must be true? I. y is an even number II. y is an odd number III. y is a multiple of 5 options: A) I only B) II only C) III and II only D) I and III E) III only SOLUTION:I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true. II. Same as above. This need not be always true. III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4) = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases. Therefore E is the answer. #### E QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2430 * 1/3 = 810 Option B #### B QUESTION:Here 10 programmers, type 10 lines within 10 minutes then 60 lines can type within 60 minutes. How many programmers are needed? options: A)16 B)10 C)6 D)60 E)50 SOLUTION:10 10 programmer 10 line 10 mins. 10 programmer 20 line 20 mins. . . . .10 programmer 60 line 60 mins. ANSWER:D #### D QUESTION:What is the Mode of the following data set M- {5,4,5,5,6,6,5,7,8,9} options: A)5 B)4 C)6 D)7 E)9 SOLUTION:Mode of a set is the data point that is repeated the most number of times. In the set given,5 is repeated Answer: A #### A QUESTION:A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives options: A)Rs. 8400 B)Rs. 11,900 C)Rs. 13,600 D)Rs. 14,700 E)NONE SOLUTION:Solution: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000. => 3x = 36000. => x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. So A's share = Rs. (35000 x 21/50) = Rs. 14,700. Answer: Option D #### D QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)30 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:Can you deduce the pattern and find the next number in the series? 3, 24,81, 192, __? options: A)276 B)277 C)278 D)279 E)375 SOLUTION:Solution: 375 Explanation: 3 = 1^1^1 + 1^1^1 + 1^1^1 24 = 2^2^2 + 2^2^2 + 2^2^2 81 = 3^3^3 + 3^3^3 + 3^3^3 192 = 4^4^4 + 4^4^4 + 4^4^4 Thus the next number will be 375 =5^5^5 + 5^5^5 + 5^5^5 Answer E #### E QUESTION:x =3 4 5 y= 27 36 9 then what is the relation between x and y options: A)1*X)^2 B)1*X)^3 C)1*X)^4 D)1*X)^5 E)1*X)^6 SOLUTION:Y=(1*X)^2 9=(1*3)^2 9=9 ANSWER:A #### A QUESTION:In the set of positive integers from 1 to 80, what is the sum of all the odd multiples of 5? options: A)180 B)245 C)320 D)260 E)270 SOLUTION:reduce to 1 - 80 5 - 15 - 25 - 35 - 45--55--65--75 are valid multiples. Add them --> 320 C #### C QUESTION:From 2005 to 2015 the world's population grew by 11.27%, and from 2005 to 2010 the world's population grew by 6.20%. What was the percentage growth in the world's population from 2010 to 2015? options: A) 5% B) 6% C) 2% D) 2.5% E) 5.5% SOLUTION:Let the world's population in 2005 = x; then, for 2005-2010, the population equation is x + 0.0620x = 1.0620x, for 2005-2015, the population equation is x + 0.1127x = 1.1127x; so, the growth from 2010 to 2015 = (1.1127x - 1.060x)/(1.062x) = 0.05 (rounded). Thus, the answer is 5%. Answer is A #### A QUESTION:A train 250 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)150m B)200m C)250m D)270m E)300 m SOLUTION:D = 72 * 5/18 = 25 = 500 – 250 = 250m ANSWER:C #### C QUESTION:If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be options: A)(1.5)^4 B)(1.05)^5 C)(1.05)^4 D)1 + (0.05)^4 E)1 + 4(0.05) SOLUTION:In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of . We'd have.... Answer :B #### B QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: 1) 80% of the team consists of spinners. 2) The opening batsmen were spinners. options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow. D #### D QUESTION:The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : options: A)144 m2 B)140 m2 C)108 m2 D)158 m2 E)None of these SOLUTION:Area of the outer rectangle = 23 × 16 = 368 m2 Area of the inner rectangle = 19 × 12 = 228 m2 Required area = (368 – 228) = 140 m2 Answer B #### B QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ? options: A)95 B)110 C)20 D)None of these E)Cannot be determined SOLUTION:Solution 2/5of 350 - 4/7of 210 = 20. Answer C #### C QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:24 machines can do a work in 10days. How many machines are needed to complete the work in 40days? options: A)10 B)6 C)4 D)7 E)5 SOLUTION:Required number of machines = 24*10/40 = 6 Answer is B #### B QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 3*1*2=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $20,000, in how many years total will the total value of the investment plus interest increase to $40,000? options: A)15 B)16 C)18 D)20 E)24 SOLUTION:5,000(1 + x)^10 = 20,000 (1+x)^10 = 4 = 2^2 (1+x)^10 = ((1+x)^5)^2 = 2^2 Therefore, (1+x)^5 = 2 5000(1 + x)^n = 40,000 (1+x)^n = 8 (1+x)^n = 2^3 (1+x)^n = ((1+x)^5)^3 = (1+x)^15 Therefore, n = 15. The answer is A. #### A QUESTION:Divide $ 1162 among A, B, C in the ratio 35 : 28 : 20. options: A)490,490,490 B)360,392,460 C)490,382,280 D)260,160,60 E)492,390,280 SOLUTION:Sum of ratio terms = (35 + 28 + 20) = 83. A's share = $ (1162 x (35/83))= $ 490; B's share = $ (1162 x(28/83))= $. 392; C's share = $ (1162 x (20/83))= $ 280. Option C #### C QUESTION:Machine A working alone can complete a job in 3 hours. Machine B working alone can do the same job in 4 hours. How long will it take both machines working together at their respective constant rates to complete the job? options: A)1.10 min B)1.714 hr C)4hr D)2hr E)1.714 hr SOLUTION:Machines ( A ) ( B ) (A+B) ---Time - 3 - ( 4 ) 1.714 ---Rate 4 --- 3 ---7 --Work 12 ---12 ---12 E #### E QUESTION:Indu gave Bindu Rs.3750 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? options: A)5 B)6 C)9 D)3 E)1 SOLUTION:3750 = D(100/4)2 D = 6 Answer: B #### B QUESTION:Jerry wrote down all the positive integers that have at most 7 digits and contain only the digits 0 and 1. How many times did he write down the digit 1 ? options: A)128 B)224 C)288 D)448 E)512 SOLUTION:Jerry wrote down a total of 27 − 1 = 127 numbers (0 is missing). Add 0 to the numbers Jerry wrote. We divide the resulting 128 numbers in pairs. If x is one of the numbers Jerry wrote then we put it in pair with 1111111 − x (whose digits are also 0s and 1s). For example 1100101 is paired with 11010. In this way, we divide the numbers into 64 distinct pairs so that each number appears exactly once. Note that there are exactly 7 digits 1 in each pair. So, Jerry wrote the digit 1 exactly 64 × 7 = 448 times. correct answer D #### D QUESTION:Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=4/5, what is the ratio of rectangle A’s area to rectangle B’s area? options: A)5/4 B)25/16 C)4/5 D)16/25 E)16/5 SOLUTION:The area of rectangle A is ab. c=5a/4 and d=5b/4. The area of rectangle B is cd=25ab/16. The ratio of rectangle A's area to rectangle B's area is ab / (25ab/16) = 16/25. The answer is D. #### D QUESTION:A starts business with Rs.3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the Capital ? options: A)24887 B)20778 C)23788 D)9000 E)2811 SOLUTION:Explanation: A invested Rs.3500 for 12 months. Let B joined with investment x. And he invested for 12 - 5 = 7 months. So there profit ratio = (3500 × 12) : (7x) = 2 : 3 ⇒ x = 9000 Answer: D #### D QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ? options: A)4/17 B)4/18 C)4/76 D)4/13 E)4/29 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer: D #### D QUESTION:A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate? options: A)270 B)360 C)480 D)600 E)400 SOLUTION:as given 3 out of every 4 bruised apple is not fit to sell or, 75% of the bruised apples are not fit to sell. as per the question 12 are not fit to sell or, 0.75x=12 x=1200/75=16 thus total number of bruised apples =16 total number of apples =25*16=400 Answer: E #### E QUESTION:The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. options: A)179 B)208 C)210 D)223 E)229 SOLUTION:Explanation: Total runs scored by the batsman = 60*46 = 2760 runs Now excluding the two innings the runs scored = 58*44 = 2552 runs Hence the runs scored in the two innings = 2760 – 2552 = 208 runs. Let the highest score be x, hence the lowest score = x – 150 x + (x - 150) = 208 2x = 358 x = 179 runs ANSWER A #### A QUESTION:If A lends Rs.4000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? options: A)112.5 B)122.5 C)132.5 D)114.5 E)180 SOLUTION:(4000*1.5*3)/100 => 180 ANSWER:E #### E QUESTION:Which 2 digit number has its digits reversed when you double it and take 1? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:reverse it and you get 73 which is 2*37-1. ANSWER:E #### E <<<Examples ends QUESTION:The average successfull Search time for sequential search on n items is options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1 SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison. Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons. Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons. so we can write total search time will be: (1+2+3+........+n) average search time will be (1+2+3+........+n)/n NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2 ANSWER: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 10,290,000, how many red beads were removed? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:10,290,000 = 2^4 * 5^4 * 1029 = 2^4 * 3 * 5^4 * 343 = 2^4 * 3 * 5^4 * 7^3 The answer is B. #### B QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)22.7 kmph B)12.7 kmph C)27.6 kmph D)12.5 kmph E)22.1 kmph SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph.Answer: D #### D QUESTION:Venus travels around the sun at a speed of approximately 21.9 miles per second. The approximate speed is how many miles per hour? options: A)64,420 B)78,840 C)83,160 D)88,970 E)94,320 SOLUTION:21.9 * 3600 = 78,840 The answer is B. #### B QUESTION:If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is: options: A)80% B)90% C)33% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12. Gain % = 3/9 * 100 = 33% Answer:C #### C QUESTION:Jacob brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%? options: A)27 B)276 C)500 D)267 E)234 SOLUTION:Let the C.P. be Rs. x. Then, 20% of x = 1100 20/100 * x = 1100 => x = 5500 C.P. = Rs. 5500, expenditure on repairs = 10% Actual price = Rs. (100 * 5500)/110 = Rs. 5000 Expenditures on repairs = (5500 - 5000) = Rs. 500. Answer: C #### C QUESTION:A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 50km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is options: A)8.95km/hr B)26.7km/hr C)27.8km/hr D)28.5km/hr E)8.45km/hr SOLUTION:average speed = (2*50*20)/50+20 km/hr =28.5 km/hr Answer (D) #### D QUESTION:Convert 50miles into yards? options: A)25630 yards B)35200 yards C)88000 yards D)42560 yards E)41520 yards SOLUTION:1 mile = 1760 yards 50 miles = 50*1760 = 88000 yards Answer is C #### C QUESTION:There are 7 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played? options: A)21 B)30 C)45 D)60 E)90 SOLUTION:7 players are there. two players play one game with one another. so 7C2=7*6/2 =21 SO OPTION A is correct #### A QUESTION:A bus started from bus stand at 8.00a m and after 30 min staying at destination, it returned back to the bus stand. The destination is 27 miles from the bus stand. The speed of the bus 50 percent fast speed. At what time it returns to the bus stand. options: A)11a.m B)12a.m C)10a.m D)10.30p.m E)11.30p.m SOLUTION:bus started after 30min ie .5hrs Now, Time=distance/speed ie Time=27/18 during going ie 1.5 hrs now during the return journey speed increasd by 50% so new speed 27mph Time=27/27 ie 1(RETURN journey) so total time=1+.5+1.5=3hrs so the bus will reach at 11am ANSWER:A #### A QUESTION:105,100,...,90,85,80,75 Insert the missing number options: A)95 B)78 C)83 D)84 E)none of the above SOLUTION:Missing number : 95 Answer : A #### A QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/91 B)33/18 C)33/29 D)33/18 E)33/12 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = 12C4/15C4 = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:A #### A QUESTION:In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class? options: A)1/2 B)1/3 C)2/3 D)1/4 E)3/4 SOLUTION:(1/2)G=(1/3)(B+G) 3G=2B+2G G=2B B/G=1/2. The answer is A. #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? options: A)250 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Answer: A #### A QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots? options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours. The answer is A. #### A QUESTION:Goldenrod and No Hope are in a horse race with 6 contestants. How many different L arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race? options: A) 720 B) 360 C) 120 D) 24 E) 21 SOLUTION:no hope finishing before goldenrod= 1/2 of the times therefore the different L arrangements are 1/2* 6! = 360 = B #### B QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:In a class of 100 students, there are 50 who play soccer, 45 who play basketball, and 50 who play volleyball. Only 15 of these students play all three sports. Everyone plays at least one of these sports. How many of the students play exactly two of these sports? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:Let S1 be the number of students who play exactly one of the three sports; S2 - the number of students who play exactly two of the three sports; and let S3 be the number of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100 (the total number of students). Also in the sum 50+45+50 (soccer players + basketball players + volleyball players), each student who plays exactly one sport is counted once, the ones who play exactly two sports are counted twice, and those who play all three sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15 correct answer A #### A QUESTION:The difference between the squares of two consecutive odd integers is a square<1000 whose root equals the combined sum of the digits of the two integers. What is the sum of the digits M of the larger integer? options: A)M=2 B)M=5 C)M=8 D)10 E)11 SOLUTION:Really hard. But let's start with few concepts: 1. Square of an odd integer will be odd. 2. Difference of odd and odd will be even. 3. Any odd integer can be expressed as difference of two squares. 4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4. Assume two odd integers to be (2x-1) and (2x+1). Difference of their squares = (2x+1)^2 - (2x-1)^2 = 4x^2 + 1 + 4x - (4x^2 + 1 - 4x) = 4x^2 + 1 + 4x - 4x^2 - 1 + 4x = 8x Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers. 8 = 2^3, so x needs to be such that itcompletesa perfect square. If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits. Let's check the options, starting with c. For sum to be 8, few possibilities are: 17, 35, 53, 71 If we take 17, the pair is 15 and 17, meaning x = 8. 8x = 64 root of 64 = 4 but 4 is not equal to 1+5+1+7. Reject. If we take 35, the pair is 33 and 35, meaning x = 17. 8x = 8*17 Reject since perfect square is not possible. If we take 53, the pair is 51 and 53, meaning x = 26. 8x = 8*26 Reject since perfect square is not possible. If we take 71, the pair is 69 and 71, meaning x = 35. 8x = 8*35 Reject since perfect square is not possible. I tried each option and the possibilities and then got lost. Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits? Starting with option a, only 2-digit odd integer whose sum is 2 is 101. If we take 101, the pair is 99 and 101, meaning x = 50. 8x = 8*50 = 400 root of 400 = 20 which is indeed equal to 9+9+1+1. Answer (A). #### A QUESTION:At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.50. What is the price of 2 doughnuts? options: A)$ 0.55 B)$ 1.00 C)$ 1.10 D)$ 1.30 E)$ 1.50 SOLUTION:3D + C = 2.25......(1) 2D + C = 1.5........(2) (1) - (2) --> D = 0.75 --> 2D = 1.5 Answer: E #### E QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/6 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)12 greater B)12 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/6 * 480 =80 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 80-68 =12>>> therfore answer is 28 fewer B #### B QUESTION:A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B? options: A)7 years. B)8 years. C)9 years. D)10 years. E)11 years. SOLUTION:EXPLANATION Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years. (2x + 2) + 2x + x = 27 5x = 25 x = 5. Hence, B’s age = 2x = 10 years. Answer D #### D QUESTION:Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work? options: A)13 B)14 C)18 D)11 E)10 SOLUTION:(5 + x)/20 + 5/25 = 1 => x = 11 days Answer:D #### D QUESTION:Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D? options: A)(5,10) B)(-3,2) C)(-1,7) D)(-1,2) E)(-3,1) SOLUTION:The slope of the line is -ve, the only point that makes the slope -ve is D. (5 - 2)/(-2 + 1) = 3/-1 Answer - D #### D QUESTION:Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together. options: A)10x11/10 B)10x10/11 C)11x10/11 D)12x10/11 E)None SOLUTION:Solution At 8 o'clock, the hour is at 8 and the minute hand is at 12,i.e. the two hands are 20 min. Spaces apart. So, the minute hand gain = (30 - 20)minute 55 minutes will be gained in 60 min. 10 minutes spaces will be gained in (60/55 x10) min. = 10x10/11 min. The hands will be in the same straight line but not together at 10x10/11 min.past 8. Answer B #### B QUESTION:if page of chemistry book is 30 more than page of physics book.if ratio of pages is 5:3.a child torn 15 pages of chemistry book.calculate new ratio. options: A)1:1 B)2:1 C)5:4 D)4:3 E)2:3 SOLUTION:chemistry page=5x, physics page=3x 5x-3x=30,2x=30,x=15 chemistry page=75, physics page=45 after torn 15 page of chemistry=60 ratio become 60/45=4:3 answer D #### D QUESTION:How long will it take for a sum of money to grow from Rs.1000 to Rs.5,000, if it is invested at 20% p.a simple interest? options: A)8 years B)20 years C)72 years D)56 years E)None SOLUTION:In this case, Rs. 1000 has become Rs.5000. Therefore, the interest earned = 5000 – 1000 =4000 Interest for Rs 1000 @ 20% for 1 year = 200 200 - 1 4000 - ? => 20 years Answer : B #### B QUESTION:If -1 < x < 0, which of the following must be true? I. x^8 < x^3 II. x^4 < 1 – x III. x^3 < x^2 options: A)III only B)II only C)I only D)I,II,III only E)II,III only SOLUTION:Answer : D #### D QUESTION:Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price? options: A)$1 B)$1.84 C)$1.92 D)$2.13 E)$2.15 SOLUTION:Ordering the data from least to greatest, we get: $1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11 The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.) B #### B QUESTION:Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A)$140 B)$141 C)$142 D)$147 E)$145 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer D)$147 #### D QUESTION:Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)80% C)100% D)180% E)200% SOLUTION:We can use fractional equivalents here to solve the problem 80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears 10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours Now we come to productivity Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour Hence the productivity is double with the assistant i.e. the increase in productivity is 180% D #### D QUESTION:The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is options: A)25 years B)30 years C)35 years D)40 years E)None SOLUTION:Sol. Let their ages of x years and (x + 10) years respectively. Then, (x + 10) - 15 = 2(x - 15) ⇔ x - 5 = 2x - 30 ⇔ x = 25. ∴ Present age of the elder person = (x + 10) = 35 years. Answer C #### C QUESTION:The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is: options: A)2200 B)5500 C)3054.9 D)1100 E)4400 SOLUTION:Cylinder volume = Ï€r(power2)h = 22/7 × 9 × 9 × 12 = 3054.9 m(power3) Answer is C. #### C QUESTION:A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result. options: A)0 B)16 C)18 D)1 E)120 SOLUTION:suppose the no is 100 first condition if it mistakenly divided the no by 2/3 ==>100/(2/3)==>150 second condition the no should multiply by 3/2 ==> 100*3/2 ==> 150 hence output should be 150 and mistakenly the output is 150 so pecentage error is zero ANSWER:A #### A QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/9 B)5/12 C)1/36 D)7/12 E)4/9 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 ANSWER:B #### B QUESTION:At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ? options: A)Rs.7.50 per kg B)Rs.8.20 per kg C)Rs.8.85 per kg D)Rs.9 per kg. E)None SOLUTION:Explanation: Total C.P of 200 kg of sugar = Rs.(80×6.75+120×8)=Rs.1500 C.P of 1 kg = Rs.[1500/200]=Rs.7.50 Gain required = 20% S.P of 1 kg = (120% of Rs.7.50) = Rs.[120/100×7.50]=Rs.9 per kg. Correct Option : D #### D QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? options: A)72 B)27 C)40 D)28 E)20 SOLUTION:800*(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer:C #### C QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is? options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5 SOLUTION:3:1 Answer:B #### B QUESTION:A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of B. options: A)250 B)450 C)750 D)800 E)None of them SOLUTION:C's 1 day's work = 1/3-(1/6+1/8)=24 A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1. A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450 C's share = Rs. [1200 - (300 + 225») = Rs. 150. Answer is B #### B QUESTION:The sum of the 1st and 3rd of 3consecutive odd integers is 131 less than three times the second integer. Find the three integers? options: A)121 B)133 C)145 D)150 E)165 SOLUTION:Let x, x + 2 and x + 4 be three integers. The sum of the first x and third x + 4 is given by x + (x + 4) 131 less than three times the second 3(x + 2) is given by 3(x + 2) - 131 "The sum of the first and third is 131 less than three times the second" gives x + (x + 4) = 3(x + 2) - 131 Solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 As an exercise, check that the sum of the first and third is 131 less than three times B #### B QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? options: A)26 B)39 C)42 D)65 E)156 SOLUTION:Here 156 has three two's two three's and one 13 rest of them must be in w so w= 13*3*4 = 156 Answer: E #### E QUESTION:When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 14? options: A)7 B)21 C)34 D)8 E)55 SOLUTION:So the number given is N = 143Q + 45 If this number is divided by 13, the remainder would be R[(143Q + 45)/13] Since 143 is divisible by 13 , the product 143Q gives no remainder This means the remainder of 45/13 should be the remainder of the entire number N which is 6 To make it divisible by 13 , the smallest number that can be added = 14 - 6 = 8 Correct Option : D #### D QUESTION:At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $8 on candy, how much did John spend at the supermarket? options: A) $60 B) $80 C) $90 D) $120 E) $180 SOLUTION:Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T. We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $8 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have: (1/2)T + (1/3)T + (1/10)T + 8 = T To get rid of the fractions we can multiply the entire equation by 30, and we obtain: 15T + 10T + 3T + 240 = 30T 28T + 240 = 30T 240 = 2T T = 120 John spent $90 at the supermarket. Answer: D #### D QUESTION:In how many W ways can 5 people from a group of 6 people be seated around a circular table options: A)56 B)80 C)100 D)120 E)144 SOLUTION:W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner) = 6 * 4! = 6 * 24 = 144 Answer - E #### E QUESTION:If x = 3d, where d is a prime number greater than 2, how many different positive even divisors does x have, including x? options: A)0 B)1 C)2 D)3 E)It cannot be determined from the information given SOLUTION:d is prime greater than 2 thus d is odd 3d is odd Thus no even factors Ans:A #### A QUESTION:Which of the following must be subtracted from 2^96 so that the resulting integer will be a multiple of 3? options: A)2 B)5 C)3 D)1 E)4 SOLUTION:{4^1} / 3 =4/3 remainder 1 {4^2} / 3 = 16/3 remainder 1 {4^3} / 3 = 64/3 remainder 1 {4^4} / 3 = 256/3 remainder 1 Actually the same remainder keeps repeating ..... Try with a diff no, say 2 {2^1}/3 = remainder 2 {2^2}/3 = remainder 1 {2^3}/3 = remainder 2 {2^4}/3 = remainder 1 Answer : D #### D QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230 m B)210 m C)260 m D)320 m E)330 m SOLUTION:Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B #### B QUESTION:A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)5.3 % B)7.6 % C)10.6 % D)12 % E)None of these SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 50 pens = Rs. 46 S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50 Profit % = (Profit /C.P.) x 100 Profit% = (3.50/46) x 100 = 7.6 % ANSWER B #### B QUESTION:Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest W? options: A) 60 B) 61 C) 62 D) 63 E) 64 SOLUTION:60 = 2*2*3*5 factor count =3 61= prime number 62 = 2*31 factor count=2 63=3*3*7 factor count=2 64=2*2*2*2*2*2 factor count=1=W answer is A. #### A QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old? options: A)231/260 B)117/130 C)51/65 D)23/32 E)11/16 SOLUTION:The number of people younger than 70 years old is 2600-800 = 1800 The number of females older than 70 years old is 0.6*850 = 510 The number of people who are either female or younger than 70 is 1800+510 = 2310. P(a person is younger than 70 or male) = 2310/2600 = 231/260 The answer is A. #### A QUESTION:A store sells four different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:4C2=6. The answer is B. #### B QUESTION:Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next? options: A)4.7 B)4.5 C)6.7 D)8.9 E)9.2 SOLUTION:In this simple addition series, each number increases by 0.8. ANSWER A #### A QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)G.C.D.=0.18 D)0.2 E)0.21 SOLUTION:Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer: Option C #### C QUESTION:At 15:00 there were 22 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ? options: A)7 B)14 C)25 D)27 E)32 SOLUTION:Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) - 8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44) 20 + 3*14 -8 * 4 = 32 E #### E QUESTION:The number of arrangements that can be made with the letters of the word PETER so that the vowels occupy the even places? options: A)18 B)20 C)40 D)12 E)14 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 4 places in 3! i.e., 24 ways. Hence the total ways are 2 * 6 = 12. Answer:D #### D QUESTION:A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. options: A)45 kmph B)50 kmph C)85 kmph D)60 kmph E)70 kmph SOLUTION:Explanation: Let the speed of the train be x kmph. Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec. Therefore 150/((x+5)×5/18)=6 <=> 30 (x + 5) = 2700 <=> x = 85 Speed of the train is 85 kmph. Answer: Option C #### C QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles. SOLUTION:Solution: 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 Answer C #### C QUESTION:By selling 20 pens for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%? options: A)8.76 B)10.76 C)8.76 D)9.76 E)5.76 SOLUTION:70% --- 20 130% --- ? 70/130 * 20 = 10.76 Answer: B #### B QUESTION:517 + 5.017 + 0.517 + 5.0017 = ? options: A)558.3657 B)527.5357 C)229.6357 D)629.5637 E)629.6753 SOLUTION:517 5.017 0.517 + 5.0017 -------- 527.5357 --------- Answer is B. #### B QUESTION:A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible? options: A)3 B)Z=4 C)Z=5 D)Z=6 E)Z=8 SOLUTION:The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)} Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with. {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)} Hence 8.E #### E QUESTION:A car covers a distance of 624 km in 3 hours. Find its speed? options: A)104 kmph B)194 kmph C)208 kmph D)174 kmph E)101 kmph SOLUTION:624/3 =208 kmph Answer:C #### C QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is? options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) M + O = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv) Subtracting (ii) from (iv), we get M = 4000. M's monthly income = Rs. 4000 C #### C QUESTION:If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. ab < 1 III. a/b < 2 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:MANHATTAN GMATOFFICIAL SOLUTION: You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term: 1 > 1 - ab > 0 0 > -a b > -1 Subtract 1 from all three terms. 0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs. Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true. Therefore, the correct answer is (D). #### D QUESTION:If “*” is called “+”, “/” is called “*”, “-” is called “/”, “+” is called “-”. 240*80 / 60 + 40 / 10 = ? options: A)-2305 B)-2407 C)2509 D)-2101 E)None of these SOLUTION:Explanation: Given : 240*80 / 60 + 40 / 10 = ? Substituting the coded symbols for mathematical operations, we get, 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = -2407 ANSWER : B #### B QUESTION:A baker sold twice as much bread in the afternoon than in the morning. If he sold 360 kilograms of bread that day, how many kilograms did he sell in the morning and how many in the afternoon? options: A)180kg B)240kg C)470kg D)641kg E)559kg SOLUTION:Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x.This must be equal to 360. 3x=360 x=3603 x=120 Therefore, the salesman sold 120 kg in the morning and 2⋅120=240 kg in the afternoon. correct answer is B)240kg #### B QUESTION:If 1^3 + 2^3 + 3^3 +......+ 10^3 = 516 then the value of 2^3 + 4^3 + 63 + ..... + 203 is options: A)1032 B)1030 C)1034 D)1035 E)1036 SOLUTION:2(13 + 23 + 33 + ---------- + 103) 2 × 516 = 1032 A #### A QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square? options: A)289 cm B)800 cm C)829 cm D)288 cm E)289 cm SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B #### B QUESTION:For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 * 5 * 5. How many two-digit positive integers have length 6? options: A)None B)One C)Two D)Three E)Four SOLUTION:The best (quickest) way I can think of to get the answer, is start with 2^6, then move on from there. 2^6=64 2^5*3=96 Obviously 2^5*5 will be more than 2 digits, as will 2^4*3^2. So 64 and 96 are it. Answer is 2 (C). #### C QUESTION:A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train. options: A)15 kmph B)36 kmph C)21 kmph D)17 kmph E)19 kmph SOLUTION:Let the speed of the goods train be x kmph. Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours 10x = 4 x 90 or x =36. So, speed of goods train = 36kmph. Ans: B #### B QUESTION:There are 3 classes having 20, 24 and 30 students respectively having average marks in an examination as 20,25 and 30 respectively. The three classes are represented by A, B and C and you have the following information about the three classes. a. In class A highest score is 22 and lowest score is 18 b. In class B highest score is 31 and lowest score is 23 c. In class C highest score is 33 and lowest score is 26. options: A)can't be determined in both cases B)definite decrease in both cases C)definite increase in both cases D)will remain constant in both cases E)will remain constant in both cases21 SOLUTION:Ans: B Explanation: Class A average is 20. And their range is 18 to 22 Class B average is 25. And their range is 23 to 31 Class A average is 30. And their range is 26 to 33 If 5 students transferred from A to B, A's average cannot be determined but B's average comes down as the highest score of A is less than lowest score of B. If 5 students transferred from B to C, C's average cannot be determined the B's range fo marks and C's range of marks are overlapping. Answer:A #### A QUESTION:At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day? options: A) 100 B) 1,800 C) 1,090 D) 200 E) 1,000 SOLUTION:Let the total number of sunlasses produced be x % of high quality sunglasses = 70% % of low quality sunglasses = 25% % of sunglasses defective = 100% - 95% = 5% But this number is given as 50 so 5% of x = 50 and x = (50)(100/5)) x = 180 Therefore there a total of 1,000 sunglasses made per day. Correct answer - E #### E QUESTION:In a bowl, the number of marbles gets doubled after every minute. If the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled. options: A)1 hour and 59 minutes B)2 hour and 59 minutes C)4 hour and 59 minutes D)4 hour and 59 minutes E)5 hour and 59 minutes SOLUTION:Solution: The correct way to solve this question is go backwards. If the number of marble gets doubled every minute and after two hours, it is filled completely, one minute ago it would be half. So, it will take 1 hour and 59 minutes for it to be filled half. Answer A #### A QUESTION:A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 3 percent and 6 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate? options: A) 3/8 B) 21/25 C) 1/2 D) 3/5 E) 3/4 SOLUTION:x * 3/100 * 1 + (20000 - x) * 8/100 * 1 = 1440 3x - 8x = 144000 - 160000 => -5x = -16000 => x = 32000 So 16800/20000 = 21/25 Answer - B #### B QUESTION:which of the following is a prime number ? options: A)17 B)18 C)15 D)20 E)25 SOLUTION:Clearly, 17 is a prime number. Option A #### A QUESTION:There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)315 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 7C2 Number of ways of selecting 2 non fiction books = 6C2 7C2 * 6C2 = 21 * 15 = 315 Answer: C #### C QUESTION:A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person? options: A)18 years B)20 years C)24 years D)32 years E)34 years SOLUTION:Explanation: Let the present age of the person be x years. Then, 3(x + 3) - 3(x - 3) = x 3x + 9 - 3x + 9 = x => x = 18 ANSWER IS A #### A QUESTION:A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos? options: A)2 films and 6 photos B)5 films and 6 photos C)5 films and 14 photos D)6 films and 4 photos E)6 films and 28 photos SOLUTION:1st photo = 0.50 Subsequent = 0.50*0.6=0.3 Price of 1 full film=0.50+0.3*35=11 Price of 2 full film = 11*2=22 24-22=2 2=0.5+0.3x x=5 24--->2 full films and 1+5=6 photos Answer: A #### A QUESTION:Select the one which is different from other Four alternatives. options: A)988 B)1140 C)1064 D)1197 E)1352 SOLUTION:E (A) 988 ÷ 19 = 52 (B) 1352 ÷ 19 = 71.15 (C) 1064 ÷ 19 = 56 (D) 1197 ÷ 19 = 63 (E) 1140 ÷ 19 = 60 #### E QUESTION:Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be 7? options: A)3/14 B)1/7 C)0 D)1/2 E)12/21 SOLUTION:METHOD-1 Probability that the number on first die is 7 = 0 Probability that the number on Second die is 7 = 1/7 [Because 1 out of 7 faces is 7] Probability that Both Dice result in odd numbers = (0)*(1/7) = 0 Answer: Option C #### C QUESTION:When 3 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number? options: A)32 B)81 C)60 D)27 E)90 SOLUTION:Explanation: Let the number be 3 + 1/2[1/3(a/5)] = a/15 => 3 = a/30 => a = 90 Answer:E #### E QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 216. What is the rate of interest per annum? options: A)8 B)2 C)9 D)4 E)12 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 216 15000[(1 + R/100)2 - 1 - 2R/100] = 216 15000[(100 + R)2 - 10000 - 200R]/10000 = 216 R2 = (216 * 2)/3 = 144 => R = 12 Rate = 12% Answer: Option E #### E QUESTION:5800 * 99 options: A)574580 B)574200 C)584250 D)576460 E)None of these SOLUTION:Explanation: 5800 * (100 - 1) = 580000 - 5800 = 574200 Option B #### B QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? options: A)22 days B)77 days C)24 days D)17 days E)18 days SOLUTION:B = 1/8 – 1/2 = 1/24 => 24 days Answer: C #### C QUESTION:A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14% while buying and by 20% while selling. What is his percentage profit? options: A)10.22% B)20.22% C)21.22% D)42.5% E)Can't be calculated SOLUTION:The owner buys 100 kg but actually gets 114kg; The owner sells 100 kg but actually gives 80kg; Profit: (114-80)/80*100=~42.5% Answer: D. #### D QUESTION:What is the Compound Interest on Rs.7000 at 8.5% p.a. compounded half-yearly for 5 years. options: A)3616.5 B)3613.5 C)3313.5 D)3616.5 E)3113.5 SOLUTION:Compound interest : A = P(1 + r/n)nt A = 10,613.50 C.I. >> 10,613.50 - 7000 >> Rs. 3613.5 Answer:B #### B QUESTION:What is the area of a square field whose diagonal of length 24 m? options: A)256 B)289 C)200 D)288 E)178 SOLUTION:d2/2 = (24 * 24)/2 = 288 Answer: D #### D QUESTION:The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is? options: A)288 B)267 C)200 D)4096 E)2771 SOLUTION:Principal = [4913 / (1 + 25/(4 * 100))3] = 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096. Answer: D #### D QUESTION:If a number is exactly divisible by 11 and 13, which of the following types the number must be? options: A)Divisible by (11 + 13) B)Divisible by (13 - 11) C)Divisible by (11 x 13) D)Divisible by (13 ÷ 11) E)None SOLUTION:Answer LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13). Correct Option: C #### C QUESTION:What should come in place of the question mark (?) in the following equation? 45789+ 34567 = 610+ ? options: A)96543 B)13678 C)23456 D)56789 E)79746 SOLUTION:45789+ 34567 = 610+ ? 45789+ 34567 – 610 = 79746 Answer E #### E QUESTION:A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have? options: A)576 B)800 C)726 D)484 E)500 SOLUTION:(4/15) * A = (2/5) * B A / B = 3 / 2 Therefore A's share is = (1210 * (3/5)) = 726 Ans - C #### C QUESTION:Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Ram's tour programme is options: A)28 Days B)24 Days C)22 Days D)20 Days E)None of these SOLUTION:Solution: Let Ram under takes a tour of x days. Then, expenses for each day = 360/x 360/x+4=360/x−3 x=20x=20 and −24−24 Hence, x= 20 days. Option(D) #### D QUESTION:A wooden box of dimensions 4 m x 2 m x 4 m is to carry rectangularboxes of dimensions 4 cm x 2 cm x 2 cm. The maximum number ofboxes that can be carried in the wooden box, is options: A)9800000 B)2000000 C)7500000 D)1200000 E)None of these SOLUTION:Explanation: Number = (400*200*400)/4*2*2 = 2000000 Answer: B #### B QUESTION:If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is? options: A)250 m B)112 m C)117 m D)125 m E)123 m SOLUTION:A A = 180 * 5/18 * 5 = 250 m #### A QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 7? options: A)56 B)112 C)224 D)448 E)425 SOLUTION:Solution: sequence of 7 lets say sequence is 7n, 7(n+1), 7(n+2), 7(n+3), 7(n+4) so range is 7n+28-7n = 28 if we put the different values of n we will get different but the range will be multiple of 28 and only 425 is not multiple of 28 Answer : E #### E QUESTION:Convert the following into a fraction: 0.3% options: A)1/3 B)2/3 C)3/10 D)1/6 E)None of the Above SOLUTION:0.3 =3/10 Answer is C. #### C QUESTION:If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? options: A)267 B)766 C)810 D)868 E)812 SOLUTION:12 men 120 acres 36 days 54 men ? 54 days 120 * 54/12 * 54/36 10 * 54 * 3/2 54 * 15 = 810 Answer:C #### C QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 130*4=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits? options: A)X-Y B)Y-X +100 C)100X-Y D)X+Y-100 E)100-XY SOLUTION:Using the simple formula 100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values. Hence Answer D #### D QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:in how many possible ways you can write 3240 as product of 3 positive integers a, b, c . options: A)450 B)420 C)350 D)320 E)300 SOLUTION:3240 => 2^3 * 3^4 * 5^1 a => 2^x1 * 3^y1 * 5^z1 b => 2^x2 * 3^y2 * 5^z2 c => 2^x3 * 3^y3 * 5^z3 a * b * c = 3240 x1 + x2 + x3 = 3 => 5C2 y1 + y2 + y3 = 4 => 6C2 z1 + z2 + z3 = 1 => 3C2 5C2 * 6C2 * 3C2 = 10 * 15 * 3 = 450 ANSWER:A #### A QUESTION:Of the 11 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 11 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man? options: A)22 B)35 C)60 D)70 E)105 SOLUTION:another approach : one scenario : [WWWM] now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women. and 6 ways to select one man so 5*4*3*6 = 360 now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways hence 360/3!= 360/6= 60 C #### C QUESTION:Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water? options: A)2 : 3 B)3 : 2 C)1 : 3 D)2 : 1 E)None of these SOLUTION:? Required ratio = 6?4 = 3 : 2 Answer B #### B QUESTION:Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive? options: A)20% B)17% C)4.0% D)3.3% E)2.8% SOLUTION:20/6 =3.33 Answer : D #### D QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work? options: A)20 B)34 C)38 D)40 E)46 SOLUTION:We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D #### D QUESTION:The moon revolves around the earth at a speed of approximately 0.9 kilometers per second. This approximate speed is how many kilometers per hour? options: A)60 B)61.2 C)3240 D)3,600 E)3,672 SOLUTION:moon revolves around the earth at a speed of 1.02kilometers per second. one hour equal to 60 minutes. one minute equals to 60 seconds. so one hour equals to 3600seconds. so one hour, speed= 0.9*3600=3240kilometers per hour. Option C is correct #### C QUESTION:A can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work? options: A)2 1/2days B)4 1/2days C)6 1/2days D)7 1/2days E)10 1/2days SOLUTION:The required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days Answer is B #### B QUESTION:In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons? options: A)200 B)210 C)230 D)250 E)270 SOLUTION:7p3 = 7 × 6 × 5 = 210 B) #### B QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ? options: A)5/16 B)5/12 C)5/19 D)5/17 E)5/15 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 Answer: B #### B QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 10 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 10 years = (20 + 10) years =30 years. Answer : A #### A QUESTION:A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)17 seconds C)40 seconds D)16 seconds E)14 seconds SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 * (2/25) = 40 seconds Answer:C #### C QUESTION:A monkey starts climbing up a tree of 20 feet tall. Each hour it hops 3 feet and slips back 2 feet. How long monkey will take to reach the top of the tree? options: A)16 hours. B)19 hours. C)12 hours. D)18 hours. E)13 hours. SOLUTION:The monkey hops 3 feet and slips down 2 feet. So for the first hour it climb 1 feet. Then for 2 hours 2 feet. Continuing the same till 17 hours, the monkey might have reached 17 feet. In 18th hour monkey hops 3 feet and reach the 20 feet. Hence the answer is 18 hours. Answer D #### D QUESTION:What is the tens digit of 36^5? options: A)1 B)7 C)5 D)3 E)9 SOLUTION:36^5 = 6^7 (6^2)=6*6 = 36 (6^3)= 36*6 = .16 (6^4)= .16*6 = ..96 (6^5) = ..96*6 = ..76 (6^6) = ..76*6 = ...56 (6^7) = ....56*6 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^7 ( dont actually calculate full values) and answer is D: 3 #### D QUESTION:A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every three leaps of the hare, the jackal takes five leaps. Find the ratio of the speed of the hare to the speed of the jackal. options: A)6:7 B)4:5 C)5:8 D)25:64 E)3:5 SOLUTION:The hare takes 3 leaps and the jackal takes 5 leaps. 1 hare leap = 4/3 jackal leaps Thus the hare's 3 leaps = 3*(4/3) = 4 jackal leaps. The ratio of their speeds is 4:5. The answer is B. #### B QUESTION:There is a certain relation between two given words on one side of : : and one word is given on another side of : : while another word is to be found from the given alternatives, having the same relation with this word as the given pair has. options: A)Landslides B)Strains C)Resistances D)Volcanoes E)Volcanoe1 SOLUTION:Explanation: Seismography is an instrument to measure the intensity of an earthquake. Similarly, taseometer is an instrument to measure strains. Answer: B) Strains #### B QUESTION:How many options are there for a code consisting of 2 even digits followed by 2 odd digits? options: A)4^5 B)5^4 C)5^5 D)4^4 E)10^4 SOLUTION:Even Numbers = 5 digits { 0 , 2 , 4 , 6 , 8 } Odd Numbers = 5 digits { 1 , 3 , 5 , 7 , 9 } EVEN EVEN ODD ODD No of ways is 5*5*5*5 = 5^4 Hence, correct, answer must be (B) 5^4 #### B QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers? options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89 SOLUTION:(5x-25):(7x-25) = 35:59 x = 12 => 60,84 Answer:D #### D QUESTION:If (a-3)(b-2) =0, which of the following must be true ? I. a=3 and b=2 II. if a is not = 3, then b=2 III. if a=3, then b is not=2 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:(a-3)(b-2)=0 So either a=3 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true. The answer is B. #### B QUESTION:In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? options: A)1/48 B)11/16 C)11/12 D)5/16 E)23/48 SOLUTION:First lets get the overview Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2) Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6) Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4) So now as above we have three events A,BC. 1st method(This is lengthy method) Possible cases in which it's a win( the highlighted green event is a win and red is loose. 1.ABC= 1/2*5/6*3/4 OR 2.ABC= 1/2*1/6*3/4 OR 3.ABC= 1/2*5/6*1/4 OR 4.ABC= 1/2*1/6*3/4 OR 5.ABC= 1/2*5/6*1/4 OR 6.ABC= 1/2*5/6*1/4 OR 7.ABC= 1/2*1/6*1/4 As we now OR means add Adding up all of them we'll get the probability of winning ie 11/16 Answer : B #### B QUESTION:Average age of students of an adult school is 42 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students. options: A)1200 B)120 C)360 D)200 E)None of these SOLUTION:Explanation : Let the original no. of students be x. According to situation, 42x + 120*32 = (x + 120)36 ⇒ x = 80 So, Required no. of students after joining the new students = x + 120 = 200. Answer : D #### D QUESTION:Three numbers are in the ratio 1:3:5 and their H.C.F is 5. The numbers are? options: A)5, 15, 35 B)5, 15, 30 C)5, 15, 25 D)5, 15, 40 E)5, 15, 20 SOLUTION:Let the required numbers be x, 3x and 5x. Then, their H.C.F = x. So, x = 5. The numbers are 5, 15, 25. Answer: C #### C QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)9 B)11 C)13 D)15 E)17 SOLUTION:Explanation : Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer : Option C #### C QUESTION:A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule? options: A)18 B)81 C)56 D)72 E)24 SOLUTION:IMO 'E' is the answer. Matches will be in multiples of 5x+4. The answer that satisfies this condition is E #### E QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8:7 Answer: B #### B QUESTION:Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 4 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)18 D)12 E)6 SOLUTION:21-12 < no of hrs < 21-6 9< no of hrs < 17. D #### D <<<Examples ends QUESTION:A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500? options: A)s. 1991 B)s. 2991 C)s. 3991 D)s. 4991 E)s. 5991 SOLUTION:Explanation: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009. Required sale = Rs. [ (4500 x 6) – 24009 ] = Rs. (27000 – 24009) = Rs. 2991. Answer B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An plane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of ? options: A)100 B)720 C)1100 D)940 E)860 SOLUTION:We know Distance = speed * time = 240 * 5 = 1200 km Now to cover 1200 km in 5/3 hrs , speed = distance / time = 1200 / (5/3) = 720 KMPH Ans- B #### B QUESTION:A woman is 18 years older than her son. In 4 years, her age will be twice the age of her son. The present age of her son is options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Explanation: Let the son's present age be x years. Then, woman's present age = (x + 18) years => (x + 18) + 4 = 2(x + 4) => x + 22 = 2x +8 So, x = 14 Answer: B #### B QUESTION:If (5+k)(5-k)=(5^2)-(2^3),then what is the value of K? options: A)1 B)3 C)4 D)2 E)6 SOLUTION:Obviously,It is in the formula a^2-b^2=(a+b)(a-b) So k is 2 Option D #### D QUESTION:Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 5, what is the probability that one of the two cards drawn is numbered 3 ? options: A)1/3 B)1/2 C)1/4 D)1/5 E)1/6 SOLUTION:(3,2) (2,3) (4,1) (1,4) – only 4 possible scenarios for sum to be 5. One from this 4 has already happened. From this four cases, only in two we have 3. So, the probability is 2 chances out of 4 that the one that occurred had 3: P=2/4.=1/2 Answer: B. #### B QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time W will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did? options: A)2 minute and 12 seconds. B)two minutes. C)44 seconds. D)20 seconds. E)12 seconds. SOLUTION:Tom is running alone for 20 seconds. So he will cover a distance of 20*2.5 = 50 m in 20 seconds=W Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side D is the answer #### D QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock? options: A)30000 B)20000 C)23000 D)21020 E)28211 SOLUTION:Explanation: Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 400 => x = 20000 Answer: B #### B QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten? options: A)15 B)18 C)21 D)23 E)29 SOLUTION:There are two conditions: 1. Angel got at least one score of each of 1, 2, 3, and 4. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18. Answer: B. #### B QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? options: A)72 min B)25.11628 min C)70 min D)74.11682 min E)76 min SOLUTION:x=time for type B prolems 2x=time for type A problem total time=3hrs=180min 185x+15*2x=180 x=180/215 x=0.837209 time taken for type A problem=15*2*0.837209=25.11628min ANSWER:B #### B QUESTION:Which of the following numbers is divisible by 4? options: A)27767 B)10224 C)26778 D)26679 E)26711 SOLUTION:10224. This is the only option with last two digits divisible by 4 Answer:B #### B QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:Mr. Sane invested a total amount of 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was 3,620, what was the amount invested in scheme B? options: A)8,000 B)8,600 C)8,150 D)Data inadequate E)None of these SOLUTION:% interest on total amount per annum = 3620×100/16500×2=362/33% Now, use Alligation method. Hence, ratio of amount invested in schemes A and B = (12 - 362⁄33) : (362⁄33 - 10) = 17 : 16 Hence, amount invested in B = 16×16500/(17+16)=8000 Answer A #### A QUESTION:AB +BA ___ 101 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)10 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. only 10 fits in.. C #### C QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)*100}=4% Answer is A. #### A QUESTION:If x=kc and y=kt,then 2y+x =? options: A)k(t-c) B)k(c-t) C)c(k-t) D)k(2t+c) E)k(1-t) SOLUTION:Just put in the given values of y and x 2y +x =2 kt +kc Now take k common 2y + x = k(2t +c) You get (D) as your answer. #### D QUESTION:A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person? options: A)18 years B)20 years C)24 years D)32 years E)34 years SOLUTION:Explanation: Let the present age of the person be x years. Then, 3(x + 3) - 3(x - 3) = x 3x + 9 - 3x + 9 = x => x = 18 ANSWER IS A #### A QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order? options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2 SOLUTION:RT = W Given: R = 1/3 + 1/3 = 2/3 T = ? W = 1 T = 1 / (2/3) = 3/2 = 1 1/2 Answer: E #### E QUESTION:The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers? options: A)12/35 B)1/35 C)35/8 D)7/32 E)7/33 SOLUTION:Let the numbers be a and b. Then, a + b = 12 and ab = 35. (a + b)/ab = 12/35 = (1/b + 1/a) = 12/35 Sum of reciprocals of given numbers = 12/35. ANSWER:A #### A QUESTION:A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle? options: A)96 km B)100 km C)106 km D)116 km E)126 km SOLUTION:Distance covered in first two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in next two hours = 14 × 2 = 48 km Distance covered in first six hours 20 + 24 + 48 = 92 km Remaining distance = 8 km 92 + 8 = 100 km Answer B #### B QUESTION:How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once? options: A)21 B)42 C)120 D)600 E)200 SOLUTION:Vowel: E O Consonants: V R M N T First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel) Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant) Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter Second letter can be filled in 5 Ways Third letter can be filled in 4 Ways So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200 Answer E #### E QUESTION:The average of first 10 odd numbers is? options: A)22 B)10 C)98 D)66 E)88 SOLUTION:Sum of 10 odd no. = 100 Average = 100/10 = 10 Answer:B #### B QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony? options: A)1:4 B)3:5 C)3:9 D)3:7 E)1:3 SOLUTION:Number of men in the colony = 4/7 (70) = 40 Number of women in the colony = 3/7 (70) = 30 Number of educated women in the colony = 1/5 (30) = 6 Number of uneducated women in the colony = 4/5 (30) = 24 Number of educated persons in the colony = 8/35 (70) = 16 As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 40 - 10 = 30 Number of educated men and uneducated men are in the ratio 10:30 => 1:3 Answer:E #### E QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: options: A)27% B)87% C)15% D)66% E)88% SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900. Face value = Rs. (50 x 20) = Rs. 1000. Dividend = Rs. 27 x 1000 = Rs. 135. 2 100 Interest obtained = 135 x 100 % = 15% 900 View Answer Discuss in Forum Answer: C #### C QUESTION:A,B and C started a business by investing Rs.800/- , Rs.1,000/- and Rs.1,200/- respectively for two years. Total profit is Rs.1000/-. Find the C's share? options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 800 E)Rs. 900 SOLUTION:Solution: A : B : C = (800 * 2) : (1,000 * 2) : (12,000 * 2) = 4 : 5 : 6. So C's share = Rs. (1000 * 6/15) = Rs. 400. Answer: Option C #### C QUESTION:What is the tens digit of 36^12? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:36^10 = 6^24 (6^2)=6*6 = 36 (6^3)= 36*6 = .16 (6^4)= .16*6 = ..96 (6^5) = ..96*6 = ..76 (6^6) = ..76*6 = ...56 (6^7) = ....56*6 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9 #### E QUESTION:A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1? options: A)A-20. B)A-12. C)A-9. D)A-10. E)A-13. SOLUTION:We could use the following logic: since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n). The condition here should now be 11K + 1 = <operation> such that it gives us an integer 11k +1 = A -20 => A = 11K + 21 Not divisible by 11 11K +1 = A -12 => A = 11K + 31 Not Divisible by 11 11K +1 = A -9 => A = 11K + 10 Not Divisible by 11 11K +1 = A -10 => A = 11K + 11Divisible by 11 11K +1 = A -13 => A = 11K + 14 Not Divisible by 11 Answer therefore is A -10 (D) #### D QUESTION:What is the difference between the local values of 4 in the number 54404? options: A)2992 B)3996 C)2877 D)2077 E)1211 SOLUTION:Explanation: 4000 – 4 = 3996 Answer:B #### B QUESTION:How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number. options: A)1875 B)2000 C)2375 D)2500 E)3875 SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375 ANSWER:C #### C QUESTION:Four persons enter the lift of a six storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor options: A)625 B)1296 C)1540 D)1478 E)360 SOLUTION:Each person out of 4 has 5 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 5*5*5*5=5^4=625. Answer: A. #### A QUESTION:A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze? options: A)154 cm2 B)113 m2 C)123 m2 D)115 m2 E)None of these SOLUTION:Area of the shaded portion = 1⁄4 × π × (12)2 = 113 m2 Answer B #### B QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)25 B)15 C)18 D)47 E)26 SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d? options: A) 5/6*d B) 7/3*d C) 10/3*d D) 7/2*d E) 9/2*d SOLUTION:Favid has d books; Jeff has d/3 books; Paula has 2d books; Total = d+d/3+2d=10d/3. Answer: C. #### C QUESTION:In a kilometer race, A can give B a 100 m start and C a 150 m start. How many meters start can B give to C? options: A)50 B)50/9 C)8500/9 D)500/9 E)None of these SOLUTION:A can give B a 100 m start and C a 150m. Start means when A runs 1000m, B runs 900m and C runs 850m. When B runs 1000m, C will run 1000 x (850/900) m (i.e. 8500/9 m) Thus, B can give C a start of - 1000 - (8500/9), i.e. 500/9 m. Answer: D #### D QUESTION:Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved? options: A)56% B)64% C)62.2% D)68% E)61% SOLUTION:If initial cost is Rs 100, then Final cost will be 100*0.7*0.6*0.9 = Rs. 37.8 savings = 100-37.8=62.2 so 62.2% ANSWER:C #### C QUESTION:Which of the following equations has a root in common with x^2−3x+2=0 ? options: A)x^2-2x+1=0 B)x^2-2x-1=0 C)x^2-x+1=0 D)x^2-3x+3=0 E)x^2-7x=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-2)= 0 so the two roots are 1 and 2. Now put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. A is the answer. #### A QUESTION:A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain? options: A)12.5% B)16.7% C)22.5% D)27.5% E)33.3% SOLUTION:Let x be the original number of each color so there are a total of 5x candies. Kaz eats all of the green candies and half of the orange ones. There are 0 green candies and 0.5x orange candies remaining. He eats half of the remaining pieces of each color. There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies. He eats red and yellow candies in equal proportions. orange+blue+red+yellow = 0.75x + red + yellow = 1.2x red + yellow = 0.45x red = 0.225x, since red = yellow. The answer is C. #### C QUESTION:E and F have a data plan which gives them 200 GB every month. If E uses 7 GB every 9 days and F uses 5 GB every 4 days, how many GB will be unused after a 30 day month? Answer in fractions. options: A)365/6 B)73/6 C)35/6 D)835/6 E)200/6 SOLUTION:Number of GB that E uses every day: 7/9 Number of GB that F uses every day: 5/4 Number of GB that E and F use every day: 7/9+5/4=73/36 Number of GB that E and F use in 30 days: 30x(73/36)=365/6 Number of GB remaining: 200-365/6=835/6 Answer is D #### D QUESTION:30 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days? options: A)87 B)18 C)17 D)36 E)10 SOLUTION:Binders Books Days 30 1400 21 x 1600 20 x/30 = (1600/1400) * (21/20) => x = 36 Answer:D #### D QUESTION:The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.2 the sixth number is? options: A)10.3 B)11.3 C)11.8 D)11.5 E)11.1 SOLUTION:1 to 11 = 11 * 10.9 = 119.9 1 to 6 = 6 * 10.5 = 63 6 to 11 = 6 * 11.2 = 67.2 63 + 67.2 = 130.2 – 119.9 = 10.3 6th number = 10.3 Answer: A #### A QUESTION:What sum of money put at C.I amounts in 2 years to Rs.7000 and in 3 years to Rs.9261? options: A)4000 B)8877 C)2877 D)2678 E)1011 SOLUTION:7000 ---- 2261 100 ---- ? => 32.3% x *1323/100 * 1323/100 = 7000 x*1.75=7000 x=7000/1.75 => 3999.25 Answer: A #### A QUESTION:The number of arrangements that can be made with the letters of the word LUCK so that the vowels occupy the even places? options: A)5 B)3 C)6 D)1 E)2 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways. Hence the total ways are 1 * 6 = 6. Answer:C #### C QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Method #1: Using the permutation formula # of 5 letter code words: nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6 # of 4 letter code words: nPr = 10! / (10 – 4)! = 10*9*8*7 # of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7) = 6 = 6/1 Answer is E. #### E QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2400? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2400 * 1/3 = 800 Option A #### A QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.2 x = 3.2 Alternate solution: Try to backsolve. Initial volume = 3.2 After one hour --> (1/4)3.2 = 0.8 After two hours --> (1/4)0.8 = 0.2 Answer: B #### B QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:60*5:36*6:75*3 100: 72: 75 72/247 * 7410 = 2160 Answer: A #### A QUESTION:In the faculty of Reverse-Engineering, 240 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total? options: A)515. B)545. C)661. D)644. E)666. SOLUTION:Answer is C :661 Solution : Total number of students studying both are 423 + 240 - 134 = 529 (Subtracting the 134 since they were included in the both the other numbers already). So 80% of total is 529, so 100% is approx. 661. #### C QUESTION:The sale price sarees listed for Rs.528 after successive discount is 20% and 10% is? options: A)288 B)277 C)380 D)290 E)262 SOLUTION:528*(80/100)*(90/100) = 380 Answer: C #### C QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:If a and b are integers and (2^a)(3^b) is a factor of 900^40, what is the largest possible value of ab? options: A)2a B)5a C)20a D)40a E)80a SOLUTION:(2^a)(3^b) is a factor of 900^40 We need to find the largest possible value of ab. We know that 900 = 2^2*5^2*3^2 Therefore 900^40 will have 2 powers of 3 in it. Hence in (2^a)(3^b), b has to 2 Therefore value of ab = 2a Correct Option: A #### A QUESTION:If the simple interest on a certain sum of money for 2 years is one–fifth of the sum, then the rate of interest per annum is options: A)14% B)7% C)10% D)15% E)3% SOLUTION:Explanation: Let the Principal(P) be x Then, Simple Interest(SI) = x/5 Time(T) = 2 years Rate of interest per annum(R) = (100×SI)/PT = (100 × (x/5)/(x × 2) = 20/2 = 10% Answer: Option C #### C QUESTION:The present ratio between the ages of Paul and Ben is 5:2. In 4 years time Paul will be 28. What is the present age of Ben? options: A)13 B)12 C)11 D)15 E)10 SOLUTION:Let the present ages of Paul and Ben be 5x years and 2x years respectively 4x+4 = 28 4x = 24 x = 6 Ben's age = 2x = 12 years Answer is B #### B QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 6 years older than B the present age of B is options: A)37 B)36 C)39 D)40 E)41 SOLUTION:let present age of A be a and B be b a+10 = 2*(b-10) => 2b-a = 30 ......(i) a = b+6 =>2b-b-6 = 30 b=36 so the present age of b is 36 years ANSWER:B #### B QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours? options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44) SOLUTION:Explanation: Here clock-wise and anti-clockwise arrangements are same. Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}} Answer: C) 18!(6 x 24) #### C QUESTION:What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad? options: A)814 B)266 C)287 D)999 E)661 SOLUTION:Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = Required number of tiles = = 814 Answer: A) 814 #### A QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number W of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:Circular arrangements= (n-1)! Hence (4!) = 24=W Answer is C #### C QUESTION:Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)16.80 × 4.50 + 4.4 B)1600 ÷ 40 + 16 × 2 C)5.5 × 8.4 + 34.6 D)1620 ÷ 20 – 1 E)1856.95 – 1680.65 – 96.3 SOLUTION:Others equal 80 whereas (c) equals 80.8. Answer C #### C QUESTION:If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars? options: A)3⁄20 B)11⁄60 C)9⁄40 D)1⁄5 E)2⁄15 SOLUTION:Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car. Half of them are men, and the other half are women, more precisely 60. It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total. Answer E #### E QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit? options: A)2777 B)2999 C)2799 D)2781 E)10500 SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 24500 * 3/7 = Rs. 10500.Answer: E #### E QUESTION:There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 4. If all 27 of the integers were listed, what would their sum be? options: A)6693 B)6793 C)6893 D)6993 E)7093 SOLUTION:There must be nine 1's in the hundreds place, nine 1's in the tens place, and nine 1's in the units place. This is also true for the 2's and 4's. Then the sum is: 9(111+222+444)=9*(777)=6993. The answer is D. #### D QUESTION:100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads? options: A)33/100 B)41/101 C)51/101 D)87/101 E)98/101 SOLUTION:Let aa be the number of coins showing heads Then, P(A=50)=P(A=51)P(A=50)=P(A=51) ⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101 C #### C QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent? options: A)75% B)67% C)29% D)55% E)45% SOLUTION:600 --- 400 100 --- ? => 67% Answer: B #### B QUESTION:If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r? options: A)2 B)3 C)4 D)5 E)Cannot be determined SOLUTION:\frac{15^r( 1+ 15)}{4^y} = 15^y (15^r . 4^2 ) / 4^y = 15^y. 4^0 15^r . 4^(2-y) = 15^y. 4^0 Equating the powers, r = y; 2-y = 0; So r = y = 2=A #### A QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speed∗Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:90, 180, 12, 50, 100, 80, ?, 3, 20, 4, 25, 2, 6, 30, 3 options: A)100 B)150 C)180 D)90 E)60 SOLUTION:30*3=90 6*30=180 6*2=12 25*2=50 4*25=100 20*4=80 3*20=60 ans is 60 ANSWER:E #### E QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of B. options: A)250 B)450 C)750 D)800 E)None of them SOLUTION:C's 1 day's work = 1/3-(1/6+1/8)=24 A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1. A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450 C's share = Rs. [1200 - (300 + 225») = Rs. 150. Answer is B #### B QUESTION:6x − 12 = 6y 5y + 5x = 10 Which of the following is the number of solutions to the system of equations shown above? options: A)More than three B)Exactly three C)Exactly two D)Exactly one E)None SOLUTION:6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 5y + 5x = 10 =>x + y = 2 -- 2 From equation 1 and 2 , we get 2x = 4 => x=2 y=0 Therefore , the given system will have Exactly one solution D #### D QUESTION:If each side of a square is increased by 20%, find the percentage change in its area? options: A)40% B)42% C)46% D)44% E)38% SOLUTION:let each side of the square be a , then area = a x a New side = 120a / 100 = 6a / 5 New area =(6a x 6a) / (5 x 5) = (36a²/25) increased area== (36a²/25) - a² Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44% answer :D #### D QUESTION:ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region? options: A)1:1 B)2:1 C)3:1 D)5:3 E)8:3 SOLUTION:Let's join the midpoints as shown in the figure then we'll get four small squares... AODX be 1 and similarly all squares..and we can split the unit 1 into half and half as per the mid points... Then shaded will be 1+1/2+1/2+1/2 = 5/2 and unshaded is 1/2+1/2+1/2 = 3/2.. shaded : unshaded is 5:3.. ANS option D. #### D QUESTION:The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 3: 00 p.m., at what time were there 32 million bacteria in the dish? options: A)6: 00 p.m. B)9: 00 p.m. C)6: 00 a.m. D)8: 00 a.m. E)10: 00 a.m. SOLUTION:Given: The number of bacteria in a petri dish increased by 50 percent every 2 hours There were 108 million bacteria in the dish at 2: 00 p.m Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours. Required: At what time were there 32 million bacteria in the dish? Assume that there were n intervals of 2 hours between 32 million and 108 million. 32 * (1.5)^n = 108 (3/2)^n = 108/32 = 27/8 = (3/2)^3 Hence n = 3 intervals. Each interval was of 2 hours. Therefore, the number of hours = 6 Subtracting 6 hours from 3 PM, we get 9 AM as the answer. Option B #### B QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 8 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 5 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 8 days; So for 4 days, it will be = 8 x 5 / 4 = 10 So, 10-5 = 5 Answer A #### A QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3600 C)Rs. 3900 D)Rs. 4000 E)Rs. 4100 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C #### C QUESTION:Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178? options: A)2277 B)2669 C)2200 D)2766 E)2998 SOLUTION:Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178. => (90%) of (110%) of x = Rs. 2178. => (90/100)(110/100)x = 2178 => x = (2178 * 100)/(9 * 11) => x = Rs. 2200 Answer: C #### C QUESTION:The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer? options: A)5 B)3 C)4 D)2 E)1 SOLUTION:Let the second integer be x and the fourth be a. Then [3x + x + (x+2) + a]/4 = 9 => 5x + 2 + a = 36 => 5x + a = 34 => a = 34 - 5x From the above equation we can see that a is minimum when x is maximum, provided both are positive The maximum value that x can take in the above equation while still keeping a positive is x=6 This gives us a= 34 - 30 = 4 Therefore the minimum value that the fourth integer can have is 4. Answer:C #### C QUESTION:9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90.5% B)87.5% C)80.5% D)77.5% E)70.5% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.212; 10+0.3} = {9.788; 10.212}. From the 8 listed numbers, 7 are within this range so 6/8=87.5%. Answer: B. #### B QUESTION:What is 35% of 4/13 of 585? options: A)52 B)63 C)74 D)85 E)96 SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate. The number 585 is between 540 and 630, so (1/9)*585 will be about 65. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently. The closest answer is 63, so this is the answer to choose. The answer is B. #### B QUESTION:A train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. options: A)45 kmph B)50 kmph C)55 kmph D)60 kmph E)70 kmph SOLUTION:Explanation: Let the speed of the train be x kmph. Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec. Therefore 100/((x+5)×5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55 Speed of the train is 55 kmph. Answer: Option C #### C QUESTION:If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b = options: A) −48 B) −2 C) 2 D) −7 E) 48 SOLUTION:a(a + 7) = 18 and b(b + 7) = 18 => a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively => a+b = -7 Ans: D #### D QUESTION:At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes? options: A)2150 B)2600 C)3120 D)1500 E)1895 SOLUTION:Winner votes = 100-30 = 70 polled votes = [(100*1000)/2*70-100]+100 = 2600 Answer is B #### B QUESTION:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there. It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week). We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat). => 3* odd is again odd. 2 * age of students is always even. So final equation is even +odd = odd. Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer A. #### A QUESTION:There are three departments having students 64,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required? options: A)73 B)74 C)75 D)76 E)77 SOLUTION:WE NEED TO TAKE GCD WHICH IS 2 THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT 1) 64/2 = 32 2) 58/2 = 29 3) 24/2 = 12 TOTAL NO. OF MIN ROOMS REQD = 32+12+29 = 73 ANSWER:A #### A QUESTION:A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy options: A)s. 600 B)s. 800 C)s.500 D)s.900 E)s. 1300 SOLUTION:Let the cost of one toy = X. Then, cost of 18 toys = 18X. Gain = 3X. SP of 18 toys = Rs. 27300. Gain = SP – CP 3X = 27300 – 18X 21X = 27300 X = Rs. 1300. ANSWER : OPTION E #### E QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? options: A)10 B)99 C)787 D)62 E)22 SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18 T = 50 D = 50 * 100/18 = 2500/9 RS = 60 + 40 = 100 * 5/18 T = 2500/9 * 18/500 = 10 sec Answer: A #### A QUESTION:A man can row upstream at 10kmph and downstream at 24 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)7 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(24 -10) kmph = 7 kmph. Answer C #### C QUESTION:Some of the 50% solution of acid was removed and this was replaced with an equal amount of 14% solution of acid. As a result, a 23% solution of acid was obtained. What fraction of the original solution was replaced? options: A)1/2 B)1/3 C)2/3 D)3/4 E)4/5 SOLUTION:Let x be the fraction of the original solution that was replaced. 0.5*(1-x)+0.14(x)=0.23 0.36x=0.27 x=3/4 The answer is D. #### D QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these SOLUTION:Explanation: Let their ages be x and (x + 24) years. 5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11. Their present ages are 35 years and 11 years Option D #### D QUESTION:Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: options: A)175.5 B)170 C)169.5 D)180 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. average price = 126+135/2 = 130.50 o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x - 153 = 22.50 x = 175.50 ANSWER A #### A QUESTION:S1 = 5 S2 = 8 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50? options: A)15 B)14 C)13 D)12 E)16 SOLUTION:term 16 = 3*16+4 = 52 Answer : E #### E QUESTION:The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 80%? I will see what is the quickest way to solve it then I will provide the explanation options: A)6 B)7 C)9 D)10 E)11 SOLUTION:The following approach might be the easiest one and less error prone. We need on-time departure rate to be higher than 8/10, so it should be at least 9/11, which means that 9 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 9-3=6 subsequent flights need to depart on-time. Answer: A #### A QUESTION:A certain telescope increases the visual range at a particular location from 70 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ? options: A) 30% B) 33 1/2% C) 40% D) 60% E) 114.28% SOLUTION:Original visual range = 70 km New visual range = 150 km Percent increase in the visual range by using the telescope = (150-70)/70 * 100% = 8/7 * 100% = 114.28 % Answer E #### E QUESTION:A company pays 12.5% dividend to its investors. If an investor buys Rs.40 shares and gets 25% on investment, at what price did the investor buy the shares? options: A)20 B)66 C)18 D)19 E)01 SOLUTION:Explanation: Dividend on 1 share = (12.5 * 40)/100 = Rs.5 Rs.25 is income on an investment of Rs.100 Rs.5 is income on an investment of Rs. (5 * 100)/25 = Rs.20 ANSWER: A #### A QUESTION:You roll N (N > 1) number of M (M > 1) sided dice at once. What is the probability they will all land on the same number? options: A)N/(M^N) B)M/(N^M) C)1/(M^(N-1)) D)1/(N^(M-1)) E)1/(M-1)^N SOLUTION:The correct rolls are any M-ples: 11...1, 22...2, ..., MM...M. This is makes M possibilities. The N dice can roll M*M*...*M (M^N) number of ways. Thus the probability of landing on the same number is M/(M^N) = 1/(M^(N-1)). Answer: C. #### C QUESTION:There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. options: A)300 B)T=400 C)T=500 D)600 E)None of these SOLUTION:{Managers} = {Female Managers} + {Male Managers}; We are told that the total number of managers in the company is 2/5 of all the employees , thus {Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively. Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200; Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500. Answer: C. #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches were made? options: A)84 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 240 / 20 = 12 sandwiches in one part For bologna we have 7 parts so: 7 *12 = 84 Answer is A #### A QUESTION:A die is tossed. Find the probability of getting a multiple of 2 ? options: A)1/5 B)2/3 C)1/6 D)1/3 E)1/2 SOLUTION:S = {1,2,3,4,5,6} E= event of getting a multiple of 2 = {2,4,6} P(E) = 3/6 = 1/2 Answer is E #### E QUESTION:How much is 80% of 60 is greater than 4/5 of 25? options: A)15 B)28 C)16 D)12 E)73 SOLUTION:(80/100) * 60 – (4/5) * 25 48 - 20 = 28 Answer: B #### B QUESTION:If circles x and y have the same area and circle x has a circumference of 14π, half of the radius of circle y is: options: A)16 B)8 C)4 D)3.5 E)1 SOLUTION:x be radius of circle x y be radius of circle y given: pi*x^2 = pi*y^2 also, 2*pi*x = 14*pi x =7 thus y =7 y/2 = 3.5 Ans: D #### D QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day. options: A)20 B)10 C)25 D)15 E)24 SOLUTION:work completed in a day by one men = 1/25 = (1/5)*(1/5) So it takes 25 men to complete this job = 25 * (1/25) = 1 Answer: C #### C QUESTION:a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12 options: A)7 B)8 C)9 D)10 E)11 SOLUTION:add 44+12=56 now 56divided by 12 so we get 8 as reaminder ANSWER:B #### B QUESTION:The sector of a circle has radius of 35 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)91.8 cm D)92.5 cm E)152.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 35) + 2(35) = 49.5 + 70 = 152.5 cm Answer:E #### E QUESTION:A scuba diver descends at a rate of 30 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 2400feet below the sea level..how long will he take to reach the ship? options: A)70 minutes B)72 minutes C)80 minutes D)76 minutes E)77 minutes SOLUTION:Time taken to reach = 2400/30= 80 minutes ANSWER:C #### C QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:Mr Katial buys a house for Rs 1,00,000 and rents it. He puts 12.5% of each month’s rent aside for upkeep and repairs, pays Rs 325 per year as taxes and realizes 5.5% annually on his investment . Find the monthly rent? options: A)Rs 634.76 B)Rs 554.76 C)Rs 654.76 D)Rs 664.76 E)none of these SOLUTION:Let the monthly rent be Rs X. We have, 5.5% of 100000 = 12 (X - 12.5% of X) - 325 5500/12 = X - (X/8) - 325/12 5500/12 + 325/12 = 7/8 x X X = 5825/12 x 8/7 Rs 554.76 per month ANSWER:B #### B QUESTION:A "word" is defined as a sequence of three dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed? options: A)3 B)5 C)6 D)8 E)9 SOLUTION:there are two ways of possibilities.. 1) all three same colour- YYY or BBB- 2 ways 2) two of one colour and one of different colour- 3!/2!-3ways.. now two /one could be Y/B or B/Y.... so 3*2=6.. total 6+2=8 ans D #### D QUESTION:A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? options: A)3 B)4 C)5 D)8 E)2 SOLUTION:M = 4 S = 2 US = 4 - 2 = 2 D = 6 T = 6/2 = 3 Answer: A #### A QUESTION:A ranch has both horses and ponies. Exactly 3/10 of the ponies have horseshoes, and exactly 5/8 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? options: A)116 B)132 C)148 D)164 E)180 SOLUTION:3/10*P are ponies with horseshoes, so P is a multiple of 10. 5/8*3/10*P = 3/16*P are Icelandic ponies with horseshoes, so P is a multiple of 16. The minimum value of P is 80. Then H = P+4 = 84. The minimum number of horses and ponies is 164. The answer is D. #### D QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer: A #### A QUESTION:What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11, 60 and 61? options: A)6.5 B)12.5 C)28 D)30.5 E)40 SOLUTION:Some of pyhtagron triplets we need to keep it in mind. Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61). So now we know the triangle is an right angle triangle. The circle circumscribes the triangle. The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5 Ans. D #### D QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 14 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)17 E)72 SOLUTION:Explanation: As there is meal for 70 adults and 14 have their meal, the meal left can be catered to 56 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 56 adults = 72 children Hence, the meal can be catered to 72 children. ANSWER: E #### E QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:A train 120 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)16 kmph B)88 kmph C)54 kmph D)18 kmph E)27 kmph SOLUTION:S = 120/16 * 18/5 = 27 kmph Answer: E #### E QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%? options: A)5% B)28% C)27% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 70 2/3 SP1 = 70 SP1 = 105 100 --- 5 => 5% Answer:A #### A QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2. options: A)Cannot be determined B)1 C)2 D)3 E)4 SOLUTION:take square of any prime number remainder will be 1 Ans B #### B QUESTION:A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many Q apples did each person get before 45 people joined the feast? options: A)20. B)21. C)22. D)23. E)24. SOLUTION:Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13. Since number of apples per person * total persons Q= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C #### C QUESTION:What is the HCF of 2/3, 4/15 and 6/5 options: A)7/45 B)2/45 C)4/15 D)8/45 E)2/15 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 4, 6)/(LCM of 3, 15, 5) = 2/15 Answer: Option E #### E QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)40 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:Tough and Tricky questions: Combinations. Seven contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? options: A)6 B)7 C)12 D)16 E)21 SOLUTION:Number of ways First-place medal can be awarded to four contestants = 7 Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3 Therefore number of possibilities = 7*3 =21 Answer:E #### E QUESTION:How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest? options: A)2.35 years B)4.25 years C)7 years D)1.25 years E)2 years SOLUTION:Explanation: Time = (100 x 60)/(400 x 12) years = 1.25 years. Answer: D #### D QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision? options: A)2008 B)2004 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008. Answer: A. #### A QUESTION:What is the largest 4 digit number exactly divisible by 88? options: A)9944 B)9999 C)9988 D)9900 E)9987 SOLUTION:Largest 4 digit number = 9999 9999 ÷ 88 = 113, remainder = 55 Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 Answer: Option A #### A QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.988] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ? options: A)0 B)1 C)27 D)54 E)Cannot be determined SOLUTION:It cannot be determined.As we do not know the actual value of K. however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer K=[lCM of 80 and 45] * (any integer) for value of k(60) * any integer unit value will be always zero . A #### A QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:If -5 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy? options: A)-42 < xy < 30 B)-42 < xy < 24 C)-28 < xy < 18 D)-24 < xy < 21 E)-24 < xy < 24 SOLUTION:The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-5)*(-6)=30. Therefore -42 < xy < 30. Answer: A. #### A QUESTION:If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 25% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? options: A)50% B)75% C)120% D)133 1/3% E)150% SOLUTION:The price on June 1st = 12 (assume); The price on May 1st = 2/3*12 = 8; The price on July 1st = 8*1.25 = 10. The average price of the bond on May 1st and July 1st = (8+10)/2 = 9. The price of the bond on June 1st (12) is 4/3 times (134%) the average price of the bond on May 1st and July 1st. Answer: D. #### D QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ? options: A)95 B)110 C)20 D)None of these E)Cannot be determined SOLUTION:Solution 2/5of 350 - 4/7of 210 = 20. Answer C #### C QUESTION:If x is an integer and 2.134 × 10^x is less than 21000, what is the greatest possible value for x? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:If x=4 2.134 × 10^4 = 21340 > 21000 So, x = 3 Answer : E #### E <<<Examples ends QUESTION:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there. It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week). We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat). => 3* odd is again odd. 2 * age of students is always even. So final equation is even +odd = odd. Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer A. #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book? options: A)229 B)270 C)877 D)266 E)281 SOLUTION:Let xx be the total number of pages in the book, then she finished 23⋅x23⋅x pages. Then she has x−23⋅x=13⋅xx−23⋅x=13⋅x pages left. 23⋅x−13⋅x=9023⋅x−13⋅x=90 13⋅x=9013⋅x=90 x=270x=270 So the book is 270 pages long. Answer:B #### B QUESTION:A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 370440, then population in 1978 was? options: A)320000 B)120029 C)187899 D)178968 E)789698 SOLUTION:X * (105/100) * (105/100) * (105/100) = 370440 X = 370440/1.157625 X = 320000 Answer:A #### A QUESTION:If P * Q implies (P2 + Q2), 8 * (3 * 2) = ? options: A)239 B)278 C)233 D)2697 E)771 SOLUTION:Explanation: We have, P * Q = (P2 + Q2) ......... Given 8 * (3 * 2) = ? 8 * 13 = (64 +169) = 233 ANSWER: C #### C QUESTION:Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is: options: A)30% B)100/3% C)35% D)44% E)None of these SOLUTION:Explanation : C.P. of 6 articles = Rs. 5 => C.P. of 1 article = Rs. 5/6 S.P. of 5 articles = Rs. 6 => S.P. of 1 article = Rs. 6/5 Profit earned per article = 6/5 - 5/6 = 11/30 % Profit = 11/30∗6/5∗100% = 44% Answer : D #### D QUESTION:A can do a piece of work in 10 days and B alone can do it in 15 days. How much time will both take to finish the work ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea. Time taken to finish the job = XY / (X + Y) = 10 x 15 / (10 + 15) = 150 / 25 = 6 days Answer: B #### B QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow? options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10% So 8100+15100⋅x+10100⋅(8100−x)=9100 Therefore 8100+320x+110(8100−x)=9100 120x=190 x=3800 Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres correct answer is D)4370 lt #### D QUESTION:If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new numbers is : options: A)22 B)40 C)88 D)27 E)11 SOLUTION:Explanation: Let the numbers are By Hypothesis , ......(i) Mean of new numbers = By (i) Answer: B) 40 #### B QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4*side = 4* (3p/5) = 12p/5 Answer is C. #### C QUESTION:The sale price sarees listed for Rs.528 after successive discount is 20% and 10% is? options: A)288 B)277 C)380 D)290 E)262 SOLUTION:528*(80/100)*(90/100) = 380 Answer: C #### C QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is? options: A)150 m B)778 m C)200 m D)276 m E)971 m SOLUTION:2(l + 150) = 600 => l = 150 m Answer:A #### A QUESTION:If it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed? options: A)400 B)420 C)480 D)500 E)600 SOLUTION:Minimum no of mail to be sent for getting 300 responses at 50% = 300/0.5 = 600 Option E #### E QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)26% C)42% D)27% E)22% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer: A #### A QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.4 B)3.9 C)4.1 D)4.2 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| = options: A)ab-4+b B)2b-ab-4 C)ab+4 D)ab-2b+5 E)4-ab SOLUTION:Given: |ab| = ab and |a| = -a Question: |b-3| + |ab-b| = ? **** Looking at |ab| = ab tells us that a and b are either both positive or negative **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: a and b are both negative values Let a=-1 and b=-1 |b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5 Test a) ab-4 = (-1)(-1)-4 = -5 Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7 Test c) ab+4 = 1 + 4 = 5 Answer: C #### C QUESTION:Which of the following is satisfied with |x-4|+|x-3|<6? options: A)1<x<5 B)2<x<5 C)0.5<x<6.5 D)0.5<x<4 E)3<x<4 SOLUTION:--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5 Therefore, the answer is C. #### C QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/5 meter and also 1/8 meter, and then if the cable were cut at each mark, how many different size length of cable would result? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:In this particular example length (10 meter) is just extraneous information. The location of the marks for 1/3 meter would be 8/40, 16/40, 24/40, 32/40, 40/40, etc... The location of the marks for 1/8 meter would be 5/40, 10/40, 15/40, 20/40, 25/40, 30/40, 35/40, 40/40, etc... The distances between marks are 5/40, 3/40, 2/40, 1/40, and 4/40. The answer is E. #### E QUESTION:If x:y=9:4 then (7x-3y) : (7x+3y)=? options: A)51:76 B)6:13 C)51:75 D)51:76 E)None of these SOLUTION:Explanation: x/y = 9/4 (Given) (7x − 3y)/(7x + 3y) 7(x/y) − 3/7(x/y)+3 ( on dividing Nr and Dr by y) (7(9/4) − 3)/(7(9/4) + 3) (63/4 − 3/1)/(63/4 + 3/1) [(63 − 12)/4]/[(63 + 12)/4] = 51/75 (7x-3y) : (7x+3y) = 51:75 Answer: Option C #### C QUESTION:Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton? options: A)330 B)300 C)252 D)225 E)210 SOLUTION:Baker Ram is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5. To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210. Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210. #### E QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water? options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3 SOLUTION:G = 10W C = 5W Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy 1gm gold + x gm copper = x+1 gm of alloy 10W+5Wx = x+1 * 6W 10+5x = 6(x+1) x = 4 Ratio of gold with copper = 1:4 = 1:4 Answer is B #### B QUESTION:If y > 0, (8y)/20 + (3y)/10 is what percent of y? options: A)40% B)50% C)60% D)70% E)80% SOLUTION:can be reduced to 4y/10+3y/10 =7y/10=70% Answer D #### D QUESTION:Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood? options: A)a) 90 B)b) 100 C)c) 110 D)d) 130 E)e) 140 SOLUTION:C. 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3rd piece (sorted in increasing length) length = 140 (median) for sum of first 2 wood length to become max, last two should be least. let 4th, 5th wood also have length 140 each. total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220/2 = 110 Answer C #### C QUESTION:Find the length of the wire required to go 12 times round a square field containing 104976 m2. options: A)15840 B)3388 C)2667 D)8766 E)15552 SOLUTION:a2 = 104976 => a = 324 4a = 1296 1296 * 12 = 15552 Answer: E #### E QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)18 B)24 C)42 D)81 E)28 SOLUTION:Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 * 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. ANSWER:B #### B QUESTION:Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 3 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? options: A)1/24 B)1/8 C)1/4 D)1/3 E)3/8 SOLUTION:I hope you are familiar with basic probability fundas - Let's say you have just ONE letter and TWO envelopes ONE of which is correctly addressed and the other addressed incorrectly. What's the probability of putting the Letter in the correctly addressed envelope - To answer this question - we see IN HOW MANY WAYS can the letter be put into the envelope - you could put it (assuming you don't know which envelope is which) in either of the two - so in total you have TWO ways of shoving the letter in. However, there's only ONE way in which it can go into the correctly addressed envelope - so 1/2 is the prob of putting in correct envelope. This is easy. Now in our current problem - let's say we have just ONE letter but FOUR envelopes. Only one of these envelopes has the address corresponding to the letter. The remaining three envelopes are incorrectly addressed. So the probability that you will put the letter correctly is 1/4. Right? What happens if i ask you the reverse question? what is the prob for putting it in the incorrect envelope. Suddenly you have three envs that are incorrect so you can put the letter incorrectly with a prob of 3/4. Right? The whole problem can be broken down into Four Events that will fulfill the requirement of the question Event 1 - E1 We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the first letter goes into the correct envelope) we have the remaining THREE Letters and THREE envelopes. Event 2 - E2 Let's take letter number 2 now - what is the probability that it LANDS in the INCORRECT envelope. Again by the same logic as above - there are 3 envelopes remaining out of which ONLY ONE has the correct address for LETTER number 2. The remaining 2 have INCORRECT address and LETTER NUMBER 2 could go in either of these 2 to meet our condition. Thus the probability of this event is 2/3 So till now what we have done is - we have calculated the prob of shoving Letter number 1 in correct env -- 1/4 we have calculated the prob of shoving Letter number 2 in INcorrect env --- 2/3 Event 3 - E3 Now let's take letter number 3 - again according to question we want to shove this in the WRONG envelope. There are 2 remaining envelopes and hence the prob of shoving this in the wrong env (or equally in the RIght env) is 1/2. Finally we come to event E4 - the Letter number 4. This has only one way of going in so its probability of being put into the WRONG envelope is 1. ok so we can see that our grand event is actually a combination of FOUR EVENTS happening - each with a probability of its own. So to calculate the total probability of the Grand Event itself we just multiply the individual probabilities since each event happens INDEPENDENTLY of each other Egrand = 1/4 * 2/3 * 1/2 * 1/1 = 1/12 However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result. If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 and worked thru the remaining letters, we could have equally well started out with letter L2 or L3 or L4. Thus since each of these events ARE MUTUALLY EXCLUSIVE, meaning THEY CAN NEVER HAPPEN ALL THE SAME TIME BUT ONLY ONE LETTER AT A TIME, to calculate the TOTAL PROBABILITY of we will add the individual probabilities 1/12 + 1/12 + 1/12 + 1/12 which works out to 1/8. B #### B QUESTION:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts? options: A)6 B)14 C)19 D)20 E)81 SOLUTION:< 6 hours sleep>= 6 hours sleepTOTAL Tired75-- Not Tired-0.7*X? TOTAL80X100 Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5; TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14; Interns who areNot Tired S= 5 + 14 = 19. Answer: C. #### C QUESTION:Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.72000 after completion of one year. What will be Jose's share of profit? options: A)20000 B)10000 C)25000 D)34000 E)40000 SOLUTION:SoL = ~s- So Anju’s share = [5/9] x 72000 = 40000 E #### E QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)12% C)22% D)24% E)21 SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer:A #### A QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 21,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 147% D) 150% E) 225% SOLUTION:The percent increase is (21947-8902)/8902=13045/8902=1.47 So the approximate answer is C #### C QUESTION:Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 5 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes? options: A) 5.5% B) 3.6% C) 4.4% D) 5.2% E) 6.0% SOLUTION:Let amount spent by Jill = 100 Clothing=50, Food=20, others=30 Tax on clothing= 2.5 Tax on others=3 Percentage= 5.5/100=5.5% Answer: A #### A QUESTION:The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score. options: A)172 B)173 C)174 D)175 E)None of the above SOLUTION:Total runs = 40 × 50 = 2000 Let his highest score be = x Then his lowest score = x – 172 Now 200−x−(x−172)/38=48 ⇒ 2x = 2172 – 1824 ⇒ x = 174 Answer C #### C QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 24 metre of cloth ? options: A)175 seconds B)195 seconds C)155 seconds D)188 seconds E)115 seconds SOLUTION:Explanation: Let the time required by x seconds. Then, More cloth means More time (Direct Proportion) So, 0.128 : 1 :: 24 : x => x = {\color{Blue} \frac{24\times 1}{0.128}} => x = 187.5 So time will be approx 188 seconds Answer: D #### D QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)287 m B)350 m C)187 m D)197 m E)186 m SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer: B #### B QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is: options: A)233 B)37 C)25 D)27 E)11 SOLUTION:Explanation: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x Gain = (5x - 4x) = Rs. x Gain % = (x * 100)/ 4x = 25%. Answer: C #### C QUESTION:In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ? options: A)12 B)27 C)26 D)11 E)22 SOLUTION:Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11. Answer: D #### D QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)276 m B)279 m C)240 m D)207 m E)285 m SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 39 = 15 x + 300 = 585 x =285m. Answer: E #### E QUESTION:The average of first 18 even numbers is? options: A)19 B)18 C)16 D)11 E)17 SOLUTION:Sum of 18 even numbers = 18 * 19 = 342 Average = 342/18 = 19 Answer:A #### A QUESTION:A and B finish the job in 15 days.while A,B and C can finish it in 12 days . C alone will finish the job in options: A)40 days B)30 days C)60 days D)70 days E)50 days SOLUTION:Explanation: 12 = (15 * x)/(15 + x) 180+12x=15x 3x=180 X=60 Answer: Option C #### C QUESTION:A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work? options: A)30 days B)20 days C)25 days D)35 days E)45 days SOLUTION:Work done by A in 10 days = 10/80 = 1/8 Remaining work = (1 - (1/8)) = 7/8 Now, work will be done by B in 42 days. Whole work will be done by B in (42 x 8/7) = 48 days Therefore, A’s one day’s work = 1/80 B’s one day’s work = 1/48 (A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30 Hence, both will finish the work in 30 days. ANSWER:A #### A QUESTION:What percentage of numbers from 1 to 20 have squares that end in the digit 9? options: A)1 B)14 C)20 D)21 E)22 SOLUTION:Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 18 are 3,7,13,17. Number of such numbers = 4. Required percentage = (4/18 * 100) = 22% ANSWER:E #### E QUESTION:Maddie has 15 apples, if she give 8 to mike, how many does she have left? options: A)1 B)7 C)3 D)4 E)5 SOLUTION:15-8=7 B. 7 #### B QUESTION:In how many different orders can the people Alice, benjamin Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, David, Charlene must be on the line before each of Frederick, Gale, and Harold? options: A)2016 B)1,296 C)1,512 D)2,018 E)2,268 SOLUTION:Place B and E first: 8 options for B, 7 options for E. We are left with 6 empty places. A, D and C must take first 3 places and F, G, H must take the remaining three. A, D and C can be arranged in their places in 3! ways. The same for F, G, and H. Total = 8*7*3!*3! = 2,016. Answer: A #### A QUESTION:There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks? options: A)5,15 B)4,15 C)5,10 D)4,10 E)5,20 SOLUTION:Assume you have locks 1-5 and keys A-E. Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum. Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D #### D QUESTION:Mr. Hernandez, who was a resident of State X for only 9 months last year, had a taxable income of $42,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year? options: A) $900 B) $1275 C) $1200 D) $1300 E) $1060 SOLUTION:Total tax for the year = 42,500 x 4% = 1700 As stated Annual tax is prorated as per the duration of stay. Prorated Tax = 1700 (9/12) = 1275 Answer B #### B QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)35 SOLUTION:Speed of the train relative to man = (63 - 3) km/hr = 60 km/hr =(60 x(5/18)) m/sec =50/3 m/sec. Therefore Time taken to pass the man =(500 x(3/50))sec = 30 sec. Answer :B #### B QUESTION:log(a(a(a)^1/4)^1/4)^1/4 here base is a. options: A)0 B)21/64 C)1 D)22/63 E)23/65 SOLUTION:log(a(a(a^1/4)^1/4)^1/4 => log(a(a^1+1/4)^1/4)^1/4 => log(a(a^5/4)^1/4)^1/4 =>log(a(a^5/16)^1/4 =>log(a^1+5/16)^1/4 =>log(a^21/16)^1/4 =>log(a^21/64) =>21/64 log(a) =>21/64 ANSWER:B #### B QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits? options: A)36 B)77 C)88 D)99 E)22 SOLUTION:Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1) Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2) Multiplying equation (1) by 2 and subtracting it from equation (2), we get => 2r = 72 => r = 36. Answer: A #### A QUESTION:A man has Rs.680 in the denominations of two-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)160 B)40 C)680 D)120 E)180 SOLUTION:Let number of notes of each denomination be x. Then 2x + 5x + 10x = 680 17x = 680 x = 40 Hence, total number of notes = 3x = 120. Answer is D #### D QUESTION:In how many different ways can change be provided for a one dollar bill using pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents), if at least two of each type of coin must be included? options: A)0 B)6 C)8 D)10 E)15 SOLUTION:I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any other coins. We cannot have all four coins represented if we have four quarters. Case I does not allow any ways. II. Case II = Three Quarters (75 cents) This does not allow for two each of the other coins. Case II does not allow any ways. III. Case III = Two Quarters (50 cents) This allows for 2-3 dimes. Subcase 1 = 2 Q, 3 D (80 cents) (2 ways) we could have 2-3 nickels Subcase 2 = 2 Q, 2 D (70 cents) (4 ways) we could have 2-5 nickels Case III allows for a total of 6 ways There's no other case, because we have to have at least two quarters and two dimes. The total over the cases equals Total = 0 + 0+ 6 =6 ways. OA =(B) #### B QUESTION:If 0.6 : x :: 5 : 8, then x is equal to: options: A)A)0.96 B)B)1.2 C)C)1.25 D)D)1.3 E)E)0.8 SOLUTION:(x * 5) = (0.6 * 8) x = 4.8/5 x = 0.96 Answer = A #### A QUESTION:A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture? options: A)1 kgs B)3 kgs C)5 kgs D)6 kgs E)None of these SOLUTION:Explanation : If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg. We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg. Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C. Step 1: Find out the ratio Qa:Qc using alligation rule. Qa/Qc=(30−25)/(25−20)=1/1. Step 2: Find out the ratio Qb:Qc using alligation rule. Qb/Qc=30−25/(25−24)=5/1. Step 3: Qc is found by adding the value of Qc in step 1 and step 2 =1+1=2. Therefore, the required ratio =1:5:2. If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture. Answer : C #### C QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 24*5= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 24*5 + 2y =124 then y=2 24*4 + 2y = 124 then y=14 24*3 +2y = 124 then y= 26 24*2 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:A certain street contains 100 buildings.They are numbered from 1 to 100. How many 9s are used in numbering these buildings? options: A)21 B)20 C)19 D)18 E)9 SOLUTION:9,19,29,39,49,59,69,79,89,90,91,92,93,94,95,96,97,98,99 so number of 9's=20 ANSWER:B #### B QUESTION:10 books are placed at random in a shelf. The probability that a pair of books will always be together is? options: A)1/0 B)1/3 C)1/5 D)1/2 E)1/1 SOLUTION:10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Answer: C #### C QUESTION:The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)80 kg B)85 kg C)90 kg D)100 kg E)110 kg SOLUTION:Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. B) #### B QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these SOLUTION:Reqd ratio 4 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100 = 4 × 140 : 7 × 150 : 8 × 175 = 8 : 15 : 20 Answer C #### C QUESTION:If the height of a right cone C is 3 and the diameter of the base of C is 8, what is the distance from the apex of C to any point on the circumference of the base of C? options: A)3√2 B)5 C)5√2 D)√(67) E)√(73) SOLUTION:height of cone=3 radius of base=4 so the distance from the apex of C to any point on the circumference of the base of C will be a right angled triangle Hence the distance is sqrt(3^2+4^2)= 5 ANSWER:B #### B QUESTION:Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ? options: A)500 B)600 C)450 D)550 E)None of these SOLUTION:Explanation: Let the lent at 5% be 'A' (A x 5 x 1)/100 + [(1500 - A)x 6 x 1]/100 = 85 5A/100 + 90 – 6A/100 = 85 A/100 = 5 => A = 500 ANSWER IS A #### A QUESTION:Ramu bought an old car for Rs. 43000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)22% E)of these SOLUTION:Total CP = Rs. 43000 + Rs. 13000 = Rs. 56000 and SP = Rs. 64900 Profit(%) = (64900 - 56000)/55000 * 100 = 16% ANSWER:B #### B QUESTION:Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 8 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score? options: A)24 B)30 C)40 D)50 E)60 SOLUTION:One way to do this would be weighted average method.. 1) let the average of 5 mocks be x... so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67... By alligation/weighted average.. the difference in 760 and 726.67 is 5/6 of difference of 760 and x.. 760-726.67 = 5/6 * (760-x) 760-x= 33.33*6/5=40... so x = 720.. the last of mock test will be 720+8+8=736... so ans = 760-736=24 A #### A QUESTION:Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he: options: A)broke even, B)lost 4 cents C)gained 4 cents D)lost 10 cents E)gained 10 cents SOLUTION:Solution: 20 % profit on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Similarly, 20 % loss on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24. Since both profit and loss amount is same so, it’s broke even. Answer: A #### A QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? options: A)289 B)132 C)279 D)277 E)278 SOLUTION:2 * 22/7 * 14 = 88 88 * 1 1/2 = Rs.132 Answer: B #### B QUESTION:Several people are sitting around a round table playing a card game with a deck of 67 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table? options: A)4 B)5 C)7 D)11 E)13 SOLUTION:Let n be the number of people at the table. If Martin gets the first and the last card, it means Martin got one more card than the others. Thus 67/n has a remainder of 1 and so 67-1 = 66 is a multiple of n. The answer is D. #### D QUESTION:In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)32% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 38 are employed males,hence 26% are employed females. (employed females)/(total employed people)=26/64=40% Answer: D. #### D QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. #### C QUESTION:If a man walks at the rate of 4 kmph, he misses a train by only 6 min. However, if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is options: A)3 km B)4 km C)5 km D)6 km E)7 km SOLUTION:Let the distance covered be d and time taken to reach the station in time t d/4 = t+6/60---(1) d/5 = t-6/60---(2) (1)-(2) gives d/4 - d/5 = (6+6)/60 d/20 = 12/60 d = 12*20/60 =4 km ANSWER:B #### B QUESTION:Find the number of solutions for 3x+4y=60, if x and y are positive integers options: A)1 B)2 C)3 D)4 E)5 SOLUTION:3x+4y=60 =>x=(60-4y)/3 as x and y are positive integers, put y=1,2,3,... & find x y=3,x=16 y=6,x=12 y=9,x=8 y=12,x=4 (x,y)=(4,12),(8,9),(12,6),(16,3) only 4 solution ANSWER:D #### D QUESTION:{3, 5, 8, y} For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y options: A)16/5, 28/3 B)4, 16/5 C)4, 16/5, 28/3 D)4, 28/3 E)3, 4, 5 SOLUTION:The set can have the following forms: 1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3 2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4 3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4 4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case. Thus the possible values are 4 and 28/3. D is the correct answer. #### D QUESTION:How many numbers are there between 200 and 800 which are divisible by both 5 and 7? options: A)35 B)16 C)17 D)can’t be determined E)None of these SOLUTION:Answer C Solution In the given range, the last number which is divisible by both 5 and 7. i.e., 35 is 210 and the highest number is 770. So the total number of numbers between 200 and 800 which are divisible by both 5 and 7 is (770-210/35)+ 1 = 17 Hence option C #### C QUESTION:Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)NOne SOLUTION:Sol. Average = 66 + 65 + 77 + 62 + 75 / 5) = (345 / 5) = 69. Answer B #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is options: A)1/4 B)1/2 C)3/4 D)3/5 E)None of these SOLUTION:The number of exhaustive outcomes is 36. Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2 P(E) = 1 - 1/2 = 1/2. Answer : B #### B QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price? options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 140 % ------> 560 (140 * 4 = 560) Selling price = Rs.560/- A #### A QUESTION:A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube? options: A)8p B)pq C)pq + 27 D)-p E)(p - q)^6 SOLUTION:A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject. B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject. C. Hold. D. since p is a perfect cube, -p will also be a perfect cube. reject. E. (p-q)^6, is a perfect cube, so reject. By elimination C is the answer. Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube. ANSWER:C #### C QUESTION:John deposited $10,000 to open a new savings account that earned 2 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened? options: A)$10,100.25 B)$10,101.50 C)$10,200.75 D)$10,201.00 E)$10,400.35 SOLUTION:2 percent annual interest compounded quarterly --> 0.5% in 3 moths. For the first 3 moths interest was 0.5% of $10,000, so $50; For the next 3 moths interest was 0.5% of $10,000,plus0.25 earned on previous interest of $100, so $50+$0.25=$50.25; Total interest for 6 months was $50+$50.25=$100.25, hence balance after 6 months was $10,000+ $100.25=$10,100.25. Answer: A. #### A QUESTION:Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = options: A)18 B)15 C)-13 D)-21 E)-24 SOLUTION:f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = f(4) = 0= 16+4b+c--- Taking 16 to the other side -> 4b+c= -16 f(-3) = 0= 9-3b+c --- taking -3b+c to the other side -> 3b-c=9 When we add these 2 equations, we get 7b= -7---> b= -1 And while substituting b= -1 we get c= -12. b+c= -13--- Answer C #### C QUESTION:In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary options: A)42,000 B)43,000 C)44,000 D)45,000 E)46,000 SOLUTION:as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned) Rest amounts are in the form of greater than or lesser than , Hence C $45000 answer is D #### D QUESTION:The average of 11numbers is 50. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number? options: A)A)188 B)B)65 C)C)58 D)D)62 E)E)48 SOLUTION:6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s answer = 6*58+6*65-11*50= 188 Answer is A #### A QUESTION:If the sum of a set of 5 different positive prime numbers is 94, what is the difference between largest and smallest prime numbers between them? options: A)53 B)51 C)47 D)41 E)31 SOLUTION:All prime numbers apart from 2 are odd. Even + Even = Even Odd + Even = Odd Odd + Odd = Even We are given 5 different prime numbers, whose sum is 94 i.e even If we include 2, we will have 4 odd prime numbers and one even. This sum would be odd If we exclude 2, we will have 5 odd numbers. This sum would be even Hence 2 is included. The possible 5 no. are = 11+7+2+43+31 = 94 the difference between largest and smallest prime numbers between them = 43 - 2 = 41 Ans - D #### D QUESTION:The reflex angle between the hands of a clock at 10.25 is: options: A)180º B)192 1/2 º C)195º D)197 1/2 º E)197 º SOLUTION:Angle traced by hour hand in 125/12 hrs ={(360/12)x(125/2)}º = 312 1/2 º . Angle traced by minute hand in 25 min =(360/60)x 25 º= 150º. Reflex angle = 360º -(312 1/2- 150º )= 360º - 162 1/2º= 197 1/2º . Answer: D #### D QUESTION:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 8 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)11 D)14 E)6 SOLUTION:Given: mean=21 and SD=8 The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=13 and 2 SD below the mean ismean-2*SD=5, so the number of hours that Pat watched television was between 5 and 13 hours. Answer: C #### C QUESTION:A rainstorm increased the amount of water stored in State J reservoirs from 160 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 50 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? options: A)240 B)250 C)260 D)270 E)300 SOLUTION:Let total capacity be x we know 200 = 0.50x x = 200/0.50 = 400 Prior to storm, we had 160 bn gallons 400-160 = 240 Answer : A #### A QUESTION:Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/10 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now? options: A)$110 B)$152.3 C)$180 D)$220 E)$260 SOLUTION:Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition. A-E = 1/10*(A+E) ==> 9A = 11E ------------ (1) Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E 1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2) Substituting (1) in (2): 11E/9*11 = 220+12E or (121/9-12) E = 220 or 13/9 E =220 E = 220*9/13 =152.3 B #### B QUESTION:Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36, find P (E|F) and P(F|E) options: A)5 B)8 C)2 D)6 E)12 SOLUTION:Here, E and F are events P(E|F) = P(EnF)/P(F) = 36/36 = 1 P(F|E) = P(EnF)/P(E) = 36/24 = 2. C) #### C QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ? options: A)35 years B)45 years C)51 years D)52 years E)None of these SOLUTION:Explanation: Age of the teacher = (38 * 15 - 37 * 14) years = 52 years. Answer: D #### D QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:Three people (1 couple and 1 single) are seated at random in a row of 4 chairs. What is the probability that the couple does not sit together? options: A)3/7 B)1/2 C)2/5 D)3/4 E)5/12 SOLUTION:The total number of arrangements of 3 people is 4*3*2 = 24 Let's think of the couple as a single unit. The number of arrangements when the couple sits together is 3*2*2 = 12. Note that we multiply by 2 because the couple can switch places with each other. The number of ways the couple won't sit together is 24 - 12 = 12 P(couple won't sit together) = 12/24 = 1/2 The answer is B. #### B QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done? options: A)144 B)180 C)192 D)360 E)None of these SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options. Task 2 can be assigned to 3 or 4 So, there are only 2 options for task 2. So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6. = 2 × 3 × 4 × 3 × 2 × 1 = 144 Answer A #### A QUESTION:The area of a triangle will be when a = 3m, b = 5m, c = 10m, a, b, c being lengths of respective sides? options: A)3 B)6 C)4 D)9 E)1 SOLUTION:S = (3 + 5 + 10)/2 = 9 Answer:D #### D QUESTION:What least number must be subtracted from 9679 so that the remaining number is divisible by 15? options: A)3 B)1 C)16 D)4 E)15 SOLUTION:On dividing 9679 by 15, we get remainder = 4. Required number be subtracted = 4 ANSWER:D #### D QUESTION:Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying science? options: A)52 B)65 C)115 D)158 E)168 SOLUTION:Given, boys and girls are in the ratio of 7 : 6, So, Number of boys = 7/13 x 390 = 210 Number of girls = 390 - 210 = 180 Students studying Arts and Science are in the ratio of 3 : 7, Number of students studying Arts = 3/10 x 390 = 117 Number of students studying Science = 390 - 117 = 273 Also boys and girls studying Arts are in the ratio of 4 : 5, Number of boys studying arts = 4/9 x 117 = 52 Number of boys studying science = 210 - 52 = 158 ANSWER:D #### D QUESTION:A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B? options: A)1/3 B)2/9 C)9/46 D)7/19 E)1/6 SOLUTION:The first thing to notice is that A is faster than B and B is faster than C. Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work. If A works for 2 days, B works for 1 day and C works for only 2/3 of the day. Therefore total work done = (2*2) + (1*1) + (1/3*1/3) = 46/9 Proportion of work done by B = (1*1) / (46/9) = 9/46 Hence Answer C. #### C QUESTION:When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is options: A) 0.005 B) 0.002 C) 0.001 D) 0.0003 E) 0.0002 SOLUTION:It is very easy if x is the diameter, then the magnified length is 1000x. ince 1000x=0.3 then x=0.3/1000=0.0003. The answer is D #### D QUESTION:Four person are chosen at random form a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is: options: A)10/21 B)20/22 C)32/45 D)13/98 E)43/21 SOLUTION:Number of ways of choosing 4 persons out of 9 =9c4 =126 No.of ways of choosing 2 children out of 4 and 2 persons out of (3+2)= (4c2+5c2) =60 P(E)=60/126 =10/21 ANSWER A #### A QUESTION:Before a salary increase, the weekly salary of a worker for 44 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:Let x be the original salary per hour. Let y be the salary per hour after the increase. 40y=44x y=(44/40)x=1.1x The salary increased 10%. The answer is D. #### D QUESTION:When x is multiplied by 3, the result is 4 more than the result of subtracting x from 16. What is the value of x? options: A)-4 B)-2 C)5 D)13 E)22 SOLUTION:The equation that can be formed is: 3x-4=16-x or, 4x=20 or, x=5. Answer : C #### C QUESTION:In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race? options: A)2min 10 sec B)2min 30 sec C)2min 40 sec D)2min 50 sec E)2min 20 sec SOLUTION:100 m = 15 sec 1 m = 15/100 sec 1000 m = 15/100*1000 =150 sec =2min 30 sec ANSWER:B #### B QUESTION:What is the value of m and n ? if log3m/log3n=log 52 options: A)1,5 B)2,5 C)3,5 D)4,5 E)2,3 SOLUTION:log (base a) b=log(base n)b/log(base n)a here base are same in reverse way of formula so log(base n)m=log(base 5) 2 hence n=5,m=2 ANSWER:B #### B QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)28% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 121.60 Let marked price be Rs. x. Then, 95/100 x = 121.60 x = 12160/95 = Rs. 128 Now, S.P. = Rs. 128, C.P. = Rs. 100 Profit % = 28%. Answer: B #### B QUESTION:How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 15% solution? options: A)A)5.8 B)B)1.3 C)C)9.6 D)D)12.5 E)E)7.9 SOLUTION:Amount salt in 100kg solution = 10*100/100 = 10 kg Let x kg of pure salt be added then(10+x)/(100+x)=15/100 200+20x=300+3x 17x = 100 x = 5.8 Answer is A #### A QUESTION:How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg? options: A)36 kg B)42 kg C)54 kg D)63 kg E)60 kg SOLUTION:S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%. C.P. of 1 kg of mixture = Rs.((100/110) x 9.24) = Rs. 8.40 C.P. of 1 kg sugar of 1st kind Rs.9 Cost of 1 kg sugar of 2nd kind Rs.7 Mean Price Rs. 8.40 Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 x = (7 x 27)/3 = 63 kg. Answer:D #### D QUESTION:On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done? options: A)2880 B)2778 C)2682 D)8222 E)6282 SOLUTION:Explanation: There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways. Further, in each category (subject), books are to be arranged in different order, we get, Required number of ways: 3! * [2! * 2! * 5!] = 2880 ANSWER: A #### A QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 500. What is the manager's monthly salary ? options: A)Rs.16003 B)Rs.16029 C)Rs.1288 D)Rs.16108 E)Rs.12000 SOLUTION:Explanation: Manager's monthly salary Rs. (2000 * 21 - 1500 * 20) = Rs.12000. Answer: E #### E QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:A mixture contains alcohol and water in the ratio 2:5. If 10liters of water is added to the mixture, the ratio becomes 2:7. Find the quality of alcohol in the given mixture. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let the quantity of alcohol and water be 2x and 5x 2x/(5x+10) = 2/7 20x = 4(3x+5) x=5 Quantity of alcohol = 2*5 = 10liters. Answer is B #### B QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? options: A)16 B)24 C)60 D)120 E)150 SOLUTION:Answer=E=150 No of 4 person committees that can be formed=5C2*6C2=150 Answer E #### E QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700 P1’s income = Rs 5*700 = Rs.3500 ANSWER:D #### D QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142 options: A)23 B)25 C)46 D)49 E)50 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 30 + 16 = 46 . #### C QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:35 + 30 + 20 = 85 This number includes some people counted twice and some people counted three times. 85 - 66 = 19, and this number represents people counted twice or three times. 8% of the people are counted two extra times. The percentage of people counted one extra time is 19 - 8(2) = 3. The percentage of people who liked more than one product is 8% + 3% = 11%. The answer is C. #### C QUESTION:The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches? options: A)31.23 B)25.12 C)36.25 D)23.17 E)27.66 SOLUTION:Total score of the batsman in 22 matches = 616. Total score of the batsman in the next 13 matches = 195. Total score of the batsman in the 35 matches = 811. Average score of the batsman = 811/35 = 23.17. Answer: D #### D QUESTION:If n is an integer greater than 8, which of the following must be divisible by 8 ? options: A)n(n + 5)(n – 6) B)n(n + 2)(n – 1) C)n(n + 1)(n – 4) D)n(n + 3)(n – 5) E)n(n + 5)(n – 6) SOLUTION:If n= 9 , then (n-1) is divisible by 8 . B #### B QUESTION:A tap can fill a tank in 12 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely? options: A)5 hr 30 mins B)7 hr 30 mins C)4hr 30 mins D)2 hr 30 mins E)3 hr 30 mins SOLUTION:Explanation: A tap can fill a tank in 12 hours. Therefore the tap can fill half the tank in 6 hours. One tap take time to fill half of the tank = 6 hrs 4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins Answer : B #### B QUESTION:The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers? options: A)12/35 B)1/35 C)35/8 D)7/32 E)7/33 SOLUTION:Let the numbers be a and b. Then, a + b = 12 and ab = 35. (a + b)/ab = 12/35 = (1/b + 1/a) = 12/35 Sum of reciprocals of given numbers = 12/35. ANSWER:A #### A QUESTION:Jane makes toy bears. When she works with an assistant, she makes 53 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)70% C)100% D)180% E)200% SOLUTION:Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears/hr ([40 bears * 1.53] / [40 hrs * .90]). [(1.7 - 1)/1] * 100% = 70% ANSWER:B #### B QUESTION:On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ? options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation: Formula: (Divisor*Quotient) + Remainder = Dividend. Soln: (56*Q)+29 = D -------(1) D%8 = R -------------(2) From equation(2), ((56*Q)+29)%8 = R. => Assume Q = 1. => (56+29)%8 = R. => 85%8 = R => 5 = R. Answer B #### B QUESTION:The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)6535 B)6532 C)6725 D)6874 E)6972 SOLUTION:C 6725 CP = SP * (100/(100 + profit%)) = 8339(100/124) = Rs. 6725 #### C QUESTION:If 0.60: x : : 6 : 4, then x is equal to options: A)0.1 B)0.4 C)0.82 D)0.8 E)None SOLUTION:Sol. (x×6) = (0.60×4) ⇒ x = 2.4/6 = 0.40. Answer B #### B QUESTION:Sum of Rs.4000 is given out in 2 pieces, one at 8% S.I. and the other at 10% S.I. If the annual interest is Rs 352, the sum is given at 8% is options: A)2000 B)2200 C)2300 D)2400 E)None of these SOLUTION:Explanation : i) Given the total sum = Rs. 4000 If the sum given at 8% be Rs.a ie) P = a , n=1, R = 8% (aX18/100) = (8a/100) If the addition given at 10% be Rs. 4000 – a P = 4000-a , n=1, R = 10% (4000 – aX1X10)/(100) = (40000-10a)/100 Given Annual interest is Rs. 352 (8a/100) + (40000-10a)/100 = 352 8a – 10a = 35200 – 40000 -2a = -4800 X = (4800/2)= Rs.2400/- Answer : D #### D QUESTION:A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.) options: A)$15,360 B)$17,360 C)$25,560 D)$21,360 E)$27,360 SOLUTION:For every $3 earn above $9360, the recipient loses $1 of benefit. OR For every $1 loss in the benefit, the recipient earns $3 above $9360 If earning is; 9360+3x Benefit = 12000-x Or the vice versa If benefit is 12000-x, the earning becomes 9360+3x He lost 50% of the benefit; Benefit Received= 12000-0.55*12000 = 12000-6600 x=5400 Earning becomes 9360+3x=9360+3*5400=25560 Ans:C #### C QUESTION:What is the rate percent when the simple interest on Rs.1000 amount to Rs.400 in 4 Years? options: A)5% B)6% C)2% D)95% E)10% SOLUTION:Interest for 4yrs = 400 Interest for 1yr = 100 Interest rate = 100/1000 x 100 = 10% Answer : E #### E QUESTION:A conference is to have eight presentations over the course of one day, consisting of three long presentations, and five short presentations. If the conference organizer doesn't want consecutive long presentations, and the conference is to start with a short presentation, how many schedules of presentations are possible? options: A)1200 B)7200 C)2880 D)5760 E)11520 SOLUTION:S*S*S*S*S* 5 short presentations can be arranged in 5!=120 ways. As for 3 long presentations: each can be placed instead of any of the 5 star, so in C35=10C53=10 ways, and they also can be arranged in 3!=6 ways. Total = 120*10*6 = 7,200 Ans:B #### B QUESTION:A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? options: A)10% B)12% C)14% D)16% E)18% SOLUTION:Let x be the amount of money paid for the first purchase. The second time, the customer paid 0.8(1.1x)=0.88x. The difference is 12%. The answer is B. #### B <<<Examples ends QUESTION:The residents of the town A participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town A, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)- 30 B)- 20 C)- 6 D)- 12 E)- 16 SOLUTION:(21-6*2)<number of hours that Pat watched television last week <(21-6*1) =9<W<15 12=C. #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window? options: A)a 100 B)b 112 C)c 90 D)d 120 E)e 30 SOLUTION:D David's position is fixed. Now we need to arrange all others around David. There are 5x4x3x2x1= 120 ways to arrange five people. #### D QUESTION:I purchased a superb bike and like my bike my number plate is also superb. The number plate is a five digit number plate and its water image is 78633 more than the number plate. Also all digits are unique. Whats is my number plate number ? options: A)10935 B)10968 C)23984 D)13725 E)11332 SOLUTION:B 10968 Water image is 89601 #### B QUESTION:18 balls are numbered 1 to 18. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)2/9 B)4/17 C)6/29 D)8/35 E)10/43 SOLUTION:P(1st ball is even) = 9/18 P(2nd ball is also even) = 8/17 P(both balls are even) = 9/18 * 8/17 = 4/17 The answer is B. #### B QUESTION:What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest? options: A)Rs. 560 B)Rs. 560.75 C)Rs. 551.25 D)Rs. 550 E)Rs. 560 SOLUTION:Explanation: Present worth of Rs. x due T years hence is given by Present Worth (PW) = x/(1+R/100)T Let x be the annual payment Then, present worth of x due 1 year hence + present worth of x due 2 year hence = 1025 x(1 + 5/100)1 + x(1 + 5/100)2 = 1025 x/(21/20) + x/(21/20)2 = 1025 20x/21 + 400x/441 = 1025 820x/441 = 1025 x = (1025 × 441)/820 = (205 × 441)/164 = Rs. 551.25 Answer: Option C #### C QUESTION:A school’s annual budget for the purchase of student computers increased by 70% this year over last year. If the price of student computers increased by 30% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year? options: A)30% B)30.77% C)36% D)37% E)38% SOLUTION:Pick numbers. Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100; This year: budget = $170, price = $1.3 --> the number of computers purchased = 170/1.3 = ~130.77 Increase in the number of computers purchased = 30.77%. Answer: B. #### B QUESTION:In an examination, 34% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both? options: A)975 B)1150 C)1175 D)1243 E)1525 SOLUTION:Failed in 1st subject = 34*2500/100 = 850 Failed in 2nd subject = 42*2500/100 = 1050 Failed in both = 15*2500/100 = 375 Failed in 1st subject only = 850-375 = 475 Failed in 2nd subject only = 1050-375 = 675 Passed in either subject but not in both = 675+475 = 1150 Answer is B #### B QUESTION:The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 75 terms of set X? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:75*4 + 74*40 + 73*400 = 300 + 2960 + 29200 = 32460 The hundreds digit is 4. The answer is C. #### C QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y? options: A)3/2 B)2 C)4/3 D)4 E)9/2 SOLUTION:Its simple equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4. Thus, correct ans is E #### E QUESTION:A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is options: A)83.33 ml B)83.03 ml C)93.33 ml D)63.03 ml E)82.33 ml SOLUTION:Explanation: Profit (%) = 9.09 % = \inline \frac{1}{11} Since the ratio of water and milk is 1 : 11, Therefore the ratio of water is to mixture = 1:12 Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml] Answer: A) 83.33 ml #### A QUESTION:Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is options: A)42 B)36 C)28 D)20 E)24 SOLUTION:Explanation: Distance covered = 120+120 = 240 m Time = 12 s Let the speed of each train = v. Then relative speed = v+v = 2v 2v = distance/time = 240/12 = 20 m/s Speed of each train = v = 20/2 = 10 m/s = 10×36/10 km/hr = 36 km/hr Answer: Option B #### B QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third smallest sector? options: A)1/72 B)1/36 C)1/18 D)1/12 E)1/9 SOLUTION:Its an AP question .... it is given clearly in the question . Let the smallest angle be a and the circle has 8 sectors and hence 8 angle with a common difference d hence all the angles can be written in AP form with Cd as d , a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d, given that a+7d = 80 --------1 also a + a+d + a+2d + a+3d + a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360) which is 8a + 28d = 360 --------2 solving 1 and 2 we get a=10 We are almost done , now the question ask what fraction of the wheel’s area is represented by the smallest sector ? (30/360)( pie r*r)/ (pie r*r) = 30/360= 1/12 D ans .... #### D QUESTION:3 workers transfer a tool weighing 120kg in 12 seconds. How many men are required to transfer it in 9 seconds? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:We have, M1D1H1 = M2D2H2 3*120*12 = M2*120*9 M2 = 3*120*12/120*9 = 4 ANSWER:A #### A QUESTION:The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid. options: A)9: 8 B)9: 5 C)9: 1 D)9: 2 E)9: 4 SOLUTION:a1 : a2 = 3 : 1 6 a12 : 6 a22 = 9: 1 Answer:C #### C QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items? options: A)15% B)12.16% C)13.4% D)20.2% E)None of these SOLUTION:Explanation : Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively. And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively. Overall loss percentage of the 1st two items = 14.33% =>(0.21p+0.11q)/(p+q)=0.1433 =>p/q=1/2. Overall loss percentage of the 2nd and 3rd item =10.4% =>(0.11q+0.1r)/(q+r)=0.104. =>q/r=2/3. Therefore, the overall loss percentage is : =>(0.21p+0.11q+0.1r)x100/(p+q+r). =>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3). =>0.1216×100. =>12.16%. Answer : B #### B QUESTION:If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer? I. w + t + 2 II. w^2 + 2wt + t^2 III. w^2 + t^2 options: A)None B)I only C)II only D)III only E)I, II, and III SOLUTION:w^2–t^2 is an odd integer means that either w is even and t is odd or w is odd and t is even. Check all options: I. w + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard; II. w^2 + 2wt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard; III. w^2 + t^2 --> even+odd=odd or odd+even=odd. Discard. Answer: A. #### A QUESTION:There are 14 songs in that 5 Rock songs, 6 western songs & 3 Hindi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song & 1 western song? options: A)15624 B)16478 C)17953 D)19655 E)28958 SOLUTION:15624 A #### A QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 Then 6 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)3 D)4 E)5 SOLUTION:A 1 As stated 1=6 => 6=1 #### A QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:The value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to: options: A)0.48 B)5.8 C)0.58 D)0.058 E)0.0058 SOLUTION:= 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 = 489 x 0.05 x 2/0.09 x 93 x 100 = 489/9 x 93 x 10 = 163/279 x 1/10 = 0.58/10 = 0.058 (or) 0.06. Answer is D. #### D QUESTION:What is 2 2/3 - 1 1/4 divided by 1/5 - 1/6 ? options: A)17/36 B)36/17 C)17/6 D)85/2 E)51/4 SOLUTION:2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12 1/5 - 1/6 = (6-5)/30 = 1/30 So 17/12/1/30 = 17/12 * 30 = 85/2 Answer - D #### D QUESTION:The banker's discount on Rs.1800 at 48% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time? options: A)1 months B)4 months C)5 months D)6 months E)7 months SOLUTION:Solution S.I on Rs.1800 = T.D on Rs.1872. P.W on Rs.1872 is Rs.1800. Rs.72 is S.I on Rs. 1800 at 48%. Time =(100x72 / 48x1800) = 1/12 year = 1 months. Answer A #### A QUESTION:How much water must be added to 60 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)10 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 60 litres of milk = (1⁄4 × 60) litres = 15 litres. Answer C #### C QUESTION:Venus travels around the sun at a speed of approximately 21.9 miles per second. The approximate speed is how many miles per hour? options: A)64,420 B)78,840 C)83,160 D)88,970 E)94,320 SOLUTION:21.9 * 3600 = 78,840 The answer is B. #### B QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=0 ii. u is not equal to v iii.u > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers. Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. . Answer: A #### A QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock? options: A)20002 B)20000 C)20007 D)200018 E)20012 SOLUTION:Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 400 => x = 20000 Answer:B #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)7 B)9 C)8 D)4 E)5 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 8 Answer:C #### C QUESTION:For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.25 – 6.25*? options: A)1.5 B)0.5 C)6.25 D)0.25 E)6.0 SOLUTION:Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.25* =6 (the greatest positive even integer less than or equal to 6.25 is 6). Hence, 6.25 – 6.25* = 6.25 - 6 = 0.25 Answer: D. #### D QUESTION:A, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each. options: A)360000;180000;270000 B)270000;180000;360000 C)180000;360000;270000 D)270000;360000;270000 E)None of them SOLUTION:Let the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then, (3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5 1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5 108x /(72x+6480000)=3/4  432x = 216x + 19440000 =216x = 19440000 =x=90000 Hence, A’s initial investment = 3x = Rs. 2,70,000; B's initial investment = 2x = Rs. 1,80,000; C's initial investment = 4x = Rs. 3,60,000. Answer is B. #### B QUESTION:A man has some hens and cows. If the number of heads be 44 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)18 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x*2+y*4=140 heads: x*1+y*1=44 implies, 2x+4y=140 and x+y=44 solving these two equations, we get x=18 and y=26 Therefore, hens are 26. ANSWER:C #### C QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 2/5 Km B)3 1/5 Km C)3 1/7 Km D)4 1/5 Km E)4 2/5 Km SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km B) #### B QUESTION:For which of the following functions f is f(c) = f(1-c) for all c? options: A)f (c) = 1 - c B)f (c) = 1 - c^2 C)f (c) = c^2 - (1 - c)^2 D)f (c) = c^2*(1 - c)^2 E)f (x) = x/(1 - x) SOLUTION:I remember seeing this problem in a GMATprep test. I think choice D should be F(c)=(c^2) (1-c)^2. If that is true then substituting (1-c) for will give us the same function back and the answer choice is D, where the function is multiplicative #### D QUESTION:In climbing a round pole of 80 meters height, a monkey climbs 5 meters in a minute and slips 2 meters in the alternate minute. To get to the top of the pole, the monkey would take : options: A)51 minutes B)54 minutes C)58 minutes D)61 minutes E)63 minutes SOLUTION:a monkey climbs 5 meters in one min & slips 2m in other min. therefore the monkey reach 3meters in 2min 3m=2min 25*3m=25*2min - >75m=50min hence the remaining 5m jumps the monkey in 1min to reach original height so 51 min ANSWER:A #### A QUESTION:A boat can move upstream at 20 kmph and downstream at 34 kmph, then the speed of the current is? options: A)7 B)6 C)8 D)4 E)2 SOLUTION:US = 20 DS = 34 M = (34 - 20)/2 = 7 Answer:A #### A QUESTION:If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is: options: A)53.33 B)54.68 C)55 D)56 E)None of these SOLUTION:Explanation: Required average = (55 × 50 + 60 × 55 + 45 × 60/55 + 60 + 45) = (2750 + 3300 + 2700/160) = 8750/160 = 54.68 Answer: B #### B QUESTION:If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30? I. wb + b^2 II. (w+ b)^2 III. w + b options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30. I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK; II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD; III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK. Answer: B. #### B QUESTION:In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun? options: A)67 kg. B)68 kg. C)69 kg. D)Data inadequate E)None of these SOLUTION:EXPLANATION Let Arun’s weight by X kg. According to Arun, 65 < X < 72 According to Arun’s brother, 60 < X < 70. According to Arun’s mother, X <= 68 The values satisfying all the above conditions are 66, 67 and 68. Required Average =( 66 + 67 + 68 /3 )= (201/3) = 67 kg Answer A #### A QUESTION:A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1 SOLUTION:(4*6 + 8*6): (4*12) 72:48 => 3:2 Answer:C #### C QUESTION:A person borrows Rs.5000 for 2 years at 5% p.a. simple interest. He immediately lends it to another person at 61⁄4% p.a for 2 years. Find his gain in the transaction per year. options: A)62.5 B)150 C)225 D)112.5 E)212.5 SOLUTION:Explanation : The person borrows Rs. 5000 for 2 years at 5% p.a. simple interest Simple interest that he needs to pay = PRT/100=5000×5×2/100=500 He also lends it at 6 1⁄4% p.a for 2 years Simple interest that he gets = PRT/100=5000×25/4×2/100=625 His overall gain in 2 years = Rs.625 - Rs.500 = Rs.125 His overall gain in 1 year = 125/2 = Rs.62.5 Answer : Option A #### A QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 370440, then population in 1978 was? options: A)320000 B)120029 C)187899 D)178968 E)789698 SOLUTION:X * (105/100) * (105/100) * (105/100) = 370440 X = 370440/1.157625 X = 320000 Answer:A #### A QUESTION:On a certain farm the ratio of horses to cows is 3:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 5:3. After the transaction, how many more horses than cows would the farm own? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:Originally, there were 3k horses and k cows. 3(3k-15) = 5(k+15) 9k-5k = 75+45 4k = 120 k = 30 The difference between horses and cows is (3k-15)-(k+15) = 2k-30 = 30 The answer is B. #### B QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order? options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2 SOLUTION:RT = W Given: R = 1/3 + 1/3 = 2/3 T = ? W = 1 T = 1 / (2/3) = 3/2 = 1 1/2 Answer: E #### E QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2 = 62 m2. answer :D #### D QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 40*9/40 = 9 seconds. Answer: C #### C QUESTION:A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)224 E)E)302 SOLUTION:If x is the original number of employees, then after 13% reduction in employees number is .87x but we are given .87x = 181 x = 208 So the original number of employees is 208 Correct Answer - B #### B QUESTION:The smallest value of n, for which n+2 is not a prime number, is options: A)1,2 B)4,6 C)2,4 D)8,12 E)9,6 SOLUTION:(1 + 2) = 3. (2 + 2) = 4. (3 + 2) = 5. (4 + 2) = 6. which is not prime , n=2,4. ANSWER:C #### C QUESTION:A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ? options: A)160 B)180 C)200 D)220 E)None SOLUTION:Answer Let the number be N. Then, (N/5) + 4 = (N/4) - 4 ⇒ (N/4) - (N/5) = 8 ⇒ (5N - 4N)/20 = 8 ∴ N = 160 Option: A #### A QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph? options: A)65 sec B)88 sec C)25 sec D)88 sec E)55 sec SOLUTION:D = 100 + 150 = 250 S = 36 * 5/18 = 10 mps T = 250/10 = 25 sec Answer: C #### C QUESTION:If 200!/10^n is an integer, what is the largest possible value of n? options: A)40 B)42 C)44 D)48 E)49 SOLUTION:We have to basically count the number of 5s withing 200 200/5 =40 200/5^2=8 200/5^3=1 We know for sure that there will be at least 49 even numbers(multiples of 2)within 200 So there are 49 10s in 200! ANSWER:E #### E QUESTION:Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics? options: A)7/12 B)4/9 C)5/9 D)1/4 E)2/3 SOLUTION:Lets pick smart numbers. Total number of students: 12 Biology (1/2): 6 Chemistry (1/3): 4 Physics (1/6): 2 After leaving school Biology: 4 Chemistry: 4 Physics: 1 New Total number of students: 9 Biology and Physics: 5 Answer 5/9 or C #### C QUESTION:A certain bacteria colony doubles in size every day for 25 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit? options: A)6.33 B)7.5 C)10 D)15 E)24 SOLUTION:If there is one bacteria colony, then it will reach the limit of its habitat in 25 days. If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 24 times. Answer: E. Similar questions to practice: Hope it helps. #### E QUESTION:If 1 persons can do 1 times of a particular work in 1 day, then, 7 persons can do 7 times of that work in ? options: A)3 days B)1 day C)9 days D)11 days E)15 days SOLUTION:That is, 1 person can do one time of the work in 1 day. Therefore, 7 persons can do 7 times work in the same 1 day itself. Option 'B' #### B QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? options: A)120cc B)360cc C)450cc D)589C E)478cc SOLUTION:Explanation: r1 = x r2 = 3x Π * x2 * h = 40 Π9 x2h = 40 * 9 = 360cc Answer: B #### B QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is: options: A)233 B)37 C)25 D)27 E)11 SOLUTION:Explanation: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x Gain = (5x - 4x) = Rs. x Gain % = (x * 100)/ 4x = 25%. Answer: C #### C QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)120% B)190% C)100 percent D)200% E)101% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is : options: A)22 B)21 C)88 D)37 E)29 SOLUTION:Explanation: Lot the total number of workers be v Then, 8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21 Answer: B) 21 #### B QUESTION:A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many Q apples did each person get before 45 people joined the feast? options: A)20. B)21. C)22. D)23. E)24. SOLUTION:Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13. Since number of apples per person * total persons Q= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C #### C QUESTION:Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? options: A)5 B)3 C)4 D)6 E)1 SOLUTION:Rate of one machine = 1 job / (20*4) days let X = number of machines needed to complete the job in 10 days 1/(4*20) * 10 * X = 1 job X = 8 8-4= 4 ANSWER: C #### C QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B QUESTION:A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? options: A)A.0.6 B)B.1 C)C.2.1 D)D.3 E)E.2.4 SOLUTION:30% of 6 = 1.8 50% of 6 = 3 shortage is 1.2 so we need to have 1.2/50% to get 50% alcohol content. = 2.4 E #### E QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers? options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89 SOLUTION:(5x-25):(7x-25) = 35:59 x = 12 => 60,84 Answer:D #### D QUESTION:The cost of raw material of a product increases by 30, the manufacturing cost increases by 20 and the selling price of the product increases by 60. The raw material and the manufacturing cost, originally, formed 40 and 60 of the total cost respectively. If the original profit was one-fourth the original manufacturing cost, find the approximation new profit percentage. options: A)48.38% B)54.68% C)62.48% D)42.36% E)None of these SOLUTION:Explanation : Let, the total initial cost of the product be Rs 100. Manufacturing cost = Rs 60 Raw materials cost = Rs 40 Also, original selling price => Rs100+(60/4)= Rs 115. New raw material cost =>Rs 40+30% of 40= Rs 52. New manufacturing cost =>Rs 60+20% of 60= Rs 72 New cost of the product = Rs124 New selling price =>115+60% of 115=Rs 184 New profit percentage =>60/124×100 =>48.38%. Answer : A #### A QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)28% B)25% C)95% D)05% E)22% SOLUTION:800 --- 200 100 --- ? => 25% Answer:B #### B QUESTION:A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute? options: A)1,200 meters / minute B)1,300 meters / minute C)1,450 meters / minute D)1,550 meters / minute E)1,650 meters / minute SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 72 kilometers per hour = 72 km/hr = (72 * 1000 meters) / (60 minutes) = 1,200 meters / minute correct answer A #### A QUESTION:A university cafeteria offers 1 flavors of pizza - pepperoni. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ? options: A)4 B)8 C)12 D)1 E)32 SOLUTION:1 flavours * 1 choices = 1C1*1C1 = 1*1=1=D #### D QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 878 in 4 years. The sum is: options: A)500 B)698 C)626 D)910 E)None SOLUTION:Sol. S.I. for 1 year = Rs. (878 - 815) = Rs. 63. S.I. for 3 years = Rs. (63 * 3) = Rs. 189. ∴ Principal = Rs. (815 - 189) = Rs. 626 Answer C #### C QUESTION:In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 20 percent of revenues. The profits in 1999 were what percent of the profits in 1998? options: A)80% B)105% C)140% D)124.2% E)138% SOLUTION:0,14R = x/100*0.1R Answer C #### C QUESTION:If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is: options: A)Rs. 182 B)Rs. 190 C)Rs. 196 D)Rs. 204 E)Rs. 210 SOLUTION:Explanation: Given ratio =1/2:2/3:3/4=6:8:9 1st part = Rs. 782*6/23=Rs. 204 Answer is D #### D QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=8 and y=6, then x^2-y^2=28 and 28 is divisible only by 4 from the options, thus it must be correct. Answer: B. #### B QUESTION:If a person walks at 16 km/hr instead of 12 km/hr, he would have walked 20 km more. The actual distance traveled by him is? options: A)50 B)65 C)70 D)61 E)60 SOLUTION:Let the actual distance traveled be x km. Then, x/12 = (x + 20)/16 x - 60 =>x = 60km. Answer: E #### E QUESTION:There is a certain relation between two given words on one side of : : and one word is given on another side of : : while another word is to be found from the given alternatives, having the same relation with this word as the given pair has. options: A)Landslides B)Strains C)Resistances D)Volcanoes E)Volcanoe1 SOLUTION:Explanation: Seismography is an instrument to measure the intensity of an earthquake. Similarly, taseometer is an instrument to measure strains. Answer: B) Strains #### B QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%? options: A)5% B)28% C)27% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 70 2/3 SP1 = 70 SP1 = 105 100 --- 5 => 5% Answer:A #### A QUESTION:What could be the range of a set consisting of odd multiples of 3? options: A)21 B)24 C)35 D)62 E)70 SOLUTION:Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 3*(2n+1) where n is any positive integer. Range = 3*(2m + 1) - 3*(2n + 1) = 3*2*(m-n) = 6 * (m-n). m, n - any positive integers The answer must be divisible by 6, which is only 24. The correct answer is B #### B QUESTION:If 22 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect? options: A)125 B)187 C)231 D)375 E)460 SOLUTION:If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line. The number of ways to select 2 lines from 22 lines is 22C2 = 231 The answer is C. #### C QUESTION:Find out the next word in the series below... FAG, GAF, HAI, IAH, ...? options: A)GAK B)JAK C)HGF D)JAH E)KHG SOLUTION:In first FAG it was reodering the first and last letters and these are the continuous alphabets ANSWER:B #### B QUESTION:A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 63 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents? options: A)14 B)45 C)54 D)65 E)81 SOLUTION:Just check the answers and reverse the numbers until you get 63. 81 - 18 = 63 Answer E #### E QUESTION:Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 5 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes? options: A) 5.5% B) 3.6% C) 4.4% D) 5.2% E) 6.0% SOLUTION:Let amount spent by Jill = 100 Clothing=50, Food=20, others=30 Tax on clothing= 2.5 Tax on others=3 Percentage= 5.5/100=5.5% Answer: A #### A QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5 SOLUTION:Rate of flow of water in second hour = 18 gallons per hour Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons Answer B #### B QUESTION:3,9,27,81,.... options: A)583 B)604 C)616 D)243 E)636 SOLUTION:1*3=3 3*3=9 9*3=27 27*3=81 81*3=243 ANSWER:D #### D QUESTION:1!+2!+3!+4!+5!+.100! is divided by 24. Find the remainder from this? options: A)4 B)6 C)9 D)10 E)11 SOLUTION:By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24. So the remainder = 1 + 2 + 6 + 0 + 0....... = C #### C QUESTION:The speed of light is approximately 93 * 10^5 miles per second. This approximate speed is how many miles per hour? options: A) 3,35 * 10^8 B)70 * 10^7 C) 11 * 10^8 D) 16 * 10^8 E) 70 * 10^8 SOLUTION:The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be. (.93*10^5)*3600 = (.93*10^5)*(3.6*10^3) = some number*10^8... The key is realizing that thesome numberhas to be bigger thatn .93(because .93*3.6), and the only answer that fits that is A #### A QUESTION:All of the citizens of a country have a six-character or seven-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes? options: A)36^13 B)35(36^7) C)37(36^6) D)35(36^6) E)37(36^7) SOLUTION:The number of possible 6-digit codes is 36^6. The number of possible 7-digit codes is 36^7. The total sum is 36^6 + 36^7 = 36^6(1+36) = 37(36^6) The answer is C. #### C QUESTION:A room has both an entrance and an exit door. The room can fill up with people in 5 hours. The room can be empty of people in 15 hours. If it is desired that the room should be filled, from empty, exactly 6 hours after people begin entering the room at 9:30am, then at what time should people begin exiting the room? options: A)10:00am B)10:45am C)12:00pm D)12:30pm E)1:30pm SOLUTION:In 6 hours the entrance door is opened to fill the room equal to 6*1/5 = 6/5 of the room. So, 1/5 more than necessary, which should be compensated by people using the exit door. To empty out 1/5 of the people, the exit door needs 15/5 = 3 hours. Therefore, the exit door should be used at 9:30am + 6 hours - 3 hours = 12:30pm. Answer: D. #### D QUESTION:The fourth proportional to 5, 8, 15 is options: A)18 B)19 C)20 D)24 E)None SOLUTION:Sol. Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : : 15 : x ⇔ 5x = (8x15) ⇔ x = (8x15) / 5 = 24. Answer D #### D QUESTION:What is the remainder when 4^381 is divided by 5 ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:I also agree that the remainder is '4' (using the last digit of the powers of 7). Could we have the official answer please?E #### E QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire? options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 120,000 m : C is the circumference C = 5 meters correct answer C #### C QUESTION:When you draw 2 dices together, find the probability of getting numbers in pairs? options: A)1/5 B)1/6 C)1/7 D)1/11 E)1/12 SOLUTION:S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} N (S) = 36 Set of pairs, B = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}; N (B) = 6 P (getting numbers in pairs) = N(B)N(S)N(B)N(S) = 636636 = 1/6 B #### B QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)*100]%=50% Answer A) 50. #### A QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ? options: A)x-2 B)x-4 C)x+4 D)x-3 E)x-1 SOLUTION:Original Digits=xy i.e. Number=10x+y After reversing the digits: Digits=yx i.e. Number=10y+x 10y+x is 36 more than 10x+y 10x+y+36=10y+x 10x-x+36=10y-y 9x+36=9y x+4=y OR y=x+4 Answer : C #### C QUESTION:A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? options: A)27 B)29 C)40 D)89 E)22 SOLUTION:1/8 - 1/x = 1/10 x = 40 Answer: C #### C QUESTION:How many numbers from 10 to 40 are exactly divisible by 3? options: A)13 B)15 C)16 D)10 E)18 SOLUTION:12, 15, 18, 21, 24, 27, 30, 33, 36, 39. 10 Numbers. 10/3 = 3 and 40/3 = 13 ==> 13 - 3 = 10. Therefore 10 digits D) #### D QUESTION:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 20 terms of the sequence? options: A)201/100 B)99/100 C)100/101 D)1/10000 E)20/21 SOLUTION:Easy task and accomplish X1=1-1/2 x2=1/2-1/3 x3=1/3-1/4 ..... x20=1/20-1/21 sum=X1+X2+X3+....X20=1-1/2+1/2-1/3+.......1/20-1/21=1-1/21=20/21 E is the answer #### E QUESTION:In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is: options: A)24 B)26 C)42 D)46 E)48 SOLUTION:Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2. Sum of digits = x + (x + 2) = 2x + 2. (11x + 2)(2x + 2) = 144 22x2 + 26x - 140 = 0 11x2 + 13x - 70 = 0 (x - 2)(11x + 35) = 0 x = 2. Hence, required number = 11x + 2 = 24. Answer:A #### A QUESTION:In how many different number of ways a Committee of 2person of can be selected from 2boys and 2girls such that at least 1 girl is included in the committe options: A)3 B)4 C)2 D)5 E)9 SOLUTION:1G 1B 2G = (2C1*2C1)+2C2 = (2*2)+1 = 5 Total 2M 2W 4C2=6 2C2=1 At least one girl = total - with out girl At least one girl = 6-1=5 D) #### D QUESTION:Ravi and Kavi start a business by investing ₹ 4000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year. options: A)2 : 28 B)5 : 28 C)7 : 18 D)1 : 18 E)3 : 18 SOLUTION:Ratio of profit = Ratio of investments = 4000 : 72000 = 1 : 18 Answer : D #### D QUESTION:What is the probability that a leap year has 53 Sundays and 52 Mondays? options: A)1/9 B)1/8 C)1/3 D)1/7 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:D #### D QUESTION:When asked what the time is,a person answered that the amount of time left is 4/8 of the time already completed.what is the time. options: A)2 PM B)9 PM C)4 PM D)8 PM E)6 PM SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=4/8x⇒x=20 Time is 4 PM Answer:C #### C QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his original salary? options: A)25% B)50% C)75% D)85% E)95% SOLUTION:Salary he get after reduced 20% = 100-20% = 80% So,percentage should be added to get back his salary = (20/80)*100 = 25% ANSWER:A #### A QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9 Probability to become a secretary = (9/10 * 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work? options: A)6 days B)2 days C)4 4/5 days D)3 days E)9 days SOLUTION:Work done by A in 2 days = 2/10 = 1/5 Remaining work = 4/5 Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6 Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days. Answer: C #### C QUESTION:A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 4/16 = 1/4. The answer is B. #### B QUESTION:A book is bought for $60 and sold for $75. What is the profit in percentage? options: A)12 B)15 C)20 D)25 E)30 SOLUTION:75/60 = 1.25 The answer is D. #### D QUESTION:A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join? options: A)4 months B)5 months C)6 months D)7 months E)8 months SOLUTION:Explanation: Assume that C was there in the business for x months A:B:C =40000×12:60000×10:120000 × x =40×12:60×10:120x =40:5×10:10 x =8:10:2x =4:5:x C's share =375000 x/ 9+x=375000 x/9+x ⇒375000 x/9+x=150000 ⇒375x9+x=150 ⇒15x=6(9+x) ⇒5x=18+2x ⇒3x=18 ⇒x=6 It means C was there in the business for 6 months. Given that B joined the business after 2 months. Hence C joined 4 months after B joined. Answer: Option A #### A QUESTION:Find the compound interest on $1000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$82.43 C)$954.26 D)$745.69 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 1000*(1 + 2/100)^4 = 1000 * 51/50 * 51/50 * 51/50 * 51/50 = $1082.43 C.I. = 1082.43-1000 = $82.43 Answer is B #### B QUESTION:How many odd 4-digit positive integers W that are multiples of 5 can be formed without using the digit 3? options: A)648 B)729 C)900 D)1296 E)3240 SOLUTION:I choose A. Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded) Possible n° of 2nd digit: 9 (3 is excluded) Possible n° of 3rd digit: 9 (3 is excluded) Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0) So, W=8*9*9*1=648 (A) #### A QUESTION:A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? options: A) 16 B) 20 C) 32 D) 44 E) 48 SOLUTION:lets say x ounces of P is mixed with Q. => 67-x ounces of Q is present in the mixture (as the total = 67 ounces) given total almond weight = 15 ounces (20x/100)+(25/100)(67-x) = 15 => x = 35 => 67-35 = 32 ounces of Q is present in the mixture. Answer is C. #### C QUESTION:Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ? options: A)30 B)32 C)34 D)36 E)38 SOLUTION:First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 1*2*2*2*2*2 = 32 ANSWER:B #### B QUESTION:In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class? options: A)1/2 B)1/3 C)2/3 D)1/4 E)3/4 SOLUTION:(1/2)G=(1/3)(B+G) 3G=2B+2G G=2B B/G=1/2. The answer is A. #### A QUESTION:A student completes a 3 part exam as follows. The student completes sections A in 6 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour? options: A)7:1 B)9:2 C)8:3 D)5:2 E)6:1 SOLUTION:The time spent on section B and section C is 27 minutes each. The ratio of C to A is 27:6 = 9:2 The answer is B. #### B QUESTION:The profit earned by selling on article for 900 is double the loss incurred when the same article is sold for 450. At what price should the article be sold to make 25% profit? options: A)750 B)800 C)850 D)860 E)890 SOLUTION:Let ‘x’ be the CP of the article; Then 900 – x = 2(x – 450); :. x= 600. 25% of 600 = 150 :. New SP = 600 + 150 = 750 Option 'A' #### A QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.3 x = 4.8 Alternate solution: Try to backsolve. Initial volume = 4.8 After one hour --> (1/4)4.8 = 1.2 After two hours --> (1/4)1.2 = 0.3 Answer: C #### C QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)288 B)492 C)877 D)278 E)178 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 20 + 21 = 41 T = 12 D = 41 * 12 = 492 Answer: B #### B QUESTION:For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6? options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4. SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6 = 6*0 + 2*7.2 + 8 - 6.6 = 0 +14.4 +1.4 15.8 Answer B #### B QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)2.3 B)2.5 C)3.5 D)3.6 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:What percent is 400 gm of 1 kg? options: A)25% B)40% C)10% D)8% E)12% SOLUTION:1 kg = 1000 gm 400/1000 × 100 = 40000/1000 =40 % Answer is B #### B QUESTION:At 12:10 o'clock Bill leaves point A towards point B at a speed of 30 Km/h. At 13:40 o'clock Richi leaves from the same point towards point B also, but at a speed of 60 Km/h. At what time will Richi passes over Bill? options: A)14:40. B)15:10. C)16:10 D)15:40 E)15:30 SOLUTION:Distance travelled by Bill in 1hr 30min ( 12:10 to 13:40) = 30kmph*(90/60)hr = 45km Relative speed = Richi's speed ~ Bill's speed = 30kmph Time taken by Richi to cross Bill = 45/30 = 1.5 hrs Time at which Richi will cross Bill = 13:40 + 1:30 = 14:70 = 15:10 hrs Ans. B #### B QUESTION:A fruit seller had some apples. He sells 35% and still has 6500 apples. Originally, he had ? options: A)650apples B)600 apples C)772 apples D)700 apples E)None SOLUTION:Answer ∵ 65% of N = 800 ∴ N = (650 x 100)/65 = 1000 Correct Option: E #### E QUESTION:If n ≠ 0, which of the following must be greater than n? I. 2n II. 2 - n III. n^2 options: A)I only B)II only C)I and II only D)II and III only E)None SOLUTION:n ≠ 0 => n = negative or n = positive if n = negative: 2n < n (n = -1 then 2n = -2 => -2 < -1) n^2 > n (n =-1 then n^2 = 1 => n^2 > n) 2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n) but if n = positive: n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II 2 - n < n(n =2 then 2-2 = 0) => only III =>answer is E #### E QUESTION:If x^2+4x+3 is odd, then which one of the following could be the value of x. options: A)3 B)4 C)5 D)6 E)9 SOLUTION:for any x, 4x+3->odd so x^2 should be even, means x should be even; only ans we have 4 as even. ANSWER:B #### B QUESTION:How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/57 ? options: A)6 B)3 C)2 D)1 E)5 SOLUTION:There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options. So, we start with a=1, we get b as -ve. out a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions) a=3, we get b as 3. Yes (Now we have 3 possible solutions) a=4, we get b as fraction. Out a=5, we get b again as some fraction. Out a=6 already taken. We have A,B options left. C,D,E are out. A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b. When a=b, we have only 1 solution = 5. So, one more solution, where a=b is not possible. So, answer will be E. #### E QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles. SOLUTION:Solution: 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 Answer C #### C QUESTION:Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)300 B)368 C)375 D)337 E)639 SOLUTION:A+B+C = 1200 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1200 => 300 Answer:A #### A QUESTION:Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.400 when the rate to profit rises from 5 to 7 percent. Find the Capital of C? options: A)3377 B)2899 C)5000 D)2778 E)1991 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 400 C's capital = 30000*1/6 = 5000 Answer: C #### C QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A <<<Examples ends QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/91 B)33/18 C)33/29 D)33/18 E)33/12 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = 12C4/15C4 = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:A #### A QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)86400 D)153603 E)153604 SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1200 or x = 120. Length = 360 m and Breadth = 240 m. Area = (360 x 240) m2 = 86400 m2. Answer: C #### C QUESTION:The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 51st term in the sequence? options: A)9 B)8 C)7 D)6 E)4 SOLUTION:Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below 02,07,22,67, 202, 607, 1822, 5467... Observe the last two digits of the sequence which have the cyclicity of4and the last two digits repeat in the order {02, 07, 22, 67} Also 51st Term =6*8 +3 i.e. 51th Terms will have same Last two digits as 3rd term of the sequence = 22 i.e. Sum of lat two digits of 35th Term = 2+2 = 4 E #### E QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)34 SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER:A #### A QUESTION:3 Years ago, the average age of a family of 5 members was 16 years. A baby having been born, the average age of the family is the same today. The present age of the baby is options: A)1 year. B)1.5 Years. C)2 Years. D)3 Years. E)4 Years. SOLUTION:We're told that 3 YEARS AGO, the average age of a family of 5 members was 16 years. This means that the SUM of their ages was (5)(16) = 80 years. A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME. This means that the sum of the ages is (6)(16) = 96 years. We're asked for the PRESENT age of the baby. Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is... 80 + (5)(3) = 95. A #### A QUESTION:An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? options: A)$480 B)$489.60 C)$634.64 D)$800.32 E)$240 SOLUTION:1.04*1.04*6000 = $6489.60 The answer is B. #### B QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:John bought 2 shares and sold them for $90 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had options: A) a profit of $10 B) a profit of $8 C) a loss of $8 D) a loss of $20 E) neither a profit nor a loss SOLUTION:$ Profit of the share sold at 20% profit = 120-90 20-? $10 profit on the sale of 1 share. $ Loss of the share sold at 20% loss= 80-90 20-? $30 loss on the sale of 1 share. 10-30=Loss of $20 Answer: D #### D QUESTION:A cab driver 5 days income was $250, $400, $750, $400 , $500. Then his average income is? options: A)$440 B)$450 C)$460 D)$470 E)$480 SOLUTION:avg = sum of observations/number of observations avg income=(250+400+750+400+500)/5 = 460 Answer is C #### C QUESTION:At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock options: A)47 B)76 C)28 D)66 E)99 SOLUTION:Explanation: For ticking 6 times, there are 5 intervals. Each interval has time duration of 45/5 = 9 secs At 12 o'clock, there are 11 intervals, So total time for 11 intervals = 11 × 9 = 99 secs. Answer: E #### E QUESTION:At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples? options: A)1/12 B)5/14 C)4/9 D)1/2 E)2/3 SOLUTION:"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind). C23∗C46C49=514C32∗C64C94=514. C23C32 - # of ways to choose which 2 samples will be tasted; C46C64 - # of ways to choose 4 cups out of 6 cups of two samples (2 samples*3 cups each = 6 cups); C49C94 - total # of ways to choose 4 cups out of 9. Answer: B #### B QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)? options: A)0 B)20 C)75 D)5 E)10 SOLUTION:Explanation : Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0 Answer : A #### A QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join? options: A)6 months B)8 months C)4 months D)2 months E)5 months SOLUTION:Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000 Let investment period of Z be x months. Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x) = 240 : 300 : 30x = 8 : 10 : x The share of Z in the annual profit of Rs. 50000 is Rs. 14000. => [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7 => 25x = 7x + (18 * 7) => x = 7 months. Z joined the business after (12 - 7) months. i.e., 5 months. Answer:E #### E QUESTION:Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed? options: A)502 B)512 C)523 D)521 E)500 SOLUTION:Let n be the total number of children. More children, less notebooks(Indirect proportion) If the number children = n, number of books each child will get = n/8 If the number children = n/2, number of books each child will get = 16 Hence we can write as children n:n/2}::16:n/8 ⇒n×n/8=n/2×16 ⇒n8=16/2=8 ⇒n=8×8=64 Then, total number of notebooks those were distributed = n×n/8=(64×64)/8=64×8=512 Answer is B. #### B QUESTION:In how many a committee of 5 members can be selected from 6 men 5 ladies consisting of 3 men and 2 ladies options: A)250 B)150 C)100 D)50 E)200 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 * 5C2) = 200 ANSWER E #### E QUESTION:If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so, (105)^3 = 3 * 7 * 7 * 5 * 3 *3 *5 *b Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 *b Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2 b = 5*7 = 35 Correct answer A. #### A QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:If p, q, and r are positive numbers such that (p/(p+q))(10) + (q/(p+q))(20)=r and if p<q which of the following could be the value of r? options: A)10 B)12 C)15 D)18 E)30 SOLUTION:The answer is D. For any positive p and q, r is a number between 10 and 20. Since p < q, weight of 10 is inferior of weight of 20 -> r is > 15 -> 18 is the answer. #### D QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/12 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 2*x Hence, a1+a2+..+a20+n = 22x So, the fraction asked = 2x/22x = 1/12 B #### B QUESTION:Pavan travelled for 15 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:What is the sum of the different positive prime factors of 960? options: A)5 B)10 C)15 D)17 E)21 SOLUTION:Prime factorization of 960 =96 * 10 =16*6 * 10 =4*4 * 2*3 * 2*5 =2*2 * 2*2 * 2* 3 * 2*5 =2^6 * 3 * 5 Sum of the different positive prime factors of 960 = 2+3+5 =10 Answer B #### B QUESTION:Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 41 films, and broke even on none of them, how many of their films were profitable? options: A)18 B)19 C)20 D)21 E)40 SOLUTION:After fiddling some more, this is how I got to answer choice E...but did I get here using voodoo math or is it sound? (.60*.75) + (.40*.25) = .44 + .10 = .55 55/100 = 11/20 Then subtract from 41: 41 - 11/20 = 40 (answer E) #### E QUESTION:What is the remainder when 3^29 is divided by 5? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1} 29 has the form 4k+1, so the units digit of 3^29 is 3. The remainder when dividing by 5 is 3. The answer is D. #### D QUESTION:Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? options: A)10 B)99 C)787 D)62 E)22 SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18 T = 50 D = 50 * 100/18 = 2500/9 RS = 60 + 40 = 100 * 5/18 T = 2500/9 * 18/500 = 10 sec Answer: A #### A QUESTION:Three bottles whose capacities are as 5 : 3 : 2 are completely filled with milk mixed with water. The ratio of milk to water in the mixture of bottles are as 3 : 2, 2 : 1 and 3 : 1 respectively. Find the percentage of water in the new mixture obtained when 1/3rd of first, 1/2 of second and 2/3rd of the third bottle is taken out and mixed together options: A)66.66% B)50% C)16.66% D)33.33% E)36.33% SOLUTION:Let the percentage of water be X The quantity of new mixture = (5X/3) + (3X/2 )+ (4X/3) = 27X/6 = 9X/2. Percentage of milk = (5X/3) x (3/5) + (3X/2) x (2/3) + (4X/3) x (3/4) = 3X Percentage of water = (5X/3) x (2/5) + (3X/2) x (1/3) + (X/2) x (2/3) = 3X/2 Percentage of water = (3X/2)/(9X/2) x 100 = 100/3 = 33 (1/3)% ANSWER:D #### D QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is? options: A)150 m B)778 m C)200 m D)276 m E)971 m SOLUTION:2(l + 150) = 600 => l = 150 m Answer:A #### A QUESTION:Find the average of first 20 natural numbers? options: A)5.5 B)7.2 C)10.5 D)12.3 E)15.5 SOLUTION:Sum of first n natural numbers = n(n+1)/2 sum of first 20 natural numbers = 20*21/2 =210 average = 210/20 = 10.5 Answer is C #### C QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used options: A)12 months B)10 months C)14 months D)16 months E)None of these SOLUTION:Explanation : B received 2/3 of the profit => A : B = 1 : 2 Let the total capital = x Then A's capital = x/4 B's capital = x – x/4 = 3x/4 Assume B's money was used for b months Then A:B = (x/4)*15 : (3x/4)*b = 1 : 2 => 15/4 : 3b/4 = 1 : 2 => 15 : 3b = 1 : 2 => 5 : b = 1 : 2 => 5/b = 1/ 2 => b = 5*2 = 10. Answer : Option B #### B QUESTION:The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994? options: A)5N B)7N C)10N D)15N E)20N SOLUTION:In 1992, the company's assets were N. In 1993, the company's assets were N + 4N = 5N. In 1994, the company's assets were 5N + 5N = 10N. The answer is C. #### C QUESTION:Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they? options: A)350 B)400 C)500 D)550 E)590 SOLUTION:N * 50 = (325000 - 300000) = 25000 N = 25000 / 50 = 500 C #### C QUESTION:If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? options: A)9 B)18−3√3 C)18 D)18+3√3 E)27 SOLUTION:The altitude of an equilateral triangle is side*√3/2. As perimeter of triangle ACD is 9+3√3, AC + CD + AD = (side+side/2+side*√3/2) = 9 + 3√3 or side =6. Perimeter of equilateral triangle, ABC is 3(side) or 18. Answer:(OptionC) #### C QUESTION:The sub-duplicate ratio of 25:49 is options: A)4:3 B)5:7 C)6:4 D)1:4 E)2:3 SOLUTION:root(25):root(49)=5:7 ANSWER:B #### B QUESTION:A box contains 3 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors? options: A)1/2 B)3/5 C)7/12 D)2/3 E)7/10 SOLUTION:Total selection ways: 5C2=5!/2!3!=10 Selecting one blue chip out of two: 2C1=2!/1!1!=2 Selecting one red chip out of four: 3C1=3!/2!1!=3 Thus, (2C1*3C1)/5C2=(2*3)/10=6/10=3/5=B #### B QUESTION:An escalator moves towards the top level at the rate of 7 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length. options: A)5sec B)25sec C)20sec D)15sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (7+2) = 20sec Answer : C #### C QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money? options: A)1489 B)6845 C)2598 D)1875 E)2600 SOLUTION:P = 75(100/20)5 => P = 1875 Answer: D #### D QUESTION:If a = 105 and a^3 = 21 × 25 × 45 × q, what is the value of q? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:a=105 = 3* 5 *7 a^3 = 21 × 25 × 45 × q => a^3 = (7*3) x (5*5) x ( 3^2 * 5) x q => a^3 = 3^3 * 5^3 * 7 x q =>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x q q = 7^2 = 49 Answer D #### D QUESTION:The area of square ABCD above is 18. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9/4∗π B)18−9/2∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =18- pi*18/4 =18- pi*9/2 ANSWER:B #### B QUESTION:The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be options: A)12 years B)20 years C)25 years D)28 years E)None SOLUTION:Solution Let the present ages of son and father be x and (60 - x) years respectively. Then, (60 - x) - 6 = 5(x - 6) = 54 - x = 5x - 30 ‹=›6x = 84 ‹=›x= 14. ∴Son's age after 6 years = (x + 6) = 20 years. Answer B #### B QUESTION:Which of the number is odd one out ? options: A)84129 B)32418 C)47632 D)36119 E)67626 SOLUTION:C 47632 as 32*32 !=476 #### C QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)*100]%=50% Answer A) 50. #### A QUESTION:In how many ways the word "KIT" can be arranged? options: A)6 B)8 C)18 D)21 E)24 SOLUTION:Explanation : The required number of ways = 3! = 6 Answer : A #### A QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -7 then by what factors will the Mean,Variance and Standard Deviation respectively change ? options: A)-7,-7,-7 B)-7,7,7 C)1,1,1 D)-7,49,7 E)7,7,49 SOLUTION:Mean: If all values are multiplied by -7 then their sum will also be multiplied by -7 so Mean will also get -7 Variance: Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values When we multiply all the values by -7 then the difference between the mean and the individual values also gets multiplied by -7 and the square of that difference becomes 49. So, the variance gets multiplied by a factor of 49 SD: Standard Deviation is the square root of variance so sqrt(49)=7. So SD gets multiplied by a factor of 7. So, answer will be D. #### D QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)18 B)20 C)24 D)30 E)40 SOLUTION:Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30 Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20 Answer:B #### B QUESTION:A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.45 B)8.45 C)7.45 D)3.45 E)1.45 SOLUTION:Explanation: 40*(46/100) = 18.4 --- 64 ? --- 12 => Rs.3.45 Answer: D #### D QUESTION:n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4? options: A)3 B)2 C)1 D)0 E)None of these SOLUTION:Let n=4q+3. 2n=8q+6=4(2q+1)+2 Thus, when 2n is divided by 4, the remainder is 2. Correct Option: B #### B QUESTION:If the two hands in a clock are 11 minutes divisions apart,then the angle between them is options: A)66° B)18° C)24° D)60° E)None of these SOLUTION:In a clock, each minute makes 6° ∴ 11 minutes will make 6 × 11 = 66° Answer A #### A QUESTION:The average age of a group of 10 students was 24. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group? options: A)22 years B)36 years C)32 years D)44 years E)None of these SOLUTION:The total age of 10 students with average 24 = 240 The total age of 12 students with average 26 = 312 The total age of 2 new students = 72 Their average =36 Correct Option B #### B QUESTION:A rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown. AB = 8 cm and BC = 4 cm. The perimeter of the figure ABCPQRA (in cm) is : options: A)24 B)28 C)36 D)48 E)None of these SOLUTION:Solution Required perimeter = (AB + BC +CP + PQ + QR + RA) = AB + BC + (CP + QR) + (PQ + RA) = AB + BC + AB + BC = 2(AB + BC) = [2(8 + 4 )] cm = 24 cm. Answer A #### A QUESTION:The dimensions of a field are 10 m by 10 m. A pit 5 m long, 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ? options: A)2m B)2.5m C)1.5m D)1.25m E)1m SOLUTION:The volume of the earth removed is 5*5*3 = 75 m^3. The remaining area of the field is 10*10 - 5*5 = 75 m^2. 75 m^3 of the earth evenly spread over the area of 75 m^2 will rise the height by (height) = (volume)/(area) = 75/75 = 1 m. Answer: E #### E QUESTION:if log 2 = 0.30103, the number of digits in 2128 is options: A)22 B)39 C)88 D)28 E)11 SOLUTION:Explanation: log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4 ie, its characteristic = 38 Hence, number of digits in 2128 = 38+1 = 39 Answer: Option B #### B QUESTION:A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)Rs.3178 B)Rs.3120 C)Rs.3127 D)Rs.3121 E)Rs.3122 SOLUTION:Explanation: Let A be the amount received at the end of the three years. A = 4800[1 + 10/100][1 + 20/100][1 + 25/100] A = (4800 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.7920 So the interest = 7920 - 4800 = Rs.3120 Answer: B #### B QUESTION:Twenty four men can do a work in 32 days. How many men are required to complete the work in 12 days? options: A)32 B)10 C)64 D)40 E)60 SOLUTION:C 64 We have M1 D1 = M2 D2 So, 24 * 32 = M2 * 12 => M2 = 64. Answer is C #### C QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes options: A)18kms B)16kms C)50kms D)30kms E)40kms SOLUTION:total eastward distance= 25kmph*1/4hr=6.25 km total westward distance= 40kmph*1/4hr=10 km total distn betn them= 6.25+10=16.25km ans 16km ANSWER:B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 50 years now, the son's age five years back was? options: A)18years B)19years C)20years D)21years E)22years SOLUTION:Let the son's present age be x years. Then, (50 - x) = x 2x = 50. x = 25. Son's age 5 years back (25 - 5) = 20 years. C) #### C QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 3600 interest. The principal amount borrowed by him was. options: A)Rs 10000 B)Rs 15000 C)Rs 16000 D)Rs 17000 E)None of these SOLUTION:Explanation: S.I.=P∗R∗T/100 =>P=S.I.∗100/R∗T =>P=3600∗100/12∗3=Rs10000 Option A #### A QUESTION:If |x^2 − 12| = x, which of the following could be the value of x? options: A)-4 B)-3 C)1 D)2 E)3 SOLUTION:|x2−12|=x|x2−12|=x |x2−12||x2−12|cannot be negative; anything that comes out of mod is always positive so |x2−12|>0|x2−12|>0 Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0 Now only Option C=1 or D=2 or E=3 are contenders for right answers. A quick Cursory crude calculation will tell you that E is the right choice |−32−12|=3|−32−12|=3 |9−12|=3|9−12|=3 |−3|=3|−3|=3 3=33=3 ANSWER IS E #### E QUESTION:Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages options: A)A)35 B)B)28 C)C)45 D)D)25 E)E)26 SOLUTION:Explanation: Let the present age of P and Q be 3x and 4x respectively. Eight years ago, P was half of Q in age => 2(3x – 8) = (4x – 8) => 6x – 16 = 4x – 8 => 2x = 8 => x = 4 7x=7*4=28 Answer: Option B #### B QUESTION:For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *4 + 3 and *4 + 4, inclusive? options: A) None B) One C) Two D) Three E) Four SOLUTION:Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *4 would be divisible by all numbers from 1 to 4. => *4+3 would give me a number which is a multiple of 3 and therefore divisible (since *4 is divisible by 3) In fact adding anyprimenumber between 1 to 4 to *4 will definitely be divisible. So the answer is none (A)! Supposing if the question had asked for prime numbers between *4 + 3 and *4 + 11 then the answer would be 1. For *4 +3 and *4 + 13, it is 2 and so on... A #### A QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? options: A)1.99 km B)2.88 km C)4.49 km D)2.99 km E)7.88 km SOLUTION:M = 6 S = 1.2 DS = 6 + 1.2 = 7.2 US = 6 - 1.2 = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 Answer: B #### B QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer? options: A)55 B)25 C)85 D)45 E)35 SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer. Therefore 0+1+3+4+5+6+7+9=35 Answer is E #### E QUESTION:f a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? options: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm SOLUTION:Total distance, which should be covered by both cars is 190+35=225 miles. Let t be the time so the equation will be 46t+54t=225 thus, t=2.25 hours Answer: D #### D QUESTION:A school has received 30% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 60% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$250 C)$100 D)$350 E)$875 SOLUTION:Let us suppose there are 100 people. 60% of them donated $30000 ( 500 * 60 ) $30000 is 30% of total amount. So total amount = 30000 * 100/60 Remaining amount is 70% of total amount. 70% of total amount = 30000 * (100/60) * (70/100) = 35000 This amount has to be divided by 40 ( remaining people are 40 ) So per head amount is 35000/40 = $875; ANSWER:E #### E QUESTION:Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $4 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed? options: A)$760 B)$750 C)$810 D)$800 E)$780 SOLUTION:50 pages typed 1x 30 pages typed 2x (original + one revision) 20 pages typed 3x (original + two revisions) 50(5)+30(5+4)+20(5+4+4)=250+270+260=780 Answer - E #### E QUESTION:The population of a city increases by 6% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years? options: A)9% B)9.27% C)27% D)15.76% E)None of these SOLUTION:Actual increase in population=5% Let, earlier population=100 then the population after 3 years =100(1+5/100)^3=115.7625 ∴Required percentage=15.7625% ANSWER:D #### D QUESTION:If the Average (mean ) of 9 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A)8x B)4x C)5x/3 D)3x/2 E)3x/5 SOLUTION:Let the 5 numbers be 1,2,3,4,5,..9 (since no restrictions are given). There mean is 4 (x). Now the sum of greatest three would be 7+8+9=24 so the answer has to be 8x....that is option A #### A QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:Solve for x: 2x – y = (3/4)x + 6. options: A)(y + 6)/5 B)4(y + 6)/5 C)(y + 6) D)4(y - 6)/5 E)6(y-4)/5 SOLUTION:2x – y = (3/4)x + 6. or, 2x - (3/4)x = y + 6. or, (8x -3x)/4 = y + 6. or, 5x/4 = y + 6. or, 5x = 4(y + 6). or, 5x = 4y + 24. or, x = (4y + 24)/5. Therefore, x = 4(y + 6)/5 correct answer B #### B QUESTION:Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in? options: A)15 hours B)12 hours C)76 hours D)16 hours E)81 hours SOLUTION:The part of the tank filled by three pipes in one hour = 1/8 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12. The tank can be filled in 12 hours. Answer: B #### B QUESTION:If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is? . options: A)6 B)12 C)24 D)36 E)48 SOLUTION:72 x 1 = 72 72 x 2 = 144 14^4=12^2 Largest possible which can divide 12 is 12 Answer = B #### B QUESTION:If the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)16 E)18 SOLUTION:Let length of rectangle = L 8^2 = L*4 => L = 64/4 = 16 Answer D #### D QUESTION:John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip? options: A) 24 B) 30 C) 48 D) 54 E) 75 SOLUTION:Speed = Distance/Time Distance for John = Speed * Time = 40 * 1/2 = 20 miles Distance for Beth = Distance for John +5 = 20+5 = 25 miles Time taken by Beth = Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6 Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour Hence, B is the answer. #### B QUESTION:There are two batches A and B of a class. Batch A consists of 36 students and batch B consists of 44 students. Find the average weight of whole class, if average weight of batch A is 40 kg and that of batch B is 35 kg. options: A)29.23 kg B)32.56 kg C)35.66 kg D)37.25 kg E)NONE OF THE ABOVE SOLUTION:Given: Average weight of batch A = 40 kg , average weight of batch B = 35 kg 1) First find the total weight of all students - Weight of batch A = (36 x 40) = 1440 - Weight of batch B = (44 x 35) = 1540 Total weight of all students = (1440 + 1540) = 2980 kg 2) Find average weight of whole class (Batch A + Batch B) students = (36 + 44) = 80 students Average Weight = Total weight of all the students / No. of Students = 2980 / 80 = 37.25 kg ANSWER IS D #### D QUESTION:What approximate value should come in place of the question mark (?). 36.0001 ÷ 5.9998 × √? = 108.0005 options: A)325 B)316 C)256 D)16 E)18 SOLUTION:Using approximation, we get 36⁄6 × √? = 108 or, √? = 108⁄6 or, √? = 18 or, ? = 324 ≈ 325 Answer E #### E QUESTION:100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads? options: A)33/100 B)41/101 C)51/101 D)87/101 E)98/101 SOLUTION:Let aa be the number of coins showing heads Then, P(A=50)=P(A=51)P(A=50)=P(A=51) ⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101 C #### C QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively options: A)19 B)17 C)13 D)9 E)18 SOLUTION:Explanation: Answer will be HCF of (28-10, 128-2, 147-3) HCF of (18, 126, 144) = 18 Option E #### E QUESTION:In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 6 metres then what will be the area of the square so formed? options: A)Cannot be determined B)2600 cm2 C)5184 cm2 D)3025 cm2 E)None of these SOLUTION:Let the side of the square be x m. ∴ Perimeter of the square = 48 × 6 = 4x ∴ x = 72 m ∴ Area = (72)2 = 5184 m2 Answer C #### C QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? options: A)289 B)132 C)279 D)277 E)278 SOLUTION:2 * 22/7 * 14 = 88 88 * 1 1/2 = Rs.132 Answer: B #### B QUESTION:The factorial expression 10!/2! is not divisible by which of the following integers? options: A)3 B)5 C)6 D)7 E)None of these SOLUTION:10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3 (A) 3 Can divide 12 or 9 (B) 5 Can divide 10 (C) 6 Can divide 12 (D) 7 can divide 7,21,28 Hence answer will be (E) #### E QUESTION:21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement. options: A)7/41 B)3/41 C)9/42 D)4/51 E)5/13 SOLUTION:The probability that first toy shows the even number, =1021=1021 Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left. Hence, probability that second toy shows the even number, =920=920 Required probability, =(1021)×(920)=(1021)×(920) =9/42 C #### C QUESTION:The average height of 35 boys in a class was calculated as 185cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).? options: A)178.27 cm B)183.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 185 cm. Wrong total height of 35 boys = 185 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 185 cm - (166 cm - 106 cm)/35 =185 cm - 60 /35 cm = 185 cm - 1.71 cm = 183.29 cm. Answer: B #### B QUESTION:What is the speed of the train in km/hr whose length is 360 metres which passes a pole in 18 seconds? options: A)59/9 km/hr B)50/9 km/hr C)25/6 km/hr D)55/18 km/hr E)60/18 km/hr SOLUTION:Speed=(18x5/18)=5 m/sec. Length of the train= 360 metre Time=18s Speed=length / time Speed=(360/8)=20 m/sec = 20*5/18 km/hr = 50/9 km/hr Answer: B #### B QUESTION:The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 25 feet on a side. What will be the volume of the new building in cubic feet? options: A)3,937,500 cubic feet B)15,750 cubic feet C)11550√3 cubic feet D)7,160,947 cubic feet E)3,937,500√3 cubic feet SOLUTION:Volume of the Hexagon with side 200 and height 70 = Area * height = 6*(sqrt(3)/4)(200^2)(70) Volume of the center bull's eye that is similar in shape of a hexagon but side 25 = 6 * (sqrt(3)/4)(25^2)*70 Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(25^2)*70=7,160,947 Answer is D #### D QUESTION:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster? options: A)30 B)44 C)42 D)46 E)50 SOLUTION:Total # of students 20+28+18-(9+7+10)+4=44. Answer: B. #### B QUESTION:Mixture A is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture A, how many kilograms of mixture A must be added to make a 70% material B in the new mixture? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Old mix has 20% oil. You add 2 kgs of 100% oil. You get new mix with 30% oil (70% material B). w1/w2 = (100 - 30)/(30 - 20) = 70/10 = 7/1 For every 7 parts of mix A, you have added 1 part of oil. Since you have added 2 kgs oil, mix A must be 7*2 = 14 kgs. You already had 8 kgs of mix A, so extra mix A added must be 14 - 8 = 6 kgs. Answer (A) #### A QUESTION:How many quarters are equal to 7 dollars? options: A)1 B)28 C)12 D)9 E)7 SOLUTION:7 * 4 = 28 quarters Answer : B #### B QUESTION:In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can? options: A)65 B)44 C)86 D)29 E)26 SOLUTION:Let the capacity of the can be T litres. Quantity of milk in the mixture before adding milk = 4/9 (T - 8) After adding milk, quantity of milk in the mixture = 6/11 T. 6T/11 - 8 = 4/9(T - 8) 10T = 792 - 352 => T = 44. Answer: B #### B QUESTION:A man took loan from a bank at the rate of 10% p.a. simple interest. After 3 years he had to pay Rs. 3000 interest only for the period. The principal amount borrowed by him was: options: A)8000 B)10000 C)11000 D)12000 E)13000 SOLUTION:Principal = (100X3000)/(10X3)= Rs. 10000 answer : B #### B QUESTION:John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet? options: A)1/16 B)5/16 C)3/8 D)1/2 E)1/4 SOLUTION:John will run farther if he runs at 5 mph and Amanda runs at 4 mph. P(John runs farther) = 1/4 * 1/4 = 1/16 The answer is A. #### A QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 35 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)45 E)01 SOLUTION:Explanation: As there is meal for 70 adults and 35 have their meal, the meal left can be catered to 35 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 35 adults = 45 children Hence, the meal can be catered to 45 children. ANSWER: D #### D QUESTION:Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John’s weekly allowance? options: A)$2.40 B)$3.00 C)$3.20 D)$3.60 E)$4.80 SOLUTION:Total allowance=X Amount spent at the arcade=3/5X Amount Remaining=2/5X Amount Spent at the toy store=2/5*1/3X=2/15X Amount Remaining=2/5X-2/15X=4/15X Now, 4/15X=$0.96 Therefore, X=$3.60. Answer D #### D QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow? options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10% So 8100+15100⋅x+10100⋅(8100−x)=9100 Therefore 8100+320x+110(8100−x)=9100 120x=190 x=3800 Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres correct answer is D)4370 lt #### D QUESTION:Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time W will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did? options: A)2 minute and 12 seconds. B)two minutes. C)44 seconds. D)20 seconds. E)12 seconds. SOLUTION:Tom is running alone for 20 seconds. So he will cover a distance of 20*2.5 = 50 m in 20 seconds=W Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side D is the answer #### D QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21 Ans: B #### B QUESTION:A glass was filled with 10 ounces of water, and 0.02 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period? options: A)0.004% B)0.02% C)0.2% D)4% E)40% SOLUTION:We are given that 0.02 ounces of water evaporated EACH DAY. Furthermore, we know that this process happened over a 20-DAY PERIOD. To calculate the total amount of water that evaporated during this time frame we need to multiply 0.02 by 20. This gives us: 0.02 x 20 = 0.4 ounces Finally, we are asked for “What percent” of the original amount of water evaporated during this period. To determine this percentage, we have to make sure we translate the expression correctly. We can translate it to: (Amount Evaporated/Original Amount) x 100% (0.4/10) x 100% (4/100) x 100% = 4% Answer D #### D QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A? options: A)10.21 B)10.27 C)10.25 D)10.23 E)60.25 SOLUTION:Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs. Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs = 2 5/6 = 2 hrs 50 min Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min. So, Anna reached city A at 10.25 a.m. Answer: E #### E QUESTION:A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance? options: A)21 (1/3) kmph B)25 (1/3) kmph C)29 (1/3) kmph D)20 (1/3) kmph E)24 (1/3) kmph SOLUTION:A Let the total distance be x km total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64 Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph. #### A QUESTION:John and David work at a hospital with 8 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen? options: A)1/30 B)1/25 C)1/20 D)1/28 E)1/30 SOLUTION:Probability that John and David will both be chosen out of 8 workers = (2/8)*(1/7) = 1/28 Answer D #### D QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2 SOLUTION:Solution Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 Answer A #### A QUESTION:The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)766 m B)156 m C)245 m D)156 m E)156 m SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer: C #### C QUESTION:The sum of the squares of three number is 138,while the sum of their products taken two at a time is 131. their sum is : options: A)20 B)30 C)40 D)None of these E)Cannot be determined SOLUTION:Solution Let the numbers be a,b and c then, a 2 + b 2+ c 2 = 138 and (ab + b c + ac) = 131. (a + b+ c)2 = a 2 + b 2 + c 2 + 2(ab + b c + ca) = 138 + 2 * 131 = 400 . ⇒ (a + b + c) = 400/20= 20 Answer A #### A QUESTION:If $25,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years? options: A) compounding daily B) compounding quarterly C) compounding monthly D) compounding annually E) All four of these would produce the same total SOLUTION:This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest. This process will be repeated every day till the amount matures Compounding annually will give least returns Answer = A #### A QUESTION:A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is: options: A)42 B)43 C)46 D)47 E)49 SOLUTION:A 42 After 10 days : 150 men had food for 35 days. Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion) 125 : 150 :: 35 : x 125 x x = 150 x 35 x = (150 x 35)/125 x = 42 #### A QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:What is the sum of the numbers between 1 and 20, inclusive? options: A)310 B)200 C)215 D)285 E)210 SOLUTION:Sol. 1+2+3...17+18+19+20 answer. E #### E QUESTION:Due to construction, the speed limit along an 9-mile section of highway is reduced from 45 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 5.61 B)B) 3.42 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 9 miles stretch = 9*60/45 = 9*4/3 = 12 New time in minutes to cross 9 miles stretch = 9*60/35 = 9*12/7 = 15.42 Time difference = 3.42 Ans:B #### B QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction? options: A)5hours B)10hours C)8hours D)10hours E)12hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 20 =10 hours Answer is B #### B QUESTION:If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)? options: A)37 B)41 C)3.5e-05 D)35 E)3.5e-07 SOLUTION:99*0.35=34.65 approx. 35 Answer : B #### B QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. options: A)z=3x B)x=3z C)y=2x D)x=2y E)y=3x SOLUTION:Rovert Travelled for x,y and for z min. Total Time : x + y + z Which is equal to : 3y Equating both sides we get x+y+z = 3y => x+z =2y ........ Eqn 1 Looking out at options D Says x =2y Using it in Eqn 1 2y + z = 2y => Z = 0 mins, Which I guess is not possible. The Ans isD #### D QUESTION:If G = 775 × 778 × 781, what is the remainder when G is divided by 14? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:G 775/14 leaves a remainder 5 778/14 leaves a remainder 8 781/14 leaves a remainder 11 5*8*11 =440 So the remainder will be the remainder of 440/14 which is 6 Ans A #### A QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible? options: A)270 B)252 C)272 D)292 E)285 SOLUTION:number of astronauts with previous experience = 7 Remaining =9 we need to pick exactly one from the first group and 2 from the second group (7C1)*(9C2) =7*36= 252 Answer : B #### B QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is? options: A)2:1 B)2:8 C)2:9 D)2:5 E)2:2 SOLUTION:Let 1 man's 1 day work = x and 1 boy's 1 day work = y. Then, 12x + 16y = 1/5 and 13x + 24y = 1/4 Solving these two equations, we get: x = 1/100 and y = 1/200 Required ratio = x:y = 1/100 : 1/200 = 2:1. Answer: A #### A QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856 SOLUTION:(900*3*3)/100 = 81 920 + 81 = 1001 ANSWER:B #### B QUESTION:What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9? options: A)397 B)401 C)403 D)405 E)399 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=405. Answer: D. #### D QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:If square-root of 15 is 3.87. Then find the value of square-root of (5/3) options: A)1.29 B)1.39 C)1.49 D)1.59 E)1.69 SOLUTION:=> root 5/ root 3 = (root 5/ root 3)*(root 3/ root 3) = root 15/ root 9 = 3.87/3 = 1.29 ANSWER:A #### A QUESTION:There are 3 classes having 20, 24 and 30 students respectively having average marks in an examination as 20,25 and 30 respectively. The three classes are represented by A, B and C and you have the following information about the three classes. a. In class A highest score is 22 and lowest score is 18 b. In class B highest score is 31 and lowest score is 23 c. In class C highest score is 33 and lowest score is 26. options: A)can't be determined in both cases B)definite decrease in both cases C)definite increase in both cases D)will remain constant in both cases E)will remain constant in both cases21 SOLUTION:Ans: B Explanation: Class A average is 20. And their range is 18 to 22 Class B average is 25. And their range is 23 to 31 Class A average is 30. And their range is 26 to 33 If 5 students transferred from A to B, A's average cannot be determined but B's average comes down as the highest score of A is less than lowest score of B. If 5 students transferred from B to C, C's average cannot be determined the B's range fo marks and C's range of marks are overlapping. Answer:A #### A QUESTION:If d<0, which of the following represents a positive number? options: A)d|d| B)|d|d C)|d|/d D)-d|d| E)d/ |d| SOLUTION:Answer : D #### D QUESTION:If a - b = 3 and a^2 + b^2 = 31, find the value of ab. options: A)12 B)15 C)10 D)11 E)13 SOLUTION:2ab = (a^2 + b^2) - (a - b)^2 = 31 - 9 = 22 ab = 11. Answer is D. #### D <<<Examples ends QUESTION:John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease? options: A)90% B)30% C)40% D)70% E)80% SOLUTION:The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)*100 = (0.9)*100 = 90%. A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, is options: A)131 B)176 C)274 D)405 E)495 SOLUTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}. 6 times 40 something is approx north of 240 Hence the answer is (C) 274 #### C QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender? options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2 SOLUTION:There are two cases. All boys and all girls case 1. all boys. 1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128 case 2 .all girls. 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128 We will add the cases to get 1/64 #### A QUESTION:The sum of four consecutive even numbers is 292. What would be the smallest number? options: A)74 B)76 C)70 D)68 E)65 SOLUTION:Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) Their sum = 8x - 4 = 292 => x = 37 Smallest number is: 2(x - 2) = 70. ANSWER:C #### C QUESTION:A retail item is offered at a discount of d percent (where d > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of d, would result in the same final price? options: A)d+5/1.05 B)d/1.05 +5 C)1.05d-5 D)d-5/1.05 E)1.05(p – 5) SOLUTION:Let x be the price of the item. Final price after discount and sales tax = x * (1 - d/100) * 1.05 Let e be the percent discount which would result in the same final price. Then, x * (1 - d/100) * 1.05 = x * (1 - e/100) => 1.05 - 1.05d/100 = 1 - e/100 => e/100 = 1.05d/100 - .05 => e = 1.05d - 5 Hence ,option C is correct. #### C QUESTION:The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: options: A)10º B)75º C)90º D)130º E)180º SOLUTION:Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º. Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º. Required angle = (130 - 120)º = 10º. Answer A #### A QUESTION:A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested? options: A)25 B)37 C)36 D)29 E)21 SOLUTION:Explanation: From the information provided we know that, Principal + 8% p.a. interest on principal for n years = 180 …….. (1) Principal + 4% p.a. interest on principal for n years = 120 ……… (2) Subtracting equation (2) from equation (1), we get 4% p.a. interest on principal for n years = Rs.60. Now, we can substitute this value in equation (2), i.e Principal + 60 = 120 = Principal = Rs.60. We know that SI = , where p is the principal, n the number of years and r the rate percent of interest. In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60. Therefore, 60 =(60*n*4)/100 => n = 100/4 = 25 years. Answer: A) 25years #### A QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum z of all the even integers between 99 and 301? options: A)10,100 B)20,200 C)22,650 D)40,200 E)45,150 SOLUTION:I would solve it in a different way. First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101 Average = (301+99)/2 = 400/2 = 200 Sum z= Average*total count = 200*101 = 20,200 Answer is B #### B QUESTION:If the average (arithmetic mean) of a and b is 110, and the average of b and c is 150, what is the value of a − c? options: A)−220 B)−100 C)100 D)−80 E)It cannot be determined from the information given SOLUTION:Question: a - c = ? (a + b)/ 2 =110 ===> a + b = 220 (b + c)/2 = 150 ===> b + c = 300 (a + b) - (b + c) = 220 - 300 ===> a + b - b - c = - 80 ===> a - c = - 80 Answer: D #### D QUESTION:A card is drawn at random from a pack of 52 cards. What is the probability that it is neither a spade nor a jack? options: A)9/13 B)4/13 C)2/13 D)6/13 E)5/13 SOLUTION:There are 13 spades including a jack and 3 more jacks of other suits. Probability of getting spade or a jack: = (13 + 3)/52 = 16/52 = 4/13 Therefore, the probability of getting neither a spade nor a jack: = 1 − 4/13 = 9/13 ANSWER:A #### A QUESTION:There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 4. If all 27 of the integers were listed, what would their sum be? options: A)6693 B)6793 C)6893 D)6993 E)7093 SOLUTION:There must be nine 1's in the hundreds place, nine 1's in the tens place, and nine 1's in the units place. This is also true for the 2's and 4's. Then the sum is: 9(111+222+444)=9*(777)=6993. The answer is D. #### D QUESTION:A fellow borrowed a certain sum of money at 6% per annum at simple interest and in 6 years the interest amounted to Rs.672 less than the sum lent. What was the sum lent? options: A)1050 B)1220 C)1250 D)1060 E)1110 SOLUTION:P - 672 = (P*6*6)/100 P = 1050 Answer: A #### A QUESTION:In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N) options: A)L(L-N) /L-M B)L(N-M) / L-M C)L-N D)M-N E)M+ SOLUTION:the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers: L = 200 M = 10 N =20. So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans.. looking the the opion C to E, one can make out that they are incorrect, A. Out of which, i choose A. #### A QUESTION:Three unbased coins are tossed. the probability of getting at least two head is ? options: A)1/4 B)1/2 C)3/4 D)2/3 E)2/5 SOLUTION:S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH} E be the event of getting at least two head is {THH,HTH,HHT,HHH} P(E)=n(E)/n(S)=4/8=1/2 Answer(B) #### B QUESTION:Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 35.1 kg of zinc has been consumed in it? options: A)78 kg B)60 kg C)64 kg D)70 kg E)None SOLUTION:Sol. For 9 kg Zinc, mixture melted = (9+11) kg. For 35.1 kg Zinc, mixture, melted = [20/9 x 35.1] kg = 78 kg. Answer A #### A QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 5-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5 Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6 Ratio: 5 to 1 Answer : D #### D QUESTION:Combine terms: 15a + 26b -4b – 16a. options: A)4a + 22b B)-28a + 30b C)-a + 22b D)28a + 30b E)5a + 30b SOLUTION:Solution: 15a + 26b -4b – 16a. = 15a – 16a + 26b – 4b. = -a + 22b. Answer: (C) #### C QUESTION:What is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1200 B)1256 C)1349 D)1456 E)1590 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m? options: A)1350 B)1357 C)2025 D)2052 E)2122 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 => 675 675 * 3 = Rs.2025 Answer:C #### C QUESTION:If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer? . options: A)√n + 1 B)n + 1 C)n^2 + 1 D)n + 2√n + 1 E)n^2 + 2n + 1 SOLUTION:Let a= +ve integer such that n= a^2 (a+1)= next +ve integer (a+1)^2 = a^2 + 1 + 2a and a=n^(1/2) Therefore , (a+1)^2=n+1+2*n^(1/2) Answer D #### D QUESTION:The average of 5 quantities is 12. The average of 3 of them is 4. What is the average of remaining 2 numbers? options: A)24 B)10 C)8 D)9.5 E)None of these SOLUTION:ANSWER: A (5x12-3x4)/2=24 #### A QUESTION:A certain list has an average of 6 and a standard deviation of B (B is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than B? options: A)(-6;0) B)(0;0) C)(0;6) D)(0;12) E)(6;6) SOLUTION:Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. E) #### E QUESTION:a and b are positive integers less than or equal to 9 and multiple of 4. If a and b are assembled into the seven-digit number abaabab, which of the following must be a factor of abaabab? options: A)3 B)4 C)5 D)7 E)8 SOLUTION:The last two digit of the number are ab. Both a and b are multiple of 4,thus the last two digits are divisible by 4, which makes the number abaabab divisible by 4. Thus 4 is always a factor of abaabab. Answer: B #### B QUESTION:A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts. options: A)21:25 B)27:25 C)21:23 D)31:25 E)33:22 SOLUTION:Solution : Given SI1 = SI 2 P1 : P2 = 1/R1T1 : 1/R2T2 = 1/(10*5) : 1/(9:6) 27:25 B #### B QUESTION:It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number X? options: A)a. 2^96 + 1 B)b. 2^16 - 1 C)c. 2^16 + 1 D)d. 7 * 2^33 E)e. 2^64 + 1 SOLUTION:a³ + b³ =(a+b)(a² -ab +b²) Now, let (2^32 + 1) be (a+b) a³ + b³ = (2^96 + 1) Now, as mentioned in formula above, a³ + b³ is always divisible by (a+b) So any factor of X=(a+b) is a factor of (a³ + b³) Henca A #### A QUESTION:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of t feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(x/t) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet. The number of revolutions = distance/circumference = 5,280x/t. Answer: A. #### A QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased? options: A)8% B)7% C)10% D)6% E)9% SOLUTION:Explanation: Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol, such that Benson buys 1 litre of petrol After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125 Since Benson spends additional 15% on petrol, amount spent by Benson = 100× (100+15)/100 = Rs.115 Hence Quantity of petrol that he can purchase = 115/125 Litre Quantity of petrol reduced = (1−115/125) Litre Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8% Answer: Option A #### A QUESTION:A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is : options: A)16000 B)18000 C)20000 D)30000 E)None of these SOLUTION:Explanation: Number of bricks =Courtyard area /1 brick area =(1800×1200 /12×6)=30000 Option D #### D QUESTION:Walking with 4/5 of my usual speed, I arrive at the bus stop 8 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed? options: A)20 B)24 C)28 D)32 E)36 SOLUTION:Let t = usual time = distance / usual speed t + 8 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4 t = 32 The answer is D. #### D QUESTION:David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house? options: A)$96,000 B)$94,000 C)$88,000 D)$75,000 E)$40,000 SOLUTION:Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer. #### B QUESTION:Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $880.What was original rent of friend whose rent is increased? options: A)800 B)900 C)1600 D)1100 E)1200 SOLUTION:0.2X = 4(880-800) 0.2X = 320 X = 1600 Answer C #### C QUESTION:The number of permutations of the letters of the word 'MESMERISE' is? options: A)9!/(2!)2 3! B)9!/(2!)2 8! C)9!/(8!)2 3! D)8!/(2!)2 3! E)9!/(2!)2 1! SOLUTION:n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways. The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R. Number of arrangements = 9!/(2!)2 3! Answer: A #### A QUESTION:A box contains 4 chocobars and 4 ice creams. Tom eats 3 of them, by randomly choosing. What is the probability of choosing 2 chocobars and 1 icecream? options: A)9/3 B)1/7 C)2/8 D)2/7 E)4/7 SOLUTION:Probability of choosing 1 chocobar = 4/8 = 1/2 After taking out 1 chocobar, the total number is 7. Probability of choosing 2nd chocobar = 3/7 Probability of choosing 1 icecream out of a total of 6 = 4/6 = 2/3 So the final probability of choosing 2 chocobars and 1 icecream = 1/2 * 3/7 * 2/3 = 1/7 B #### B QUESTION:Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A)$140 B)$141 C)$142 D)$147 E)$145 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer D)$147 #### D QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)30% C)32% D)73% E)84% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 ---20 => 20% Answer:A #### A QUESTION:Express the ratio 3 2/3 : 7 1/3 in its simplest form. options: A)1:21 B)1:1 C)2:1 D)1:2 E)2:11 SOLUTION:Solution We first convert the mixed numbers 3 2/3 and 7 1/3 into fractions 3 2/3 = 3*3 / 3 + 2 / 3 = 11 / 3 7 1/3 = 7*3 / 3 + 1 / 3 = 22 / 3 The ratio 3 2/3 : 7 1/3 can be expressed as 11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22 Simplify = 11 / 22 = 1 / 2 The ratio is 1 / 2 or 1:2 ANSWER IS D #### D QUESTION:What is the number of integers from 1 to 100 (inclusive) that are divisible by neither 5 nor by 6? options: A)35 B)47 C)58 D)26 E)34 SOLUTION:In 100 consecutive numbers, number of multiples of 5 = 100/5 = 20 (Ignore decimals) In 100 consecutive numbers, number of multiples of 6 = 100/6 = 16 Number of multiples of 5*6 i.e. 30 = 100/30 = 3 Number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - (29 + 16 - 3) {Using the concept of sets here) = 58 Answer is C #### C QUESTION:9, 16, 18, 25, 36,49 options: A)9 B)16 C)18 D)25 E)36 SOLUTION:Each of the numbers except 18, is perfect square. Answer: Option C #### C QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT options: A)38 B)41 C)30 D)31 E)29 SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: C #### C QUESTION:A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 5,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 11.11% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-5,500=4,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/4,500*100=~11.11% of the remaining solution of 4,500 gallons. Answer: E. #### E QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 4y) is odd II. xy^2 is an even negative integer III. (y^2 - x) is an odd negative integer options: A)(3X-4Y) IS ODD TRUE B)II only C)I and II D)I and III E)II and III SOLUTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 4y) is odd 3x - is always negative and odd 2y - can be 0, when y=0, or always even integer (positivie or negative) odd integer +/- even integer = always odd I statement is always true II. xy^2 is an even negative integer y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true III. (y^2 - x) is an odd negative integer y can be 0 => -x will be positive => III statement is not true basing on above, only I statement will always be true answer is A #### A QUESTION:Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift? options: A)1/27 B)1/54 C)1/81 D)1/6 E)1/216 SOLUTION:Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2 Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2) Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6 Answer: option D #### D QUESTION:Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg options: A)2:0 B)2:3 C)2:1 D)2:2 E)2:8 SOLUTION:By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind Required ratio = 60 : 90 = 2 : 3 Answer: B #### B QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number? options: A)9 B)11 C)17 D)13 E)15 SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7. Given (x + 1) + (x + 7) = 28 => 2x + 8 = 28 => x = 10 The third number = x + 3 = 10 + 3 = 13. Answer: D #### D QUESTION:Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 35%. What fraction of the original paint was replaced? options: A)1/35 B)1/5 C)2/3 D)3/5 E)4/5 SOLUTION:35% is 10%-points above 25% and 15%-points below 50%. Thus the ratio of 25%-solution to 50%-solution is 3:2. 3/5 of the original paint was replaced. The answer is D. #### D QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x options: A)1 B)2 C)34 D)12 E)13 SOLUTION:46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A #### A QUESTION:The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer? options: A)5 B)3 C)4 D)2 E)1 SOLUTION:Let the second integer be x and the fourth be a. Then [3x + x + (x+2) + a]/4 = 9 => 5x + 2 + a = 36 => 5x + a = 34 => a = 34 - 5x From the above equation we can see that a is minimum when x is maximum, provided both are positive The maximum value that x can take in the above equation while still keeping a positive is x=6 This gives us a= 34 - 30 = 4 Therefore the minimum value that the fourth integer can have is 4. Answer:C #### C QUESTION:The product of n consecutive positive integers is always divisible by? options: A)n^2 -1 B)(n+1)! C)2n +1 D)n! E)n^2 + 1 SOLUTION:Plug in some vlues and check - Product of first 2 number is 2*1 Product of first 3 number is 3*2*1 Product of first 4 number is 4*3*2*1 Product of first 5 number is 5*4*3*2*1 So, The product of first n natural numbers is always divisible by n! , answer will be (D) #### D QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:With 630 ml mixture of milk & water in the ratio 7:2. How much water mustbe added to make the ratio 7:3? options: A)60 ml B)80 ml C)70 ml D)90 ml E)92 ml SOLUTION:concentration of water in mixture1 =2/9 (since the ratio of milk and water = 7:2) ...(1) concentration of water in pure water= 1 ...(2) Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3 => concentration of water in mixture2 =3/10 By rule of alligation, concentration of water in mixture1 (2/9) concentration of water in pure water (1) Mean concentration (3/10) 1−3/10=7/10 =1:19 => Quantity of water =630×1/9=70 ml C #### C QUESTION:Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he: options: A)broke even, B)lost 4 cents C)gained 4 cents D)lost 10 cents E)gained 10 cents SOLUTION:Solution: 20 % profit on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Similarly, 20 % loss on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24. Since both profit and loss amount is same so, it’s broke even. Answer: A #### A QUESTION:One of the longest sides of the triangle is 20 m,the other side is 10 m.Area of the triangle is 80m^2.What is the another side of the triangle? options: A)2sqrt(61) B)2sqrt(62) C)2sqrt(63) D)2sqrt(64) E)2sqrt(65) SOLUTION:base of triangle is 20 and area is 80 therefore height=2*80/20=8. now one side of triangle is of 10. so we can get the point were the base is divided by applying Pythagoras therm so division pt =sqrt(10^2-8^2)=sqrt(36)=6 threfore other half is 14. now second side=sqrt(14^2+8^2)=sqrt(260)=2sqrt(65) ANSWER:E #### E QUESTION:Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = options: A)18 B)15 C)-13 D)-21 E)-24 SOLUTION:f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = f(4) = 0= 16+4b+c--- Taking 16 to the other side -> 4b+c= -16 f(-3) = 0= 9-3b+c --- taking -3b+c to the other side -> 3b-c=9 When we add these 2 equations, we get 7b= -7---> b= -1 And while substituting b= -1 we get c= -12. b+c= -13--- Answer C #### C QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:If a person throw 2 dice simultaneously then find the probability of the sum of dots is 3 multiply ? options: A)1/2 B)1/3 C)2/5 D)7/9 E)1/4 SOLUTION:If 2 dies are thrown E = event of getting a prime number = 12 total number of possible out comes = 36 probability = 12/36 = 1/3 Answer is B #### B QUESTION:A company organzied a help desk.there have been done 24 hrs work on software,17 hrs on help user nd 40% on other services.find the total no. of hrs have been worked on that day? options: A)68 B)69 C)70 D)67 E)76 SOLUTION:let total no of hrs = x they have done 24+17=41 40% of x is 40/100=2/5 x=41+2x/5 x=68.3 ANSWER:A #### A QUESTION:The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly options: A)24.64 B)24.69 C)24.62 D)24.6 E)24.61 SOLUTION:Explanation: For 1st year S.I =C.I. Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200 i.e S.I on the principal for 1 year is Rs.200 Principle = = Rs.2500 Amount for 2 years, compounded half-yearly C.I = Rs.424.64 Also, Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64 Answer:A #### A QUESTION:CONVERT 2.5 hectares in ares options: A)130 ares. B)160 ares. C)180 ares. D)230 ares. E)250 ares. SOLUTION:2.5 hectares in ares 1 hectare = 100 ares Therefore, 2.5 hectares = 2.5 × 100 ares = 250 ares. ANSWER- E #### E QUESTION:What distance (in meters) will be covered by a bus moving at 54 km/hr in 15 seconds? options: A)175 B)200 C)225 D)250 E)275 SOLUTION:54 km/hr = 54 * 5/18 = 15 m/s distance = 15 * 15 = 225 meters The answer is C. #### C QUESTION:Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)21 C)25 D)26 E)24 SOLUTION:Solution Given Data 3 positive integers Average of a, b, and c = 20. So, a+b+c3a+b+c3 = 20 or a + b + c = 60 a ≤ b ≤ c Median = (a + 11) Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c Therefore, b = a + 11 Objective To find the least value of 'c' Theoretically, the least value of c is when c = b. Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11) Or 3a = 38 or a = 12.66 So, b = c = 12.66 + 11 = 23.66 However, we know that these numbers are all integers. Therefore, a, b, and c cannot take these values. So, the least value for c with this constraint is NOT likely to be when c = b Let us increment c by 1. Let c = (b + 1) In this scenario, a + (a + 11) + (a + 12) = 60 Or 3a = 37. The value of the numbers is not an integer in this scenario as well. Let us increment c again by 1. i.e., c = b + 2 Now, a + (a + 11) + (a + 13) = 60 Or 3a = 36 or a = 12. If a = 12, b = 23 and c = 25. The least value for c that satisfies all these conditions is 25. Correct answer is choice C. #### C QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:The time on a clock is 20 minutes past 5. What is the angle between the hands of the clock? options: A)60 degrees B)20 degrees C)30 degrees D)50 degrees E)40 degrees SOLUTION:The hour hand rotates 360 degrees in twelve hours. The hour hand rotates 30 degrees in one hour. The hour hand rotates 5 degrees in ten minutes. At this time, the hour hand has rotated 160 degrees. The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes. At this time, the minute hand has rotated 120 degrees. The difference is 160 - 120 = 40 degrees. The answer is E. #### E QUESTION:An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 18%. How much will an air-conditioning unit cost in November? options: A)$466 B)$470 C)$472 D)$484 E)$491 SOLUTION:if its prevoius november (before discount) then price is $470. but if its November of next year then 16% discount on $470=470(1-16/100)=$394.8 again a corrected raised price of 18% over $394.8=394.8(1+18/100)=465.86~$466 Ans A #### A QUESTION:The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is ? options: A)96 litres B)98 litres C)100 litres D)102 litres E)None SOLUTION:Answer Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12 Average = ( 110 x 7 + 86 x 5 ) / 12 =(1200 / 12 = 100 liters Correct Option: C #### C QUESTION:A car covers a distance of 624 km in 3 hours. Find its speed? options: A)104 kmph B)194 kmph C)208 kmph D)174 kmph E)101 kmph SOLUTION:624/3 =208 kmph Answer:C #### C QUESTION:A certain fraction has the same ratio to 1/18, as 2/5 does to 7/9. What is this certain fraction? options: A)1/20 B)1/25 C)1/30 D)1/35 E)1/40 SOLUTION:x / (1/18) = (2/5) / (7/9) x = 2*9*1 / 18*5*7 = 1/35 The answer is D. #### D QUESTION:Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly? options: A)Rs.1261 B)Rs.1440 C)Rs.1185 D)Rs.1346 E)Rs.1446 SOLUTION:A = 8000(21/20)3 = 9261 = 8000 --------- 1261 ANSWER:A #### A QUESTION:The price of stock decreased by 5% last year and rose by 10% this year. What is the net percentage change in the price of the stock? options: A)0.2% B)0.8% C)1.2% D)1.6% E)4.5% SOLUTION:(100% - 5%) * (100% + 10%) = 0.95 * 1.10 =1.045 = 104.5%. The net percentage change in the price of the stock is (+) 4.5% The answer is E #### E QUESTION:Amol was asked to calculate Arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged the 2 digits, say a and b,in one of these 10 integers. As a result, his answer for the Arithmetic mean was 1.8 more than what it should have been. Then b - a equals options: A)1 B)2 C)3 D)4 E)None of these SOLUTION:Explanation : Arithmetic mean is more by 1.8 means sum is more by 18. So, ba – ab = 18. b > a because sum has gone up, e.g. 31 – 13 = 18. Hence, b – a = 2. Answer : B #### B QUESTION:Find the middle one when The sum of three consecutive even numbers is 36? options: A)10 B)12 C)15 D)16 E)20 SOLUTION:3 consecutive numbers can be a - 1, a, a + 1 So sum of numbers = 3a = 36. Hence a = 12. B #### B QUESTION:A cube of edge 7 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to: options: A)1:25 B)1:49 C)1:52 D)1:522 E)None SOLUTION:Sol. Required ratio = 6 * 1 * 1 / 6 * 7 * 7 = 1/49 = 1:49. Answer B #### B QUESTION:A man buys s cycle for $100 and sells it at a loss of 10%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 90% of the $100 = 90/100 * 100 = $90 Answer is E #### E QUESTION:The average age 10 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)20 B)99 C)77 D)26 E)12 SOLUTION:10 * 2 = 20 years Answer: A #### A QUESTION:Acording to a military code, SYSTEM is SYSMET and NEARER is AENRER. What is the code for FRACTION ? options: A)CARFTINO B)CARFTION C)ARFCNOIT D)CARFNOIT E)SUIIQQWE SOLUTION:Explanation: The letter is the first half and the letter half of the word are separately reversed to obtain the code. Answer: D #### D QUESTION:A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much options: A)0.60 loss B)0.70 loss C)0.80 loss D)0.50 loss E)0.40 loss SOLUTION:CP when profit of 25% = 12.8 CP when loss of 20% = 20 Total CP = 32.8 Total SP = 32.00 Total loss = 0.80 ANSWER:C #### C QUESTION:The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5/18 = 30 m/s Hence time taken to cover 330 m = 330/30 = 11 seconds. Answer: A #### A QUESTION:If x+|x|+y=4 and x+|y|-y=6 what is x+y=? options: A)11 B)-1 C)3 D)5 E)13 SOLUTION:If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0. If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases). Answer: C. Adding both eqn we get 2x +IxI+IyI = 13 Now considering X <0 and y>0 2x-x +y = 13 we get x+y =11 Hence answer should be A #### A QUESTION:hree 6 faced dice are thrown together. The probability that all the three show the same number on them is ? options: A)1/39 B)1/36 C)1/32 D)1/287 E)1/29 SOLUTION:It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways. Hence the probability is 6/216 = 1/36 Answer: B #### B QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:What is the total surface area in square meters of a rectangular solid whose length is 8 meters, width is 7 meters, and depth is 4 meters? options: A)132 m2 B)145 m2 C)165 m2 D)152 m2 E)120 m2 SOLUTION:Surface Area of a cuboid = 2(lb+bh+lh) = 2(8*7+7*4+8*4)=2(56+28+32)=2*116=132 m2 Answer : A #### A QUESTION:The proportion of water to alcohol in Solution A is 5:4 and the proportion of water to alcohol in Solution B is 6:5. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? options: A)40.9% B)41.9% C)42.9% D)43.9% E)44.9% SOLUTION:Let V be the total volume of the new solution. Then a volume of V/2 was added from each solution A and B. The amount of alcohol added to the new solution was: (4/9)(V/2)+(5/11)(V/2)=2V/9+5V/22=89V/198. The concentration of alcohol is 89/198=44.9% The answer is E. #### E QUESTION:When a 192 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ? options: A)52 B)68 C)62 D)67 E)69 SOLUTION:Answer No. of pieces = Total length / Length of each piece = 192/3.2 = 60 Option: D #### D QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour. options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these SOLUTION:Explanation: We know Time = Distance/speed So total time taken = (120/60+160/80)=4hours Time taken for 280 Km = 280/4=70.km/hr Option A #### A QUESTION:The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z? options: A)35 B)33 C)28 D)21 E)15 SOLUTION:The smallest possible product is 33 which is 3*11. All other products are too big. The answer is B. #### B QUESTION:What is the average of xx,2x2x,and 66? options: A)x+2 B)x+2x C)x+2x+2 D)2x+2 E)x+2x-2 SOLUTION:By the definition of an average, we get: x+2x+63=3x+63x+2x+63=3x+63 =3(x+2)3=x+2.=3(x+2)3=x+2. Hence, the answer is x+2x+2 or Option C #### C QUESTION:The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)6535 B)6532 C)6725 D)6874 E)6972 SOLUTION:C 6725 CP = SP * (100/(100 + profit%)) = 8339(100/124) = Rs. 6725 #### C QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)287 m B)350 m C)187 m D)197 m E)186 m SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer: B #### B QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P? options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36 SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house. J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs Answer:B #### B QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D QUESTION:How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The numbers should be of the form 6c+3. The minimum is 3 when c=0. The maximum is 45 when c=7. There are 8 such numbers. The answer is D. #### D QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt? options: A)16.67 B)30 C)50 D)60.33 E)150 SOLUTION:let x=ounces of 60% salt solution to be added .2*50+.6x=.5(50+x) x=150 Answer E #### E QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $18,000 to $28,000, by how much will the property tax increase? options: A) $320 B) $800 C) $320 D) $600 E) $850 SOLUTION:Increase in house value = $28,000 - $18,000 =$10000 So, tax increase = 8% of$10000=$800 Answer: B #### B QUESTION:What approximate value should come in place of question mark (?) in the following equation? 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ? options: A)230 B)225 C)232 D)220 E)240 SOLUTION:? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12 = 256.3 + 40.3 – 66.12 ≈ 232 Answer C #### C QUESTION:If n + 12 is a positive odd integer, which of the following must be true about the sum of the next four integers? options: A)It is a multiple of 3 B)It is a multiple of 4 C)It is a prime number D)It is a multiple of 5 E)It is a multiple of 2 SOLUTION:n+12 is a positive odd integer. This means n will be an odd integer The next 4 integers would be: n + 12, n + 13, n + 14, n + 15 Sum = 4n + 54 This sum will always be even. Option E #### E QUESTION:Sebastian bought a meal at a restaurant and left a 15% tip. With the tip, he paid exactly $35.42. How much did the meal cost without the tip? options: A)$28.98 B)$29.91 C)$30.15 D)$30.60 E)$30.80 SOLUTION:The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip. Thus, 115% of this price equals $35.42: 1.15x = 35.42 Divide both sides by 1.15:=>x=35.42/1.15=30.80 correct answer E)$30.80 #### E QUESTION:11 is subtracted from 40% of a number and results is 23. What is the number? options: A)160 B)92 C)88 D)85 E)34 SOLUTION:(40/100) * X – 11 = 23 4X = 340 X = 85 Answer:D #### D QUESTION:The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : options: A)144 m2 B)140 m2 C)108 m2 D)158 m2 E)None of these SOLUTION:Area of the outer rectangle = 23 × 16 = 368 m2 Area of the inner rectangle = 19 × 12 = 228 m2 Required area = (368 – 228) = 140 m2 Answer B #### B QUESTION:If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ? options: A)3653 B)3657 C)2977 D)3957 E)2711 SOLUTION:Explanation: Given : Letter : T I E R B A N Code : 7 1 9 3 2 4 5 Thus, the code for RENT is 3957. ANSWER:D #### D QUESTION:A driver goes on a trip of 50 kilometers, the first 25 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour. What is the average speed of the entire trip in kilometers per hour? options: A)35 B)36 C)40 D)42 E)45 SOLUTION:The time for the first part of the trip was 25/60 = 5/12 hours. The time for the second part of the trip was 25/30 = 5/6 hours. The total time for the trip was 5/12 + 5/6 = 15/12 = 5/4 hours. The average speed for the trip was 50 / (5/4) = 40 kph The answer is C. #### C QUESTION:In what ratio should a variety of oil costing Rs. 9 per ltr be mixed with another variety of oil costing Rs. 17.25 per ltr to obtain a mixture costing Rs. 11.75 per ltr? options: A)4 : 1 B)1 : 3 C)3 : 1 D)1 : 2 E)2 : 1 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (17.25 - 11.75) / (11.75 - 9) = 22/11=2/1 ANSWER:E #### E QUESTION:If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q? options: A)6 B)4 C)3 D)2 E)1 SOLUTION:4500+10q+d+8737=13003+100q+10d 13237+10 q+d=13003+100q+10d 234=90q+9d 26=10 q+d d=6 ^ q=2 ==> d-q= 4 ANSWER B #### B QUESTION:The average of first 18 even numbers is? options: A)19 B)18 C)16 D)11 E)17 SOLUTION:Sum of 18 even numbers = 18 * 19 = 342 Average = 342/18 = 19 Answer:A #### A QUESTION:Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)491 B)481 C)471 D)441 E)445 SOLUTION:Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 3*7/100*2100 = 441. D #### D QUESTION:On dividing 22 by a number, the quotient is 7 and the remainder is 1. Find the divisor. options: A)1 B)2 C)3 D)6 E)7 SOLUTION:d = (D-R)/Q = (22 - 1)/7 = 21/7 = 3 C #### C QUESTION:The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is? options: A)240 B)235 C)245 D)250 E)260 SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec. Time = 30 sec Let the length of bridge be x meters. Then, (130 + x)/30 = 25/2 x = 245 m. Answer: Option C #### C QUESTION:Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ? options: A)2 B)5 C)1 D)9 E)4 SOLUTION:4-3=1. Answer is C #### C QUESTION:There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)675 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 10C2 Number of ways of selecting 2 non fiction books = 6C2 10C2 * 6C2 = 45 * 15 = 675 Answer: C #### C QUESTION:What is the maximum number of points that 10 circles of different radii intersect? options: A)24 B)26 C)33 D)90 E)100 SOLUTION:the maximum number of points that two circles intersect is two. therefore, each of these 10 circles intersect two point with each of the other 9 circles. as a consequence, the number of these points is equal to two times the number of combination of the 10 circles. 2∗(10!)/(2!∗10!)=90 Answer: D #### D QUESTION:A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food. options: A)$400 B)$1400 C)$3400 D)$2400 E)$4400 SOLUTION:Part of salary left =1-(2/5+3/10+1/8) =7/40 Let the monthly salary be $x Then (7/40) of x=1400 X=8000 Expenditure on food=$2400 Option D #### D QUESTION:10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day? options: A)4 days B)10 days C)20 days D)25 days E)26 days SOLUTION:Explanation: 10*12*15/20 = 24*20*x/32 X=4 Answer: Option A #### A QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2490 ? options: A)Rs. 832 B)Rs. 830 C)Rs. 822 D)Rs. 812 E)Rs. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830. Answer: B #### B QUESTION:If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since q is an integer so q cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making q^2 as a multiple of 12)) q^2 is divisible by 12 (12 = 2*2*3), So, q should have at least one 2 and one 3 so that q^2 has a 2^2 and two 3 So, q will have a 2 and a 3. Or q will be a multiple of 6 So, largest possible integer than should divide q^3 is 6^3 So, Answer will be D #### D QUESTION:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major? options: A)1/15 B)4/5 C)4/15 D)1/5 E)2/5 SOLUTION:tot students=x 1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2) 2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x) hence 1/5 D #### D QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ? options: A)95 B)110 C)20 D)None of these E)Cannot be determined SOLUTION:Solution 2/5of 350 - 4/7of 210 = 20. Answer C #### C QUESTION:Claire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have? options: A)39 B)50 C)66 D)57 E)60 SOLUTION:G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300 G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66 C #### C QUESTION:If a and b are the roots of the equation x2 - 9x + 20 = 0, find the value of a2 + b2 + ab? options: A)10 B)25 C)36 D)61 E)87 SOLUTION:Explanation: a2 + b2 + ab = a2 + b2 + 2ab - ab i.e., (a + b)2 - ab from x2 - 9x + 20 = 0, we have a + b = 9 and ab = 20. Hence the value of required expression (9)2 - 20 = 61. Answer D #### D QUESTION:Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? options: A)5/5 B)5/9 C)3/4 D)5/7 E)5/2 SOLUTION:In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27 The probability = 27/36 = 3/4. Answer: C #### C QUESTION:Q. How many 9-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6, 6, 7? options: A)180 B)140 C)210 D)270 E)300 SOLUTION:the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2 i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _ case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6 when the units digit is 2 i.e 1 _ _ _ _ _ 2 number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60 when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30 case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6) number of ways this can be done would be 5! / (2!) for 2 =60 and 5! / 2! for 6 ... = 60 adding all of these ... gives the answer 140 ... the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat B #### B QUESTION:What is the area of a square field whose diagonal of length 24 m? options: A)256 B)289 C)200 D)288 E)178 SOLUTION:d2/2 = (24 * 24)/2 = 288 Answer: D #### D QUESTION:The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is: options: A)60 kg B)59 kg C)62 kg D)63 kg E)61 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (75 x 3) = 225 …. (i) A + B = (88 x 2) = 176 …. (ii) B + C = (72 x 2) = 144 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 288 …. (iv) Subtracting (i) from (iv), we get : B = 63. B’s weight = 63 kg. Answer D #### D QUESTION:Evaluate: 20 - 12÷12×2 = options: A)A)4 B)B)8 C)C)12 D)D)16 E)E)20 SOLUTION:According to order of operations, 12÷12×2 (division and multiplication) is done first from left to right 12÷12×2 = 1 × 2 = 2 Hence 20 - 12÷12×2 = 20 - 12 = 8 correct answer is B) 8 #### B QUESTION:A sum of Rs.4000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)2888 B)3120 C)2877 D)2600 E)1277 SOLUTION:Let A be the amount received at the end of the three years. A = 4000[1 + 10/100][1 + 20/100][1 + 25/100] A = (4000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.6600 So the interest = 6600 - 4000 = Rs.2600 Answer: D #### D QUESTION:What is the speed of the train in km/hr whose length is 360 metres which passes a pole in 18 seconds? options: A)59/9 km/hr B)50/9 km/hr C)25/6 km/hr D)55/18 km/hr E)60/18 km/hr SOLUTION:Speed=(18x5/18)=5 m/sec. Length of the train= 360 metre Time=18s Speed=length / time Speed=(360/8)=20 m/sec = 20*5/18 km/hr = 50/9 km/hr Answer: B #### B QUESTION:In a class, the average age of 28 boys is 12 years and the average of 20 girls is 8 years. what is the average age of the whole class? options: A)10.3 Years B)12.3 Years C)12.6 Years D)13 Years E)15 Years SOLUTION:Total age of 48 students (28X 12+20 X 8) = 496 Average = 496/48 = 10.3 Years A #### A QUESTION:Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount? options: A)$1200 B)$1400 C)$1600 D)$1800 E)$2000 SOLUTION:0.7(x-600)=0.6(x-400) 0.1x=420-240 x=1800 The answer is D. #### D <<<Examples ends QUESTION:I lost Rs 68 in two races. My loss in the second race is Rs 6 more than my lose in the first race. My friend lost Rs 4 more than me in the second race. Then what is the amount lost by my friend in the second race? options: A)Rs 41 B)Rs 40 C)Rs 31 D)Rs 51 E)Rs 81 SOLUTION:I lost Rs 68 in two races. My loss in the second race is Rs 6 more than my lose in the first race. so I lost Rs 31 in first race and Rs 37 in 2nd race. My friend lost Rs 4 more than me in the second race. My friend lost 37+4= Rs 41 in the second race. ANSWER:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)10 B)20 C)21 D)22 E)23 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days ANSWER : OPTION B #### B QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? options: A)35 B)36 C)37 D)43 E)39 SOLUTION:James worked for 41 hours hence he earned 40*x+5*2x=50x dollars; We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours. Answer: D. #### D QUESTION:Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there? options: A)20 toys B)30 toys C)40 toys D)60 toys E)50 toys SOLUTION:x : the total number of toys x/10 : the number of toys for first child x/10 + 12 : the number of toys for second child x/10 + 1 : the number of toys for the third child 2(x/10 + 1) : the number of toys for the fourth child x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x x = 30 toys : solve for x correct answer B #### B QUESTION:if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no. options: A)24 B)25 C)26 D)27 E)28 SOLUTION:25 m^3 = (3+1)(3+1) = 16 then m^4 = (4+1)(4+1)=25 ANSWER:B #### B QUESTION:If the number 24*32 is completely divided by 6. what is the smallest whole number in the place of * ? options: A)4 B)3 C)1 D)2 E)5 SOLUTION:Solution The number is divisible by 6 means it must be divisible by 2 and 3. Since the number has 2 as its end digit it is divisible by 2. Now, 2+4+x+3+2=11+x which must be divisible by 3. Thus x=1 Answer C #### C QUESTION:A single discount equivalent to the discount series of 20%, 15% and 8% is? options: A)37.4 B)31.8 C)31.6 D)31.3 E)31.1 SOLUTION:100*(80/100)*(85/100)*(92/100) = 62.6 100 - 62.6 = 37.4 Answer:A #### A QUESTION:The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.8,517 for a cell phone, then what was the cost price of the cell phone? options: A)Rs.5,845 B)Rs.6,750 C)Rs.5,700 D)Rs.6,925 E)None of these SOLUTION:Explanation: 123% of CP =SP Therefore, CP = Rs.8,517x100/123 = Rs.6925 Answer: Option D #### D QUESTION:A reward of $1400 was divided among a group of 36 rescue workers such that each male in the group received $50. How much did each of the 16 females receive? options: A)$10 B)$12.50 C)$25 D)$37.50 E)$50 SOLUTION:x = amount each female received amount each male received = 50 number of females = 16 number of males = 36 - 16 = 20 total to males = 20(50) = 1000 total to females = 16x reward = total to males + total to females 1400 = 1000 + 16x 1400 - 1000 = 16x 400 = 16x 25 = x Answer: C #### C QUESTION:A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running? options: A)2 1/7 hours B)2 1/2 hours C)2 7/2 hours D)4 1/2 hours E)2 1/5 hours SOLUTION:Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours. Answer:B #### B QUESTION:When asked what the time is,a person answered that the amount of time left is 1/5 of the time already completed.what is the time. options: A)2 B)9 C)3 D)8 E)6 SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=15x⇒x=2024−x=15x⇒x=20 Time is 8 PM Answer:D #### D QUESTION:A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 12 cups of tea are prepared, 6 in one way and 6 in other. Find the different possible ways of presenting these 12 cups to the expert. options: A)252 B)240 C)300 D)924 E)None SOLUTION:Solution: Since, there are 6 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is, [12!/(6!x 6!)]= 924 Answer: Option D #### D QUESTION:By selling a house for Rs.45000, it was found that 1/2 of the outlay was gained, what ought the selling to price to have been in order to have lost 2 p.c? options: A)38020 B)38000 C)38028 D)29400 E)38192 SOLUTION:CP + CP/2 = 45000 CP = 30000 SP = 30000*(98/100) =29400 Answer:D #### D QUESTION:The third proportional to 2 and 6 is? options: A)18 B)17 C)14 D)15 E)13 SOLUTION:(6*6)/2 = 18 Answer:A #### A QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share? options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164 SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B #### B QUESTION:The number of permutations of the letters of the word 'MESMERISE' is? options: A)9!/(2!)2 3! B)9!/(2!)2 8! C)9!/(8!)2 3! D)8!/(2!)2 3! E)9!/(2!)2 1! SOLUTION:n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways. The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R. Number of arrangements = 9!/(2!)2 3! Answer: A #### A QUESTION:A retailer buys 80 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)115 C)112 D)118 E)120 SOLUTION:let the market price of each pen be $1 then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20 profit %=((43.20*100)/36) %=120% Answer E)120 #### E QUESTION:What is the units digit of (52^5)(37^3)(71^9)? options: A)3 B)4 C)6 D)7 E)8 SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2. The units digit of 37^3 is the units digit of 7^3 which is 3. The units digit of 71^9 is the units digit of 1^9 which is 1. The units digit of 2*3*1 is 6. The answer is C. #### C QUESTION:A furniture dealer purchased a desk for $100 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? options: A)40% B)45% C)50% D)55% E)60% SOLUTION:Anyway, in this question, there is no discount but the mark up is given as 40% of the selling price. So it is not 40% of $100 but instead, 40% of Selling price which is obtained by adding mark up to $100. So if selling price is S, 100 + 40% of S = S or 100 = 0.6S therefore S = 100/0.6 = S = Profit = 100/0.6- 100 which is calculated on cost price in % terms. So 40/100 * 100 = 40% is profit. A #### A QUESTION:Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance. What is the distance traveled by each tyre? options: A)75000 B)80000 C)90000 D)67800 E)50000 SOLUTION:B 80,000. The distance traveled by each tyre: 4/5 * 1, 00, 000km = 80,000 km. #### B QUESTION:A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.15,000 earned at the end of 2years from the startingof the business? options: A)s. 5,000 B)s. 4,500 C)s. 5,700 D)s. 6,500 E)s. 7,500 SOLUTION:A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3. B's share = Rs. 15000 x 3/10 = Rs. 4,500. B #### B QUESTION:The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall’s revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n? options: A)100n/(150 – n) B)200n/(250-n) C)200n/(300-n) D)250n/(400-n) E)300n/(500-n) SOLUTION:Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold. Total revenue= Revenue due to A + Revenue due to B = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B) = n *1 + (100-n) *1.5 = n + (150-1.5n) --- (1) 2. But we know, revenue due to A = m%. of the total revenue --- (2) 3. To express m in terms of n we need to relate (1) and (2) 4. m% = n / ( n + (150-1.5n)) or m= 100n / 150-0.5n = 200n/(300-n) ANSWER:C #### C QUESTION:which of the following is a prime number ? options: A)17 B)18 C)15 D)20 E)25 SOLUTION:Clearly, 17 is a prime number. Option A #### A QUESTION:For any 5 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3? I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. II. Dividing each of the numbers by 3 and then adding the results together. III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. options: A)I only B)II only C)I and II only D)II and III only E)None of the above SOLUTION:Let the 3 numbers be x, y and z. Question: Which of the following is equivalent to (x + y + z)/3 I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141 II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent Answer: C #### C QUESTION:In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people? options: A)11C6 * 9! *4! B)11C3 * 6! *3! C)15C4 * 9! *3! D)15C2 * 10! *3! E)16C5 * 10! *4! SOLUTION:7 people can be selected from 11 people in 11C7 ways. Remaining 4 people can be selected from 4 people in 4C4 ways. Now, arranging 7 people on a round table = (7-1) ! = 6! Arranging 4 people on a round table = (4-1) ! = 3! Hence, total number of ways = 11C7 * 6! * 4C4 * 3! = 11C3 * 6! * 3! B #### B QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 * 72 = 48 Answer: B #### B QUESTION:Salesperson A's compensation for any week is $350 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation? options: A)$21,000 B)$18,000 C)$15,000 D)$ 14,500 E)$4,000 SOLUTION:sometime, setting up an equation is an easy way to go with: 350 + 0.06 (x - 1000) = 0.08 x x = 14,500 Ans : D #### D QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be: options: A)20 cm B)25 cm C)35 cm D)50 cm E)None of these SOLUTION:Explanation: Total volume of water displaced =(4 x 50) m3 = 200 m3 Rise in water level = 200/40×20= 0.25m = 25cm Answer: B #### B QUESTION:Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%? options: A)30000 B)40000 C)50000 D)60000 E)70000 SOLUTION:let first parrt is x and second part is y then x+y=50000----------eq1 total profit=profit on x +profit on y 7000=(x*10*1)/100 + (y*20*1)/100 70000=x+2y-----------------------------------eq2 70000=50000+y so y=20000 then x =50000-20000=30000 first part =30000 ANSWER:A #### A QUESTION:Today is Tuesday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come? options: A)Saturday B)MONDAY C)TUESDAY D)WEDNESDAY E)FRIDAY SOLUTION:Today is Tuesday after three days--->Friday now, (Friday)after before day--->Thursday then, (Thursday)day after tomorrow--->Saturday ANSWER:A #### A QUESTION:A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum N of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ? options: A) 5 B) 7 C) 9 D) 10 E) 14 SOLUTION:Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum N of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D #### D QUESTION:Tom can hit a target 3 times in 6 shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4shots. What is the probability that at least 2 shots hit the target ? options: A)1/2 B)2/5 C)2/3 D)3/7 E)3/11 SOLUTION:Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by Karan hits tha target and Raja not hit the target. or Karan does not hit the target and Raja hits the target. or. Karan hits the target and Raja hits the target = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6 = 24/36 = 2/3 C #### C QUESTION:A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected? options: A)1/3 B)2/5 C)2/7 D)3/7 E)3/8 SOLUTION:Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected) = = 2/5 B #### B QUESTION:Sandy bought 65 books for $1480 from one shop and 55 books for $920 from another shop. What is the average price that Sandy paid per book? options: A)$38 B)$18 C)$99 D)$27 E)$20 SOLUTION:average price per book = (1480 + 920) / (65 + 55) = 2400 / 120 = $20 The answer is E. #### E QUESTION:CONVERT 2.5 hectares in ares options: A)130 ares. B)160 ares. C)180 ares. D)230 ares. E)250 ares. SOLUTION:2.5 hectares in ares 1 hectare = 100 ares Therefore, 2.5 hectares = 2.5 × 100 ares = 250 ares. ANSWER- E #### E QUESTION:Three hoses work to fill a tub at at different rate. Hose Q and B, working together, can fill the tub in 6/5 of an hour. Hoses Q and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub? Edited for accurate solution options: A)3/10 B)2/5 C)1/2 D)1 E)6/5 SOLUTION:Convert the given time to rate and you will be able to add it up. Total Rate of Q and B = Rate of Q + Rate of B = 1/(6/5) = 5/6 Total Rate of Q and C = Rate of Q + Rate of C = 1/(3/2) = 2/3 Total Rate of B and C = Rate of B + Rate of C = 1/2 Adding all three, 2(Rate of Q + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2 = 2 Rate of Q + Rate of B + Rate of C = 1 tub/hour Time taken by all three together to fill up the tub is 1 hour=D #### D QUESTION:The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers? options: A)10 B)12 C)14 D)15 E)16 SOLUTION:Solution Let the number be x and (28 - x) = Then, x (28 - x) = 192 ‹=›x2 - 28x + 192 = 0. ‹=›(x - 16) (x - 12) = 0 ‹=›x = 16 or x = 12. Answer B #### B QUESTION:Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is? options: A)10 B)30 C)40 D)50 E)60 SOLUTION:Let the numbers be 3x,4x and 5x their L.C.M. = 60x 60x =600 x = 10 The numbers are 3*10 , 4*10 , 5*10 Hence required H.C.F. = 10 Answer is A #### A QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)18 B)20 C)24 D)30 E)40 SOLUTION:Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30 Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20 Answer:B #### B QUESTION:The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers? options: A)15 B)17 C)19 D)21 E)23 SOLUTION:x,x+2,x+4 are three odd numbers (x+x+2+x+4)/3=12+(x/3) x=15 last no.=x+4=19 ANSWER:C #### C QUESTION:Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $880.What was original rent of friend whose rent is increased? options: A)800 B)900 C)1600 D)1100 E)1200 SOLUTION:0.2X = 4(880-800) 0.2X = 320 X = 1600 Answer C #### C QUESTION:A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in. options: A)17 days B)97 days C)19 days D)60 days E)15 days SOLUTION:A = 140 days B = 105 days 1/140 + 1/105 = 7/420 = 1/60 =>60 days Answer: D #### D QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is S? options: A)50+A/200 B)50+3S/100 C)50+S/40 D)100+S/50 E)100+3S/100 SOLUTION:50+S/40=C #### C QUESTION:What is 30% of 210? options: A)61 B)63 C)65 D)67 E)69 SOLUTION:X/210 = 30/100 100X = 210X30 X =(210X30)/100 X =6300/100 = 63 ANSWER = B = 63 #### B QUESTION:In your classes you counted 120 hands. How many students were at the class? options: A)60 B)61 C)85 D)86 E)88 SOLUTION:Total number of hands = 120 We have 2 hands. To find how many students were at the class, divide the total number of hands by the number of hands we have. We get, divide 120 by 2 220 ÷ 2 = 60 Therefore, there were 60 students at the class. ANSWER IS A #### A QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence? I. w-6,x-6,y-6,z-6 II. 5w,2x,3y,5z III. 5w,5x,5y,5z options: A)II and III B)III only C)I and III D)I and II E)II only SOLUTION:lets look at the three choices... I. w-6,x-6,y-6,z-6 since the difference is constant, it is an arithmetic sequence... II. 5w,2x,3y,5z since the difference is not constant, it is not an arithmetic sequence III. 5w,5x,5y,5z since the difference is constant it is an arithmetic sequence... Answer is A) #### A QUESTION:The sector of a circle has radius of 24 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)104.6 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 24) + 2(24) = 56.6 + 48 = 104.6 cm Answer:C #### C QUESTION:If the length of a rectangular field is 30 metres more than its breadth and the perimeter of the field is 540 metres, what is the area of the field in square metres? options: A)18000 B)40000 C)31000 D)19000 E)16000 SOLUTION:Let breadth is x then length is 30+x Now the perimeter=2(x+30+x)=540 solving this we get x=120 Now the area is 120*150=18000 ANSWER:A #### A QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:18 C)18:22 D)18:39 E)18:39 SOLUTION:Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer:A #### A QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded? options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :- letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..) Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get IDAATRE ANSWER:D #### D QUESTION:What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 6), (x, 6)? options: A)64 B)81 C)125 D)196 E)225 SOLUTION:To find the area of a square, knowing the length of one side is sufficient. From the coordinates given, we can see that one side equals 14. The area is 14*14 = 196. The answer is D. #### D QUESTION:A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees? options: A)$20,200 B)$20,500 C)$20,800 D)$21,000 E)$21,400 SOLUTION:average = 2(19000)+(21000)+3(22000) / 6 = $20,833 The answer is C. #### C QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale? options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these SOLUTION:Let the original price be x and sale be of y units. Then, the revenue collected initially = x × y Now, new price = 0.8x, new sale = 1.8y Then, new revenue collected = 1.44xy % increase in revenue = 0.44xy/xy×100 = 44% increase Answer A #### A QUESTION:In a survey of parents, exactly 7/8 of the mothers and 3/4 of the fathers held full-time jobs. If 60 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs? options: A)25.5% B)21.5% C)17.5% D)13.5% E)9.5% SOLUTION:Fathers without full-time jobs are 1/4*2/5 = 2/20 of all the parents surveyed. Mothers without full-time jobs are 1/8*3/5 = 3/40 of all the parents surveyed. The percent of parents without full-time jobs is 2/20 + 3/40 = 7/40 = 17.5% The answer is C. #### C QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:Find the product of place value and face value of 5 in 65231 options: A)28000 B)25000 C)27000 D)26000 E)28000 SOLUTION:Place value of 5 in 65231 = 5 x 1000 = 5000 Face value = 5 required product = 5000 x 5 = 25000 Answer :B #### B QUESTION:The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds? options: A)4 B)9 C)39 D)48 E)63 SOLUTION:Given: z=s^2+2s for 0≤s≤7 z(4) = 4^2 + 2*4 = 24 z(7) = 7^2 + 2*7 = 63 Therefore z(7) - z(3) = 63 - 24 = 39 km/hr Option C #### C QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)Rs.6620 B)3378 C)2768 D)2999 E)2771 SOLUTION:A = 20000(11/10) 3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king? options: A)1/13 B)2/15 C)4/13 D)3/17 E)1/19 SOLUTION:Here, n(S) = 52 There are 13 cards that are diamond (including one king) and there are 3 more kings. Let E = event of getting a diamond or a king. Then, n(E) = (13 + 3) = 16 P (E) = 16 / 52 = 4/13 C #### C QUESTION:John earned 40% more per month than Oscar. If john salary is decreased 10% and Oscar’s salary is increased by 10%, then john would be earning what percent more than Oscar? options: A)10% B)9.09% C)15.54% D)14.54% E)It cannot be determined from the information given. SOLUTION:This Q is all about taking the correct BASE for taking %s.. the very first step requires taking some numbers for each.. ONE should be 100... it is easy to take 60 and 100 here.. but the BASE is 100 here, so the salary can be 100 and 140.. 100 increases 10% =110.. 140 decreases 10%=126.. so the increase is 16.. again the BASE is 110, so answer 16/110 * 100= 14.54% C without calculations, answer cannot be equal to or greater than 16, as 16 is on 110.. so D is the only one left #### D QUESTION:How many numbers from 10 to 1000 are exactly divisible by 9? options: A)100 B)10 C)11 D)12 E)14 SOLUTION:10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100 Answer : A #### A QUESTION:(0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is: options: A)0.8 B)0.4 C)0.96 D)0.69 E)0.76 SOLUTION:Given expression = (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2) = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2) = (a - b) = (0.5 - 0.1) = 0.4 Answer is B #### B QUESTION:What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x options: A)35678 B)73205 C)75653 D)86554 E)87565 SOLUTION:(B) 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205 #### B QUESTION:For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? options: A)12% B)26% C)29% D)32% E)60% SOLUTION:In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated. In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated. Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%. Answer: D. #### D QUESTION:A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? options: A)13 8/3 days B)13 1/3 days C)13 6/3 days D)63 1/3 days E)13 5/3 days SOLUTION:5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days Answer:B #### B QUESTION:The average salary/head of allthe workers in a workshop is Rs.750, if the average salary/head of 5 technician is Rs.900 and the average salary/head of the rest is Rs.700, the total no. of workers in the work-shop is ? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:Let the total number of workers be y. So sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y -5 workers. 5 x 900 + 700(y -5) = 750 y ⇒ 4500 + 700y - 3500 = 750y ⇒ 50y = 1000 ∴ y = 20 So total number of workers = 20 B #### B QUESTION:Preeti covers a distance in 40 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 50%. options: A)60 km/h B)70 km/h C)117.64 km/h D)100 km/h E)125.25 km/h SOLUTION:Given Speed = 60 Kmph. It means Preeti covered 60 km in 60 min (1 hour). So, in 40 min he will cover 40 km. 50% time reduced = 40 - 50% of 40 = 20 min. Thus, Preeti needs to cover 40 km in 20 min (0.34 hour). Speed * Time = Distance. Speed * 0.34 = 40 Speed = 117.64 kmph. ANSWER : OPTION C #### C QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:Tough and Tricky questions: Exponents. If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy? options: A)4, 2, 8, 6 B)4 and 2 C)2 and 8 only D)6 and 4 E)8 and 6 SOLUTION:Only Units digit of X and Y contribute to the Units digit of XY. Finding all values of X for positive values of a When, a=1; X=2 a=2; X=4 a=3; X=8 a=4; X=16 a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4...... Similarly, Finding all values of Y for positive values of b When, b=1; Y=3 b=2; Y= 9 b=3; Y= 27 b=4; Y=81 b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9.... So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y When X=2 and Y=3: Units digit of XY = 6 When X=2 and Y=9: Units digit of XY = 18 When X=2 and Y=7: Units digit of XY = 14 When X=2 and Y=1: Units digit of XY = 2 When X=4 and Y=3: Units digit of XY = 12 When X=4 and Y=9: Units digit of XY = 36 When X=4 and Y=7: Units digit of XY = 28 When X=4 and Y=1: Units digit of XY = 4 When X=8 and Y=3: Units digit of XY = 24 When X=8 and Y=9: Units digit of XY = 72 When X=8 and Y=7: Units digit of XY = 56 When X=8 and Y=1: Units digit of XY = 8 When X=6 and Y=3: Units digit of XY = 18 When X=6 and Y=9: Units digit of XY = 54 When X=6 and Y=7: Units digit of XY = 42 When X=6 and Y=1: Units digit of XY = 6 There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6 Ans: A #### A QUESTION:The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? options: A)3:5 B)3:9 C)3:2 D)2:2 E)3:8 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r1^2 . h1/r2^2. h2 => 1/15 = (1)^2h1/(2)^2h2 => h1/h2 = 3/5 i.e. h1 : h2 = 3:5 Answer: A #### A QUESTION:How many numbers from 29 to 79 are exactly divisible by 11? options: A)4 B)6 C)8 D)5 E)7 SOLUTION:Numbers=(79/11)-(29/11) =7-2 =5 numbers Option D is answer #### D QUESTION:x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days? options: A)x2/y2 units B)y3/x2 units C)x3/y2 units D)y2/x2 units E)None SOLUTION:Explanation: Let amount of work completed by y men working y hours per in y days = w units More men, more work(direct proportion) More hours, more work(direct proportion) More days, more work(direct proportion) Hence we can write as (men)x:y (hours)x:y (days)x:y }::x:w ⇒x^3w=y^3x ⇒w=y^3x/x^3 =y^3/x^2 Answer: Option B #### B QUESTION:There are 3 classes having 20, 24 and 30 students respectively having average marks in an examination as 20,25 and 30 respectively. The three classes are represented by A, B and C and you have the following information about the three classes. a. In class A highest score is 22 and lowest score is 18 b. In class B highest score is 31 and lowest score is 23 c. In class C highest score is 33 and lowest score is 26. options: A)can't be determined in both cases B)definite decrease in both cases C)definite increase in both cases D)will remain constant in both cases E)will remain constant in both cases21 SOLUTION:Ans: B Explanation: Class A average is 20. And their range is 18 to 22 Class B average is 25. And their range is 23 to 31 Class A average is 30. And their range is 26 to 33 If 5 students transferred from A to B, A's average cannot be determined but B's average comes down as the highest score of A is less than lowest score of B. If 5 students transferred from B to C, C's average cannot be determined the B's range fo marks and C's range of marks are overlapping. Answer:A #### A QUESTION:If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 5. II. x is an integer multiple of 3 III. x is an integer multiple of 6 options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6. Let us take example n, n+1, n+2 as 3 three consecutive positive integers. In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12 Hence in a product of 3 consecutive integers, the product is always divisible by 3. Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also. Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even Answer E #### E QUESTION:A firm has 3 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.) options: A)42 B)46 C)50 D)54 E)58 SOLUTION:The number of ways to form a group of 3 is 8C3 = 56 The number of groups with no senior partner is 5C3 = 10 The number of groups with at least one senior partner is 56-10 = 46 The answer is B. #### B QUESTION:When you draw 2 dices together, find the probability of getting numbers in pairs? options: A)1/5 B)1/6 C)1/7 D)1/11 E)1/12 SOLUTION:S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} N (S) = 36 Set of pairs, B = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}; N (B) = 6 P (getting numbers in pairs) = N(B)N(S)N(B)N(S) = 636636 = 1/6 B #### B QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11 SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify. As for your question, it is very simple and straightforward with number plug in. Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E QUESTION:There are 3 teams each with 8 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)192 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 64 possibilities (8*8) since each team has 8 players. So there are a total of 192 possibilities (64*3). I hope this method is easier for you to understand. #### C QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs. 51.25 B)Rs. 51.22 C)Rs. 51.219 D)Rs. 51.18 E)Rs. 51.11 SOLUTION:Explanation: Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer:A #### A QUESTION:Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 7 meters, and the interior of tank B has a height of 7 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? options: A)70% B)80% C)100% D)120% E)125% SOLUTION:The radius of tank A is 7/(2*pi). The capacity of tank A is 10*pi*49 / (4*pi^2) = 245 / (2*pi) The radius of tank B is 10 / (2*pi). The capacity of tank B is 7*pi*100 / (4*pi^2) = 350 / (2*pi) Tank A / Tank B = 245/350 = 7/10 = 70% The answer is A. #### A QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)40 B)41 C)48 D)67 E)45 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: Option C #### C QUESTION:A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a red ball is selected? options: A)x/(x + 4) B)y/(x + 5) C)(x + 5)/(x + y + 9) D)(y + 4)/(x + y + 9) E)(x + 4)/(x + y + 9) SOLUTION:x red balls y green balls x+4+y+5 is the total =x+y+9 x+5 is the number of red balls so (x + 5)/(x + y + 9) the answer is C #### C QUESTION:The greatest number of four digits which is divisible by 7, 10, 40 and 60 is: options: A)9200 B)9300 C)9400 D)8400 E)7400 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 7, 10, 40 and 60 is 4200. On dividing 9999 by 4200, the remainder is 1599. Required number (9999 - 1599) = 8400. ANSWER :D #### D QUESTION:At a circular table for nine will sit seven adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the nine people be arranged around the table. options: A)120 B)240 C)480 D)600 E)720 SOLUTION:Consider the two parents and two children as one unit. Then there are five adults and one family unit. The number of ways 6 can form a line is 6! Around a circular table, there would be 6 rotations so we divide this number by 6. There are 5! ways for 6 to sit around the circular table. Then the two children have two options and the two parents have two options. Then the total number of ways is 5!*2*2= 480 The answer is C. #### C QUESTION:If a number is exactly divisible by 11 and 13, which of the following types the number must be? options: A)Divisible by (11 + 13) B)Divisible by (13 - 11) C)Divisible by (11 x 13) D)Divisible by (13 ÷ 11) E)None SOLUTION:Answer LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13). Correct Option: C #### C QUESTION:A wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face? options: A)52.9% B)55.4% C)58.3% D)61.7% E)64.5% SOLUTION:There are a total of 9*9*9 = 729 cubes. All the exterior cubes will have at least one face painted red. The interior is formed by 7*7*7 = 343 cubes. The number of cubes with at least one side painted red is 729 - 343 = 386 cubes The probability that a cube has at least one side painted red is 386/729 which is about 52.9% The answer is A. #### A QUESTION:The divisor is 12, the quotient is 4 and the remainder is 1. What is the dividend? options: A)48 B)49 C)96 D)97 E)72 SOLUTION:D = d * Q + R D = 12 * 4 + 1 D = 48 + 1 D = 49 Answer: B #### B QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 6 years ago? options: A)152460 B)214560 C)131632 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^6 Answer is C #### C QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 30¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)66 E)49.5 SOLUTION:Total price of six cans = 6*36.5 = 219 Total price of 4 cans = 4*30 = 120 Total rice of two cans = 219 - 120 = 99 Average price of two cans = 99/2 = 49.5 c Another way to do it is this: Assume that the four leftover cans were of 30c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 2*36.5 + 4*6.5 = 99 Avg cost of the two cans = 99/2 = 49.5c Answer (E) #### E QUESTION:A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse. options: A)2200 B)1800 C)1200 D)1000 E)1500 SOLUTION:Let the C.P of the horse be Rs. X, Then, C.P of the carriage = Rs.(3000- x). 20% of x - 10% of ( 3000-x ) =2% of 3000 = 60, x/5 - ( 3000-x )/10 = 60, 3x - 3000 = 600, 3x =3600, x = 1200. Hence, C.P of the horse = Rs. 1200 ANSWER:C #### C QUESTION:Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought? options: A)20 B)18 C)24 D)26 E)28 SOLUTION:Smallest gumballs = (19-16) + (19-14) +19= 27 Largest gumballs = (25-16) + (25-14) +25= 45 Difference = 45 - 27 = 18 B #### B QUESTION:In how many years will a sum of money double itself at 10% per annum? options: A)2 years 4 months B)4 years 2 months C)8 years 4 months D)10 years 8 months E)None SOLUTION:Sol. Let sum = x. Then, S.I. = x ∴ Time = [100 * S.I. / P*R] = [100 * x / x * 12] years = 8 1/3 years = 8 years 4 months. Answer C #### C QUESTION:If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$72.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 60.50 = (20/100)*60.50 = $12.1 Total spent 60.50 + 12.1 = $72.6 correct answer B #### B QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students? options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9 SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760 Sum of the marks for the class of 45 students = 45 * 70 = 3150 Sum of the marks for the class of 85 students = 2760 + 3150 = 5910 Average marks of all the students = 5910/85 = 69.5.Answer: D #### D QUESTION:Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage X. options: A)16.8% B)17.4% C)17.9% D)18.5% E)19.1% SOLUTION:Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20 Selling price of an orange = 10 --> Cost price = 10/1.25 = 8 A > O 23*(A) + 10*(O) = 653 653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0 Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value Between 11 and 21, If A = 11, O = 30 --> Not possible If A = 21, O = 17 --> Possible Cost price = 20*21 + 8*17 = 420 + 136 = 556 Profit = 653 - 556 = 97 Profit% X= (97/556)*100 = 17.4% Answer: B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: options: A)14 B)67 C)56 D)89 E)34 SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer:A #### A QUESTION:Jerry, an electrician, worked 5 months out of the year. What percent of the year did he work? (round answer to the nearest hundredth) What percent 12 is 5? 12 months = 1 year options: A)58.33% B)68.33% C)78.33% D)88.33% E)41.66% SOLUTION:1. Multiply the opposites 5 x 100 = 500 100=5/12 Divide by the remaining number 41.66% (rounded to hundredth) correct answer E #### E QUESTION:The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet? options: A)33 B)37 C)27 D)28 E)23 SOLUTION:Explanation: Other side = = = = 6 ft Area of closet = (6 x 4.5) sq. ft = 27 sq. ft. Answer: C) 27 #### C QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ? options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these SOLUTION:solution: Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)] =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4. ∴ Required average =8.4/2 = 4.2 Answer B #### B QUESTION:x =1 2 3 y= 4 5 18 then what is the relation between x and y options: A)1*X)^1 B)1*X)^6 C)1*X)^7 D)1*X)^4 E)1*X)^2 SOLUTION:Y=(1*X)^2 4=(1*2)^2 4=4 ANSWER:E #### E QUESTION:The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994: options: A)7N B)8N C)9N D)12N E)15N SOLUTION:Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets. In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992: $100 + 4x$100 = $100 + $400 =$500 In 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993: $500 +2x$500 = $500 + $1000 =$1500 This is 15 times the 1992 number, so the correct answer is 15N. #### E QUESTION:One pipe can fill a pool four times faster than a second pipe. When both pipes are opened, they fill the pool in eight hours. How long would it take to fill the pool if only the faster pipe is used? options: A)5 hr B)8 hr C)10 hr D)16 hr E)20 hr SOLUTION:fast pipe + slow pipe = together One pipe fills the pool four times faster than the other pipe so, hourly fill rates: 1/x + 1/4x = 1/8 Let x = number of hours it would take the fast pipe to fill the pool thus, x=10 hours Answer: C #### C QUESTION:What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81? options: A)1020600 B)1020593 C)56693 D)28343 E)18900 SOLUTION:14 = 2 * 7 25 = 5 * 5 36 = 2 * 2 * 3 * 3 81 = 3 * 3 * 3 * 3 So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C. #### C QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer: A #### A QUESTION:The diagonals of a rhombus are 12 cm and 10 cm. Find its area? options: A)158 B)129 C)150 D)123 E)60 SOLUTION:1/2 * 12 * 10 = 60 Answer:E #### E QUESTION:The H.C.F. and L.C.M. of 0.63, 1.05 and 2.1 options: A)(i)0.20(ii)6.31 B)(i)0.21(ii)5.30 C)(i)0.21(ii)6.30 D)(i)1.21(ii)6.50 E)None of these SOLUTION:Explanation : Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10. Without decimal places, these numbers are 63, 105 and 210. Now, H.C.F. of 63, 105 and 210 is 21. H.C.F. of 0.63, 1.05 and 2.1 is 0.21. L.C.M. of 63, 105 and 210 is 630. L.C.M. of 0.63, 1.05 and 2.1 is 6.30. ANSWER IS C #### C QUESTION:If 4 men and 1 boy working together, can do two times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:4M + 1B =2(1M + 1B) 4M + 1B = 2M + 2B 2M = 1B The required ratio of work done by a man and a boy = 1:2 D #### D QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)26 B)22 C)12 D)24 E)20 SOLUTION:Explanation: Let the required number of days be x More men, less days (indirect proportion) Hence we can write as (men) 36 : 27 :: x : 18 ⇒36×18=27 × x ⇒12×18=9 × x ⇒12×2=x ⇒x=24 Answer: Option D #### D QUESTION:Insert the missing number ..., 4, 8, 16, 32, 64, 128, 256 options: A)6 B)5 C)2 D)3 E)8 SOLUTION:series is 2* Previous Number. ANSWER:C #### C QUESTION:Calculate the rate on a principal of Rs.1500 which yields a simple interest of Rs. 220.50 in 3 Years? options: A)6.9% B)2.9% C)9.9% D)5.9% E)4.9% SOLUTION:220.50 = (1500*3*R)/100 R = 4.9% Answer: E #### E QUESTION:Two pipes can fill a tank in 10 hours & 12 hours respectively. While 3rd pipe empties the full tank n 20 hours. If all the three pipes operate simultaneously,in how much time will the tank be filled? options: A)6 hrs 43 min B)2 hrs 25 min C)7 hrs 30 min D)6 hrs 32 min E)7 hrs 10 min SOLUTION:tank filled in 1 hr = 1/10 + 1/12 - 1/20 = 8/60 = 2/15 part so full tank is filled in 15/2 hrs = 7 hr 30 min.. ANSWER:C #### C QUESTION:Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them? options: A)5/7 B)5/3 C)5/1 D)5/6 E)5/2 SOLUTION:P(at least one graduate) = 1 - P(no graduates) = 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6 Answer: D #### D QUESTION:Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? options: A)66 B)70 C)72 D)75 E)78 SOLUTION:Let the distance one way be x Time from home to work = x/60 Time from work to home = x/100 Total time = 2 hrs (x/60) + (x/100)= 2 Solving for x, we get x = 75 Time from home to work in minutes= (75)*60/60 = 75 minutes Ans= D #### D QUESTION:1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus? options: A)98 B)99 C)97 D)96 E)95 SOLUTION:Let x be the no of initial passenger no of passengr left in 1st stop (2x/3)+30 no of passenger in the 2nd stop 3/4((2x/3)+30) + 12 which is equal to 84 (passngr on last stop) so final eqn....3/4((2x/3)+30) + 12 = 84 Ans x = 99 ANSWER:B #### B QUESTION:There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)Rs. 30 B)Rs. 34 C)Rs. 42 D)Rs. 48 E)Rs. 50 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1 or, 35x + 42 = 42x – 42 or, x = 12 Thus the original expenditure of the mess = 35 x 12 = Rs. 42 C #### C QUESTION:The number of arrangements that can be made with the letters of the word MEADOWSS so that the vowels occupy the even places? options: A)14 B)144 C)720 D)992 E)221 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 5 places in 5! i.e., 120 ways. Hence the total ways are 120 * 6 = 720. Answer:C #### C QUESTION:The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is: options: A)1677 B)2523 C)1683 D)3363 E)3567 SOLUTION:L.C.M. of 5, 6, 7, 8 = 840. Required number is of the form 840k + 3 Least value of k for which (840k + 3) is divisible by 9 is k = 2. Required number = (840 x 2 + 3) = 1683. Answer: Option 'C' #### C QUESTION:The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is options: A)62 kg B)60 kg C)64 kg D)72 kg E)None of these SOLUTION:Explanation : Let the weight of student be x kg. Given, Difference in average weight = 8 kg => (96-x)/4 = 8 => x = 64 Answer : C #### C QUESTION:A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)36 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=288/32=9 m/s Distance covered by B in 4 seconds = Speed × time =9×4=36 metre i.e., A beat B by 36 metre Answer is E #### E QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(6900*6)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:A part-time employee whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? options: A)9 B)13 C)17 D)20 E)33.33 SOLUTION:Let original hourly wage be x and let the no of hours worked be y Total wage will be =x*y After the increment the wage will be=1.5 x Now we need to find number of hours worked so that x*y=1.5x*z i.e z=1/1.5 y = 2/3y %decrease = (y-2/3y)/y *100=100/3=33.33%. Thus my answer is E. #### E QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1055 B)1050 C)1057 D)1060 E)1070 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055. A #### A QUESTION:There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men? options: A)1932 B)1933 C)1934 D)1935 E)1936 SOLUTION:(5c3*11c3)+(5c4*11c2)+(5c5*11c1) 1936 ANSWER:E #### E QUESTION:Which of the following is an integer? I. 9! / 6! II. 9! / 8! III. 9! / 7!5! options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:9!/6! = 9*8*7 which is an integer. 9!/8! = 9 which is an integer. 9!/7!5! = 9*8 / 5*4*3*2 = 3/5 which is not an integer. The answer is D. #### D QUESTION:If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000? options: A)$3500 B)$5000 C)$3150 D)$7200 E)$10000 SOLUTION:Saving = (45-30)% of 48000 = 7200. Answer:D #### D QUESTION:There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is: options: A)9 B)13 C)15 D)12 E)19 SOLUTION:Explanation: abc/bcd=385/1001=>a/d=5/13 So d = 13 Option B #### B <<<Examples ends QUESTION:In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)3.75 sec D)12.5 sec E)6 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 150/40 = 3.75 sec. ANSWER:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score. options: A)172 B)173 C)174 D)175 E)None of the above SOLUTION:Total runs = 40 × 50 = 2000 Let his highest score be = x Then his lowest score = x – 172 Now 200−x−(x−172)/38=48 ⇒ 2x = 2172 – 1824 ⇒ x = 174 Answer C #### C QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is? options: A)10 years B)11 years C)12 years D)13 years E)14 years SOLUTION:Total age of 3 boys = 24*3 =72 ratio of their ages = 1:2:3 Age of the youngest = 72*1/6 = 12 years Answer is C #### C QUESTION:How many digits are in (12×10^14)(10×10^15)? options: A)24 B)25 C)26 D)27 E)32 SOLUTION:The question simplfies to (12×10^14)(10^16) => 12*10^30 => Will contain 30 zeros +2 digit 12 =>32 Ans E #### E QUESTION:16, 23, 19, 19, 22, 15, 25, ? What number should replace the question mark? options: A)13 B)11 C)16 D)18 E)19 SOLUTION:B 11 There are two alternate sequences: +3 and –4; #### B QUESTION:The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? options: A)3:4 B)3:0 C)3:1 D)7:3 E)3:7 SOLUTION:Let the present ages of A and B be 4.5x and 3x years respectively. Then, (4.5x - 4)/(3x + 4) = 1/1 1.5x = 8 => x = 5.33 Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: D #### D QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article? options: A)2777 B)2987 C)1200 D)1240 E)1671 SOLUTION:CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 Answer: D #### D QUESTION:In September, John sold 2323 more soap than in February. In November, he sold 5 percent more than in September. John's November sales were what percent greater than his February sales? options: A)10/3% B)65% C)214/3 % D)75% E)514/3% SOLUTION:Let february sale= x september sale= x+2/3x= 5x/3 November sale= 5x+3 + 5*5/100*3x 21/12x= 1.75 x Hence November sale is 75% > February sale D is the answer #### D QUESTION:The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price? options: A)40% B)8% C)25% D)16.66% E)9% SOLUTION:Original cost before weight adjustment: X Cost after 90% weight adjustment: 9/10 X 20% profit on 9/10X: (120/100)(9/10)(X) or 108X/100 Mark up on original cost of X: (108X/100)/X-1 = 8/100 ANSWER:B #### B QUESTION:At 6'o clock clock ticks 6 times. The time between first and last ticks was 30sec. How much time it takes at 10'o clock. options: A)60sec B)62sec C)66sec D)64sec E)54sec SOLUTION:At 6'0 clock, clock ticks 6 times. So, there must be 5 intervals between clock ticks. Time Between first and last ticks = 30sec So, 1 interval = 30/5 = 6sec So 6'o clock 5 *6=30sec 7'o clock 6 *6=36sec . . 9'o clock 8 *6=48sec 10'o clock 9 *6=54sec So, 54sec at 10'o clock. ANSWER:E #### E QUESTION:A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these SOLUTION:Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: C #### C QUESTION:There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)108 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand. #### C QUESTION:The true discount on a bill of Rs.1080 is Rs.180.The banker's discount is options: A)210 B)212 C)214 D)216 E)None of these SOLUTION:Solution P.W = Rs.(1080 - 180) = Rs. 900 S.I on Rs. 1080 =Rs.(180/900 x 1080) = Rs. 216. Answer D #### D QUESTION:Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $45,000 higher than Store B's revenues. In the second month, Store A's revenues were $8,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue? options: A) $14,000 B) $15,000 C) $42,000 D) $47,000 E) $50,000 SOLUTION:Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +45 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +8 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T): (45 + 8 + T)/3 = 2 53 + T = 6 T = -47 Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -47 represents a $47,000 advantage in favor of Store B. Choice (D) is correct. #### D QUESTION:What percent of 120 are 90? options: A)33 B)66 C)75 D)44 E)31 SOLUTION:(?% /100) * 120 = 90 ? = 75% Answer: C #### C QUESTION:Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B QUESTION:Find the value of a from (15)^2 x 8^3 ÷ 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 ÷ 256 = a = 225 x 512 ÷ 256 = 450 E #### E QUESTION:if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr). options: A)18 kmph B)15.5 kmph C)12.5 kmph D)13.5 kmph E)22.5 kmph SOLUTION:Speed in still water = (16 + 9)1/2 kmph = 12.5 kmph. answer :C #### C QUESTION:What is the sum of the different positive prime factors of 380? options: A)5 B)10 C)15 D)17 E)26 SOLUTION:Prime factorization of 380 =38 * 10 =2*19 * 10 =2*19 * 2*5 =2^2 * 5 * 19 Sum of the different positive prime factors of 380 = 2+5+19 =26 Answer E #### E QUESTION:Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages options: A)30 B)35 C)37 D)41 E)42 SOLUTION:Explanation: Let A's age 10 years ago = x years. Then, B's age 10 years ago = 2x years. (x + 10) / (2x+ lO) = 3/4 => x = 5. So, the total of their present ages =(x + 10 + 2x + 10) = (3x + 20) = 35 years Option B #### B QUESTION:A right triangle has sides of a, b, and 7, respectively, where a and b are both integers. What is the value of (a + b)? options: A)40 B)42 C)46 D)48 E)49 SOLUTION:LET a= hypotenuse , b =base ,7 = perpendicular . therefore a^2 -b^2 =7^2 or (a+b)(a-b) = 49 a+b =49/a-b ' a-b cannot be zero ..therefore a+ b =49 where a-b is equal to 1 E #### E QUESTION:if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no. options: A)24 B)25 C)26 D)27 E)28 SOLUTION:25 m^3 = (3+1)(3+1) = 16 then m^4 = (4+1)(4+1)=25 ANSWER:B #### B QUESTION:Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day? options: A)Rs. 120 B)Rs. 150 C)Rs. 250 D)Rs. 400 E)None of these SOLUTION:Solution: Ratio of number of men, women and children, = (18/6): (10/5):(12/3) = 3:2:4 Total (Men +Women +Children) = 18 3X +2X +4X = 18 9X = 18 X = 2 Hence, number of women = 2X = 2*2 = 4 Share of all women = (10*4000)/40 = Rs. 1000 [18+10+12 =40] Thus, share of each woman = 1000/4 = Rs. 250. Answer: Option C #### C QUESTION:How many different subset of the set of the 12 Calendar Month will not have the Month of March. options: A)1951 B)1948 C)1953 D)1947 E)1949 SOLUTION:This is a combination solution Since we have 11 different Month other than the Month of March we can take any Month from the set of 11 Months to make a subset. 11C1 +11C2 + 11C3 + 11C4 + 11C5 + 11C6 + 11C7 + 11C8 + 11C9 + 11C10 + 11C11 = 1948 Plus the one set that is null that is the Set having no element in it which is 11C0 =1 = 1948 + 1 = 1949 E = 1949 #### E QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 7:3. If 70% of the Toyota bought and 30% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? options: A)76% B)58% C)68% D)89% E)49% SOLUTION:let total no of Vehicles bought be 100, Toyota 70 and Honda 30, so total number of SUV's bought for Toyota and Honda respectively 70* 70/100=49 and 30* 30/100=9 so total 58 SUV's were bought out of 100 Vehicles bought..so required % is 58% ANSWER:B #### B QUESTION:At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? options: A)62.5 B)62.8 C)62.1 D)62.9 E)32.5 SOLUTION:Explanation: CP = 47.50 SP = 47.50*(125/100) = 59.375 MP*(95/100) = 59.375 MP = 62.5 Answer: A #### A QUESTION:Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock? options: A)60 miles B)70 miles C)90 miles D)120 miles E)400 miles SOLUTION:Answer = B. 70 miles Relational speed = 130 - 100 = 30 miles per hour In 3 hours, difference = 30 * 3 = 90 miles Fast train trailing 20 miles, so effective difference = 90 - 20 = 70 miles #### B QUESTION:Simple interest on a sum at 5% per annum for 2 years is Rs.120. The C.I. on the same sum for the same period is? options: A)81.6 B)81.9 C)121.5 D)121.3 E)121.1 SOLUTION:SI = 60 + 60 CI = 60 + 60 + 1.5= 121.5 Answer: C #### C QUESTION:Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%. options: A)429.3 B)270 C)177 D)166 E)111 SOLUTION:Explanation: Cost of each share = (20 + 2.5% of 20) = Rs.20.5 Therefore, number of shares = 8800/20.5 = 429.3 ANSWER:A #### A QUESTION:X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join? options: A)6 months B)8 months C)4 months D)2 months E)5 months SOLUTION:Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000 Let investment period of Z be x months. Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x) = 240 : 300 : 30x = 8 : 10 : x The share of Z in the annual profit of Rs. 50000 is Rs. 14000. => [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7 => 25x = 7x + (18 * 7) => x = 7 months. Z joined the business after (12 - 7) months. i.e., 5 months. Answer:E #### E QUESTION:Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)80% C)100% D)180% E)200% SOLUTION:We can use fractional equivalents here to solve the problem 80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears 10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours Now we come to productivity Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour Hence the productivity is double with the assistant i.e. the increase in productivity is 180% D #### D QUESTION:If n is a positive integer, which of the following is a possible value of |36 - 5n|? options: A)7 B)14 C)12 D)15 E)20 SOLUTION:When 36>5n, then |36- 5n| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1 When 36<=5n, then |36- 5n| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits. Answer: B #### B QUESTION:If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following? options: A)m/3 B)9m C)9m^2 D)m^2/3 E)m^2/9 SOLUTION:m = 9 ^ (X-1) m = 3 ^ (2x-2) m^2 = 3 ^ (4x-4) m^2/9 = 3 ^ (4x-6) Answer E #### E QUESTION:What will come in place of the x in the following Number series? 75, 225, x, 2025, 6075 options: A)675 B)752 C)300 D)400 E)1200 SOLUTION:(A) 25 x 3 = 75, 75 x 3 = 225 , 225 x 3 = 675, 1675 x 4 = 2025. #### A QUESTION:90, 180, 12, 50, 100, 80, ?, 3, 20, 4, 25, 2, 6, 30, 3 options: A)100 B)150 C)180 D)90 E)60 SOLUTION:30*3=90 6*30=180 6*2=12 25*2=50 4*25=100 20*4=80 3*20=60 ans is 60 ANSWER:E #### E QUESTION:courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose? options: A)22 B)77 C)877 D)99 E)88 SOLUTION:3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters=525 cm = 5 × 5 × 3 × 7 Hence common factors are 3 and 7 Hence LCM = 3 × 7 = 21 Hence largest size of square tiles that can be paved exactly with square tiles is 77 cm. Answer:B #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent? options: A)28% B)25% C)55% D)17.6% E)55% SOLUTION:850 --- 150 100 --- ? => 17.6% Answer: D #### D QUESTION:If (1 – 1.5)N = 1, then N = options: A) −400 B) −140 C) −2 D) 4 E) 400 SOLUTION:(1 – 1.5)N = 1 Simplify to get: -0.5N = 1 Rewrite as (-1/2)N = 1 Multiply both sides by -2 to get: N = -2 Answer: C #### C QUESTION:The height of the wall is 4 times its width and length of the wall is 3 times its height .if the volume of the wall be 10368 cu.m.its width is options: A)4m B)5m C)6m D)7m E)8m SOLUTION:Explanation: Let width = x Then, height=4x and length=12x 12x × 4x × x = 10368 x = 6 Answer: C #### C QUESTION:Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many litres of tomato puree will be obtained from 20 litres of tomato juice? options: A)2 litres B)2.4 litres C)2.5 litres D)6 litres E)4 litres SOLUTION:Tomato Juice has 90% water and 10% tomato Tomato puree has 20% water and 80% tomato So 20 liter of tomato juice has 20*90/100=18 liters of water and 2 liters of tomato. As tomato puree has 80% content of tomato, so 2 liters of tomato from 20 liter juice corresponds to 80% so tomato purees that can be obtained=100*2/80=2.5 ANSWER:C #### C QUESTION:A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is options: A)250 B)276 C)280 D)285 E)None SOLUTION:Solution since the month begins with a sunday , so there will be five sundays in the month. Required Average = (510x5+240x25 / 30) = (8550 / 30) = 285 Answer D #### D QUESTION:In how many ways can you line up 7 apples in a row if one of them cannot be in the middle or at the either end? options: A)1,790 B)52 C)2,880 D)98 E)2,560 SOLUTION:Since the apple cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880. Answer: C. #### C QUESTION:A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is? options: A)1250m B)1750m C)950m D)1000m E)1300m SOLUTION:Speed = 15*5/18 = 15/18 m/sec Distance covered in 35 minutes = 15/18 *35 *60 = 1750 m Answer is B #### B QUESTION:A train 420 m long is running at a speed of 48 km/hr. In what time will it pass a bridge 60 m long? options: A)40 sec B)36sec C)60 sec D)48 sec E)18 sec SOLUTION:total length= 420+60=480 speed=48km/h=(48*5)/18= 40/3 m/s time=(480*3)/40=36 sec. ANSWER:B #### B QUESTION:A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck? options: A)2:1 B)3:4 C)4:3 D)1:4 E)5:6 SOLUTION:Given; 4 duck = 3 hen; Or, duck/hen = 3/4; Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter. Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''Answer: 2:1; #### A QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is? options: A)299 m B)777 m C)200 m D)167 m E)128 m SOLUTION:2(l + 100) = 600 => l = 200 m Answer:C #### C QUESTION:If n is an integer and 5^n > 4,000,000, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:When you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8 2 to the ^ 8 = 256 so its 256 x 5^6 that means 5^6 x 5^x must be greater 5^x > 256 5^1=5 5^2=25 5^3= 125 5^4= 625 - > so x must be at least 4 5^(6+4)= 5^10 ANSWER:D #### D QUESTION:If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF options: A)13 - 11 - 9 - 7 - 8 B)13 - 11 - 9 - 7 - 6 C)13 - 11 - 9 - 7 - 7 D)13 - 11 - 9 - 7 - 3 E)13 - 11 - 9 - 7 - 1 SOLUTION:MLIGF = 13 - 11 - 9 - 7 - 8 Note: this is a dummy question. Dont answer these questions Answer:A #### A QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 2/5 Km B)3 1/5 Km C)3 1/7 Km D)4 1/5 Km E)4 2/5 Km SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km B) #### B QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)*(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)*(r+4)/(y+r+6) D)(y+3)/(y+r+7)*(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much percent should he reduce the quantity of gasoline that he buys? options: A)6.66% B)8% C)10% D)12% E)12.5% SOLUTION:Let price of original price of gasoline = 10$ and let original consumption of gasoline = 10 Amount spend on gasoline originally = 10*10 = 100$ the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline Increased price of gasoline = 12.5$ Now Ron intends to spend on gasoline =1.15*100 = 115$ Consumption of gasoline needs to be = 115/12.5 = 1150/125 = 46/5 = 9.2 Reduction in consumption of gasoline = 10-9.2 = .8 % reduction in consumption of gasoline = .8/10 * 100% = 8% Answer B #### B QUESTION:Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately. options: A)12 , 18 B)8 , 10 C)18 , 20 D)20 , 25 E)None of these SOLUTION:Explanation : Let speed of ram and shakil be x and y resp. Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute. 2000/x - 1800/y= -60 2000/x= 1800/y -60---------------------(1) Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters 1000/x = (2000- 360y)/y------------------(2) Solve equation 1 and 2 to obtain x and y Answer is x = 8 minutes, y = 10 minutes Hence (B) is the corret answer. Answer : B #### B QUESTION:Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y 1997- x1---- y1-- x1+y1 x1= a*x .....(P) y1= 1.07*y...(Q) x1+y1/x+y = 1.01 solve using P and Q and find x/y #### A QUESTION:X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13750 ? options: A)3200 B)4000 C)3250 D)3825 E)3985 SOLUTION:Ratio of investment, as investments is for different time. Investment x Number of units of time. Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8. X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16. Ratio of investments => X : Y : Z = 18 : 21 : 16. Investment Ratio = Profit sharing Ratio. Z = 13750 × 16/55 = Rs.4000. Share of Z in the profit is Rs.4000. Option B #### B QUESTION:Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ? options: A)500 B)600 C)450 D)550 E)None of these SOLUTION:Explanation: Let the lent at 5% be 'A' (A x 5 x 1)/100 + [(1500 - A)x 6 x 1]/100 = 85 5A/100 + 90 – 6A/100 = 85 A/100 = 5 => A = 500 ANSWER IS A #### A QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 7 robots altogether, if the robots build only one robot at a time? options: A)70 1/7 min B)94 1/7 min C)110 1/7 min D)112 1/7 min E)131 1/7 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) Now the 4 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2 = 5/2 so they complete one robot in 2/5th of an hour - (3) Now the 5 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2+1/2 = 3 so they complete one robot in 1/3th of an hour - (4) Now the 6 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2 so they complete one robot in 2/5th of an hour - (5) And now we have 7 robots So Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes Answer - E #### E QUESTION:A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A options: A)26.2 km B)25.7 km C)23.2 km D)26.67 km E)None of these SOLUTION:Explanation: Distance travelled by each of them is to be made equal. => Distance travelled walking = Distance covered cycling. Let after 4 hours of walking, A walk for x hours more before B catches up with him. => Distance = Speed * Time (4+x)4 = 10x x = 8/3 Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67 ANSWER: D #### D QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)767 m B)467 m C)245 m D)567 m E)544 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C #### C QUESTION:A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)17% B)25% C)69% D)31% E)19% SOLUTION:Let the price be 100. The price becomes 130 after a 30% markup. Now a discount of 10% on 130. Profit=117-100 17% answer A #### A QUESTION:Find the least number of complete years in which a sum of money put out at 15% compound interest will be more than double of itself? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:5 years Answer: A #### A QUESTION:A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 8, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? options: A)20 B)22 C)24 D)27 E)30 SOLUTION:Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes Answer: D. #### D QUESTION:One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card? options: A)1/4 B)1/7 C)1/8 D)1/5 E)2/5 SOLUTION:Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12/48 = 1/4 A #### A QUESTION:In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 8,000 have been vaccinated against both, how many have been vaccinated only against rubella? options: A)2,5000 B)7,500 C)10,000 D)15,000 E)16,000 SOLUTION:Use a single variable as far as possible. Number vaccinated only against mumps = x Number vaccinated against both = 2x = 8000 (so x = 4000) Then, number vaccinated against mumps (including both) = x + 2x = 3x Number vaccinated against rubella = 2*3x = 6x Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*4000 = 16,000 Answer (E) #### E QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)10 B)20 C)21 D)22 E)23 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days ANSWER : OPTION B #### B QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 34, what is the minimum possible range in scores of the three test-takers? options: A)a 17 B)b) 34 C)c) 35 D)d) 45 E)e) 80 SOLUTION:It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have: A- 0 and 17 B- 0 and 28 C- 0 and 35 therefore the minimum range is 34, it cant be any lower however you play with the numbers. B #### B QUESTION:How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 26%? options: A)100 ml B)60 ml C)120 ml D)130 ml E)150 ml SOLUTION:we can also go by answer choices Tke 100 ml for eg 400 (old)+100 (new concentr)ml 500*26/100 = 130 ml (30ml is de old concentration +100 ml (newly added) Answer D #### D QUESTION:Set D consists of 19 elements. The average of set D is L. If a new element is added to the set and the average grows by K, what is the value of the new element? options: A)a) L(1 + K / 5) B)b) L * (K/100) - 20L C)c) 20L(1+K/100) D)d) 20(1+K/100)-19L E)e) L*(K/5)-19 SOLUTION:Let's assume the value of new element to bea. So converting the word problem into equation, (19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K But according to the answer options, problem writer wanted to conveyk% percent rise in average value. If we consider this case than resulting equation will be, (19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100] ==> a= 20L + KL/5 -19L ==> a= L + KL/5 , which is equivalent to option [A] #### A QUESTION:Concentrated pineapple juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated pineapple juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:A certain number of men can finish a piece of work in 10 days. However, if there were 10 less men it will take 10 days more for the work to be finished. How many men were there originally? options: A)10 men B)30 men C)40 men D)20 men E)none of these SOLUTION:Let x be the number of men originally Thus, 10x=(10+10)(x-10) 10x=20(x-10) x=2(x-10) x = 20 ANSWER:D #### D QUESTION:Bookman purchased 55 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 360, how many paperback copies were sold? options: A)8 B)10 C)12 D)19 E)16 SOLUTION:The bookman had 10 hardback ad 55-10=45 paperback copies; 14 copies were sold, hence 55-14=41 copies were left. Let # of paperback copies left be p then 10p+20(41-p)=560 --> 10 p=260 --> p=26 # of paperback copies sold is 45-26=19 Answer: D #### D QUESTION:Vijay bought 160 shirts at the rate of Rs. 255 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? options: A)Rs. 321 B)Rs. 270 C)Rs. 277.5 D)Rs. 285 E)None of these SOLUTION:Total CP per shirt = 255 + 1400/160 + 1.75 + 320/160 = Rs. 267.5 SP = CP[(100 + profit%)/100] = 267.5 * [(100 + 20)/100] = Rs. 321. ANSWER:A #### A QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places? options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5 SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset. Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300 Number CA possible = 1C1 = 1 Number FL possible = 1C1 = 1 Number HI possible = 1C1 = 1 Number other possible = 47C1 = 47 Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes) P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900 Answer: D #### D QUESTION:judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 6th position from either end of the row. Can you find out how many girls are practicing together? options: A)4 B)9 C)11 D)6 E)8 SOLUTION:As judith is 6th from either end of the row, it means that 5 girls are on one of her sides and 5 are present on the other. 5 + 5 + 1(judith herself) = 11. Hence, 11 girls are practicing the dance together. correct answer is C)11 #### C QUESTION:Two clocks are set at 3 0'clock in the morning. If one clock gains 10 minutes per hour and when it shows 6:30 in the morning what does the correct clock show? options: A)5:30 B)5:25 C)7:00 D)6:15 E)6:00 SOLUTION:The faster clock gains 10 minutes per hour. The two clocks at at 3:00 at 3 0'clock in the morning At 4 0'clock - The correct clock is at 4:00 The faster clock is at 4:10 (1 hour + gains 10 minutes) At 5 0'clock - The correct clock is at 5:00 The faster clock is at 5:20 (2 hours + gains 20 minutes) In three hours the faster clock gains 3*10=30 minutes When the faster clock is at 6:30 the correct clock is at 6:00 in the morning. Answer is E #### E QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)9 D)2 E)9 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:At a meeting of 8 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table? options: A)2400 B)2800 C)3200 D)3600 E)4000 SOLUTION:8 people can be arranged around a table in 7! ways. Consider the two chiefs who will not sit together as a single unit. The number of ways to arrange 7 units around a table is 6! We need to multiply this by 2 as the two people can be switched in each arrangement. The total number of ways to arrange the chiefs is 7! - 2*6! = 5*6! = 3600 The answer is D. #### D QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is? options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) M + O = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv) Subtracting (ii) from (iv), we get M = 4000. M's monthly income = Rs. 4000 C #### C QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 – 4xy (x- y)2 = 625 – 576 => (x – y) = 7 ANSWER: A #### A QUESTION:If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years? options: A)(1+k/100)^n B)(1+k)^n C)(1+kn/100) D)(1+k/100)^4n E)(1+kn) SOLUTION:Amount after 7n years will be = x ( 1 + k/100)^4n Amount after 3n years will be = x ( 1 + k/100)^3n So, required ratio will be - { x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n Hence answer will be a. (1+k/100)^4n D #### D QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender? options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2 SOLUTION:There are two cases. All boys and all girls case 1. all boys. 1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128 case 2 .all girls. 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128 We will add the cases to get 1/64 #### A QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of five rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes? options: A)11 min B)12 min C)10 min D)15 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 5 - 1 = 4 rounds per hour. Time taken to complete one round at this speed = 1/4 hr = 15 min. D #### D QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? options: A)700 B)666 C)600 D)400 E)800 SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C #### C QUESTION:Every student at Parcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Parcy School? options: A)63 B)69 C)74 D)82 E)86 SOLUTION:the total number of students at Parcy School The answer is 86 or any multiple of 43.E #### E QUESTION:As a bicycle salesperson, David earns a fixed salary of $25 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>1 options: A)I,III only B)III only C)I only D)II only E)II,III only SOLUTION:II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week); III. y>1 --> if David sold 3 bicycles this week then this week he earned 25+3*6=$43, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $25. So y must be more than 1; I. y<3x --> is not always true. Answer: E #### E QUESTION:which of the following inequalities indicates the set of all values of d for which the lengths R of the three sides of a triangle can be 3,4, and d? options: A)0<d<1 B)0<d<5 C)0<d<7 D)1<d<5 E)1<d<7 SOLUTION:This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c . Thus, |a-b| < c < a+b |b-c| < a < b+c |c-a| < b < a+c Thus, if the sides of the triangle are 3,4 and d, 4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer. #### E QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B? options: A)128228 B)12800 C)12819 D)12818 E)12812 SOLUTION:16*8: x*4 = 5:2 x = 12.8 => Rs.12800 Answer: B #### B QUESTION:A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:If n is a perfect square and a perfect cube, then n = a^6 for some integer a. The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625. The answer is B. #### B QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs? options: A)11 B)12 C)22 D)24 E)44 SOLUTION:22 times in a day. 12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes) ANSWER:C #### C QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 3*1*2=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A #### A QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/55000 * 100 = 21.6% ANSWER:D #### D QUESTION:A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)28 sec B)16 sec C)36 sec D)18 sec E)17 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 240 + 120 = 360 m. Time taken = 360/10 = 36 sec. Answer:C #### C QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 *12=45,000*8 1:1 Madhu's share=1/2*60,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)Monday SOLUTION:Explanation: Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer: Option C #### C QUESTION:A man invests Rs. 4,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? options: A)Rs. 1200 B)Rs. 1300 C)Rs. 1500 D)Rs. 2000 E)None of these SOLUTION:Explanation : Interest on Rs.4000 at 5% per annum = ( 4000 × 5 × 1) / 100 = Rs. 200 Let his additional investment at 8% = x Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25. To earn 6% per annum for the total, interest = (4000 + x) × 6 × 1/100. => 200 + 2x/25 = (4000 + x) × 6 × 1/100. => 20000 + 8x = (4000 + x) × 6. => 20000 + 8x = 24000 + 6x. => 2x=4000. => x=2000. Answer : D #### D QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit? options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62 SOLUTION:Explanation: We are given selling price = Rs. 580 and expected profit of 15 % Therefore, we can easily solve this numerical, considering basic formulae of profit and loss. Let cost price = x Selling price = C.P. + Profit S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price) 580 = x + (0.15 x) 580 = 1.15 x Therefore, x = 504.347 Cost Price = Rs. 504.35 Now, we have the cost price and hence, Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65 The trader gets a profit of Rs. 75.65 ANSWER IS A #### A QUESTION:A reduction of 30% in the price of oil enables a house wife to obtain 6kgs more for Rs.940, what is the reduced price for kg? options: A)72 B)47 C)40 D)28 E)20 SOLUTION:940*(30/100) = 282 ---- 6 ? ---- 1 => Rs.47 Answer:B #### B QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it? options: A)Rs. 8400 B)Rs. 8721 C)Rs. 8856 D)Rs. 9000 E)None of these SOLUTION:Explanation: Actual price = 95% of 90% of 85% of Rs. 12000 = 95/100 * 90/100 * 85/100 * 12000 = Rs. 8721. ANSWER IS B #### B QUESTION:If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a? options: A)2 B)1 C)3 D)7 E)9 SOLUTION:(a5,608 + 584)/88 = a6,192/88 Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 192/8 = 24 => So, we want divisible by 11. Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11. a619-2 => a61-7 => a5-4 => a1 => 11/11. So a = 1. Answer: B #### B QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? options: A)25 days B)24 C)22 days D)27 days E)21 days SOLUTION:B 24 days B = 1/8 – 1/2 = 1/24 => 24 days #### B QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (750 ~ 1020)/1020 = 26% Loss A #### A QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive? options: A)$444 B)$445 C)$446 D)$447 E)$448 SOLUTION:A+B+C = 1200 Given ratio 10:12:13 Let us say the shares of A,B,C deducting 10,20,15 be a,b,c a+b+c = 1200-45= 1155 = 35K c share = (1155X13)/35 = 429 C = chandran share = 429+15 = 444 Option A #### A QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)247 m B)256 m C)245 m D)527 m E)725 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C #### C QUESTION:If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r? options: A)2 B)3 C)4 D)5 E)Cannot be determined SOLUTION:\frac{15^r( 1+ 15)}{4^y} = 15^y (15^r . 4^2 ) / 4^y = 15^y. 4^0 15^r . 4^(2-y) = 15^y. 4^0 Equating the powers, r = y; 2-y = 0; So r = y = 2=A #### A QUESTION:Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 48 seconds. Find the length of the faster train? options: A)270 B)288 C)266 D)299 E)480 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 48 * 10 = 480 m. The length of the faster train = 480 m. Answer: E #### E QUESTION:How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together. options: A)17280 B)4320 C)720 D)80 E)None of thsee SOLUTION:Explanation: word SIGNATURE contains total 9 letters. There are four vowels in this word, I, A, U and E Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now So total letter are 6. 6 letters can be arranged in 6! ways = 720 ways Vowels can be arranged in themselves in 4! ways = 24 ways Required number of ways = 720*24 = 17280 Option A #### A QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point. options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10) SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A #### A QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)10 min B)20 min C)30 min D)40 min E)60 min SOLUTION:Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/3*60/55 = 40 min D #### D QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true? (i) x is prime (ii) y is even (iii) xy is positive options: A)ii only B)iii only C)i and iii only D)ii and iii only E)i, ii and iii SOLUTION:Effectively y = 36x/41 (i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x is not necessarily prime. (ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN. (iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer. ANSWER:B #### B QUESTION:While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%) options: A)4.09 B)4.0 C)4.04 D)4.02 E)4.01 SOLUTION:Explanation: Given Error = 2% while measuring the side of a square. If the correct value of the side of square is 100, the measured value: => 100 + 2% *100 = 100+2=102 The area of square with edge 100 = side*side => 100*100 => 10000 The area of square with side 102 = 102*102= 10404 Error in area calculation = 10404-1000 = 404 % error= (404/10000)*100 = 4.04% ANSWER: C #### C QUESTION:Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid? options: A)D + 40 B)D + H – 1 C)D + 2H D)6.93H E)1.21D SOLUTION:before Discount price was: 1.4D+1.5H After Discount: 1.4D +1.5H-.42D-.45H substitute D=6H final value: 6.93H Ans Is D #### D QUESTION:A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train? options: A)230 m B)250m C)643m D)832m E)270m SOLUTION:Speed = (72 x 5/18)m/sec = 20 m/sec. Time = 26 sec. Let the length of the train be x metres. Then, x + 270/26 = 20 x + 270 = 520 x = 250. Answer:B #### B QUESTION:The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : options: A)Rs. 113.5 B)Rs. 119.7 C)Rs. 124.75 D)Rs. 130.75 E)Rs. 134.45 SOLUTION:For an income of Rs.756, investment = Rs.9000 For an income of Rs., investment = = Rs.125 For a Rs.100 stock, investment = Rs.125. Market value of Rs. 100 stock = = Rs. 124.75 C #### C QUESTION:A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? options: A)5/8 B)6/13 C)5/16 D)5/13 E)5/11 SOLUTION:Two balls can be picked from thirteen balls in 13Câ‚‚ ways. We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵ ways. The required probability = (9 * 4) = 36/78 = 6/13 Answer: B #### B QUESTION:In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can? options: A)52 B)56 C)60 D)64 E)68 SOLUTION:Let C be the capacity of the can. (5/8)*(C-20)+20=(3/4)*C 5C-100+160=6C C=60 The answer is C. #### C QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made? options: A)1:4 B)1:3 C)2:3 D)3:4 E)None of these SOLUTION:Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B #### B QUESTION:In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was: options: A)2500 B)2520 C)3000 D)3100 E)None of these SOLUTION:Explanation : Number of valid votes = 70% of 9000 = 6300. Valid votes polled by other candidates = 40% of 6300 (40/1006300) = 2520. Harsh Mishra a year ago 0 upvotes Answer : B #### B QUESTION:From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The distance traveled by Ferry P is 18 km. Then the distance traveled by Ferry Q is 54 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 54/9 = 6 hours, which is 3 hours more than Ferry P. The answer is C. #### C QUESTION:The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is: options: A)31 kg B)32 kg C)33 kg D)35 kg E)None of these SOLUTION:Explanation: Let A, B, C represent their respective weights. Then, we have: A + B + C = (45 x 3) = 135 …. (i) A + B = (40 x 2) = 80 …. (ii) B + C = (45 x 2) = 90 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv) Subtracting (i) from (iv), we get : B = 35. B’s weight = 35 kg. Answer: D #### D QUESTION:Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is? options: A)6 km B)8 km C)9 km D)11 km E)12 km SOLUTION:Let total distance =D=D Distance travelled at 4 kmph speed =(23)D=(23)D Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr We know, Time=DistanceSpeedTime=DistanceSpeed Total time 2115=2/34D+1/35D2115=2/34D+1/35D 2115=2D12+D152115=2D12+D15 84=14D84=14D D=6 km Option A is correct #### A <<<Examples ends QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {1,2,3}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)2/3 D)1/2 E)5/6 SOLUTION:The product to be even either one or both must be even, so: P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3; Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1. Answer: C. #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:R and S start walking each other at 10 AM at the speeds of 3 km/h and 4 km/h respectively. They were initially 17.5 km apart. At what time do they meet? options: A)2 : 30 PM B)11 : 30 AM C)1 : 30 PM D)12 : 30 PM E)None of these SOLUTION:Let after t hours they meet then, 3t + 4t = 17.5 ⇒ t = 25 ∴ Time = 10 am + 2.5 h = 12 : 30 am Answer D #### D QUESTION:12,?,68,129,220,347,516 options: A)129 B)220 C)347 D)31 E)520 SOLUTION:2*2*2 + 4 = 12 4*4*4 + 4 = 68 5*5*5 + 4 = 129 6*6*6 + 4 = 220 7 *7 *7 + 4 = 347 8 *8 *8 + 4 = 516. 3*3*3 +4 = 31 ANSWER : D #### D QUESTION:If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)R of x, x^2, x^3, x^4 and x^5 is equal to which of the following? options: A)12x B)13x C)14x D)16x E)20x SOLUTION:1 + x^4 + x^3 + x^2 + x = 81 i.e. 1 +x+ x^2+ x^3+ x^4 = 81 x+ x^2+ x^3+ x^4 = 80 x(1 +x+ x^2+ x^3) = 80 x(81-x^4) = 80 81x - x^5 = 80 x^5 = 81x -80 Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x Average of R{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x AnswerD #### D QUESTION:If the integer w is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when w is rounded to the nearest ten. which of the following is a possible value of w? options: A)64 B)67 C)99 D)133 E)147 SOLUTION:We have to check options 1 by 1. 64 rounded to nearest hundred = 100 64 rounded to nearest ten = 60 now difference = 40 the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. therefore 40/60)*100 = 66 2/3 ==>this is the answer. 99 rounded to nearest ten = 100 133 rounded to nearest ten = 130 133 rounded to nearest hundred w= 100=A #### A QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)2 C)3 D)4 E)6 SOLUTION:The distance between the nest and the ditch is 200 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 200 = 6000. D = ST 6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km) D) #### D QUESTION:180 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? options: A)1~10 B)10~20 C)35~45 D)65~75 E)85~95 SOLUTION:180 = 2^2*3^3*5 There are factors in each range except for 65~75 The answer is D. #### D QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)3 B)2.5 C)2.25 D)1.5 E)4 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 - x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 ANSWER:B #### B QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 7. options: A)18 B)20 C)17.5 D)30 E)32 SOLUTION:Solution Average = (7+14+21+28)/4) = 70 / 4 = 17.5. Answer C #### C QUESTION:A committee of 3 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee? options: A)1/28 B)3/28 C)1/14 D)4/28 E)3/14 SOLUTION:3/8*4/7*1/6*3! = 3/14. We are multiplying by 3! because we can choose secretary, economist, and accountant is several way: SEA, SAE, ESA, EAS, ASE, AES. Answer: E. #### E QUESTION:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output? options: A)17% B)24% C)30% D)32% E)79% SOLUTION:take it as original output =100. to meet demand increase by 10%, then output=110. to meet holiday demand , new output increase by 10% then output equals 121 To restore new holidy demand output to original 100. final -initial/final*100 =21/121*100=8/33*100=17% approxiamately. option A is correct. #### A QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer: B #### B QUESTION:If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? options: A)9 B)18−3√3 C)18 D)18+3√3 E)27 SOLUTION:The altitude of an equilateral triangle is side*√3/2. As perimeter of triangle ACD is 9+3√3, AC + CD + AD = (side+side/2+side*√3/2) = 9 + 3√3 or side =6. Perimeter of equilateral triangle, ABC is 3(side) or 18. Answer:(OptionC) #### C QUESTION:In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people? options: A)11C6 * 9! *4! B)11C3 * 6! *3! C)15C4 * 9! *3! D)15C2 * 10! *3! E)16C5 * 10! *4! SOLUTION:7 people can be selected from 11 people in 11C7 ways. Remaining 4 people can be selected from 4 people in 4C4 ways. Now, arranging 7 people on a round table = (7-1) ! = 6! Arranging 4 people on a round table = (4-1) ! = 3! Hence, total number of ways = 11C7 * 6! * 4C4 * 3! = 11C3 * 6! * 3! B #### B QUESTION:The price of pulses has fallen by 18%. How many quintals can be bought for the same amount which was sufficient to buy 16 quintals at the higher price? options: A)20.5 B)22.5 C)19.5 D)18.4 E)32.5 SOLUTION:80% of original price can buy = 16 quintals. Therefore, he can buy ( 16 x 100 )/ 82 = 19.5 quintals at the lower price. ANSWER:C #### C QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 130*4=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible? options: A)230 B)360 C)420 D)840 E)5,040 SOLUTION:we have 6 letters out of which 3 are of one kind, 2 are of another kind.. so total ways = 6!/2!1!=360 ans B #### B QUESTION:In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 93% of the products of M3 III are not defective. What is the percentage of defective in the stockpile? options: A)3% B)5% C)2.5% D)4% E)3.6% SOLUTION:Explanation : Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3. Products from M1 = 40, from M2 = 30 and from M3 = 30. Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.07 x 30 = 2.1 Therefore, total number of defective products = 3.6 Answer : E #### E QUESTION:A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)75 ways B)87 ways C)66 ways D)108 ways E)21 ways SOLUTION:Explanation: The boy can select one trouser in five ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 5 * 15 = 75 ways. Answer: A #### A QUESTION:What is 2 2/3 - 1 1/4 divided by 1/5 - 1/6 ? options: A)17/36 B)36/17 C)17/6 D)85/2 E)51/4 SOLUTION:2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12 1/5 - 1/6 = (6-5)/30 = 1/30 So 17/12/1/30 = 17/12 * 30 = 85/2 Answer - D #### D QUESTION:A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have? options: A)576 B)800 C)726 D)484 E)500 SOLUTION:(4/15) * A = (2/5) * B A / B = 3 / 2 Therefore A's share is = (1210 * (3/5)) = 726 Ans - C #### C QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers? options: A)180 B)128 C)276 D)297 E)236 SOLUTION:Let the five numbers be P, Q, R, S and T. => P + Q + R + S + T = 655. (P + Q)/2 = 85 and R = 125 P + Q = 170 and R = 125 P + Q + R = 295 S + T = 655 - (P + Q + R) = 360 Average of the last two numbers = (S + T)/2 = 180. Answer:A #### A QUESTION:find out the probability to get 1Rs coin head, 2Rs coin Tail and 5Rs coin head?? options: A)1/2 B)1/8 C)1/16 D)1/4 E)None of these SOLUTION:1Rs coin head=1/2 2Rs coin Tail=1/2 5Rs coin head=1/2 =(1/2)*(1/2)*(1/2) =1/8 ANSWER:B #### B QUESTION:Find the value of (28 + 48/69) × 69 options: A)1980 B)1982 C)1930 D)1988 E)1680 SOLUTION:=(28 + 48/69) × 69 =(1932+ 48)/69× 69 =1980/69× 69 =1980 Answer is A. #### A QUESTION:Based on this year's costs, a builder budgets P dollars for planing N new buildings next year. If the average cost of building each building were to increase 10% from this year's cost, then the greatest number of buildings that the builder could build next year using P dollars would be: options: A)9% less than N B)11% less than N C)Equal to N D)9% greater than N E)11% greater than N SOLUTION:Correct answer is (A). This year, the price of a building is price1=P/N. If this price increases by 50% it becomes Price2=P/N*1.1 Then with P dollars, you can build P/Price2 buildings i.e. P/(P/N*1.1) i.e. N/1.1 i.e. 0.91*N Which is 9% less than N. #### A QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:If x = 3 and y = 2, what is the value of 5(x-y)^2 - xy ? options: A)-8 B)-7 C)-1 D)-2 E)-5 SOLUTION:x = 3 and y = 2 x-y = 3 - 2 = 1 x*y = 3 * 2 = 6 Now we apply it in the equation 5(x-y)^2 - xy =5 (1)^2-6 ==>5*1 -6 = 5-6 =-1 Answer : C #### C QUESTION:9 people decided to split the restaurant bill evenly. If the bill was $514.16 dollars, how much money did they 1 cent is the smallest unit? options: A)$514.16 B)$514.17 C)$514.18 D)$514.19 E)$514.20 SOLUTION:This is equivalent to finding the first number that is divisible by 9 that occurs after 51416. In order to divide the sum in 9 parts, the amount must be divisible by 9 Divisibility rule of 9: The sum of the digits must be divisible by 9 Sum of digits of 51416 = 17 and 18 is divisible by 9. Hence, we need to add 1 to this number for it to be divisible by 9 Correct Option: B #### B QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number? options: A)10 B)60 C)30 D)40 E)50 SOLUTION:Explanation: 6:7 6x + 10 : 7x + 10 = 7 : 8 8[6x + 10] = 7[7x + 10] 48x + 80 = 49x + 70 49x - 48x = 80 - 70 x = 10 Then smallest number is = 6 6x = 60 Answer: Option B #### B QUESTION:How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)52 sec B)50 sec C)51 sec D)55 sec E)58 sec SOLUTION:B 50 sec The distance to be covered = Sum of their lengths = 200 + 300 = 500 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 500/10 = 50 sec. #### B QUESTION:Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment? options: A)1200 B)3000 C)1000 D)3600 E)2400 SOLUTION:Let the additional invested amount for 8% interest be x; Equation will be; 2400+0.05*2400+x+0.08x = 2400+x+0.08(2400+x) 0.05*2400+0.08x = 0.06x+0.08*2400 0.02x = 2400(0.08-0.05) x = 2400*0.03/0.02 = 3600 Ans:D #### D QUESTION:Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A)$140 B)$141 C)$142 D)$147 E)$145 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer D)$147 #### D QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)16 km/hr B)17 km/hr C)60 km/hr D)15 km/hr E)19 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer: C #### C QUESTION:If 200!/10^n is an integer, what is the largest possible value of n? options: A)40 B)42 C)44 D)48 E)49 SOLUTION:We have to basically count the number of 5s withing 200 200/5 =40 200/5^2=8 200/5^3=1 We know for sure that there will be at least 49 even numbers(multiples of 2)within 200 So there are 49 10s in 200! ANSWER:E #### E QUESTION:Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds? options: A)22 B)24 C)99 D)27 E)17 SOLUTION:Explanation: Less Cogs more turns and less time less turns Number of turns required=80 × × = 24 times Answer: B) 24 #### B QUESTION:Three different containers contain 496 litres, 403 litres and 713 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ? options: A)29 litres B)31 litres C)35 litres D)19 litres E)26 litres SOLUTION:M1 = 496 litres M2 = 403 litres M3 = 713 litres Required measurement = H.C.F. of M1,M2,M3 = 31 litres Answer is B #### B QUESTION:1.5, 2.3, 3.1, 3.9, ..? options: A)0.6 B)0.8 C)0.4 D)0.24 E)0.15 SOLUTION:1.5+0.8=2.3 2.3+0.8=3.1 3.1+0.8=3.9 3.9+0.8=4.7 ANSWER:B #### B QUESTION:How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 7? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The numbers should be of the form 7c+3. The minimum is 3 when c=0. The maximum is 45 when c=6. There are 7 such numbers. The answer is C. #### C QUESTION:In how many ways can five boys and three girls sit in a row such that all boys sit together? options: A)A)2888 B)B)2885 C)C)2880 D)D)2876 E)E)2224 SOLUTION:Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways. Required number of arrangements = 4! * 5! = 24 * 120 = 2880. Answer:C #### C QUESTION:The average (arithmetic mean) of the integers from 100 to 400, inclusive, is how much greater than the average of the integers from 50 to 250, inclusive? options: A) 100 B) 175 C) 200 D) 125 E) 300 SOLUTION:For an AP the mean or average of series is average of first and last term. So, average of numbers between 100 to 400, inclusive = (100+400)/2 = 250 average of numbers between 50 to 250, inclusive = (50+250)/2 = 150 difference = 250 - 150 = 100 Answer is A #### A QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day 5 miles per hour for 6 hours. How many miles in total did she walk? options: A)68 B)44 C)58 D)60 E)62 SOLUTION:First day - 18 miles with 3 miles per hours then total - 6 hours for that day Second day - 4 miles per hour and 5 hours - 20 miles Third day - 5 miles per hour and 6 hours - 30 miles Total 18+20+30 = 68 Answer: option A. #### A QUESTION:How much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)40 sec B)50 sec C)60 sec D)70 sec E)80 sec SOLUTION:The distance to be covered = Sum of their lengths = 400 + 300 = 700 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 700/10 = 70 sec. ANSWER:D #### D QUESTION:If points A and B are (8-3) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:I. The area of a square region with side AB --> side=AB=(8-3) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. #### A QUESTION:A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? options: A)1/3 B)2by3 C)2/5 D)3/5 E)4/5 SOLUTION:Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol. Let x ml be the amount removed ---> total alcohol left = 4-0.4x New quantity of whiskey added = x ml out of which 0.19 is the alcohol. Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml. Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3. Hence, B is the correct answer. #### B QUESTION:How many diagonals does a polygon with 23 sides have, if one of its vertices does not connect to any diagonal? options: A)201 B)159 C)179 D)189 E)209 SOLUTION:If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals n= 23-1 then 22*(22-3)/2 = 209 Correct Option:E #### E QUESTION:An inspector rejects 0.06% of the meters as defective. How many will he examine to reject 2? options: A)A)1500 B)B)2000 C)C)2500 D)D)3000 E)E)3333 SOLUTION:Let the number of meters to be examined be x Then, 0.06% of x = 2 (6/100)*((1/100)*x = 2 x = 3333 Answer is E #### E QUESTION:A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially? options: A)25 B)21 C)20 D)10 E)15 SOLUTION:Suppose the can initially contains 7x and 5x litres mixtures A and B respectively Quantity of A in mix. left =[7x –7/12 * 9 ] =[7x –21/4] Quantity of B in mix. left =[5x –5/12 *9 ] = [ 5x - 15/4 ] Therefore [ 7x-21/4 ] =7/9 or 28x-21 = 7/9 [5x-15/4]+9 20x+21 252x -189 =140x+147 or 112x =336 , x = 3. Quantity of A in the can initially =7*3 =21 ANSWER:B #### B QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2360 TD = Rs. 360 PW = F - TD = 2360 - 360 = Rs. 2000 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2000 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2360 for unexpired time =360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally? options: A)11 B)77 C)12 D)99 E)887 SOLUTION:x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 3*4 = 12 Answer: C #### C QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E? options: A)60 B)80 C)40 D)120 E)160 SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30 (9/8)x - (3/4)x = 30 x = 80=E Answer: B #### B QUESTION:In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed? options: A)5 B)4 C)3 D)2 E)0 SOLUTION:= 147,000 = 147 x 1000 = (3) x (7 x 7) x (2x2x2) x (5x5x5) = 2^3 x 3^1 x 5^3 x 7^2 red = 7^2 = 49 ANSWER:D #### D QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? options: A)5040 B)2520 C)360 D)120 E)42 SOLUTION:6! = 720 720/2=360 half the time carmelo is in front, vice versa Answer: (C) 360 #### C QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full? options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes SOLUTION:1/20 - 1/40 = 1/40 40 minutes Answer:C #### C QUESTION:What is the greatest prime factor of 4^16 - 2^30? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:4^16 - 2^30 =(2^2)^16 - 2^30 = 2^32 - 2^30 = 2^30 (2^2 -1) = 2^30 * (4-1) = 2^30 * 3 The greatest prime factor is 3. The answer is B. #### B QUESTION:The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ? options: A)35 years B)45 years C)51 years D)52 years E)None of these SOLUTION:Explanation: Age of the teacher = (38 * 15 - 37 * 14) years = 52 years. Answer: D #### D QUESTION:A football field is 9600 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards? options: A)450 B)600 C)700 D)2400 E)3200 SOLUTION:Answer C) 9600 yards need 1200 lbs 1 Yard will need 1200/9600 = 1/8 lbs 3600 Yards will need 1/8* 5600 Yards = 700lbs #### C QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 40 miles per gallon, and from Town B to Town C, the car averaged 50 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)42.85 B)40 C)35 D)41 E)39 SOLUTION:step 1) took LCM of 40 and 50.. came as 200. step 2) 200 distance between B to C... do 200/50 hence 4 gallons used step 3) twice distance.. hence 200*2= 400... do as above.. 400/40= 10 gallons used step 4) total gallons.. 4+10= 14 gallons step ) total miles= 200+400= 600 miles hence.. average of whole journey = 600/14 which comes to 42.85 Answer : A #### A QUESTION:Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bicycle to work. If it takes him exactly 8 minutes more to walk to work than to ride his bicycle, then x equals options: A)4 B)7 C)12 D)15 E)20 SOLUTION:The best way would be... Per km, he takes 40 secs extra if he walks So he will take 8 mins or 8*60 secs in 8*60/40 =12 km ANSWER:C #### C QUESTION:Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $45,000 higher than Store B's revenues. In the second month, Store A's revenues were $8,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue? options: A) $14,000 B) $15,000 C) $42,000 D) $47,000 E) $50,000 SOLUTION:Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +45 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +8 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T): (45 + 8 + T)/3 = 2 53 + T = 6 T = -47 Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -47 represents a $47,000 advantage in favor of Store B. Choice (D) is correct. #### D QUESTION:How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? options: A)15 kg B)18 kg C)20 kg D)24 kg E)None of these SOLUTION:Here, cost price of mixture = 100×100/100+25 = 32 paise ∴q1q2=32−24/42−32=810=45 and hence q1 = 4⁄5 × 25 = 20 kg Answer C #### C QUESTION:If w and t are positive integers, wt + w + t cannot be options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let wt + t + w = x Add 1 on both sides: wt + t + w + 1 = x + 1 t(w + 1) + w + 1 = x + 1 (w + 1)(t + 1) = x + 1 Minimum value of (w + 1) = 2 Minimum value of (t + 1) = 2 Hence x + 1 cannot be prime Substitute x from the given options: 6 + 1 = 7 --> prime --> wt + t + s cannot be 6 Answer: B #### B QUESTION:Whats the reminder when 58,458,965,231,457,895,684,525,465,985,445 is divided by 16 options: A)5 B)7. C)2. D)3 E)9 SOLUTION:A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16. Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it. 58,458,965,231,457,895,684,525,465,985,445 = 58,458,965,231,457,895,684,525,465,980,000+5,445 The first number is divisible by 16. You just have to find the remainder when you divide 5445 by 16. That will be the remainder when you divide the original number by 16. 5445/16 gives remainder 5. Answer (A) #### A QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is: options: A)3000 B)3200 C)3450 D)4000 E)3570 SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5 = 105 : 40 : 36. Let the initial investments be 105x, 40x and 36x. => A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12) = 1680x : 480x : 432x = 35 : 10 : 9. Hence, A2's share = Rs. 21600 x 10/54 = Rs. 4000. Answer : D #### D QUESTION:Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm? options: A)602 sq.cm B)620 sq.cm C)200 sq.cm D)605 sq.cm E)600 sq.cm SOLUTION:Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus. BE2 + AE2 = AB2 252 = 152 + AE2 AE = √(625 - 225) = √400 = 20, AC = 20 + 20 = 40 cm. Area of a rhombus = 1/2 * d1d2 = 1/2 * 40 * 30 = 600 sq.cm. Answer: E #### E QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between? options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2 SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest. Answer (E) #### E QUESTION:Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible? options: A)5 B)6 C)9 D)24 E)26 SOLUTION:Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A #### A QUESTION:Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 40 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute? options: A)4:5 B)9:25 C)5:4 D)25:9 E)Cannot be determined from the information provided SOLUTION:Same circumferential rate means that a point on both the gears would take same time to come back to the same position again. Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B Time A = 2*pi*25/Speed A Time B = 2*pi*20/Speed B Since the times are same, 50pi/Speed A = 40pi/Speed B SpeedA/Speed B = 50pi/30pi = 5/4 Correct Option: C #### C QUESTION:If x percent of 400 is 20 percent of 700, then x = options: A)200 B)350 C)700 D)400 E)1,400 SOLUTION:x/100(400) = 2/10(700) x = 400. Option D. #### D QUESTION:From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? options: A)756 B)700 C)600 D)500 E)450 SOLUTION:We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only). Required number of ways = (7C3 x 6C2) + (7C4 x 6C1) + (7C5) = (525 + 210 + 21) = 756. ANSWER A #### A QUESTION:A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp? options: A)248 B)312.5 C)346.5 D)392.5 E)424 SOLUTION:Area covered by lamp = Pi*r^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot) where r= 21 m = length of part lit So area = (22/7)*21*21/4 = 346.5 sq m answer :C #### C QUESTION:A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k? options: A)3/4 B)1 C)4/3 D)2 E)7/2 SOLUTION:This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k. {{k + 4}/4} = k k + 4 = 4k 4 = 3k k = 4/3 Answer = C #### C QUESTION:After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day? options: A)$1.25 million B)$80,000 C)$750,000 D)$27,000 E)$10,000 SOLUTION:Let sales in previous month = X 1.25 X=2,000,000 5/4 X= 2,000,000 ..........> X=2,400,000 sales per day= 2,400,000/30= less than 80,000 Answer:B #### B QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)16 B)17 C)10 D)18 E)15 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 2 = 26 => x = 8 Deepak's age = 3x = 18 years. Answer: D #### D QUESTION:Sixty percent of a number is 21 less than four fifth of that number. What is the number ? options: A)240 B)140 C)230 D)130 E)105 SOLUTION:Let the number be x. Then, 4*x/5 –(60% of x) = 21 4x/5 – 60x/100 = 21 x = 105. Answer E. #### E QUESTION:Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 10x boxes? options: A)13 minutes B)14 minutes C)15 minutes D)16 minutes E)20 minutes SOLUTION:Rate = Work / Time Given Rate of Machine A = X / 10 min Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min . Rate of Machine B = 4x / 10 we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates let's first find the combined Rate of Machine A and B Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10 Now combine Time = combine work needs to be done / Combine Rate = 10x/5x * 10 = 6 Min Ans: E #### E QUESTION:Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? options: A)66 B)74 C)78 D)80 E)None of these SOLUTION:Explanation: Number of subjects = 6 Average of marks in 6 subjects = 74 Therefore total marks in 6 subjects = 74 * 6 = 444 Now, No. of subjects = 5 Total marks in 5 subjects = 74 * 5 = 370 Therefore marks in 6th subject = 444 – 370 = 74 ANSWER B #### B QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? options: A)122443 B)154546 C)165454 D)186545 E)220030 SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 E #### E QUESTION:In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:6C3 = 6!/(3! . 3!) = (6 × 5 × 4)/(3 × 2) = 5 × 4 = 20 B) #### B QUESTION:In measuring the sides of a rectangle, one side is taken 14% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)8.3% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000. Now, the area obtained with wrong measurements would be 114*95=10,830, which is 8.3% greater than the actual area. Answer: C. #### C QUESTION:There are three foam generators in the factory, each of the first two can generate 8 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)146. D)154. E)115 SOLUTION:Let the foam generators capacity be - A = 8 lit/hr B = 8 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 34 lit ( 8 + 8 + 18 ) ; since in 1 and 1/2 hr they will generate 34 + 17 => 51 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 8 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 52 litres {2 (8+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 8 => 12 litres So, total foam generated will be 115 Litres ( 51 + 52 + 12 ) ; hence answer will be (E) #### E QUESTION:In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ? options: A)3990 B)1540 C)1995 D)3672 E)None of these SOLUTION:In order that two books on French are never together, we must place all books as under X E X E X E X E X E .....X E X where E denotes the position of an English book and X that of a French book. Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in 22C19 = 22C3 = (22x21x20)/(3x2x1) = 1540 ways Answer B. #### B QUESTION:If (2/3)^n=(3/2)^3, what is the value of n? options: A)-3 B)-2 C)-1 D)0 E)1 SOLUTION:(2/3)^n = (3/2)^3 = (2/3)^-3 n = -3 (Answer = A) #### A QUESTION:The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles? options: A)20° B)70° C)60° D)120° E)140° SOLUTION:If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence 3x + 6x = 90 9x = 90 x = 10 Measures of the two acute angles are 3x = 3 × 10 = 30° 6x = 6 × 10 = 60° C #### C QUESTION:Two dice are thrown together.What is the probability that the sum of the number on the two faces divided by 4? options: A)3/9 B)4/9 C)1/9 D)2/9 E)5/9 SOLUTION:n(s)=6*6=36 Let e be the event that the sum of the numbers on the two faces is divisible by 4 E={(1,3),(2,2),(3,1),(2,6),(3,5),(4,4),(5,3),(6,2)} n(e)=8 p(e)=n(e)/n(s) =8/36 =2/9 Answer is option D #### D QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)8 B)9 C)7 D)5 E)4 SOLUTION:Explanation: x – y = 5 4x – 6y = 6 x = 12 y = 7 Answer:C #### C QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)? options: A)85/365∗84/364 B)13/65∗13/64 C)1 - 85!/365! D)1 - {365!}/{280!(365^8^5)} E)1 - 85!/(365^8^5) SOLUTION:Probability(At Least 2 share a bday) = 1 - Probability(All 85 have distinct birthdays) total ways to pick 85 birthdays = 365^85 Ways to pick distinct 85 out of the 365 & distribute it to 85 people = C(365,85)*85! Hence Probability = 1−365!/280!36585 ANswer is D #### D QUESTION:A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)6 ½ sec B)6 ½ sec C)9 ½ sec D)8 sec E)7 ½ sec SOLUTION:D 8 sec D = 160 S = 72 * 5/18 = 20 mps T = 160/20 = 8 sec #### D QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:What is the next number of the following sequence 7, 0, 1, 8, 5, 12, 9, 26, 3, 2, 23, ? options: A)28 B)29 C)30 D)31 E)32 SOLUTION:7,0,1,8,5,12,9,26,3,2,23,X (7,0,1,8),(5,12,9,26),(3,2,23,X) 7+0+1=8 5+12+9=26 3+2+23=X => X=28 ANSWER:A #### A QUESTION:The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is: options: A)1439 B)1440 C)1459 D)1449 E)1549 SOLUTION:LCM = 1440 1440 - 1 = 1439 ANSWER:A #### A QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture? options: A)294 B)235 C)350 D)288 E)580 SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A QUESTION:The average of first 11 prime numbers is? options: A)14.55 B)11.11 C)12.11 D)13.11 E)14.11 SOLUTION:Sum of 11 prime no. = 160 Average = 160/11 = 14.55 ANSWER: A #### A QUESTION:If the price of petrol increases by 44, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? options: A)25% B)20% C)16.67% D)33.33% E)None of these SOLUTION:Explanation : let us assume before increase the petrol will be Rs. 100. After increase it will be Rs (100+44) i.e 144. Now, his consumption should be reduced to :- =(144−100)/144 ∗ 100. Hence, the consumption should be reduced to 30.6%. Answer : E #### E QUESTION:How many different ways can you select a pilot and a co pilot if you have 30 people to choose from? options: A) 870 B) 920 C) 1398 D) 4950 E) 9900 SOLUTION:You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot. So the answer is in a sense (30C2) x 2 = 870. Ans A #### A QUESTION:Sandy bought 65 books for $1480 from one shop and 55 books for $920 from another shop. What is the average price that Sandy paid per book? options: A)$38 B)$18 C)$99 D)$27 E)$20 SOLUTION:average price per book = (1480 + 920) / (65 + 55) = 2400 / 120 = $20 The answer is E. #### E QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:Workers at a campaign office have 2500 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day? options: A)300 B)800 C)1500 D)1200 E)1900 SOLUTION:(1/5)*2500 = 500 Remaining = 2500-500 = 2000 (1/4) of remaining = (1/4)*2000 = 500 Remaining now = 2000-500 = 1500 Answer: Option C #### C QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘POWER’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word ‘POWER’ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 5*4*3*2*1 = 120 ANSWER:E #### E QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 66. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 55 C)(c) 82 D)(d) 83 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (66-6)/6+1=11 such multiples. So, final number of sets is 11*5=55 Answer : B #### B QUESTION:A car takes 6 hours to cover a distance of 504 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? options: A)48 Kmph B)50 Kmph C)52 Kmph D)56 Kmph E)60 Kmph SOLUTION:Time = 6 Distence = 504 3/2 of 6 hours = 6 * 3/2 = 9 Hours Required speed = 504/9 = 56 Kmph D #### D QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? options: A)10000 B)12000 C)13000 D)10860 E)14400 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7800 × 118/100 × 118/100 = 10860 D #### D QUESTION:I came across this problem in the GMATprep software and got it totally wrong! A company consists of 6 senior and 4 junior staff officers. If a committee is created with 4 senior and 1 junior staff officers, how many possible committees are there? options: A)12 B)44 C)56 D)60 E)200 SOLUTION:6C4*4C1 =60=D #### D QUESTION:A project scheduled to be carried out over a single fiscal year has a budget of $12,000, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,540. By how much was the project over its budget? options: A) $380 B) $540 C) $1,050 D) $1,380 E) $1,430 SOLUTION:Difficulty level: 600 Each month's budget = 12000/12 = 1000 Budget for 4 months = 4*1000 = 4000 Actual amount spent = 4540 Amount spent over the budget = 4540 - 4000 = 540 Answer (B), Regards, #### B QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? options: A)12 B)15 C)16 D)18 E)19 SOLUTION:one day work done by A=1/20 work done by A in 2 days=1/10 work done by A,B,C on 3rd day=1/10+1/10=1/5 1/5th of the work will be completed at the end of 3 days the remaining work =1-1/5=4/5 1/5 of work is completed in 3 days total work wiil be done in 3*5=15 days ANSWER:B #### B QUESTION:In a test containing 16 questions , contestants get a base core of 20 points for taking the test. 5 points for each correctly answered question and 2 points for each unanswered question.An incorrectly answeredquestion is worth 0 points.Of the following scores which one is not attainable options: A)96 B)97 C)94 D)95 E)93 SOLUTION:1. 15 corrected and 1 uncorrected 20+5*15+0=95 2.15 corrected and 1attempted 20+5*15+2=97 3. 14corrected+2attempted 20+14*5+2*2=94 so 96 is not possible ANSWER:A #### A QUESTION:18 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. options: A)190 B)153 C)210 D)220 E)230 SOLUTION:1st person will shake hand with 17 people 2nd person will shake hand with 16 people 3rd person will shake hand with 15 people ...... total no. of handshakes = 17+...+3+2+1 = 17*(17+1)/2 = 153 or, if there are n persons then no. of shakehands = nC2 = 18C2 = 153 ANSWER:B #### B QUESTION:One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number? options: A)4 B)6 C)0 D)9 E)19 SOLUTION:Answer: Option D x/2 – x/3 = 6 => x =6 3 + 6 = 9 #### D QUESTION:what is next number in sequence 212 427 303 336 394 ? options: A)123 B)345 C)560 D)567 E)245 SOLUTION:E 245 space them properly as 21 24 27 30 33 36 39 42 45 ? #### E QUESTION:If xy > 0, which of the following must be negative? options: A)-x/-y B)x/y C)-x/y D)2xy E)x+y SOLUTION:- / + = - Answer : C #### C QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment? options: A)1200 B)3000 C)1000 D)3600 E)2400 SOLUTION:Let the additional invested amount for 8% interest be x; Equation will be; 2400+0.05*2400+x+0.08x = 2400+x+0.06(2400+x) 0.05*2400+0.08x = 0.06x+0.06*2400 0.02x = 2400(0.06-0.05) x = 2400*0.01/0.02 = 1200 Ans: "A" #### A QUESTION:One boy forgot the last digit of a 7 digit no. If he randomly dialthe final 3 digits aftercorrectly dialing the 1st 4, then what is the chance of dialing the correct no.? options: A)1/890 B)2/465 C)1/1000 D)1/3453 E)2/1454 SOLUTION:it is given that last 3 digits are randomly dialed Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability = 1/(10)3 = 1/1000 C #### C QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 10800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)60000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 10800 ( 18 × 600 = 10800) 100% -------> 60000 votes (100 × 600 = 60000) C #### C QUESTION:The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is? options: A)1/2 B)3/4 C)3/5 D)3/7 E)4/9 SOLUTION:Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D 1 2 3 1 =iXiX71=4; 1 3 Required probability 3/4 B #### B QUESTION:If one-third of one-fourth of a number is 15, then three-tenth of that number is options: A)35 B)15 C)60 D)54 E)57 SOLUTION:Let the number be x. then 1/3 of ¼ of x=15 X=15x12=180 The required number=(3/10)*180=54 ANSWER D 54 #### D QUESTION:A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? options: A)22 B)28 C)25 D)82 E)34 SOLUTION:M = 20 S = 5 DS = 20 + 5 = 20.Answer:C #### C QUESTION:Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: options: A)175.5 B)170 C)169.5 D)180 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. average price = 126+135/2 = 130.50 o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x - 153 = 22.50 x = 175.50 ANSWER A #### A QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 36. What is the value of x? options: A)80 B)96 C)100 D)108 E)120 SOLUTION:y = 0.5*0.5*x = x/4 y%*x = 36 (y/100)*x = 36 (x/400)*x = 36 x^2 = 36*400 x = 120 The answer is E. #### E QUESTION:A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? options: A)3:3 B)3:4 C)3:8 D)3:1 E)3:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by A and B = 6000 : 8000 => 3:4.Answer: B #### B QUESTION:What distance (in meters) will be covered by a bus moving at 54 km/hr in 15 seconds? options: A)175 B)200 C)225 D)250 E)275 SOLUTION:54 km/hr = 54 * 5/18 = 15 m/s distance = 15 * 15 = 225 meters The answer is C. #### C QUESTION:10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 2 women and 10 children take to complete the work? options: A)4 B)5 C)7 D)8 E)10 SOLUTION:1 women's 1 day work = 1/70 1 child's 1 day work = 1/140 (2 women + 10 children)'s 1 day work = (2/70 + 10/140) = 1/10 2 women and 10 children will complete the work in 10 days. E #### E QUESTION:SCORE INTERVAL----------------NUMBER OF SCORES 50-59-------------------------- 2 60-69--------------------------10 70-79--------------------------16 80-89--------------------------5 90-99--------------------------2 The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 35 scores? options: A)16th B)20th C)22th D)24th E)18th(70-79) SOLUTION:Total scores= 2+10+16+5+2 = 35, which is odd, therefore the median is the Floor(35/2)+1 = 18th score. And the 18th score is in the 70-79 range, because 50-69 only reference 12 scores. E #### E QUESTION:In the xy-coordinate system, line k passes through points (-7m, 0) and (0, 3m). Which of the following is a possible equation of line k? options: A)y = -7/3*x + 3m B)y = 3/7*x - 7m C)y = 7/3*x + 3m D)y = 3/7*x + 3m E)y = -3/7*x - 7m SOLUTION:The slope of the line is 3m/7m=3/7. The y-intercept is 3m. the equation of the line is: y = 3/7*x +3m The answer is D. #### D QUESTION:When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[8] = ? options: A)[22] B)[44] C)[75] D)[88] E)[90] SOLUTION:[7]*[8]=(7*2+1)(8/2+1) =[75]. Ans -C #### C QUESTION:A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2? options: A)Rs.45 B)Rs.48 C)Rs.44 D)Rs.43 E)Rs.41 SOLUTION:π (152 - 132) = 176 176 * 1/4 = Rs.44 Answer:C #### C QUESTION:There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks? options: A)5,15 B)4,15 C)5,10 D)4,10 E)5,20 SOLUTION:Assume you have locks 1-5 and keys A-E. Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum. Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D #### D <<<Examples ends QUESTION:Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 75 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains? options: A)93% B)97% C)100% D)107% E)99% SOLUTION:Say Arthur's fortune was $100. Then: A = 20*1.5*1.1 = 33 B = 20*1.5*1.1 = 33 C = 20*1.5*0.4 = 12 D = 20*0.6*1.75 = 21 E = 0 Total 33 + 33 + 12 + 21 = 99. Answer: E. #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| = options: A)ab-4 B)2b-ab-4 C)ab+4 D)ab-2b+4 E)4-ab SOLUTION:Given: |ab| = -ab and |a| = -a Question: |b-4| + |ab-b| = ? **** Looking at |ab| = -ab tells us that either one of a or b is negative. **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: b is positive Let a=-1 and b=1 |b-4| + |ab-b| = |1-4| + |-1-1| = 5 Test a) |ab-4| = |(1)(-1)-4| = |-5|=5 Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1 Test c) ab+4 = -1 + 4 = 3 Test d) ab-2b+4 = -1-2(1)+4=1 test e) 4-1=3 ANSWER=A #### A QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer: A #### A QUESTION:There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes? options: A)18 B)21 C)35 D)42 E)56 SOLUTION:Note that each handshake includes two people. The total number of handshakes is 14*3/2 = 21 The answer is B. #### B QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 13260, how much money did he borrow? options: A)13000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 13260 18x + 45x + 39x = (13260* 100) 102x = 1326000 => x = 13000. Answer:A #### A QUESTION:A 6 litre sol is 40% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? options: A)A.0.6 B)B.1.2 C)C.2.1 D)D.3 E)E.5.4 SOLUTION:40% of 6 = 2.4 50% of 6 = 3 shortage is 0.6 so we need to have 0.6/50% to get 50% alcohol content. = 1.2 B #### B QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet. The number of revolutions = distance/circumference = 5,280z/y. Answer: A. #### A QUESTION:The least number, which when divided by 12, 31, 20 and 54 leaves in each case a remainder of 8 is: options: A)448 B)488 C)16748 D)548 E)560 SOLUTION:Required number = (L.C.M. of 12, 31, 20, 54) + 8 = 16740+ 8 = 16748. answer :C #### C QUESTION:Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 2/3 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem? options: A)1/16 B)7/8 C)9/64 D)5/64 E)3/64 SOLUTION:P(Xavier will solve)=1/4 P(Yvonne will solve)=2/3 P(Zelda will NOT solve) = 1- 5/8 = 3/8. Now, we need to multiply all this Ps to find an answer: p= (1/4)*(2/3)*(3/8) = 1/16. Ans. A. #### A QUESTION:Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt? options: A)25/33 B)31/44 C)41/55 D)53/66 E)65/77 SOLUTION:Total possible ways to choose 4 students out of 12 = 12C4 = 495 The number of ways to choose 4 students with no green shirts = 9C4 = 126 P(no green shirts) = 126/495 = 14/55 P(at least 1 green shirt) = 1 - 14/55 = 41/55 The answer is C. #### C QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum. options: A)800 B)700 C)600 D)500 E)None of them SOLUTION:Let the sum be Rs. x Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40 = (7x/20)-(3x/10)=40 x = (40 * 20) = 800. Hence, the sum is Rs. 800. Answer is A. #### A QUESTION:A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 25 per kg, then his gain percent is options: A)12% B)33% C)14% D)15% E)16% SOLUTION:Explanation: Suppose he bought 5 kg and 3 kg of tea. Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150. Selling price = Rs. (8 x 25) = Rs. 200. Profit = 200 - 150 = 50 So, Profit % = (50/150) * 100 = 33% Option B #### B QUESTION:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue? options: A)25/153 B)28/153 C)5/17 D)E=4/9 E)E=12/17 SOLUTION:P(at least one blue) = 1 - P(0 blue) = 1 - 10/18*9/17 = 12/17. Answer: E. #### E QUESTION:In a party attended by 13 persons, each clinch their glass with every other. How many glass clinches? options: A)51 B)52 C)78 D)54 E)55 SOLUTION:Total no. of person = 11 Total no. of glass clinches = n(n-1)/2 =13*12/2 = 78 ANSWER:C #### C QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)10 m B)16 m C)245 m D)19 m E)235 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: E #### E QUESTION:A searchlight on top of the watchtower makes 4 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds? options: A)5/6 B)4/5 C)3/4 D)2/3 E)1/2 SOLUTION:The searchlight completes one revolution every 15 seconds. The probability that the man's area will be lit up is 5/15=1/3. The probability that he will stay in the dark is 1-1/3=2/3 The answer is D. #### D QUESTION:If the denominator of a fraction is increased by 4, then the fraction becomes 5/8. If the numerator is 11 less than the denominator, find the numerator. options: A)25 B)20 C)30 D)15 E)35 SOLUTION:iniatial fraction=x/y; after increasing deno..by 4=> x/(y+4)=5/8; given x = y - 11; then (y-11)/(y+4)=5/8=>y=36; x = 36-11 = 25 ANSWER:A #### A QUESTION:There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)5/9 D)4/9 E)2/3 SOLUTION:total 9 from take one. 9c1=9 red 5 from one 5c1=5 5/9 ANSWER:C #### C QUESTION:1395 x 1395 options: A)1946025 B)1981709 C)18362619 D)2031719 E)None of these SOLUTION:1395 x 1395 = (1398)2 = (1400 - 2)2 = (1400)2 + (5)2 - (5 x 1400 x 5) = 1946025. Answer: Option A #### A QUESTION:1401 x 1401 = ? options: A)1962800 B)1962801 C)1960000 D)1951611 E)1951613 SOLUTION:1401 x 1401 = (1401)2 = (1400+1)2 = (1400)2 + (1)2 + (2 x 1400 x 1) = 1960000 + 1 + 2800 = 1960001+ 2800 = 1962801. B) #### B QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many W digits does this integer consists of? options: A)150 B)339 C)342 D)359 E)362 SOLUTION:Number of single digit integers = 9 Number of 2 digit integers = 99 - 10 + 1 = 90 Number of 3 digit integers = 150 - 100 + 1 = 51 Number of digits in the integer W= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C SOLUTION:Let temperature on 4th day be X°C Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1 => X = 41.9 Therefore, temperature on 4th day = 41.9°C. ANSWER:D #### D QUESTION:Calculate the distance covered by 350 revolutions of a wheel of radius 25.3 cm. options: A)558.6 m B)556.6 m C)516.6 m D)156.6 m E)256.6 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 350 resolutions. =350 * 2 * 22/7 * 25.3 = 55660 cm = 556.6 m ANSWER:B #### B QUESTION:At a meeting of the 8 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 8 Chiefs of Staff be seated around a circular table? options: A)120 B)480 C)960 D)2520 E)5080 SOLUTION:Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E #### E QUESTION:If x + y = 8 and y − 3x = 7, then what is the value of y-x? options: A)1/7 B)3 C)15 D)15/2 E)60/7 SOLUTION:x+y=8 ...equation 1 -3x+y=7 ...equation 2 adding both the equations -2x+2y=15=>y-x=15/2 correct answer option D #### D QUESTION:If the cost price of 60 boxes is equal to the selling price of 50 boxes, the gain percent is options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let C.P. of each box be Re. 1. Then, C.P. of 50 boxes = Rs. 50; S.P. of 50 boxes = Rs. 60. Gain % = 10/50 * 100 = 20% Answer:D #### D QUESTION:A firm has 5 senior partners and 7 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.) options: A)145 B)155 C)165 D)175 E)185 SOLUTION:The number of ways to form a group of 3 is 12C3 = 220 The number of groups with no senior partner is 7C3 = 35 The number of groups with at least one senior partner is 220-35 = 185 The answer is E. #### E QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? options: A)508 B)500 C)800 D)570 E)503 SOLUTION:We can select one boy from 20 boys in 20 ways. We select one girl from 25 girls in 25 ways We select a boy and girl in 20 * 25 ways i.e., = 500 ways. Answer:B #### B QUESTION:Five carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if four of the carpenters work together at their respective rates ? options: A)11/15 B)3/5 C)11/30 D)47/75 E)5/9 SOLUTION:Farmer A, B, C, and D A's rate: 1/3 job/hour B's rate: 1/4 job/hour C's rate: 1/5 job/hour D's rate: 1/7 job/hour By intuition we know that the three fastest farmers are A B and C. As such (1/3 + 1/4 + 1/5)*(4/5) = ? 47/75 or (D) #### D QUESTION:In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? options: A)30% B)70% C)100% D)250% E)300% SOLUTION:cp = 100 profit = 320 ans SP = 420 new CP = 125% of RS 100 = Rs 125 New SP = 420 profit = (420-125) = 295 req % (295/420*100)% = 1475/21% = 70% ANSWER B #### B QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 4. What is the ratio of their heights? options: A)A)2:5 B)B)2:7 C)C)2:2 D)D)2:1 E)E)4:3 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(4)2h2 => h1/h2 = 4/3 i.e. h1 : h2 = 4 : 3 Answer: E #### E QUESTION:The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool? options: A)1400 B)1600 C)1800 D)1500 E)2000 SOLUTION:volume of pool = 80*150*10 cu.ft ,100% full = 60*100*10*1 cu.ft water is available to drain. draining capacity =60 cu.ft /min therefore time taken = 80*150*10*1/ 60 min= 2000 min E #### E QUESTION:Two letters from the word KYANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant? options: A)14/27 B)15/28 C)27/28 D)16/28 E)30/28 SOLUTION:There are 6 consonants and 2 vowels in KYANTKAR . probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels) Probability of both vowels = 2C2/8C2 = 1/28 So,Answer is 1 - 1/28 = 27/28 Answer : C #### C QUESTION:Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 6. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased? options: A)3, 8, 24 B)7, 9, 17 C)6, 9, 12 D)5, 15, 18 E)9, 10, 13 SOLUTION:I didnt get your point on eliminating A. The number of stamps only one purchased was divisible by 6.Could that not be Cecilia with 9 stamps. I choose this and marked A. #### A QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:Find the value of 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] options: A)800 B)3200 C)900 D)1600 E)None SOLUTION:Answer 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] = 4 x [(36 x 48 x 250) / (12 x 9 x 5)] = 4 x 4 x 4 x 50 = 3200 Correct Option: B #### B QUESTION:Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: options: A)2:3 B)4:3 C)7:3 D)9:3 E)4:2 SOLUTION:Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3. #### B QUESTION:The value of Underrot 32pi/4 + Underrot 25 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question) options: A)6 B)35 C)41 D)30 E)23 SOLUTION:Under root (32pi/4) ~ 25 Under root (25) = 5 Hence, 25+5 = 30 is the approx answer. D is the correct answer. #### D QUESTION:The LCM and HCF of two numbers are 100 and 10 respectively. Find the larger of the two numbers if their sum is 110. options: A)100 B)12 C)35 D)466 E)56 SOLUTION:There are 2 approaches in solving this. Methode 1. HCF * LCM = The Actual Number. 100* 10= 1000 So the answer which we are looking for has to be a factor of 1000. So among the options shortlist the answers by eliminating those numbers which is not divisible by 1000. and then take the highest number as the answer as the question asks abt the highest number. answer is A #### A QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 6000, brokerage being 1/4%, is: options: A)83.08 B)114 C)114.75 D)124 E)124.75 SOLUTION:Face Value = Rs. 6000. Dividend = 10.5%. Annual Income = Rs. 756. Brokerage per Rs. 100 = Rs. 0.25. Dividend is always paid on the face value of a share. Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income. = 6000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100. = Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 83.33. = Market Value of Rs. 100 stock = Rs. 83.33 - Re. 0.25. = Market Value of Rs. 100 stock = Rs. 83.08 answer : A #### A QUESTION:Grace has 18 jellybeans in her pocket. She has 10 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? options: A)4 B)8 C)12 D)13 E)15 SOLUTION:The worst scenario is when she takes 10 red and 4 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. Answer: E. #### E QUESTION:If C + D = 9 and C and D are positive integers, which of the following is a possible value for 5C + 8D? options: A)55 B)61 C)69 D)90 E)97 SOLUTION:c + d = 11 5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 45 + 3d=D=15 D=15 c+d=9=C+15=9=C=9-15=-6 C=-6 5C + 8D=5(-6)+8(15)=-30+120=90 Hence, D is the right answer. #### D QUESTION:In how many years will a sum of money doubles itself at 30% per annum on simple interest? options: A)7% B)3% C)5% D)8% E)2% SOLUTION:P = (P*30*R)/100 R = 3% Answer:B #### B QUESTION:Evaluate: 20 - 12÷12×2 = options: A)A)4 B)B)8 C)C)12 D)D)16 E)E)20 SOLUTION:According to order of operations, 12÷12×2 (division and multiplication) is done first from left to right 12÷12×2 = 1 × 2 = 2 Hence 20 - 12÷12×2 = 20 - 12 = 8 correct answer is B) 8 #### B QUESTION:A shopkeeper sold an article offering a discount of 4% and earned a profit of 26%. What would have been the percentage of profit earned if no discount was offered? options: A)24 B)28 C)31 D)32 E)34 SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 126 Let marked price be Rs. x. Then, 96/100 x = 126 x = 12600/96 = Rs. 131.25 Now, S.P. = Rs. 131.25, C.P. = Rs. 100 Profit % = 31%. ANSWER:C #### C QUESTION:On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 48 centimeters assuming that 1-inch is 2.54 centimeters? options: A)174.2 B)212 C)288.1 D)296 E)302 SOLUTION:1.5 inch = 2.54*1.5 cm. So, 2.54*1.5 represents 24 miles. So for 48 cm.: 48/(2.54*1.5) = x / 24 ---> x = 24*47/(3.81) = 302 Answer will be E. #### E QUESTION:The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places options: A)34 B)35 C)56 D)67 E)23.57 SOLUTION:Let the side of the square be a cm. Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm i.e. 4a = 60 A = 15 Diameter of the semicircle = 15 cm Circimference of the semicircle = 1/2(∏)(15) = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places Answer: Option E #### E QUESTION:The triplicate ratio of 1:3 is? options: A)1:0 B)1:8 C)1:27 D)1:2 E)1:1 SOLUTION:13: 33 = 1:27 Answer: C #### C QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) options: A)27 B)30 C)33 D)36 E)39 SOLUTION:33/4 ÷ 4 = 33/16 pounds in each container 33/16 pounds * 16 ounces / pound = 33 ounces in each container The answer is C. #### C QUESTION:5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3294, how much was it in the beginning? options: A)2988 B)2776 C)4079 D)2871 E)881 SOLUTION:X * (95/100) * (85/100) = 3294 X = 4079 Answer:C #### C QUESTION:A car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+336*6=448c =>c=336*6/112=18 Answer B. #### B QUESTION:Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. options: A)z=3x B)x=3z C)y=2x D)x=2y E)y=3x SOLUTION:Rovert Travelled for x,y and for z min. Total Time : x + y + z Which is equal to : 3y Equating both sides we get x+y+z = 3y => x+z =2y ........ Eqn 1 Looking out at options D Says x =2y Using it in Eqn 1 2y + z = 2y => Z = 0 mins, Which I guess is not possible. The Ans isD #### D QUESTION:The cost of 3 kg of sugar is $30. What will the cost of 8 kg of sugar be? options: A)20 B)40 C)80 D)160 E)180 SOLUTION:3 kg costs $30 1 kg costs $10 8 kg costs $80 The answer is C. #### C QUESTION:Mr. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck options: A)$145 B)$250 C)$300 D)$175 E)$150 SOLUTION:Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A) #### A QUESTION:Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between: options: A)40 to 100 B)80 to 140 C)160 to 260 D)220 to 260 E)220 to 300 SOLUTION:260-X+X+300-X+GT60 = 400 =>X = GT 620-400 => X = GT 220 => X >= 220 (Here GT means Greater than) So Min value of X is 220 coming to options D/E X's maximum value cannot exceed 260 as per the venn diagramsince 'W' circle cannot accomodate 'X' More than 260 ANSWER:D #### D QUESTION:Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)100 C)110 D)130 E)140 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C QUESTION:Find the fourth proportion to 2,4,6 options: A)18 B)12 C)9 D)6 E)8 SOLUTION:Explanation: 2:4 :: 6:x => 2/4= 6/x => x = 24/2 => x = 12 Answer:B #### B QUESTION:How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4? options: A)288 B)173144 C)144 D)297 E)2181 SOLUTION:Explanation: If a number has to be divisible by 4, the last two digit of that number should be divisible by 4. So _ _ _ x y. Here xy should be a multiple of 4. There are two cases: Case 1: xy can be 04, 20 or 40 In this case the remaining 3 places can be filled in 4×3×2 = 24. So total 24×3 = 72 ways. Case 2: xy can be 12, 24, 32, 52. In this case, left most place cannot be 0. So left most place can be filled in 3 ways. Number of ways are 3×3×2 = 18. Total ways = 18×4 = 72. Total ways = 144 Answer:C #### C QUESTION:Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes? options: A) 911 B) 100 C) 101 D) 160 E) 785 SOLUTION:Let's take the approach that uses the answer choices to eliminate wasted time. 32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt. Looking at the answers it is clear...we can only choose (D) THE CORRECT ANSWER IS D. #### D QUESTION:A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 310 m long? options: A)34 Seconds B)22 Seconds C)41 Seconds D)24 Seconds E)27 Seconds SOLUTION:27 Seconds Distance travelled = 140 + 310m = 450m Speed = 60 * 5/8 = 50/3m Time = 450 * 3/50 = 27 Seconds ANSWER E #### E QUESTION:A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? options: A)63 B)336 C)567 D)3024 E)5040 SOLUTION:All the cordinates are integer hence, possible AT values are {-1,0}, {-1,1} ....{-1,7}: 8 ways .... {7,-1}, {7,0} ......{7,6}: 8 ways 9*8 ways = 72 for AC values can be {1,2}, {1,3} .... {1,7} : 6ways ...... {7,1}, {7,2} ..... {7,6} : 6 ways 7*6 = 42 Total = 72 * 42 = 3024 hence D #### D QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0. What is the difference between the two greatest possible values of x? Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. options: A)124 B)241 C)394 D)421 E)842 SOLUTION:Ratio of a:b:c= 2:4:1 Two possible greatest single digit values for b are 8 and 4 if b is 8, then x= 482 if b is 4, then x= 241 difference= 482-241= 241 B is the answer #### B QUESTION:If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days? options: A)47.6 kg B)52.6 kg C)59.6 kg D)56.6 kg E)57.6 kg SOLUTION:(3 * 5)/48 = (9 * 2)/ x x = 57.6 kg ANSWER:E #### E QUESTION:The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles? options: A)20° B)70° C)60° D)120° E)140° SOLUTION:If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence 3x + 6x = 90 9x = 90 x = 10 Measures of the two acute angles are 3x = 3 × 10 = 30° 6x = 6 × 10 = 60° C #### C QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 Then 6 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)3 D)4 E)5 SOLUTION:A 1 As stated 1=6 => 6=1 #### A QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is: options: A)587 × 10<10>(exponent) miles B)587 × 10<-12> (exponent) miles C)587 × 10<-10>(exponent) miles D)587 × 10<12>(exponent) miles E)587 × 10<8>(exponent) miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 ×10<12>(exponent) miles #### D QUESTION:Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 550. The income of the deceased was? options: A)Rs. 692.80 B)Rs. 820 C)Rs. 990 D)Rs. 1385 E)None SOLUTION:Answer Income of the deceased = Total income of 4 members - total income of remaining 3 members. = 735 x 4 - 550 x 3 Rs. = 1290 Rs. Correct Option: E #### E QUESTION:If Renee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased? options: A)1/4 B)1/5 C)1/10 D)2/25 E)1/20 SOLUTION:5% is 5/100 = 1/20 10% is 10/100 = 1/10 The increase must be greater than 1/20 and less than 1/10. 1/4, 1/5, and 1/10 are not less than 1/10. 1/20 is not greater than 1/20. The only option left is 2/25, which is in the specified range. ANSWER:D #### D QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there? options: A)20 coin B)30 coins C)28 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 35 ⇒ 1.75x = 35 ⇒ x = 20 coin Answer A #### A QUESTION:What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7? options: A)397 B)401 C)403 D)405 E)364 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=364. Answer: E. #### E QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:If x is divisible by 2 and 7, which of the following must divide evenly into x? I. 60 II. 32 III. 14 options: A)I,II only B)I,III only C)I only D)III only E)II only SOLUTION:If x is divisible by 2,7 means it will be = or > 14, 28,42 etc... That are not divisible by 60, 32. So, the answer is D #### D QUESTION:Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)NOne SOLUTION:Sol. Average = 66 + 65 + 77 + 62 + 75 / 5) = (345 / 5) = 69. Answer B #### B QUESTION:A sum of money becomes 7/6 of itself in 6 years at a certain rate of simple interest. The rate per annum is? options: A)50/9 B)50/13 C)50/17 D)25/9 E)5 5/1 SOLUTION:Let sum = x. Then, amount = 7x/6 S.I. = 7x/6 - x = x/6; Time = 6 years. Rate = (100 * x) / (x * 6 * 6) = 25/9 %. Answer:D #### D QUESTION:A box contains 3 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black? options: A)4/7 B)3/5 C)5/8 D)2/3 E)3/4 SOLUTION:Each ball has an equal chance (1/9) of being selected fourth. The probability that a black ball is selected fourth is 6/9 = 2/3. The answer is D. #### D QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit? options: A)2388 B)2380 C)2888 D)2663 E)2922 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 6970 * 14/41 = Rs. 2380. Answer: B #### B QUESTION:A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? options: A)9/30 B)14/30 C)4/9 D)3/5 E)6/25 SOLUTION:I guess it's mean that square B is placed within rectangle A entirely. Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16; Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30. Answer: B. #### B QUESTION:A solution of 60 ounces of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar? options: A)20 ounces B)80 ounces C)100 ounces D)120 ounces E)180 ounces SOLUTION:20% sugar in 60 oz solution; Sugar = 60*20/100 = 12 oz Water = 60-12 = 48 oz Now; let's add "x" oz of water in the solution; Total solution = 60+x oz Sugar = 12 oz.(Sugar's amount will not change as we are not adding or subtracting sugar) 12 = (60+x) * 5/100 60+x = 240 x = 240 - 60 = 180 oz Answer: "E" #### E QUESTION:If you roll one fair six-sided die, what is the probability that the number is even or less than 4? options: A)1/6 B)1/3 C)2/ 3 D)3/4 E)5/6 SOLUTION:Total favourable outcomes: 1,2,3 (less than 4), 4,6(even) = 5 Total possible outcome= 6 Probability=5/6. Answer: Option E #### E QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B QUESTION:In a sequence of 40 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 282, what is the smallest term in the sequence? options: A)2 B)-2 C)0 D)8 E)9 SOLUTION:Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term. An = 282 + (40 - 1)*(-7) An = 282 - 273 = 9 E #### E QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 6300 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 17500 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×6300 / 12×3) => Rs. 17500. Answer : B #### B QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 3/3% C)33 1/3% D)39 1/3% E)33 4/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once? options: A)9/100 B)1/10 C)11/100 D)19/100 E)1/5 SOLUTION:Probability = No of balls with exactly one 1 / total number of balls = {1,10,12 to 19, 21,31,41,51,61,71,81,91,100}/100 = 19/100 Answer is D #### D QUESTION:If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following? options: A)m/3 B)9m C)9m^2 D)m^2/3 E)m^2/9 SOLUTION:m = 9 ^ (X-1) m = 3 ^ (2x-2) m^2 = 3 ^ (4x-4) m^2/9 = 3 ^ (4x-6) Answer E #### E QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years? options: A)2500 B)2800 C)3500 D)3600 E)2050 SOLUTION:P = 4032 R = 20% Required population of town = P/(1 + R/100)^T = 4032/(1 + 20/100)^2 = 4032/(6/5)^2 = 2800(approximately) Answer is B #### B QUESTION:A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work? options: A)18 days B)11 days C)77 days D)188 days E)66 days SOLUTION:8/12 + 6/x = 1 X = 18 days Answer: A #### A QUESTION:A box contains four cents, of which two centss have heads on both their faces, one cent has tail on both its faces and the fourth cent is a normal one. A cent is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the cent tossed is also a head. options: A)4/5 B)3/5 C)2/5 D)3/4 E)1/2 SOLUTION:There are four ways (2 heads in one two-headed cent and 2 heads in the other two-headed cent) How many ways can you get heads from this entire set of cents? There are five ways (four as identified above and one from the normal coin) Therefore probability = 4/5 Option A #### A QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics? options: A) 20% B) 42% C) 44% D) 66% E) 84% SOLUTION:You are correct. People who cover local politics are a subset of people who cover politics. 25% of reporters who cover politics do not cover local politics so 75% DO cover local politics. Reporters covering local politics= 75% of reporters covering politics= 25% of all reporters Reporters covering politics/All Reporters = 25/75 = 1/3 Reporters not covering politics/All Reporters = 2/3 = 66%=D #### D QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse? options: A)A)5 B)B)8 C)C)10 D)D)15 E)E)30 SOLUTION:Total number of ways to choose 6 chairs from 5= 6C2=15 Total number of combination=150 That means we need get 10 combinations from the selection of tables.... Screening through the answers.... 5C3=10..... 10*15=150 Answer is 5... A #### A QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)28% D)68% E)48% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:5216 x 51 = ? options: A)266016 B)212016 C)266436 D)216314 E)None of these SOLUTION:Explanation : Normal way of multiplication may take time. Here are one alternative. 5216 x 51 = (5216 x 50) + 5216 = (5216 x 100/2) + 5216 = 521600/2 + 5216 = 260800 + 5216 = 266016. Answer : Option A #### A QUESTION:At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate? options: A)134 B)178 C)195 D)166 E)194 SOLUTION:C 195 The number of votes the winning candidate received was 963 + 53 + 79 + 105 /4= 300. The second received 300 – 53 = 247, The third received 300 – 105 = 195. #### C QUESTION:Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in? options: A)6 B)12 C)28 D)42 E)21 SOLUTION:The part of the tank filled by three pipes in one hour = 1/14 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/14= 1/21. The tank can be filled in 21 hours. Answer:E #### E QUESTION:There are 6 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set? options: A)15 B)30 C)69 D)78 E)90 SOLUTION:We can select from 0 to 6 pens and from 0 to 9 books. Thus the total possible ways to select objects is 7*10 = 70 We must subtract 1 for the case with 0 pens and 0 books. The answer is C. #### C QUESTION:From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 13 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ? options: A)38 B)39 C)40 D)41 E)42 SOLUTION:Soln:- 13x=45 --> 87/77*x=45 --> x=45*77/87=677/17=~40. Answer: C. #### C QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)22 B)45 C)66 D)88 E)12 SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer: B #### B QUESTION:If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above? A. B. C. D. E. options: A)(−8,8) B)(4,−4) C)(5,−5) D)(2,−2) E)(−4,4) SOLUTION:Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A) Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B) Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C) Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D) Answer: Option C #### C QUESTION:In how many ways can 4 black and 4 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct. options: A)144 B)24 C)576 D)48 E)16 SOLUTION:4 black chess pieces can be arranged in 4! ways and 4 white pieces can be arranged in 4! ways. W_W_W_W Number of ways = 4!*4! = 24 * 24 = 576 Answer C #### C QUESTION:The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees. options: A)$2291.7 B)$1546.8 C)$2546.5 D)$1879.3 E)$3125.3 SOLUTION:mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7 Answer is A #### A QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)19% B)11% C)18% D)218% E)14% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer:C #### C QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double (5,5)? options: A)1/24 B)1/36 C)1/12 D)1/18 E)1/3! SOLUTION:total no. in two dice (1,1) ,(2,2) .....(6,) Total number of events= 6*6 Total events of getting same pair(5,5) = 6 Probability= 6/6*6= 1/6=1/3! E #### E QUESTION:A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour? options: A)15 kmph B)5 kmph C)10 kmph D)Data inadequate E)None of these SOLUTION:Here downstream speed = 15 km/hr and upstream speed = 5 km/hr ∴ Speed of the boat = 15+5/2=10km/h Answer C #### C QUESTION:A five-year promissory note with a face value of $3500, bearing interest at 11% compounded semiannually, was sold 21 months after its issue date to yield the buyer 10% compounded quarterly.What amount was paid for the note options: A)$4336.93 B)4336.99 C)4336.96 D)4336.92 E)4336.91 SOLUTION:Explanation: i=j/m Maturity value = PV (1 + i)^n Term = 5 years - 21 months= 3.25 years Price paid = FV(1+ i )^-n Answer: A) 4336.93 #### A QUESTION:If $600 is deposited into a savings account at an annual interest rate of 4% that compounds monthly, what is the value of the investment after 7 years? options: A)$750.00 B)$823.50 C)$973.25 D)$100.25 E)$793.49 SOLUTION:Using CI Formula: A=P(1+r/n)^n*t A=600(1+4/7)^4*7 A=793.49 Option: E #### E QUESTION:161?85?65?89=100 then use + or - in place of ? and take + as m,- as n then find value of m-n options: A)3 B)-1 C)1 D)-3 E)2 SOLUTION:161-85-65+89=100 so m=1, n=2 => (m-n)=-1 ANSWER:B #### B QUESTION:A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 6%. What was its profit on the items sold in February? options: A)27.5% B)30% C)35% D)37.5% E)41% SOLUTION:Assume the total price = 100x Price after 20% markup = 120x Price after 25%further markup = 1.25*120x = 150x Price after the discount = 0.94*150x = 141x Hence total profit = 41% Option E #### E QUESTION:What least number must be added to 1056, so that the sum is completely divisible by 23 ? options: A)2 B)3 C)16 D)18 E)23 SOLUTION:23) 1056 (45 92 --- 136 115 --- 21 --- Required number = (23 - 21) = 2. Answer: Option A #### A QUESTION:Find the unit digit in the product 274*318*577*313 options: A)5 B)2 C)10 D)26 E)89 SOLUTION:Explanation: Required digit=Unit digit is in(4*8*7*3)=2 Answer B #### B QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.4 B)3.9 C)4.1 D)4.2 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together? options: A)16 days B)12 days C)3 days D)5 days E)9 days SOLUTION:Sol. (A + B)'s 1 day's work = (1/18) (B + C)'s 1 day's work = (1/24) and (A + C)'s 1 day's work = (1/36) Adding, we get: 2 (A + B + C)'s 1 day's work =¬(1/18 + 1/24 + 1/36) =9/72 =1/8 (A +B + C)'s 1 day's work =1/16 Thus, A, Band C together can finish the work in 16 days. Ans: A #### A QUESTION:A shipment of 8 TV sets contains 6 black and white sets and 2 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set? options: A)1/7 B)1/4 C)5/14 D)11/28 E)27/28 SOLUTION:2/8 * 1/7 = 2/56 1-(2/56) = 54/56 = 27/28 Answer E #### E QUESTION:A company spends an average of $500 for its 20 employees's salaries and an average of $100 for its 5 drivers' salaries. What is the average expenditure of the company? options: A)$360 B)$290 C)$420 D)$600 E)$240 SOLUTION:Number of employees is 20 Their average salary is $500 Number of drivers is 5 Their average salary is $100 Total salary of the employees is 20*500=$10,000 Total salary of the drivers is 5*100=$500 Total expenditure for company is 10,000+500=$10,500 Average expenditure is 10,500/20+5=$420 Answer is C #### C QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be? options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999. 366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday Answer: A #### A QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)1 B)7 C)3 D)8 E)5 SOLUTION:40*(40/100) = 16 --- 64 ? --- 12 => Rs.3 Answer: D #### D QUESTION:Each of the integers from 1 to 18 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even options: A)19 B)12 C)11 D)10 E)3 SOLUTION:Out of the 18 integers: 9 are odd and 9 are even. If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case: 1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first 2. 10th number will be the first even number So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even. So, answer will be 10. (D) #### D QUESTION:What is the height of the tower ? A man standing at a distance of 1km from the bottom of the tower makes an angle 300 degrees with the top of the tower .An insect starts from the bottom of the tower and reaches the top in 25sec. options: A)0.577km B)0.477km C)0.677km D)0.577k7 E)0.977km SOLUTION:tan = opp side/adj side tan 30= height/1 ht=0.577km ANSWER:A #### A QUESTION:The value of (34.31*0.473*1.5)/(0.0673*23.25*7.57) is close to options: A)2 B)1.15 C)2.01 D)2.06 E)2.35 SOLUTION:(34.31*0.473*1.5)/(0.0673*23.25*7.57) = 24.343/11.845 = 2.06 ANSWER:D #### D QUESTION:The product of the prime numbers between 0 and 20 is closest to... options: A)10^5 B)10^6 C)10^7 D)10^8 E)10^9 SOLUTION:Write out the primes 1 - 20 2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 Round the numbers off in multiples of 5. Try to alternate rounding up and down 5 x 5 x 5 x 5 x 10 x 10 x 20 x 20 25 x 25 x 10 x 10 x 20 x 20 pull out 10 from each number 10^6 (2.5 x 2.5 x 2 x 2) 10^6 (5 x 4) 10^7 (2) round off the 2. answer is C #### C QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)12 B)45 C)77 D)88 E)51 SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer: B #### B QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is? options: A)12 B)14 C)15 D)19 E)10 SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank. 1/x + 1/(x - 5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x- 15)(x - 3) = 0 => x = 15. Answer:C #### C <<<Examples ends QUESTION:According to the 2001 census,the population growth rate of Lucknow is going to be an increasing AP with first year's rate as 5% and common difference as 5% but simultaneously the migration,rate is an increasing GP with first term as 1% and common ratio of 2.If the population on 31 december 2000 is 1 million,thn find in which year will Lucknow witness its first fall in population? options: A)2006 B)2007 C)2005 D)2008 E)2009 SOLUTION:population growth rate according to the problem year 1 = 5% year 2 = 10% year 3 = 15% year 4 = 20% year 5 = 25% year 6 = 30% population decrease due to migration year 1 = 1% year 2 = 2% year 3 = 4% year 4 = 8% year 5 = 16% year 6 = 32% Thus, the first fall would happen in year 2006 ANSWER:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:10 men working 6 hrs per day manufacture 200 shoes in 18 days. How many hours a day must 15 men work to manufacture the same 200 shoes in 12 days? options: A)6 B)10 C)12 D)15 E)18 SOLUTION:Let the required number of hours be x. More men, less hours per day (Indirect proportion) Less days, more working hours per day (Indirect proportion) men 15 : 10 } : : 6 : x days 12 : 18 .'. 15*12*x = 10*18*6 = x = 10*18*6/(15*12) = x = 6 ANSWER : A #### A QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)2/215 B)3/155 C)1/216 D)2/213 E)3/212 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as q(a+l)/2----------------1) q= total no. of terms =80 a= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)100 kg B)102.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 3.5) kg = 35 kg. Weight of new person = (65 + 35) kg = 100 kg. Answer: A #### A QUESTION:A data set with a mean of 40 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)18 B)36 C)59 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=40-3.5=36.5 to{mean}+{deviation}=40+3.5=43.5. The smallest number within this range from the options is 36. Answer: B. Hope this helps. #### B QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:Set A: {1, 3, 4, 6, 9, 12, 16} If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 4? options: A)3/14 B)2/7 C)9/14 D)5/7 E)1/35 SOLUTION:using probability you can solve: 3/7*2/6*1/5=1/35. Ans E #### E QUESTION:A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse. options: A)2200 B)1800 C)1200 D)1000 E)1500 SOLUTION:Let the C.P of the horse be Rs. X, Then, C.P of the carriage = Rs.(3000- x). 20% of x - 10% of ( 3000-x ) =2% of 3000 = 60, x/5 - ( 3000-x )/10 = 60, 3x - 3000 = 600, 3x =3600, x = 1200. Hence, C.P of the horse = Rs. 1200 ANSWER:C #### C QUESTION:what is next number in sequence 212 427 303 336 394 ? options: A)123 B)345 C)560 D)567 E)245 SOLUTION:E 245 space them properly as 21 24 27 30 33 36 39 42 45 ? #### E QUESTION:There are between 500 and 510 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection? options: A) 501 B) 503 C) 506 D) 507 E) 510 SOLUTION:Let number of cards = x If the cards are counted 3 at a time , there are 2 left over- x= 3p+2 x can take values 503 , 506 , 510 If the cards are counted 4 at a time , there is 1 left over x= 4q+1 x can take values 501 , 506 Therefore , x = 506 Answer C #### C QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:The average of first four prime numbers greater than 30 is? options: A)38 B)20 C)30 D)40 E)50 SOLUTION:31 + 37 + 41 + 43 = 152/4 = 38 ANSWER:A #### A QUESTION:A train running at 1/3 of its own speed reached a place in 9 hours. How much time could be saved if the train would have run at its own speed? options: A)8hrs B)10hrs C)12hrs D)15hrs E)6hrs SOLUTION:time taken if run its own speed = 1/3*9 =3 hrs Time saved = 9 - 3 = 6 hrs Answer : E #### E QUESTION:A square with sides of 15 units each. What would be the area of the square. Consider a square as a combination of two right angled triangles. options: A)100 B)256 C)225 D)81 E)144 SOLUTION:A square can be considered as a set of two right angled triangles joined from the hypotenuse. Since the sides are 10 units each. The height and base of both the triangles is 10 each. Area of a right angled triangle is 1/2 * base * height Area of both the triangles is 2 * 1/2 * base * height. Since both triangles are similar. = base * height = 15*15 =225 Ans: C #### C QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)2528 B)2526 C)2522 D)2722 E)2426 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261? options: A)8000 B)8077 C)2776 D)2976 E)2971 SOLUTION:8820 ---- 441 100 ---- ? => 5% x *105/100 * 105/100 = 8820 x*1.1025=8820 x=8820/1.1025 => 8000.Answer: A #### A QUESTION:How much 60% of 50 is greater than 40% of 30? options: A)18 B)28 C)26 D)27 E)23 SOLUTION:(60/100) * 50 – (40/100) * 30 30 - 12 = 18 Answer:A #### A QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20 SOLUTION:5p3 =5 x4= 20 Option 'E' #### E QUESTION:What approximate value should come in place of question mark (?) in the following equation? 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ? options: A)230 B)225 C)232 D)220 E)240 SOLUTION:? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12 = 256.3 + 40.3 – 66.12 ≈ 232 Answer C #### C QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)6 B)5 C)8 D)9 E)4 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8.Answer: C #### C QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)9% B)4% C)6% D)3% E)5% SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer:B #### B QUESTION:A boat crossed a lake from East to West at the speed of 5 km/h, entered a river and covered twice as much distance going upstream at 4 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.6 km/h that day, what was its approximate downstream speed? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:One way of solving this is: Speed of boat on still water (lake)=5kmph Speed upstream = 4kmph = speed in still water - speed of river => speed of river = 1kmph =>Speed downstream = speed in still water + speed of river = 5+1 =6kmph Ans is C #### C QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B QUESTION:The speed of a boat in still water in 20 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is: options: A)10.6 B)5.2 C)10.8 D)5.4 E)5.0 SOLUTION:Speed downstream = (20 + 6) = 26 kmph Time = 24 minutes =12/60 hour = 1/5 hour Distance travelled = Time × speed =1/5×26 = 5.20 km Answer is B. #### B QUESTION:A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 30% profit on the cost of the item? options: A)18 B)21.6 C)22 D)25.7 E)27 SOLUTION:Producer price = $15; The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 30% of the final price --> (final price)*0.7 = $18 --> (final price) = $25.7. Answer: D. #### D QUESTION:Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is? options: A)17/65 B)17/29 C)17/21 D)P(EᴜP) =17/20 E)17/212 SOLUTION:n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D #### D QUESTION:If x > y and y > z, which of the following represents the greatest number W? options: A) x − z B) x − y C) y − x D) z − y E) z − x SOLUTION:Because x>y>z thus W=x- z wil lbe greatest Ans: A #### A QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 740 will be: options: A)Rs. 300 B)Rs. 200 C)Rs. 240 D)Rs. 350 E)None of these SOLUTION:Z share = Z, Y = 1.2Z X = 1.25×1.2Z, X+Y+Z =740 (1.25× 1.2+1.2+1)Z=74 3.7Z=740, Z=200 Answer: . B. #### B QUESTION:What is the unit digit of (6!*3! / 3!*4!)? options: A)5 B)6 C)0 D)3 E)4 SOLUTION:(6!*3! /3!*4!) =(6! / 4!) =5*6 =30 Units digit of the above product will be equal to 0 Answer C #### C QUESTION:Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries? options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140 SOLUTION:Probability of basket = 3/5 Probability of no basket = 2/5 Required probability=3* 3/5*2/5*2/5 =36/125 A is the answer . #### A QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:Fathers age is 5 times his son’s age. 4 years back the father was 9 times older than son.Find the fathers’ present age. options: A)40 years B)33 years C)22 years D)33 years E)44 years SOLUTION:Ans. 40 years #### A QUESTION:9, 16, 18, 25, 36,49 options: A)9 B)16 C)18 D)25 E)36 SOLUTION:Each of the numbers except 18, is perfect square. Answer: Option C #### C QUESTION:The purchase price of an article is $48. In order to include 30% of cost for overhead and to provide $12 of net profit, the markup should be options: A)15% B)25% C)35% D)40% E)55% SOLUTION:Cost price of article = 48$ % of overhead cost = 30 Net profit = 12 $ We need to calculate % markup Net profit as % of cost price = (12/48)*100 = 25% Total markup should be = 25 + 30 = 55% Answer E #### E QUESTION:A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there? options: A)15 B)30 C)28 D)24 E)32 SOLUTION:number of workers = 10* (25-10)/10 = 15 Answer is A #### A QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 * 1300 = 1040 Option D #### D QUESTION:Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? options: A)21 B)16 C)16 D)28 E)12 SOLUTION:Speed Ratio = 1:7/6 = 6:7 Time Ratio = 7:6 1 -------- 7 4 --------- ? è 28 m Answer: D #### D QUESTION:A small college reduced its faculty by approximately 15 percent to 195 professors. What was the original number of faculty members? options: A)182 B)208 C)224 D)229 E)302 SOLUTION:If x is the original number of faculty members, then after 15% reduction in faculty members number is .85x but we are given .85x = 195 x = 229 So the original number of faculty members is 229 Correct Answer - D #### D QUESTION:The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.90 per metre. options: A)2399 B)3888 C)2999 D)5808 E)6468 SOLUTION:Explanation: Area = (13.86 x 10000) sq.m = 138600 sq.m Circumference = Cost of fencing = Rs. (1320 x 4.90) = Rs. 6468. Answer: E) 6468 #### E QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? options: A)20 B)18 C)12 D)14 E)15 SOLUTION:A's 2 day's work = 1/20 x 2 = 1/10 (A + B + C)'s 1 day's work = 1/20 + 1/30 + 1/60 = (3+2+1)/60 = 1/10 Work done in 3 days = A's 2 day's work + (A + B + C)'s 1 day's work Work done in 3 days = 1/10 + 1/10 Now, work is done in 3 days = 2/10 = 1/5 So, 1/5 cork is done in 3 days. So, work will be done in (3 x 5) = 15 days. So, correct answer is E #### E QUESTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. options: A)6 B)6.5 C)7 D)7.5 E)5 SOLUTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total) Hour miles/hour Total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 It takes a total of nine hours to cover the 210 mile distance. ANSWER: A 6 #### A QUESTION:A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village? options: A)10km B)50km C)30km D)25km E)20km SOLUTION:Average speed = 2xy/x+y = 2*25*4/25+4 = 200/29km/hr Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km Distance of the post office from the village = 40/2 = 20km Answer is E #### E QUESTION:If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above? A. B. C. D. E. options: A)(−8,8) B)(4,−4) C)(5,−5) D)(2,−2) E)(−4,4) SOLUTION:Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A) Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B) Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C) Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D) Answer: Option C #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)26 B)22 C)12 D)24 E)20 SOLUTION:Explanation: Let the required number of days be x More men, less days (indirect proportion) Hence we can write as (men) 36 : 27 :: x : 18 ⇒36×18=27 × x ⇒12×18=9 × x ⇒12×2=x ⇒x=24 Answer: Option D #### D QUESTION:Two trains are moving in the same direction at 126 kmph and 54 kmph. The faster train crosses a man in the slower train in 14 seconds. Find the length of the faster train? options: A)280 B)290 C)300 D)310 E)320 SOLUTION:Relative speed = (126 - 54) * 5/18 = 4 * 5 = 20 mps. Distance covered in 27 sec = 14 * 20 = 280 m. The length of the faster train = 280 m. Answer:A #### A QUESTION:Carol spends 1/4 of her savings on a stereo and 1/2 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? options: A)1/4 B)2/7 C)5/12 D)3/8 E)7/12 SOLUTION:Total Savings = S Amount spent on stereo = (1/4)S Amount spent on television = (1-1/2)(1/4)S = (1/2)*(1/4)*S = (1/8)S (Stereo + TV)/Total Savings = S(1/4 + 1/8)/S = 3/8 Answer: D #### D QUESTION:How many positive integers less than 100 are neither multiples of 2 or 3? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:1) multiples of 2 till 100 = 100/2 = 50 2) multiples of 3 till 100 = 100/3 = 33.33= 33 add the two 50+33=83 ; subtract common terms that are multiple of both 2 and 3.. LCM of 2 and 3 = 6 Multiples of 6 till 100 = 100/6 = 16.66 = 16 so total multiples of 2 and 3 = 83-16 = 67 100-67 = 33 Answer : D #### D QUESTION:How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number? options: A)26 B)30 C)34 D)38 E)42 SOLUTION:The first number is 22 = 16+6(1). We can continue adding 6 to make a list: 22, 28, 34,... The last number is 196 = 16+6(30) There are 30 numbers in the list. The answer is B. #### B QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is: options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 20 : 8 :: 12 : x => 8 x 20 x x = 10 x 8 x 12 => x = 10 x 8 x 12 / (8 x 20) => x = 6 Answer : C #### C QUESTION:A man buys s cycle for $100 and sells it at a loss of 30%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 70% of the $100 = 70/100 * 100 = $70 Answer is C #### C QUESTION:A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k? options: A)3/4 B)1 C)4/3 D)2 E)7/2 SOLUTION:This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k. {{k + 4}/4} = k k + 4 = 4k 4 = 3k k = 4/3 Answer = C #### C QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning? options: A)39 B)88 C)3 D)7 E)62 SOLUTION:Let the average after 7th inning = x Then average after 16th inning = x - 3 \inline \fn_jvn \therefore 16(x-3)+87 = 17x \inline \fn_jvn \therefore x = 87 - 48 = 39 Answer:A #### A QUESTION:A given line L has an equation 3x+4y=5. Which of the following is the equation of line which is parallel to the above line? options: A) 4x + 3y = 5 B) 3x + 4y = 10 C) 3x + 5y = 5 D) 3x + 5y = 3 E) 3x – 4y = 5 SOLUTION:3x+4y=5 --- equation 1 2 lines are parallel if a1/a2 = b1/b2 ≠ c1/c2 Comparing the original line with option B 3x+4y = 10 -- equation 2 From equations 1 and 2 , we get 5=10 which is not possible Hence our answer is 3x + 4y = 10 Answer B #### B QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:40, 45, 50, 50, 60, 75, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:If (x-13)(x-3) < 0, which of the following must be true? options: A)x^2 + 5x + 6 < 0 B)x^2 + 5x + 6 > 0 C)5 - x < 0 D)x - 5 < 0 E)13 - x > 0 SOLUTION:(x-13)(x-3)<0 can be written as (13-x)(x-3)>0 So,to inequality hold true multiple of (13-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<13 Answer Choice E matched which says 13-x>0 or x<13,which must be true (I started to look from E to A for making easy decision first) Correct Answer E #### E QUESTION:The maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is options: A)91 B)81 C)1001 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 891 and 810. ‹=› 81. Answer B #### B QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:If a committee of 2 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? options: A)24 B)40 C)50 D)80 E)120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 4C2=6. But these 2 chosen couples can send two persons (either husband or wife): 2*2=2^2=4. Total # of ways: 4C2*2^2=24. Answer: A #### A QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions? options: A)754 m B)704 m C)708 m D)706 m E)204 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m Answer:B #### B QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value W of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer W is 342. The correct answer is E. #### E QUESTION:A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $3200 and the total price paid for type B products was $5800. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year? options: A)$14,755 B)$15,325 C)$11,129 D)$16,225 E)$17,155 SOLUTION:cost of type A products next year = 1.3 * 3200 = 4160 cost of type B products next year = 1.2 * 5800 = 6960 total 4169 + 6960 = 11129 ANSWER:C #### C QUESTION:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar? options: A) 9 B) 12 C) 15 D) 18 E) 21 SOLUTION:(Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins) í.ẹ. Red*White = Blue*Total Coins Let, Red = 3a White = 3b Blue = 3c Total Coins = 3(a+b+c) í.ẹ. 3a * 3b = 3c*3(a+b+c) í.ẹ. a*b = c*(a+b+c) For smallest values of a, b and c 2*3 = 1*(1+2+3) í.ẹ. Minimum Total Coins = 3*(1+2+3) = 15 Answer: Option C #### C QUESTION:How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 30% iodine solution? options: A)30.5 B)49 C)100 D)105 E)140 SOLUTION:Solution 1: Assume the iodine solution to be mixed = x lts. Iodine = 0.4x lts, Water = 0.6x lts. Solution 2: 35 liters of a 20% iodine solution Iodine = 7 lts, Water = 28 lts. Total iodine = 0.4x + 7 Total water = 0.6x + 28 The resultant is a 35% idoine solution. Hence (0.4x + 7) / (x + 35) = 30/100 40x + 700 = 30x + 1050 10x = 305 x = 30.5 lts Correct Option: A #### A QUESTION:A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %? options: A)62 2/3% B)64 2/3% C)66 2/3% D)66 5/3% E)68 2/3% SOLUTION:Gain=40 lemons Total 100 lemons CP 100-40=60 (40/60)*100 =66 2/3% Ans C #### C QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 46 years, was replaced by a new person. Find the age of the new person? options: A)18 B)56 C)16 D)17 E)14 SOLUTION:Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 46 + Q => Q = 16 Answer:C #### C QUESTION:If x = 3d, where d is a prime number greater than 2, how many different positive even divisors does x have, including x? options: A)0 B)1 C)2 D)3 E)It cannot be determined from the information given SOLUTION:d is prime greater than 2 thus d is odd 3d is odd Thus no even factors Ans:A #### A QUESTION:In how many ways can the letters of the word "SATURN" be arranged? options: A)560 B)640 C)720 D)800 E)880 SOLUTION:The total ways of arranging the letters = 6! = 720 The answer is C. #### C QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)*100]%=50% Answer A) 50. #### A QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? options: A)250 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Answer: A #### A QUESTION:AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 16.0 grams 4:00 P.M. x grams 7:00 P.M. 20.4 grams Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.? options: A)12.0 B)18.1 C)12.2 D)12.3 E)18.0 SOLUTION:The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours. Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm: Fractional increase from 1 PM to 4 PM = X / 16.0 Fractional increase from 4 PM to 7 PM = 20.4 / X X \ 16 = 20.4 \ X X^2 = 20.4 * 16 X = 18 answer : E #### E QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12*100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:A,B,C invested the capitals in a business. If A invested Rs. 20,000 more than B and C invested Rs.10,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000 options: A)5500, 2500, 6000 B)5200, 2800, 6000 C)4250, 2250, 7500 D)5250, 1750, 7000 E)5300, 2700, 6000 SOLUTION:A==30,000 B==10,000 C==40,000 so, ration are3:1:4 profit 14000 so,, 14000/8==1750 so,, A==5250, B==1750,, C==7000 ANSWER:D #### D QUESTION:There are three foam generators in the factory, each of the first two can generate 8 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)146. D)154. E)115 SOLUTION:Let the foam generators capacity be - A = 8 lit/hr B = 8 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 34 lit ( 8 + 8 + 18 ) ; since in 1 and 1/2 hr they will generate 34 + 17 => 51 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 8 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 52 litres {2 (8+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 8 => 12 litres So, total foam generated will be 115 Litres ( 51 + 52 + 12 ) ; hence answer will be (E) #### E QUESTION:The banker's discount on Rs.1800 at 48% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time? options: A)1 months B)4 months C)5 months D)6 months E)7 months SOLUTION:Solution S.I on Rs.1800 = T.D on Rs.1872. P.W on Rs.1872 is Rs.1800. Rs.72 is S.I on Rs. 1800 at 48%. Time =(100x72 / 48x1800) = 1/12 year = 1 months. Answer A #### A QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage? options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3% SOLUTION:Explanation: Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 33 pens = Rs. 33 Profit% = 33/99 * 100 = 33 1/3% Answer: A #### A QUESTION:You need to climb 10 stairs. At each support, you can walk one stair or you can jump two stairs. In what number alternative ways you'll climb ten stairs? options: A)99 B)79 C)55 D)89 E)66 SOLUTION:D #### D QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit? options: A)2388 B)2380 C)2888 D)2663 E)2922 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 6970 * 14/41 = Rs. 2380. Answer: B #### B QUESTION:A lamp is put on one corner of a square plot of side 50m. It's light reaches 21m. Find the area of that plot that is lit by that lamp? options: A)248 B)312.5 C)346.5 D)392.5 E)424 SOLUTION:Area covered by lamp = Pi*r^2/4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1/4 part lit is of the plot) where r= 21 m = length of part lit So area = (22/7)*21*21/4 = 346.5 sq m answer :C #### C QUESTION:Which of the following equations has a root in common with x^2−3x+2=0 ? options: A)x^2-2x+1=0 B)x^2-2x-1=0 C)x^2-x+1=0 D)x^2-3x+3=0 E)x^2-7x=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-2)= 0 so the two roots are 1 and 2. Now put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. A is the answer. #### A QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 6*6 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ? options: A)2015 B)2088 C)270 D)1881 E)1781 SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4 .............. f(2014) = 2015 Ans: A #### A QUESTION:The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid. options: A)9: 8 B)9: 5 C)9: 1 D)9: 2 E)9: 4 SOLUTION:a1 : a2 = 3 : 1 6 a12 : 6 a22 = 9: 1 Answer:C #### C QUESTION:What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected? options: A)76 ways B)66 ways C)30 ways D)56 ways E)43 ways SOLUTION:The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5 = 30 ways. Answer: C #### C QUESTION:What is greatest positive integer n such that 2^n is a factor of 12^11? options: A)a)10 B)b)12 C)c)22 D)d)20 E)e)60 SOLUTION:The given number is 12^11 =(2*2*3)^11 =(2^22)*(3^11) So the greatest possible value for n such that 2^n can be factor of given number is 22. Answer C #### C QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)69 E)71 SOLUTION:1/2 * d (12 + 8) = 690 d = 69 Answer: D #### D QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)8 B)10 C)12 D)11 E)15 SOLUTION:Speed = 120/10 = 12 m/sec speed of the second train = 120/5 = 8 m/sec relative speed = 12+8 = 20 m/sec Req time = 120+120/20 = 12 sec ANSWER C #### C QUESTION:Two wheels are connected via a conveyor belt. The larger wheel has a 48cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r? options: A)90r B)75r C)48r D)24r E)(64π)/3 SOLUTION:Interesting to note that the larger wheel has a diameter of 48 (8*6) while the smaller one has a diameter of 32 (8*4)... If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 48pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.5 = 15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.5 = 900 revolutions per hour. If r = 10, then the answer choice must be b. A. 90r #### A QUESTION:If G = 775 × 778 × 781, what is the remainder when G is divided by 14? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:G 775/14 leaves a remainder 5 778/14 leaves a remainder 8 781/14 leaves a remainder 11 5*8*11 =440 So the remainder will be the remainder of 440/14 which is 6 Ans A #### A QUESTION:A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of B. options: A)250 B)450 C)750 D)800 E)None of them SOLUTION:C's 1 day's work = 1/3-(1/6+1/8)=24 A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1. A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450 C's share = Rs. [1200 - (300 + 225») = Rs. 150. Answer is B #### B QUESTION:Twelve telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of five members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? options: A)120 B)126 C)792 D)1200 E)1260 SOLUTION:My ans is 12C5 = 792 C #### C QUESTION:The triplicate ratio of 1:3 is? options: A)1:27 B)1:8 C)1:3 D)1:1 E)1:2 SOLUTION:1^3: 3^3 = 1:27 Answer: A #### A QUESTION:If Albert’s monthly earnings rise by 20%, he would earn $560. If, instead, his earnings rise by only 21%, how much (in $) would he earn this month? options: A)643 B)652 C)660 D)564 E)693 SOLUTION:=560/1.2∗1.21 =564=564 Answer is D #### D QUESTION:2 friends A n B running up hill and then to get down length of road 440 yads A on his return journey met B going up at 20 yards from top if A has finished race 5 minute earlier than B then how much time A had taken to complete the race ? options: A)100 minute B)110 minute C)120 minute D)130 minute E)140 minute SOLUTION:total journey= 440*2=880 A meet B 20 yards from top in getting down it means he has covered 440+20=460 yards while B is 420 yards.so he is 40 yards ahead of B which is equals to 5 minute. so 40 yards in 5 min 880 yards will be in 5*880/(40)=110 minute ANSWER:B #### B QUESTION:Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Tuesday, how many croissants will Marina eat on the 24th of that month? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:She eat as follow Mon - 1 Tue - 2 Wed - 3 Thr - 5 Fri - 1(since she had more than 4 previous day) sat - 6 sunday - 1 (since she had more than 4 previous day) so 24th day of month she will have 5. Answer is D #### D QUESTION:The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%? options: A)16 2/7% B)16 2/6% C)16 2/3% D)16 7/3% E)12 2/3% SOLUTION:10 CP = 12 SP 12 --- 2 CP loss 100 --- ? => 16 2/3% Answer: C #### C QUESTION:The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is: options: A)60 kg B)59 kg C)62 kg D)63 kg E)61 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (75 x 3) = 225 …. (i) A + B = (88 x 2) = 176 …. (ii) B + C = (72 x 2) = 144 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 288 …. (iv) Subtracting (i) from (iv), we get : B = 63. B’s weight = 63 kg. Answer D #### D QUESTION:Rohit spent 30 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Rohit have left over? options: A)29% B)35% C)46% D)47% E)52% SOLUTION:SayRohit's earning last month was $100. Rohit spent 30 percent of his earning last month on rent --> $30 on rent; 20 percent less than what he spent on rent to purchase a new dishwasher --> $30*0.8=$24 on the dishwasher. Left over amount 100 - (30 + 24) = $46 Answer: C #### C QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/91 B)33/18 C)33/29 D)33/18 E)33/12 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = 12C4/15C4 = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:A #### A QUESTION:How many bricks, each measuring 125 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm? options: A)1280 B)2400 C)5500 D)7400 E)3400 SOLUTION:Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (125 x 11.25 x 6) = 1280 ANSWER:A #### A QUESTION:Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own? options: A)6 B)7 C)8 D)12 E)14 SOLUTION:Lets suppose Anne and Bruce take A and B hrs working separately So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours) After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 3 hours) Solving these 2 equations we can find B as 12 ANSWER:D #### D QUESTION:The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: options: A)10º B)75º C)90º D)130º E)180º SOLUTION:Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º. Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º. Required angle = (130 - 120)º = 10º. Answer A #### A QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)Rs.500 B)Rs.1000 C)Rs. 3630 D)Rs.2500 E)Rs.6000 SOLUTION:Explanation: 6300:4200:10500 3:2:5 3/10 * 12100 =Rs. 3630 ANSWER:C #### C QUESTION:The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ? options: A) 10^9 B) 10^8 C) 10^2 D) 10^6 E) 10^5 SOLUTION:P = 2*3*5*7 ~ 10^ 2 Answer : C #### C QUESTION:Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck. options: A)150 B)160 C)170 D)180 E)190 SOLUTION:Let the 1st paycheck be x (integer). Dawson got a weekly raise of $ 160. So after completing the 1st week she will get $ (x+160). Similarly after completing the 2nd week she will get $ (x + 160) + $ 160. = $ (x + 160 + 160) = $ (x + 320) So in this way end of every week her salary will increase by (B)$ 160. #### B QUESTION:A shop owners pays an average salary of $400 to his 10 employees and $100 to the 2 accountants. What is the average salary for the shop owner? options: A)$350 B)$500 C)$460 D)$120 E)$800 SOLUTION:Number of employees in the shop is 10 Their average salary is $400 Number of accountants in the shop is 2 Their average salary is $100 Total salary of the employees is 10*400=$4,000 Total salary of the accountants is 2*100=$200 Total salary for the shop owner is $4,200 Average salary for the shop owner is 4,200/12=$350 Answer is A #### A QUESTION:The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is? options: A)5 kmph B)1 kmph C)6 kmph D)2 kmph E)3 kmph SOLUTION:The current of a stream = 1 The speed of the motor boat in still water= x Speed downstream = x + 1 Speed upstream = x - 1 since distance = speed × time, we have 35/(x + 1) + 35/(x - 1) = 12 kmph=6 kmph Answer : Option C #### C QUESTION:In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 210 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ? options: A)40 ml B)70 ml C)20 ml D)20/3 ml E)10 ml SOLUTION:There are 0.3*100=30 ml of element X in the initial solution. We need X to be 1/3rd of 210 ml in the resulting solution, so 70 ml. Thus out of 110 ml of solution added, 40 must be X (in order it to become 70 ml) ans the remaining 70 must be Y. Answer: B #### B QUESTION:A train 440 meters long is running with a speed of 65 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)40.338 sec B)41.338 sec C)42.338 sec D)40 sec E)34.338 sec SOLUTION:D = 440 + 180 =620 S = 65 * 5/18 = 18.05556 mps T = 620/18.05556 =34.33846 E #### E QUESTION:A was born when B was 1 year and 3 months old. C was born when A was 2 years 1 month old. What is the age of B when C is 4 years and 6 months old? options: A)4 yr 10 month B)6 yr 10 month C)7 yr 11 month D)7 yr 10 month E)8 yr 10 month SOLUTION:When C is 4yr 6 month i.e. 54 months old A is 79 month old.. B is 15 month older than A When A is 79 months old then, B is 94 months old i.e. 7yr 10 month ANSWER:D #### D QUESTION:There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)Rs. 30 B)Rs. 34 C)Rs. 42 D)Rs. 48 E)Rs. 50 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1 or, 35x + 42 = 42x – 42 or, x = 12 Thus the original expenditure of the mess = 35 x 12 = Rs. 42 C #### C QUESTION:A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. options: A)15/7 B)4/17 C)7/18 D)19/6 E)7/15 SOLUTION:Let S be the sample space Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45 Let E=event of getting both balls of same colour Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4) =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21 P(E)=n(E)/n(S)=21/45=7/15 Option E #### E QUESTION:There are 8 magazines lying on a table; 4 are movie magazines and the other 4 are education magzines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the movie magazine will be selected? options: A)9/14 B)11/14 C)13/14 D)1/14 E)3/14 SOLUTION:1- (4c3/8c3) = 13/14 Answer : C #### C QUESTION:A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed? options: A)30days B)35days C)40days D)44days E)45days SOLUTION:Explanation: (A+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5 A complete remaining work in 2/5*50 = 20 Total work = 10+20= 30days Answer: Option A #### A QUESTION:A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 1.25 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 40 worth of diesel fuel? options: A)20 seconds B)1 minute C)1 minute 20 seconds D)20 minutes E)1 hour 20 minutes SOLUTION:No. of gallons = 40 / 1.25 = 32 for 2 gallons it takes 5 secs for 32 gallons it will take 80 secs = 1 min and 20 secs Answer: C #### C QUESTION:In how many different ways can the letters of the word 'CAREER' be arranged? options: A)10 ways B)20 ways C)180 ways D)60 ways E)40 ways SOLUTION:Totally there are 6 letters on the word CAREER. it contains 1C,1A,2R,2E. The no of ways is 6!/2!2!=180 ways. ANSWER:C #### C QUESTION:For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y? options: A)14 B)12 C)10 D)16 E)18 SOLUTION:we know that : x > 1, y > 1, and x + 3y < 1000, and it is given that length means no of factors. for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal. hence, lets start with smallest no 2. 2^1 =2 2^2 =4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256 2^9=512 2^10 =1024 (it exceeds 920, so, x can't be 2^10) so, max value that X can take is 2^9 , for which has length of integer is 9. now, since x =512 ,x+3y<920 so, 3y<408 ==> y<136 so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7 for 2^7 has length of integer is 7. SO, combined together : 9+7 = 16. D #### D QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? options: A)700 B)666 C)600 D)400 E)800 SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C #### C QUESTION:A fill pipe can fill 1/3 of cistern in 20 minutes in how many minutes, it can fill 3/4 of the cistern? options: A)15 min B)45 min C)25 min D)40 min E)50 min SOLUTION:1/3 of the cistern can fill in 20 min 3/4 of the cistern can fill in = 20*3*3/4 = 45min Answer is B #### B QUESTION:Which of the following has the most number of divisors? options: A)99 B)101 C)176 D)182 E)179 SOLUTION:Explanation: 99 = 1 x 3 x 3 x 11 101 = 1 x 101 176 = 1 x 2 x 2 x 2 x 2 x 11 182 = 1 x 2 x 7 x 13 So, divisors of 99 are 1, 3, 9, 11, 33, .99 Divisors of 101 are 1 and 101 Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176 Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Hence, 176 has the most number of divisors. Answer: C #### C QUESTION:How many of the integers between 25 and 45 are even ? options: A)21 B)20 C)11 D)10 E)9 SOLUTION:Number start between 25 to 45 is 20 numbers half of them is even..which is 10 ANSWER:D #### D QUESTION:If you are given $5, and the amount doubles every day, how much money will you have after 4 days? options: A)$256 B)$512 C)$1024 D)$625 E)$720 SOLUTION:5^4=625 The answer is D #### D QUESTION:Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? options: A)66 B)70 C)72 D)75 E)78 SOLUTION:Let the distance one way be x Time from home to work = x/60 Time from work to home = x/100 Total time = 2 hrs (x/60) + (x/100)= 2 Solving for x, we get x = 75 Time from home to work in minutes= (75)*60/60 = 75 minutes Ans= D #### D QUESTION:If c and d are prime numbers, which of the following CANNOT be the sum of c and d? options: A)5 B)9 C)13 D)23 E)33 SOLUTION:All answer choices but D are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd. Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers. Answer: D #### D <<<Examples ends QUESTION:JERRY has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If JERRY needs to pay exactly $128, what is the least number of bills he will need to use? options: A)16 B)35 C)46 D)577 E)576 SOLUTION:128 is the total sum of money. as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils 128-120 = 8 so now we need to get 8 from either 5 dollar bills or 1 dollar bills 8 - 5 (use only 1 5 dollar bill) = 3 so we can get 3 from using 3 $1 bills. Hence 16 ( 12+1+3 ) ANSWER IS A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 3. If 1 < m < 300, what is the greatest possible value of m? options: A)173 B)203 C)233 D)263 E)293 SOLUTION:13*9 = 117 Let's start with 3, and keep adding 13 until we find a number with the form 9k+2. 3, 16, 29 = 9*3+2 The next possible number is 29 + 117 = 146 The next possible number is 146 + 117 = 263 The next possible number would be greater than 300. The answer is D. #### D QUESTION:Find the value of 72515 x 9999 = m? options: A)345434667 B)246465757 C)465767867 D)725077485 E)645354643 SOLUTION:72515 x 9999 = 72515 x (10000 - 1) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 D #### D QUESTION:3^7+3^7+3^7=? options: A)a) 81^2 B)b) 81^4 C)c) 81^5 D)d) 81^6 E)e) 81^15 SOLUTION:The correct answer is A 81^2 #### A QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (5*27) - (4*25) = 135-100 = 35 Answer: Option A #### A QUESTION:A scuba diver descends at a rate of 32 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 6400feet below the sea level..how long will he take to reach the ship? options: A)200 minutes B)240 minutes C)220 minutes D)210 minutes E)77 minutes SOLUTION:Time taken to reach = 6400/32= 200 minutes ANSWER:A #### A QUESTION:P sells an article to Q at 10 % profit. Q sells it to R at 25 % profit. If R pays Rs. 250 for it, What did P pay for it ? options: A)Rs. 181.81 B)Rs. 181.88 C)Rs. 181.82 D)Rs. 181.89 E)Rs. 181.812 SOLUTION:Explanation: Selling price of P = Cost price of Q Selling Price of Q = Cost price of R = Rs. 250 ….. Given Q sold it to R with 25 % profit. Cost price of Q = 100/125 * 250/1 = Rs. 200 = Selling price of P. P sold it to Q with 10 % profit. Cost price of P = 100 / 110 * 200 / 1 = Rs. 181.81 ANSWER: A #### A QUESTION:V and B are integers. The expression (V+1)(B+1) is even. What can be said about V and B? options: A)They are both even numbers. B)At least one of them is even. C)At least one of them is odd. D)They are both odd. E)Nothing can be said surly on V and B SOLUTION:Odd x Odd = Odd Odd x Even = Even Even x Even = Even To fulfill condition Either (V+1) or (B+1) needs to be Even So either V or B needs to be odd Or At least one of them is odd. At least one of them is odd=C #### C QUESTION:What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest? options: A)Rs. 560 B)Rs. 560.75 C)Rs. 551.25 D)Rs. 550 E)Rs. 560 SOLUTION:Explanation: Present worth of Rs. x due T years hence is given by Present Worth (PW) = x/(1+R/100)T Let x be the annual payment Then, present worth of x due 1 year hence + present worth of x due 2 year hence = 1025 x(1 + 5/100)1 + x(1 + 5/100)2 = 1025 x/(21/20) + x/(21/20)2 = 1025 20x/21 + 400x/441 = 1025 820x/441 = 1025 x = (1025 × 441)/820 = (205 × 441)/164 = Rs. 551.25 Answer: Option C #### C QUESTION:A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)22 B)20 C)88 D)71 E)10 SOLUTION:x ------- 12 (x + 10) ---- 6 x * 12 = (x + 10)6 x = 10 \Answer: E #### E QUESTION:If you roll one fair six-sided die, what is the probability that the number is even or less than 4? options: A)1/6 B)1/3 C)2/ 3 D)3/4 E)5/6 SOLUTION:Total favourable outcomes: 1,2,3 (less than 4), 4,6(even) = 5 Total possible outcome= 6 Probability=5/6. Answer: Option E #### E QUESTION:A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture? options: A)14 liters B)76 liters C)10 liters D)11 liters E)12 liters SOLUTION:Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters. P liters of water added to the mixture to make water 25% of the new mixture. Total amount of water becomes (30 + P) and total volume of mixture is (150 + P). (30 + P) = 25/100 * (150 + P) 120 + 4P = 150 + P => P =10 liters. Answer: C #### C QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5 B)6 C)7 D)1 E)2 SOLUTION:160 = (180*4*R)/100 R = 5% Answer: A #### A QUESTION:A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger? options: A)46 B)36 C)18 D)22 E)23 SOLUTION:Explanation: Distance to be covered = 240+ 120 = 360 m Relative speed = 36 km/hr = 36×10/36 = 10 m/s Time = distance/speed = 360/10 = 36 seconds Answer: Option B #### B QUESTION:One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish. options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Fast's 1 hr work = 1/2 slow's 1 hr work = 1/3 1/2 + 1/3 = 5/6 they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins ANSWER:C #### C QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 10P pots? options: A)M/10 B)6/M C)600M D)M/6 E)10M SOLUTION:The time it takes to wash 10P pots is 10M minutes which is 10M / 60 = M/6 hours. The answer is D. #### D QUESTION:30 carrots on a scale weigh 5.94 kg. When 3 carrots are removed from the scale, the average weight of the 27 carrots is 200 grams. What is the average weight (in grams) of the 3 carrots which were removed? options: A)165 B)170 C)175 D)180 E)185 SOLUTION:27*200=5400. The other 3 carrots weigh a total of 540 grams. The average weight is 540/3 = 180 grams. The answer is D. #### D QUESTION:What distance will be covered by a bus moving at 72 kmph in 30 seconds? options: A)287 B)600 C)289 D)276 E)207 SOLUTION:72 kmph = 72 * 5/18 = 20 mps D = Speed * time = 20 * 30 = 600 m. Answer:B #### B QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)68 km/hr. B)32 km/hr. C)34 km/hr. D)35 km/hr. E)72 km/hr. SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240 )/12 2x = 40 x = 20. Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr. answer :E #### E QUESTION:What is the remainder when 1274 * 1275 * 1277 *1285 is divided by 12? options: A) 0 B) 6 C) 11 D) 9 E) 7 SOLUTION:1271*1275*1277*1285 = (1272 - 2)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1) Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-2)(3)(-7)(1) = 42. Thus the question becomes: what is the remainder upon division of 42 by 12? The answer to this question is 6. Answer: B #### B QUESTION:A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The rate on interest per annum is. options: A)4% B)5% C)6% D)7% E)10% SOLUTION:Explanation: S.I. on Rs 800 for 1 year = 80 Rate = (100*80)/(800*1) = 10% Answer: E #### E QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:A, B and C started a business with a total investment of Rs. 72000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find C's share. options: A)Rs. 3240 B)Rs. 2520 C)Rs. 2880 D)Rs. 3360 E)None of these SOLUTION:Explanation: Let C's investment = Rs. x B's investment = Rs. (x - 3000) A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000) Now, (A + B + C)'s investment = Rs. 72000 => x + (x - 3000) + (x + 3000) = 72000 => 3x = 72000 => x = 24000 Hence, A's investment = Rs. 27000 B's investment = Rs. 21000 C's investment = Rs. 24000 Ratio of the capitals of A, B and C = 27000 : 21000 : 24000 = 9 : 7 : 8 A's share = Rs. [(8/24) × 8640] = Rs. 2880 Answer: Option C #### C QUESTION:Two trains each 170m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 55km/h while the other travels at 50km/h. how long will it take for them to pass each other completely. options: A)15 sec B)11.6 sec C)31.6 sec D)12.6 sec E)23 sec SOLUTION:Explanation: D = 170 m + 170 m = 340 m RS = 55 + 50 = 105 * 5/18 = 146/5 T = 340 * 5/146 = 11.6 sec Answer: Option B #### B QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced? options: A)70% B)15% C)20% D)25% E)30% SOLUTION:price of a coat in a certain store = $500 the price of the coat is to be reduced by $350 % change = (Final Value - Initial Value)*100 / Initial Value % Reduction= (Reduction in Price)*100 / Initial Value i.e. % Reduction= (350)*100 / 500 = 70% Answer: Option A #### A QUESTION:In the quadrilateral PQRS d=10 cm, h1=4.6 cm and h2=2.3 cm. Find the area options: A)21 B)22 C)23 D)34.5 E)25 SOLUTION:area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona) so 1/2*10*(4.6+2.3)=34.5 ANSWER:D #### D QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work? options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work .. Therefore, Y will do the remaining 1/10 th work alone.. As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job... ans 10 E #### E QUESTION:A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay? options: A)270 B)360 C)276 D)271 E)272 SOLUTION:12*8 :16*9 = 18*6 8: 12: 9 12/29 * 870 = 360 Answer: B #### B QUESTION:In how many W ways can 5 people from a group of 6 people be seated around a circular table options: A)56 B)80 C)100 D)120 E)144 SOLUTION:W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner) = 6 * 4! = 6 * 24 = 144 Answer - E #### E QUESTION:A starts a business with a capital of Rs. 9,000. B joins in the business with Rs.18,000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? options: A)2 months B)6 months C)7 months D)8 months E)None of these SOLUTION:Explanation : Let B joins for x months. Then A:B = 9000*12 : x* 18000 = 3 : 1 => 9*12 : 18x= 3 : 1 => 9*12/ 18x = 3/1 = 3 => 9*4 /18x = 1 => 2/x = 1 => x = 2. Answer : Option A #### A QUESTION:A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute? options: A)1,200 meters / minute B)1,300 meters / minute C)1,450 meters / minute D)1,550 meters / minute E)1,650 meters / minute SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 72 kilometers per hour = 72 km/hr = (72 * 1000 meters) / (60 minutes) = 1,200 meters / minute correct answer A #### A QUESTION:A sum of money is sufficient to pay B's wages for 12 days and C's wages for 24 days. The same money is sufficient to pay the wages of both for? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Let the total money be $x B's 1day work = $ x/12 C's 1day work = $ x/24 A+B 1day work = $ x/8 Money is sufficient to pay the wages of both for 8days Answer is C #### C QUESTION:We are given the positive numbers a,b,c, which form an arithmetic progresion in the given order. We know that a+b+c=9. The numbers a+1,b+1,c+3 form a geometric progression in the given order. Find c. options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Solution: Since a,b,c form an arithmetic progression, c=b+d=a+2d and a+b+c=a+a+d+a+2d=3a+3d=9, so a+d=b=3 and a+c=6=>c=6−a. Since a+1,b+1,c+3 form a geometric progression, we have (b+1)2=(a+1)(c+3), or 16=(a+1)(6−a+3)=(a+1)(9−a) 16=9a+9−a2−a a2−8a+7=0, therefore a=7 or a=1. But if a=7, c=6−a=6−7=−1<0 and by definition c is positive, so a=7 is not a solution. Therefore a=1 and c=6−a=6−1=5. Answer A #### A QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5. options: A)140 B)142 C)146 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:If Susan can paint a house in 4 hours, and Jeff can paint the same house in 6 hours, how long will it take for both of them to paint the house together? options: A)2.4 hr B)2.6 hr C)3.0 hr D)5.0 hr E)5.2 hr SOLUTION:If Susan can paint the house in 4 hours, then in 1 hour she can paint 1/4 of the house. If Jeff can paint the house in 6 hours, then in 1 hour he can paint 1/6 of the house. Let x = number of hours it would take them together to paint the house so, 1/4 + 1/6 = 1/x x=12/5 or 2.4 hours Answer: A #### A QUESTION:The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot? options: A)1 B)17 C)88 D)12 E)15 SOLUTION:Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer: B #### B QUESTION:A numberais squared and then multiplied by negative 3. The result of this operation Q is equal to three times the sum of three timesaand two. What is one possible value ofa? options: A)-3 B)-2 C)1 D)2 E)3 SOLUTION:Q=-3*a^2=3(3a+2) a= -2 or -1 a=-2=B #### B QUESTION:The average age of a husband, wife and their child 12 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is? options: A)19.01 years B)5.25 years C)16 years D)15 years E)4.75 years SOLUTION:Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years. Required average = 57/12 = 4.75 years. Answer:E #### E QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 4 cm, and the point of contact is 6 cm above the ground, what is the radius of the other ball? options: A)10 cm B)12 cm C)14 cm D)16 cm E)18 cm SOLUTION:similar triangle properties.. 2/r+4 = 4/r-4 giving r = 14. Answer: C #### C QUESTION:I came across this problem in the GMATprep software and got it totally wrong! A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there? options: A)12 B)44 C)56 D)120 E)200 SOLUTION:6C3*4C2 =120=D #### D QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 * (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 650 = 13 Answer: E #### E QUESTION:A man can row upstream at 10kmph and downstream at 24 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)7 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(24 -10) kmph = 7 kmph. Answer C #### C QUESTION:40, 45, 50, 55, 60, 70, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.3, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 55, 60, 70, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.3 = 47.2. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat? options: A)5! B)8! C)9! D)12! E)11! SOLUTION:Ans.(B) Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways #### B QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:let no. of right ques be x, then no. of wrong ques will be= 26 - x now, according to ques 8x - (26-x)5 = 0, hence x=10...no. of right ques is 10 ANSWER:B #### B QUESTION:How many digits are in (8×10^10)(10×10^5)? options: A)17 B)25 C)26 D)27 E)28 SOLUTION:The question simplfies to (8×10^10)(10^6) => 8*10^16 => Will contain 16 zeros +1 digit 8 =>17 Ans A #### A QUESTION:P is three times as old as Q. In 10 years, P will be twice as old as Q. How old was P three years ago? options: A)27 B)30 C)33 D)36 E)39 SOLUTION:P = 3Q so Q = P/3 P+10 = 2(Q+10) = 2(P/3+10) P/3 = 10 P = 30 Three years ago, P was 27. The answer is A. #### A QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio E of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture. Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water. Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1. Shortcut. We are essentially replacing water in the mixture with pure milk. Let W_o be the amount of water in the mixture originally = 8 litres. Let W_r be the amount of water in the mixture after the replacements have taken place. Then,{W_r}/{W_o}= (1-R/M)^n where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated. Hence, {W_r}/{W_o} =(1/2)^2  =1/4 Therefore E,W_r ={W_o}/4= 8/4 = 2 litres.B #### B QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.2 feet C)3.3 feet D)3.0 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+2=36 36/12=3.0 feet ANSWER:D #### D QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)3 B)5 C)8 D)13 E)15 SOLUTION:Total # of students = 40 Avg # of books per student = 2 Total # of books = 40*2 = 80 # of student borrowed at least 3 books = 40-2-12-10 = 16 # of books borrowed by above 16 students = 80-(12*1)-(10*2) = 48 Considering that 15 out of above 16 students borrowed only 3 books, # of books borrowed = 15*3 = 45 So maximum # of books borrowed by any single student = 48-45 = 3 option A #### A QUESTION:The product of two numbers a and b equals one-quarter their average. What is a in terms of b? options: A)a= b/(8b-1) B)a= b/(7b-1) C)a= b/(8b) D)a= b/(8b-4) E)a= 2b/(8b-1) SOLUTION:a*b = ( a+b)/8 8ab =a+b a= b/(8b-1) ANSWER:A #### A QUESTION:Robert ate 7 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel? options: A)A)4 B)B)7 C)C)9 D)D)5 E)E)2 SOLUTION:7-5=2. Answer is E #### E QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? options: A)315min B)325min C)335min D)345min E)None of these SOLUTION:Explanation: Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = (19+16)=(518) So both punctures will make the type flat in (185)mins=335mins Answer: C #### C QUESTION:154 pencils are distributed to children with the same number. What can’t be the range including the number of children? options: A)50~60 B)10~20 C)20~30 D)1~10 E)70~80 SOLUTION:154 candies are distributed to children with the same number. What can’t be the range including the number of children? A. 1~10 B. 10~20 C. 20~30 D. 40~50 E. 70~80 -> In 154=1*154=2*77=7*22=11*14, you can come up with 4 cases. One is distributing 77 candies to 2 children each. Another is distributing 2 candies to 77 children each. Also, you can distribute 22 candies to 7 children. The other is distributing 7 candies to 22 children. Amongst these cases, what is not included is a. 50~60. Therefore, the answer is A. #### A QUESTION:A person starting with Rs.64 and making 6 bets, wins 3times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is? options: A)Rs.37 B)Rs.45 C)Rs.47 D)Rs.53 E)Rs.59 SOLUTION:As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order). The overall resultant will remain same. So final amount with the person will be (in all cases): =64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727 Hence the final result is: 64−27=3764−27=37: A loss of Rs.37 A #### A QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)? options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5 SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57) 4.5/(4.5 - 2) = 9/5 (1.8) 3.5/(3.5 - 2) = 7/3 (~2.33) 2.5/(2.5-2) = 5 1.5/(1.5 - 2) = -3 Thus, the answer is D. #### D QUESTION:If 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days? options: A)127 B)237 C)360 D)450 E)281 SOLUTION:Explanation: Let the required no of hectares be x. Then Men --- Hectares---Days 10---------80---------24 36---------x---------30 More men, More hectares (Direct proportion) More days, More hectares (Direct proportion) x=36/10*30/24*80 x= 360 Answer: C #### C QUESTION:In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ? options: A)45 B)48 C)52 D)58 E)None SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 Correct Option: B #### B QUESTION:How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)52 sec B)50 sec C)51 sec D)55 sec E)58 sec SOLUTION:B 50 sec The distance to be covered = Sum of their lengths = 200 + 300 = 500 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 500/10 = 50 sec. #### B QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ? options: A)6 B)4 C)2 D)5 E)1 SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B #### B QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:Can you find next number in tricky mathematical series below? 111 , 113 , 117 , 119 , 123 , 137 ? options: A)151 B)161 C)171 D)131 E)121 SOLUTION:Solution: 151 (131+20) Explanation: 1st 7 prime numbers post 100 are 101 , 103 , 107 , 109 , 113 , 127 , 131 ...Adding 20 to numbers 121 , 123 , 127 , 129 , 133 , 147 , 151 Answer A #### A QUESTION:The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ? options: A) 10^9 B) 10^8 C) 10^2 D) 10^6 E) 10^5 SOLUTION:P = 2*3*5*7 ~ 10^ 2 Answer : C #### C QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:Which of the following is a pair of co–primes? options: A)(16, 62) B)(18, 25) C)(21, 35) D)(23, 92) E)none SOLUTION:Solution H.C.F. of 18 and 25 is 1. So, they are co-primes. Answer B #### B QUESTION:Which of the following is satisfied with |x-4|+|x-3|<6? options: A)1<x<5 B)2<x<5 C)0.5<x<6.5 D)0.5<x<4 E)3<x<4 SOLUTION:--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5 Therefore, the answer is C. #### C QUESTION:Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving. options: A)180% B)124% C)160% D)154% E)140% SOLUTION:Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24% correct answer - B #### B QUESTION:Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are options: A)11, 42 B)12, 24 C)15, 42 D)16, 19 E)33, 44 SOLUTION:A 11, 42 Let the age of Priya = x years Then, the age of her father = (x+ 31) years ATQ, (x+ 8) + (x+ 31 + 8) = 69 2x+ 47 = 69 2x= 69 – 47 = 22 x= 11 The age of Priya = 11 years The age of her father = 11 + 31 = 42 years #### A QUESTION:A certain list of 100 data has an average (arithmetic mean) of 8 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 106 data with standard deviation less than d? options: A)-8 and 0 B)0 and 0 C)0 and 8 D)0 and 16 E)8 and 8 SOLUTION:Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 8 and 8 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. Answer: E. #### E QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? options: A)15% B)25% C)35% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(300) / 1000 = 15% The answer is A. #### A QUESTION:How many of the positive factors of 19 are not factors of 29? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 19 - 1, 19 factors of 29- 1, 29 Comparing both, we have three factors of 19 which are not factors of 29- 19, The answer is B #### B QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? options: A)120cc B)360cc C)450cc D)589C E)478cc SOLUTION:Explanation: r1 = x r2 = 3x Π * x2 * h = 40 Π9 x2h = 40 * 9 = 360cc Answer: B #### B QUESTION:A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.? options: A)30 min B)35 min C)45 min D)50 min E)55 min SOLUTION:there are 9 hours in between 9 a.m. to 6 p.m. 9*5=45 minutes. ANSWER:C #### C QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:David obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? options: A)75 B)27.6 C)66.6 D)16.5 E)11 SOLUTION:Explanation: Average = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6. Answer:C #### C QUESTION:A man rows his boat 90 km downstream and 70 km upstream, taking 3 hours each time. Find the speed of the stream? options: A)76 kmph B)6 kmph C)3.5 kmph D)4.5 kmph E)4 kmph SOLUTION:Speed downstream = d/t = 90/(3) = 30 kmph Speed upstream = d/t = 70/(3) = 23 kmph The speed of the stream = (30 - 23)/2 = 3.5 kmph Answer:C #### C QUESTION:What is the 9th term in this sequence? 2,4,6,13,22,35,60 options: A)138 B)148 C)158 D)168 E)178 SOLUTION:2+4 =6 +0 =6 6+4 =10+3 =13 13+6 =19+3 =22 22+13=35+0 =35 35+22=57+3 =60 60+35=95+3 =98 98+60=158+0=158 so 9th term is 158 ANSWER:C #### C QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:14 times a number gives 210. The number is options: A)11 B)12 C)15 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 14×N=210⇒N=15 Correct Option: C #### C QUESTION:Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age. options: A)60 years B)80 years C)70 years D)76 years E)86 years SOLUTION:Let Kumar’s present age be x years and Sailesh’s present age be y years. Then, according to the first condition, x - 10 = 3(y - 10) or, x - 3y = - 20 ..(1) Now. Kumar’s age after 10 years = (x + 10) years Sailesh’s age after 10 years = (y + 10) (x + 10) = 2 (y + 10) or, x - 2y = 10 ..(2) Solving (1) and (2), we get x = 70 and y = 30 Kumar’s age = 70 years and Sailesh’s age = 30 years. ANSWER:C #### C QUESTION:2. The value of x + x(xx) when x = 2 is: options: A)5 B)10 C)8 D)15 E)20 SOLUTION:x + x(xx) Put the value of x = 2 in the above expression we get, 2 + 2(22) = 2 + 2(2 × 2) = 2 + 2(4) = 2 + 8 = 10 Answer : B #### B QUESTION:An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? options: A)$480 B)$489.60 C)$634.64 D)$800.32 E)$240 SOLUTION:1.04*1.04*6000 = $6489.60 The answer is B. #### B QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)9 C)4 D)1 E)3 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:There are 2 positive integers x and y. What is the probability that x+y is odd? options: A)1/4 B)1/2 C)1/3 D)1/5 E)1/9 SOLUTION:Explanation : The addition of two integer results in an odd number only if any one of the integers is an odd number. The probability of an odd among the two integer is 1/2. Hence, the required probability is 1/2. Answer : B #### B QUESTION:A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 37 years and that of the grandchildren is 6 years. What is the average age of the family? options: A)28 4⁄7 years B)31 5⁄7 years C)32 2⁄7 years D)27 1⁄2 years E)None of these SOLUTION:Required average = (67×2+37×2+6×3/2+2+3) =226/7 = 32 2⁄7 years Answer C #### C QUESTION:The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ? options: A)35 years B)45 years C)51 years D)52 years E)None of these SOLUTION:Explanation: Age of the teacher = (38 * 15 - 37 * 14) years = 52 years. Answer: D #### D QUESTION:What is x if x + 5y = 24 and y = 2? options: A)1 B)3 C)5 D)7 E)14 SOLUTION:Substitute y by 2 in x + 5y = 24 x + 5(2) = 24 x + 10 = 24 If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence x = 14 correct answer E #### E QUESTION:A and B start a business with Rs.6000 and Rs.18000 respectively. Hoe should they share their profits at the end of one year? options: A)3:5 B)3:4 C)3:1 D)1:3 E)3:9 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by A and B = 6000 : 18000 => 1:3 Answer:D #### D QUESTION:A train is running with a speed of 60 kmph and its length is 110 metres. Calculate the time by which it will pass a man running opposite with speed of 6 kmph options: A)2 second B)4 second C)6 second D)8 second E)10 second SOLUTION:Explanation: From the given question, we will first calculate the speed of train relative to man, => ( 60 + 6 ) = 66 km/hr ( we added 6 because man is running opposite ) Convert it in metre/second =66×5/18 =55/3m/sec Time it will take to pass man =110×3/55 =6 seconds ANSWER IS C #### C QUESTION:A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball? options: A)5/7 B)9/14 C)13/21 D)17/28 E)23/35 SOLUTION:P(no red balls) = 6/8*5/7*4/6 = 5/14 P(at least one red ball) = 1 - 5/14 = 9/14 The answer is B. #### B QUESTION:835, 734, 642, 751, 853, 981, 532 options: A)751 B)853 C)981 D)532 E)None of these SOLUTION:Solution In each number except 751,the difference of third and first digit is the middle one. Answer A #### A QUESTION:The ratio of two quantities is 1 to 2. If each of the quantities is increased by 15, what is the ratio of these 2 new quantities? options: A)5:6 B)25:27 C)15:16 D)20:21 E)It cannot be determined from the information given SOLUTION:The ratio cannot be straight way added any quantity... 1:2means 1X:2X... So when you add a quantity, it becomes 1x + 15 : 2x +15.. So value of x is must.. Ans E #### E QUESTION:Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y? options: A)15.5 sec B)8.4 sec C)33.6 sec D)31.11 sec E)16.8 sec SOLUTION:Z--------------------------------------|----------------------------Y Car A(20mps)------------------------->P<---------------Car B(15mps) Let 2 cars meet each other at point P in t seconds. Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t. From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further. so, 15t/20 = 10 So t=40/3 sec and total distance = (35*40)/3 Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx. Answer D #### D QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased? options: A) 100% B) 500% C) 300% D) 600% E) 800% SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%. Answer: B. #### B QUESTION:A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)7 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph Answer:D #### D QUESTION:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ? options: A)3x+32 B)5x-1 C)(7x+15)/2 D)(9x-4)/2 E)6x+2 SOLUTION:We can take X+1 = 9 X= 8 So 4c envelopes will be 6 and 5c envelopes will be 3 So total cost will be 39 Then that is our target Plug x =8 in answer choices Only B works Correct Answer : B #### B QUESTION:If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:If A = B/C, -1 < C < 0 and 4 < B, which of the following is correct? options: A)A > 4. B)0 < A <4. C)-4 < A < 0. D)A < -4. E)A < -20. SOLUTION:B is +veC is -ve Eliminate AB For min. value max. numerator and minimize dinominator take B=4.1A=-0.9 A=4.1/-0.9 A<-4 Ans D #### D QUESTION:What approximate value should come in place of the question mark (?) in the following equation? 1.542 × 2408.69 + 5134.632 = ? options: A)4600 B)4800 C)5200 D)6400 E)8800 SOLUTION:Explanation 3700 + 5100 = 8800 Answer E #### E QUESTION:0.05 x 0.40=? options: A)3.15e-05 B)0.000315 C)0.315 D)0.02 E)0.002 SOLUTION:5 x 40 = 200 Sum of decimal places =4 Therefore, 0.05x 0.44 = 0.0200 Answer is D. #### D QUESTION:Find the odd man out 4, 15, 40, 121, 364, 1093, 3280 options: A)4 B)15 C)121 D)364 E)3280 SOLUTION:1*3+1 = 4 4*3+1 = 13 13*3+1 = 40 40*3+1 = 121 121*3+1 = 364 364*3+1 = 1093 1093*3+1= 3280 ANSWER:B #### B QUESTION:In what time a debt of Rs.7920 due may be cleared by immediate cash down payment of Rs.3600 at 1/2% per month options: A)10years B)20years C)30years D)40years E)50years SOLUTION:Explanation: PW=100x Amount/100+(RxT) Answer: B #### B QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price? options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3% SOLUTION:Let the price of the article be Rs. 100. 20% of 100 = 20. New price = 100 + 20 = Rs. 120 Required percentage = (120 - 100)/120 * 100 = 20/120 * 100 = 50/3 = 16 2/3%. Answer:A #### A QUESTION:The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation? options: A)1 B)5 C)7 D)8 E)11 SOLUTION:Let me define terms: in g(p) = R p is argument, R is result, g() is function, in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1:1 Even g2: 1*(Even,Odd ) =1 Even 1 Odd g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8 Ans D it is! #### D QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer: A #### A QUESTION:Find the value of 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] options: A)800 B)3200 C)900 D)1600 E)None SOLUTION:Answer 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] = 4 x [(36 x 48 x 250) / (12 x 9 x 5)] = 4 x 4 x 4 x 50 = 3200 Correct Option: B #### B QUESTION:The population of a bacteria colony doubles every day. If it was started 11 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? options: A)512 B)768 C)1024 D)2048 E)4096 SOLUTION:2^11(2) = 2^12 = 4096 The answer is E. #### E QUESTION:In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County? options: A)200 B)210 C)216 D)224 E)235 SOLUTION:The number must be a multiple of both 8 and 7 so the answer is 224. The answer is D. #### D QUESTION:A firm has 3 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.) options: A)42 B)46 C)50 D)54 E)58 SOLUTION:The number of ways to form a group of 3 is 8C3 = 56 The number of groups with no senior partner is 5C3 = 10 The number of groups with at least one senior partner is 56-10 = 46 The answer is B. #### B QUESTION:There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is options: A)10 B)15 C)16 D)13 E)18 SOLUTION:Explanation: abcbcd=3851001=>ad=513 abcbcd=3851001=>ad=513 So d = 13 D #### D QUESTION:Three partners A, B, C in a business invested money such that 3(A’s capital) = 6(B’s capital) = 9(C’s capital) then, The ratio of their capitals is options: A)63 : 45 : 34 B)6 : 3 : 2 C)36 : 54 : 28 D)63 : 45 : 35 E)None of these SOLUTION:Explanation: Let3(A’s capital) = 6(B’s capital) = 9(C’s capital) = Rs.x Then, A’s capital = Rs x/3, B’s capital = Rs. x/6 and C’s capital = Rs. x/9. A : B : C = x/3 : x/6 : x/9 6 : 3 : 2 Answer: Option B #### B QUESTION:If Shreehari walks in the speed of 4.5 km/hr from his house, in what time will he reach his school which is 750 m long from his house? options: A)5 B)30 C)10 D)12 E)15 SOLUTION:Speed = 4.5 * 5/18 = 1.25 m/sec Time taken = 750/1.25 = 600 sec ie. 10 mins. Answer:C #### C QUESTION:If Albert’s monthly earnings rise by 20%, he would earn $560. If, instead, his earnings rise by only 21%, how much (in $) would he earn this month? options: A)643 B)652 C)660 D)564 E)693 SOLUTION:=560/1.2∗1.21 =564=564 Answer is D #### D QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years? options: A)587 × 108 miles B)587 × 10-12 miles C)587 × 1010 miles D)587 × 10-10 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 × 1012 miles. Answer is B. #### B QUESTION:A division of a company consists of six men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/11 D)5/12 E)7/15 SOLUTION:Total number of ways to select 2 members = 11C2 = 55 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/55 = 2/11 The answer is C. #### C QUESTION:A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system correct answer D #### D QUESTION:If a function f is defined by f(x)= (1-x)/x for all non zero numbers x. If f(a) = 1 and f(a/b) = 3 then b= ? options: A)3 B)1/3 C)2 D)1/2 E)-2 SOLUTION:Given that f(x)= (1-x)/x and f(a) = 1, then f(a) =(1-a)/a=1 ===> a=1/2, then backsolve using the answer choices: f(a/b) = f(1/2b) = 3 A) 3 ===> f(1/2*3) = f(1/6) = 5 B) 1/3 ===> f((1/2)/(1/3)) = f(3/2) = (-1/2)/(3/2) = -1/3 C) 2 ===> f(1/2*2) = f(1/4) =3 WINS D) 1/2 ===> f((1/2)/(1/2)) = f(1) = 0 E) -2 ===> f((1/2)/-2) = f(-1/4) = (5/4)/(-1/4) = -5 Answer: C #### C QUESTION:The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A? options: A)1000 B)1500 C)2000 D)3000 E)4000 SOLUTION:Let monthly income of A = a monthly income of B = b monthly income of C = c a + b = 2 × 5050 .... (Equation 1) b + c = 2 × 6250 .... (Equation 2) a + c = 2 × 5200 .... (Equation 3) (Equation 1) + (Equation 3) - (Equation 2) => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250) => 2a = 2(5050 + 5200 - 6250) => a = 4000 i.e., Monthly income of A = 4000 Answer is E. #### E QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)2 cm B)7 cm C)1 cm D)4 cm E)9 cm SOLUTION:Explanation: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer: Option E #### E QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days? options: A)47.6 kg B)52.6 kg C)59.6 kg D)56.6 kg E)57.6 kg SOLUTION:(3 * 5)/48 = (9 * 2)/ x x = 57.6 kg ANSWER:E #### E QUESTION:If a and b are positive integers of C such that a/b=2.86, which of the following must be a divisor of a? options: A)10 B)B.13 C)18 D)26 E)50 SOLUTION:The prompt gives us a couple of facts to work with: 1) A and B are positive INTEGERS 2) A/B = 2.86 We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in). The simplest place to start is with... A = 286 B = 100 286/100 = 2.86 These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)... A = 143 B = 50 143/50 = 2.86 There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A.... Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices. Final Answer: B #### B QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? options: A)10000 B)12000 C)13000 D)10860 E)14400 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7800 × 118/100 × 118/100 = 10860 D #### D <<<Examples ends QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)12 B)72 C)48 D)99 E)11 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.75 + 1.25 = 3 km = 3000 m. Required time = 3000 * 3/125 = 72 sec. Answer: B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The length of the longest tape in cm which can be used to measure exactly, the length 100cm; 2m25cm; and 7m80cm is: options: A)30 B)5 C)10 D)36 E)25 SOLUTION:The three lengths in cm are 100, 225 &780. HCF of 100, 225 &780 is 5. Hence, the answer is 5 cm. ANSWER:B #### B QUESTION:How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336 options: A)3 B)4 C)5 D)6 E)7 SOLUTION:B 4 By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4. #### B QUESTION:A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident? options: A)35 B)30 C)25 D)20 E)None of these SOLUTION:Let the truth spoken by A and B be pl and p2 respectively, i.e., pl = 3⁄4 and p2 = 4⁄5 They will contradict each other only when one speaks truth and the other is lying. i.e., 3⁄4 × 1⁄5 + 4⁄5 × 1⁄4 = 3⁄20 + 4⁄20 = 7⁄20 = 35⁄100 i.e, 35% Answer A #### A QUESTION:What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x options: A)35678 B)73205 C)75653 D)86554 E)87565 SOLUTION:(B) 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205 #### B QUESTION:(1+0.0001)/(0.04+10000) The value of the expression above is closet to which of the following? options: A)0.0001 B)0.001 C)0.1 D)1 E)10 SOLUTION:Notice that we need approximate value of the fraction. Now, the nominator is very close to 1 and the denominator is very close to 10, hence the value of the fraction is very close to 1/10000=0.0001. Answer: A #### A QUESTION:Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)0.125% D)0.2083% E)none SOLUTION:This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/60) = 20.833% and the answer is not there in the options. The correct answer is (E). #### E QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M? options: A)278 B)2890 C)270 D)2702 E)1050 SOLUTION:504/M = 384/800 (504 * 800) / 384 = M M = 1050 Answer:E #### E QUESTION:Three houses of the same type were advertised to be let in a locality. four men made separate applications for a house. What is the probability that each of them applied for the same house. options: A)1/4 B)1/6 C)1/8 D)1/9 E)3/256 SOLUTION:Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 3 houses 1/3 Let us consider case where all 4 men choose House no 1 So for First men it will be 1/4,second men 1/4 , third men also 1/4 and fourth man 1/4 So probability of selecting house no 1 is 1/4*1/4*1/4*1/4= 1/256 And since there are 3 such house so probability that each men select the same house is 3*1/256 Ans is E #### E QUESTION:A company has 2 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director? options: A)500 B)720 C)4500 D)20 E)55 SOLUTION:atleast one means exactly one and more than one. different committees with 5 people can be chosen having at least 1 director is (2c1*5c4) + (2c2*5c3) = 20; Hence D. #### D QUESTION:When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ? options: A)339 B)349 C)369 D)359 E)Data inadequate SOLUTION:Explanation: x = 13p + 11 and x = 17q + 9 13p + 11 = 17q + 9 17q - 13p = 2 q = 2 + 13p 17 The least value of p for which q = 2 + 13p is a whole number is p = 26 17 x = (13 x 26 + 11) = (338 + 11) = 349 Answer: B #### B QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%? options: A)20% B)28% C)29% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 86 2/3 SP1 = 86 SP1 = 129 100 --- 29 => 29% Answer:C #### C QUESTION:If points A and B are (6-1) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. #### A QUESTION:A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B? options: A)7 B)14 C)21 D)28 E)35 SOLUTION:In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice. With 36 liters of milk, we need a total of 48 liters of juice to make drink B. We need to add 21 liters of juice. The answer is C. #### C QUESTION:If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina Works independently at the job for 8 hours and then Ann works independently, how many hours will it take Ann to complete the remainder of the jobs? options: A)2/3 B)3/4 C)1 D)2 E)3 SOLUTION:Work done by Tina in 1 hr=1/12 Work done by Tina in 8 hr=1/12*8 which is 2/3 Now,the remaining work is 1/3 which is completed by Ann in 1/3*9 which is 3hr ANSWER:E #### E QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr options: A)25 Seconds B)28 Seconds C)30 Seconds D)35 Seconds E)40 Seconds SOLUTION:Explanation: Relative Speed = 63-3 = 60 Km/hr = 60 *(5/18) = 50/3 m/sec Time taken to pass the man will be 500∗3/50=30seconds ANSWER IS C #### C QUESTION:Find the average of first 4 multiples of 11? options: A)10 B)12.6 C)27.5 D)31.3 E)40.8 SOLUTION:average = (11+22+33+44)/4 = 27.5 Answer is C #### C QUESTION:The rate of Interest on a sum of money is 11% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is options: A)1,000 B)2,000 C)2,100 D)2,250 E)2,540 SOLUTION:Explanation: I1 = (P x 3 x 11)/100 = P/3 I2 = (P x 4 x 4)/100 = 4P/25 I3 = (P x 1 x 5)/100 = P/20 P/3 + 4P/25 + P/20 = 540 27P/50 = 540 P = 1000 Answer: Option A #### A QUESTION:A certain roller coaster ride has fewer than 110 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If riders are let on only in groups of 6 all riders will be able to get on the roller coaster. Which of the following could be the number of people in the line? options: A)7 B)22 C)52 D)67 E)72 SOLUTION:Total number of riders = 5p + 2 or 6q. The first number that fits in is 12. Numbers following will be 12 + multiple of 30 ( LCM of 5 and 6). Therefore, the total number of riders will be 30k+12. 12, 42, 72, 102 are the only possibilities as the number of riders is fewer than 110. Among the given options 72 is the answer. ANSWER:E #### E QUESTION:If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses? options: A)1/8 B)1/3 C)1/4 D)1/2 E)1 SOLUTION:P(THH) = 1/2*1/2*1/2=1/8 The answer is A. #### A QUESTION:A man is 30 years older than his son. In four years, his age will be twice the age of his son. The present age of this son is options: A)22 years B)23 years C)24 years D)25 years E)26 years SOLUTION:Explanation: Let's Son age is x, then Father age is x+30. => 2(x+4) = (x+30+4) => 2x+8 = x+34 => x = 26 years Answer: Option E #### E QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B QUESTION:Three sets of 80, 50 and 90 students appeared for an examination and the pass percentage was 75, 90 and 100 respectively. the pass percentage of the whole set is options: A)87.63% B)88.53% C)88.93% D)88.63% E)89.63% SOLUTION:Explanation: total passed student =60+45+90=195 195 is 88.63% of 220 ANSWER:D #### D QUESTION:The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red options: A)2.54% B)4.56% C)6.125% D)7.134% E)8.341% SOLUTION:Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125% C #### C QUESTION:If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$60.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10 Total spent 50.50 + 10.10 = $60.60 correct answer B #### B QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? options: A)315min B)325min C)335min D)345min E)None of these SOLUTION:Explanation: Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = (19+16)=(518) So both punctures will make the type flat in (185)mins=335mins Answer: C #### C QUESTION:On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum. options: A)33498 B)17000 C)2665 D)28876 E)313 SOLUTION:The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a. So P = (100 * 10200)/ (30 * 2) = Rs.17000 Answer:B #### B QUESTION:In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days. options: A)11 B)12 C)13 D)15 E)16 SOLUTION:Work done by Kamal in 1 day = 1/20 Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16 => Suresh can complete the work in 16 days Answer is E. #### E QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 2 rows or 7 rows or 9 rows, then no tree will be left. Find the least number of trees required options: A)22 B)60 C)126 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(2, 7, 9) = 126 Answer: C #### C QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7740 km and comes back to the starting point. The total time taken by him is: options: A)914.2 hours B)900 hours C)915 hours D)982.9 hours E)915 hours SOLUTION:Explanation: Speed downstream = (16 + 2) = 18 kmph Speed upstream = (16 - 2) = 14 kmph Total time taken = 7740/18 + 7740/14 = 430 + 552.9 = 982.9 hours Answer: Option D #### D QUESTION:A,B and C started a business by investing Rs.800/- , Rs.1,000/- and Rs.1,200/- respectively for two years. Total profit is Rs.1000/-. Find the C's share? options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 800 E)Rs. 900 SOLUTION:Solution: A : B : C = (800 * 2) : (1,000 * 2) : (12,000 * 2) = 4 : 5 : 6. So C's share = Rs. (1000 * 6/15) = Rs. 400. Answer: Option C #### C QUESTION:A and B are two partially filled buckets of water. If 7 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 7 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)77/5 B)13 C)17 D)21 E)23 SOLUTION:Let Bucket A be A and Bucket B be B Scenario 1 A-7 = 1/3 (B+7) ----> 3A-21 =B+7 Scenario 2 B-7 = 1/2 (A+7) -----> 2B-14 = A+7 From Scenario 1, B = 3A-28 Substitute B with this information in Stmt 2 2 (3A-28) -14 = A+7 ------> 6A -56-14 = A+7 ------> 6A- A = 70+7 ---> 5A= 77 A= 77/5, Answer choice A #### A QUESTION:A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)22 B)350 C)268 D)277 E)198 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer:B #### B QUESTION:a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple? options: A)225 B)228 C)230 D)231 E)235 SOLUTION:CP = 140*2+150*3+160*4+170*1=1540 SP = 1.5*1540=2310 Total no.of kgs=2+3+4+1=10 SP per kg=2310/10=231 ANSWER:D #### D QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 13000, then the share of B is? options: A)6000 B)12000 C)18000 D)24009 E)24002 SOLUTION:Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 13000 Share of B = 6/13 (13000) = Rs. 6000 Answer: A #### A QUESTION:The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 50 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons? options: A)55 B)56 C)57 D)58 E)59 SOLUTION:20x + 50 = 21(x – 5) X=55 ANSWER:A #### A QUESTION:Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter? options: A)201 B)132 C)772 D)592 E)261 SOLUTION:2 * 22/7 * 16 = 100.5 100.5 * 2 = Rs.201 Answer: A #### A QUESTION:The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : options: A)Rs. 113.5 B)Rs. 119.7 C)Rs. 124.75 D)Rs. 130.75 E)Rs. 134.45 SOLUTION:For an income of Rs.756, investment = Rs.9000 For an income of Rs., investment = = Rs.125 For a Rs.100 stock, investment = Rs.125. Market value of Rs. 100 stock = = Rs. 124.75 C #### C QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? options: A)4% B)8% C)4.2% D)4.8% E)5% SOLUTION:Let's say there is a TOTAL of100students at this college. 60 percent of the total number of students are freshmen. # of freshmen = 60% of 100 =60 40 percent of the fresh-men are enrolled in the school of liberal arts... Number of liberal arts freshmen = 40% of 60 =24 ...and, of these, 20 percent are psychology majors... Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8 What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? 4.8/100= 4.8% Answer:D #### D QUESTION:Solve 8x – 4 = 4x + 11 options: A)5(1/3) B)6(1/3) C)7(1/3) D)3(3/4) E)9(1/3) SOLUTION:Sol. 8x – 4 = 4x + 11 => 8x – 4x = 11 + 4 => 4x = 15 => x = 15/3 = 3(3/4). Answer D #### D QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse? options: A)27 B)98 C)27 D)80 E)71 SOLUTION:CP = SP + 1CP = SP - g 620 + x = 860 - 2x 3x = 240 => x = 80 Answer:D #### D QUESTION:John professes to sell his goods at the cost price but he made use of 800 grams instead of a kg, what is the gain percent? options: A)12 1/3% B)12 1/4% C)12 2/3% D)12 2/1% E)12 1/2% SOLUTION:800 --- 100 100 --- ? => 12 1/2% Answer:E #### E QUESTION:A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)22277 B)29977 C)267676 D)14000 E)18811 SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 Answer: D #### D QUESTION:What is the median from the below series 90, 93, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)85 C)93 D)97 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88, 90, 93, 93, 95, 96, 98 The median quiz score was 93. (Four quiz scores were higher than 93 and four were lower.) C #### C QUESTION:If 24 men can do a piece of work in 25 hours, in how many hours will 15 men do it ? options: A)40 hours B)45 hours C)50 hours D)55 hours E)60 hours SOLUTION:Let the required number of hours be x. Then, Less men, More hours (Indirect Proportion) 15 : 24 : : 25 : x<=>(15 x x) =(24 x 25)<=>(24 x 25)/15 = 40 Hence, 15 men can do it in 60 hours Answer is A. #### A QUESTION:If y/x is an integer, which of the following must also be an integer? I. xy II. x/y III. x options: A)I alone B)II alone C)None of the above D)I and III E)III alone SOLUTION:Lets take X = 1/6 and Y = 2/3 Then Y/X = 4 which is an integer. But XY = 1/6 * 2/3 = 1/9 --> Not an integer. X/Y = 1/6 divided by 2/3 = 1/4 --> Not an integer. X alone is 1/6. Not an integer. Hence C. None of the above. #### C QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y? options: A)3/2 B)2 C)4/3 D)4 E)9/2 SOLUTION:Its simple equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4. Thus, correct ans is E #### E QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)12 B)72 C)48 D)99 E)11 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.75 + 1.25 = 3 km = 3000 m. Required time = 3000 * 3/125 = 72 sec. Answer: B #### B QUESTION:Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home? options: A)6 B)7 C)8 D)10 E)11 SOLUTION:It's a simple geometry problem. Look at the diagram below: Answer: E. #### E QUESTION:A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball? options: A)5⁄7 B)10⁄21 C)2⁄7 D)11⁄21 E)None of these SOLUTION:Reqd probability = 5C2/7C2=5×4/7×6=10/21 Answer B #### B QUESTION:Two cars cover the same distance at the speed of 50 and 61 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)273 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 61x X = 4.55 60 * 4.55 = 273 km ANSWER:B #### B QUESTION:The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@[email protected],whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$430 per month. The salary of the new supervisor is: options: A)870 B)600 C)287 D)771 E)191 SOLUTION:Explanation: Total salary of 8 workers and supervisor together = 9 × 430 = 3870 Now total salary of 8 workers = 3870 − 870 = 3000 Total salary of 9 workers including the new supervisor = 9 × 430 = 3870 Salary of the new supervisor = 3870 − 3000 = 870 Answer: A #### A QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 40 miles per gallon, and from Town B to Town C, the car averaged 50 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)42.85 B)40 C)35 D)41 E)39 SOLUTION:step 1) took LCM of 40 and 50.. came as 200. step 2) 200 distance between B to C... do 200/50 hence 4 gallons used step 3) twice distance.. hence 200*2= 400... do as above.. 400/40= 10 gallons used step 4) total gallons.. 4+10= 14 gallons step ) total miles= 200+400= 600 miles hence.. average of whole journey = 600/14 which comes to 42.85 Answer : A #### A QUESTION:How many numbers from 10 to 40 are exactly divisible by 3? options: A)13 B)15 C)16 D)10 E)18 SOLUTION:12, 15, 18, 21, 24, 27, 30, 33, 36, 39. 10 Numbers. 10/3 = 3 and 40/3 = 13 ==> 13 - 3 = 10. Therefore 10 digits D) #### D QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)*(100%-19%) = 1.07*.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D QUESTION:A man wants to sell his scooter .There are two offers one at Rs12000 cash and other at a credit of Rs12880 to be paid after 8 months ,money being at 18% per annum which is better offer? options: A)Rs.12880 B)Rs.12000 C)Both are equally good D)None of the above E)Cannot be determined SOLUTION:Explanation: PW of Rs.12,880 due 8 months hence =Rs.[12880×100/100+(18×812)]=Rs.11500= Clearly 12000 in cash is a better offer. Answer: B #### B QUESTION:The true discount on a bill of Rs.8640 is Rs.1440.The banker's discount is options: A)1428 B)1528 C)1628 D)1728 E)None of these SOLUTION:Solution P.W = Rs.(8640 - 1440) = Rs. 720 S.I on Rs. 8640 =Rs.(1440/7200 x 8640) = Rs. 1728. Answer D #### D QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 12 machines produce in 6 minutes? options: A)1344 B)3360 C)8400 D)5040 E)67200 SOLUTION:8 machines produce 560 in 1 min 8 machines produce 560* 6 in 6 min 12 machine produce 560*6*(12/8) in 6 minutes 560*6*12/8=5040 answer is D. #### D QUESTION:Find the odd man out. 1, 16, 81, 255, 625, 1296 options: A)255 B)1296 C)81 D)1 E)625 SOLUTION:Explanation : The pattern is 1^4, 2^4, 3^4, 4^4, 5^4, 6^4 Hence, in place of 255, the right digit is 44 = 256 Answer : Option A #### A QUESTION:which of the following is a prime number ? options: A)17 B)18 C)15 D)20 E)25 SOLUTION:Clearly, 17 is a prime number. Option A #### A QUESTION:John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish? options: A) 24 B) 34.8 C) 37.8 D) 40 E) 84 SOLUTION:The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p: 0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40. Answer: D. #### D QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/4. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)5. B)7. C)9. D)10. E)17. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10 Lets take LCM of three balls 4,5 and 10 =20. The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS. Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls. IMO option C is correct. #### C QUESTION:Find the value of k for which there are infinite solutions for the given set of equations. 5x + 2y = k and 10x + 4y = 3 options: A)3/0 B)3/2 C)3/1 D)3/8 E)3/4 SOLUTION:For the two sets of equation to have infinite solutions, we have 510=24=k3510=24=k3. Hence, k = 3/2 Answer: B #### B QUESTION:Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest W? options: A) 60 B) 61 C) 62 D) 63 E) 64 SOLUTION:60 = 2*2*3*5 factor count =3 61= prime number 62 = 2*31 factor count=2 63=3*3*7 factor count=2 64=2*2*2*2*2*2 factor count=1=W answer is A. #### A QUESTION:A shopkeeper sold an article offering a discount of 4% and earned a profit of 26%. What would have been the percentage of profit earned if no discount was offered? options: A)24 B)28 C)31 D)32 E)34 SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 126 Let marked price be Rs. x. Then, 96/100 x = 126 x = 12600/96 = Rs. 131.25 Now, S.P. = Rs. 131.25, C.P. = Rs. 100 Profit % = 31%. ANSWER:C #### C QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible? options: A)30 B)42 C)120 D)360 E)720 SOLUTION:5 people ,7 seats, only 2 can drive if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways since any one can drive total ways = 24 *2= 48 ways 4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways 48*15=720 ANSWER:E #### E QUESTION:The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be options: A)37:20 B)47:20 C)47:25 D)22:25 E)97:50 SOLUTION:Sailor = 1.85 * Officer Sailor/Officer = 1.85/1 = 185/100 = 37/20 Answer will be A #### A QUESTION:A right circular cylinder has a height of 25 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? options: A)500(π – 3) B)500(π – 2.5) C)500(π – 2) D)500(π – 1) E)625(π – 1.5) SOLUTION:[quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? The square base has sides of sqrt(50) due to the 45-45-90 triangle 25*25*pi - 15*sqrt(50)^2 =625(π – 1.5) E. 500(π – 1.5) #### E QUESTION:In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions? options: A)63 B)48 C)85 D)52 E)47 SOLUTION:In the given word there 6 letters in that there are 2 vowels and 4 consonants no of ways of arranging the vowels=2p2=2 no of ways of arranging the consonants=4p4=24 total number of ways 24*2=48 Answer(B) #### B QUESTION:Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)2a2 – ab + 3b2 B)(a – b)(2a – 3b) + 4ab C)(a – b)2 + (a2 + ab + 2b2) D)(a + b)2 + (a2 + 2b2 – 3ab) E)(a + b)(a – b) + (2a2 – ab + 4b2) SOLUTION:The other parts are equal to 34. Answer E #### E QUESTION:A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum N of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ? options: A) 5 B) 7 C) 9 D) 10 E) 14 SOLUTION:Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum N of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D #### D QUESTION:In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:The total number of books the students borrowed is 20*2=40. The students who borrowed zero, one, or two books borrowed 8*1+3*2=14 books. The 7 students who borrowed at least three books borrowed 40-14=26 books. If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books. The answer is A. #### A QUESTION:If a 3-digit integer is selected at random from the integers 300 through 349, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to two more than the middle digit? options: A) 50/349 B) 1/313 C) 1/49 D) 1/100 E) 1/50 SOLUTION:Hundreds digit has to be 3 . So units digit needs to 3 as well And both Hundreds and Units digit needs to be 2 more than ten's digit The number is 313 Total numbers between 300 and 349 = (349-300)+1 = 50 Probability = 1/50 Answer E #### E QUESTION:For a lottery, three numbers are drawn, each from 1 to 40. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning? options: A)01 B)025 C)115 D)125 E)5 SOLUTION:(1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38))((1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38)) ((1/8)−(9/78))((1/8)−(9/78)) (0.125−approx.0.1111)(0.125−approx.0.1111) Approximately 0.010.01 ANSWER :A #### A QUESTION:A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey? options: A)6 B)4 C)8 D)2 E)3 SOLUTION:M = 45 S = 1.5 DS = 6 US = 3 AS = (2 * 6 * 3) /9 = 4 Answer: B #### B QUESTION:Jake wants to invite 9 friends to his 8th birthday party. Each invitation requires 2 stamps to mail, costing 12 cents each. How much will Jake have to spend on stamps to send invitations to his 9 friends? options: A)$1.08 B)$1.41 C)$1.74 D)$1.98 E)$2.16 SOLUTION:2 stamps multiplied by 12 cents = 24 cents per invitation. 24 cents multiplied by 9 invitations = 216 cents = $2.16, hence answer : E. #### E QUESTION:If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour? options: A)17/140 B)29/180 C)26/143 D)1/5 E)39/121 SOLUTION:50 apprentices can finish the job in 4 hours,thus: 10 apprentices can finish the job in 4*5 = 20 hours; In 1 hour 10 apprentices can finish 1/20 of the job. 30 journeymen can finish the same job in 4,5 hours,thus: 15 journeymen can finish the job in 7*2 = 14 hours; In 1 hour 15 journeymen can finish 1/14 of the job. Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job. Answer: A #### A QUESTION:A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 180 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year? options: A)2989 B)2765 C)6000 D)2989 E)9772 SOLUTION:Total production of salt by the company in that year = 5000 + 5180 + 5360 + .... + 6980 = 72060. Average monthly production of salt for that year = 72060/12 = 6005. Answer:C #### C QUESTION:70,76, 74,85,90,105,105,130,130,130 The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD. We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74. Answer: C. #### C QUESTION:A bike covers a certain distance at the speed of 65km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)85 km/h B)85.34 km/h C)86.66 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(C) Sol. Total distance = 65 × 8 = 520 km Now speed = 520/6 = 86.66 km/h #### C QUESTION:Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set? options: A) 87 B) 89 C) 90 D) 92 E) 95 SOLUTION:Set X = {11, 13, 17,............., 83, 89, 97} Set Y = {10, 20, 30,..............., 70, 80, 90} Combining two sets, say Set Z Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97} Range = Max Value - Min Value Range (Z) = 97 - 10 = 87 OA A is the answer. #### A QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 85. Find the third number? options: A)A)37 B)B)85 C)C)48 D)D)43 E)E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 85 6x = 85 => third number is 85. Answer: Option B #### B QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A? options: A)240 B)288 C)266 D)216 E)123 SOLUTION:(3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 630 = 240 Answer: A #### A QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14×30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×14) Ratio of the capacity of a man and woman =1/(15×14) : 1/(14×30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:The price of 10 bat is equal to that of 4 balls. The price of 15 balls and 2 bats together is Rs. 4000. The total price of 12 chairs and 3 balls is: options: A)Rs. 3200 B)Rs. 3500 C)Rs. 3700 D)Rs. 3900 E)Rs. 4000 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. D) #### D QUESTION:If c is 20% of a and 10% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 200% SOLUTION:Answer = E 20a/100 = 10b/100 b = 20a/10 = 200a/100 = 200% #### E QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in? options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr SOLUTION:Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer:D #### D QUESTION:A rainstorm increased the amount of water stored in State J reservoirs from 160 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 50 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? options: A)240 B)250 C)260 D)270 E)300 SOLUTION:Let total capacity be x we know 200 = 0.50x x = 200/0.50 = 400 Prior to storm, we had 160 bn gallons 400-160 = 240 Answer : A #### A QUESTION:A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number. He was afraid of forgetting his PIN. He wrote down the number 125 in his diary to remember his PIN. He also wrote out the way to calculate 125 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 125". Once, Prafull saw his diary in which Pinaki wrote this number 125. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN? options: A)874 B)872 C)876 D)875 E)879 SOLUTION:Explanation : Let, the PIN is x. According to the question, The card number =996 and Remainder =125. Thus, (996 × x)/997=125. =>x= 872. Answer : B #### B QUESTION:Bernice's income is 70 percent more than Cathy's income, and Cathy's income is 65 percent less than Camilla's income. What percent of Camilla's income is Bernice's income? options: A)54.5% B)52.5% C)59.5% D)51.5% E)55.5% SOLUTION:Camilla's income = 100 (assume); Cathy's income = 35 (65 percent less than Camilla's income); Bernice's income = 59.5 (70 percent more than Cathy's income). Thus, Bernice's income (59.5) is 59.5% of Camilla's income (100). Answer: C #### C QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following numbers? options: A)4 B)3 C)7 D)6 E)9 SOLUTION:Let the consecutive even integers are n and (n + 2) difference of the squares = (n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4 = 4(n + 1) which is divisible by 4 Answer is A #### A QUESTION:Two numbers have a H.C.F of 9 and a product of two numbers is 1800. Find the L.C.M of the two numbers? options: A)200 B)150 C)160 D)170 E)180 SOLUTION:L.C.M of two numbers is given by (Product of the two numbers) / (H.C.F of the two numbers) = 1800/9 = 200. ANSWER:A #### A QUESTION:The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is : options: A)15 cm B)25 cm C)35 cm D)42 cm E)62 cm SOLUTION:Solution Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C #### C QUESTION:Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube? options: A)22 B)77 C)28 D)18 E)19 SOLUTION:93 + 123 + 153 = a3 => a = 18 Answer: D #### D QUESTION:Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h options: A)20 seconds B)3 C)4 D)1 E)5 SOLUTION:swim in still water at = 3 speed of river= 1.4 US = 3 - 1.4= 1.6 Distance = 8 T = 8/1.6 = 5 Answer: E #### E QUESTION:The cost per pound of green tea and coffee were the same in June. In July, the price of coffee shot up by 100% and that of green tea dropped by 90%. If in July, a mixture containing equal quantities of green tea and coffee costs $3.15 for 3lbs, how much did a pound of green tea cost in July? options: A)$4 B)$0.1 C)$1 D)$3 E)$1.65 SOLUTION:Lets assume price of Coffee in June =100x Price of green Tea in June =100x Price of Coffee in July = 200x (because of 100% increase in price) Price of green Tea in July = 10x (because of 90% Decrease in price) Price of 1.5 pound of Coffee 1.5 pound of green Tea in July will be = 300x + 15x = 315x As per question 315x= 3.15$ x = 0.01S So the Price of green Tea in July = 10x = 10 x 0.01 = 0.1$/pound Answer B #### B QUESTION:If n = 9^11 – 9, what is the units digit of n? options: A)0 B)1 C)4 D)6 E)8 SOLUTION:Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 9^3 - 9. Now 9^3 has last digit 9. , we subtract 9 from 9 , thus 9 -9 = 0 is the answer. Option A #### A QUESTION:John bought 9.25m of cloth for $425.50. Find the cost price per metre. options: A)46 B)47 C)58 D)56 E)54 SOLUTION:Cloth bought by John = 9.25 m Cost of 9.25 m = $425.50 Cost per metre = 425.50 ÷ 9.25 The cost of the cloth per metre = $ 46 Answers: A #### A QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean? I. 13.7 II. 12.3 III. 9.3 options: A)I only B)I and II only C)II only D)III only E)I and III only SOLUTION:Mean = 12 SD = 1.3 2 SD above mean = 12+2*1.3 = 14.6 2 SD below mean = 12-2*1.3 = 9.4 12.3 and 13.7 lies in the range of 2SD from mean Answer: Option D #### D QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is options: A)91 B)910 C)61 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 671 and 610. ‹=› 61. Answer C #### C QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 10 and 100? options: A)1345 B)1576 C)2475 D)2578 E)1895 SOLUTION:numbers are 11,13,15-------,97,99 Average of the set: (largest+smallest)/2=(99+11)/2=55; # of terms: (largest-smallest)/2+1=(99-11)/2+1=45 The sum = 45*55= 2475 Answer: C #### C QUESTION:If the simple interest on a certain sum of money for 2 years is one–fifth of the sum, then the rate of interest per annum is options: A)14% B)7% C)10% D)15% E)3% SOLUTION:Explanation: Let the Principal(P) be x Then, Simple Interest(SI) = x/5 Time(T) = 2 years Rate of interest per annum(R) = (100×SI)/PT = (100 × (x/5)/(x × 2) = 20/2 = 10% Answer: Option C #### C QUESTION:In X game of billiards, X can give Y 20 points in 45 and he can give Z 30 points in 45. How many points can Y give Z in X game of 100? options: A)30 B)20 C)25 D)40 E)50 SOLUTION:X scores 45 while Y score 40 and Z scores 30. The number of points that Z scores when Y scores 100 = (100 * 30)/25 = 60. In X game of 100 points, Y gives (100 - 60) = 40 points to C. D #### D QUESTION:If a^2+b^2=177and ab=54 then find the value of a+b/a-b? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:(a+b)^2=a^2+b^2+2ab=117+2*24=225 a+b=15 (a-b)^2=a^2+b^2-2ab=117-2*54 a-b=3 a+b/a-b=15/3=5 Answer is C. #### C QUESTION:Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is the probability that none of the objects occupy the place corresponding to its number? options: A)17/24 B)3/8 C)1/2 D)5/8 E)5/3 SOLUTION:Explanation : Let a particular number (say) number 2 occupies position 1. Then all possible arrangement are given as: =>(2,1,3,4), (2,1,4,3), (2,3,4,1), (2,4,1,4), (2,4,1,3), (2,4,3,1). Out of these six, three (2,1,3,4), (2,3,1,4), (2,4,3,1) are not acceptable because numbers 3 and 4 occupy the correct positions. Hence, the required probability = 3/6 = 1/2. Answer : C #### C QUESTION:The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? options: A)A)17 B)B)18 C)C)19 D)D)22 E)E)24 SOLUTION:Explanation: 10 * 16 + 36 – 26=170 => 170/10 = 17 A) #### A QUESTION:There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle. options: A)18 B)99 C)12 D)07 E)11 SOLUTION:Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm. a2 = 784 = (4)(196) = (22).(142) a = (2)(14) = 28 a = 2l, l = a/2 = 14 l = (7/3)s Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm. Answer: C #### C QUESTION:A shop keeper marked 30% above the cost price and offered 20% discount then find it's net profit? options: A)2% B)2.5% C)3.7% D)4.6% E)5% SOLUTION:Net profit = 30-20 + (30*(-25)/100) = 2.5% Answer is B #### B QUESTION:In the Bargaining Bazar everyone purchase with a fair bargaining, so the traders markup the prices too much. A trader marked up an article at Rs. M expected huge profit if it is sold on marked price. But a customer purchased it at M/2 with his fine bargaining skills, so the expected profit of the trader diminished by 66.66%. What is the percentage discount fetched by the customer through bargaining? options: A)33.33% B)50% C)60% D)66.66% E)None of these SOLUTION:Solution: MP = M SP = M/2 % Discount = [(M/2) /M] *100 = 50%. Answer: Option B #### B QUESTION:Four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. In 18 minutes, how many times do they toll together ? options: A)43 B)44 C)45 D)46 E)47 SOLUTION:LCM of 2, 4, 6, 8 is 24. So, after each 24 seconds, they would toll together. Hence, in 18 minutes, they would toll 18*60 seconds / 24 seconds = 45 times But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second). So, total tolls together = 45+1 = 46 Answer C #### C QUESTION:A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested? options: A)$360 B)$380 C)$400 D)$420 E)$440 SOLUTION:S.I for 5 years = $680 - $480 = $200 The S.I. is $40/year S.I. for 2 years = $80 Principal = $480 - $80 = $400 The answer is C. #### C QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office? options: A)38 B)27 C)24 D)19 E)17 SOLUTION:Explanation: Let t be his usual time to reach his office and v be his usual speed. v = d/t ……….(d is the distance Ajay travels while going to his office) vt = d At v1 = 4v/5 ; t1 = t + 6 4v/5 = d/(t + 6) 4v/5* (t + 6) = d 4v/5* (t + 6) = vt On solving we get, t = 24 minutes ANSWER:C #### C QUESTION:There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 4. If all 27 of the integers were listed, what would their sum be? options: A)6693 B)6793 C)6893 D)6993 E)7093 SOLUTION:There must be nine 1's in the hundreds place, nine 1's in the tens place, and nine 1's in the units place. This is also true for the 2's and 4's. Then the sum is: 9(111+222+444)=9*(777)=6993. The answer is D. #### D QUESTION:Let X be the smallest positive integer such that 10 and 14 are factors of 250 + X, so the value of X is: options: A)0 B)10 C)20 D)30 E)40 SOLUTION:You can calculate the LCM (10,14) = 70. After that you should check which of the possible X values will result in a number divisible by 70. The only possibility for this is 30 ( because 250 + 30 = 280 = 70*4) Answer D #### D QUESTION:At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate? options: A)134 B)178 C)195 D)166 E)194 SOLUTION:C 195 The number of votes the winning candidate received was 963 + 53 + 79 + 105 /4= 300. The second received 300 – 53 = 247, The third received 300 – 105 = 195. #### C QUESTION:-64*29+468=? options: A)1430 B)1302 C)-2801 D)-1388 E)None of these SOLUTION:=> -64*(30-1)+468; => -(64*30)+64+468; => -1920+532=-1388. Correct Option: D #### D QUESTION:A man can row upstream at 15 kmph and down strem 30 kmph. He takes 9 hours to row from lower point A to upper point B and back to A. What is the total distance traveled by him in 9 hours? He must return back to base point A in remaining time. options: A)80 B)120 C)140 D)180 E)200 SOLUTION:Upward distance traveled per hour - 15 km, distance traveled after 6 hours = 90 km. He remained with 3 hours travel downward, i.e. distance traveled in remaining 3 hours downward = 90 km so total distance traveled from A to B and Back to point A = 90 km upward + 90 km downhill = 180 km (Answer : D) #### D QUESTION:If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15%, the gain is: options: A)16(2/3)% B)13(1/3)% C)15 (1/6)% D)15% E)None of these SOLUTION:Let C.P.=Rs. 100. First S.P.=Rs. 120 Now, S.P. =Rs. 120, commission=10% Therefore, Marked Price=[(100/90)X120]=Rs. 400/3. No, marked price=400/3, commission=15% Therefore, S.P.=85% of 400/3=[(85/100)X(400/3)]=340/3. Therefore, Gain%=[(340/3)-100]=40/3=13(1/3)%. ANSWER:B #### B QUESTION:30% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim? options: A)70 B)97 C)87 D)100 E)76 SOLUTION:Given, 30% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks. Given, marks of Robert = 80 30% of 80 = 30/100 * 8 = 24 Given, 30% of Ram's marks = 24. => Ram's marks = (24 * 100)/30 = 80 Also, 20% of Rahim's marks = 24 => Rahim's marks = (24 * 100)/20 = 120 Average marks of Ram and Rahim = (80 + 120)/2 = 100. Answer:D #### D <<<Examples ends QUESTION:If 1^3 + 2^3 + 3^3 +......+ 10^3 = 516 then the value of 2^3 + 4^3 + 63 + ..... + 203 is options: A)1032 B)1030 C)1034 D)1035 E)1036 SOLUTION:2(13 + 23 + 33 + ---------- + 103) 2 × 516 = 1032 A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A man can do a piece of work in 5 days, but with the help of his son he can do it in 2 days. In what time can the son do it alone ? options: A)7 1/2 days B)6 1/2 days C)5 1/3 days D)3 1/3 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/2−1/5)=(5−2)/10=3/10 So son will do whole work in 10/3 = 3 1/3 days Answer: D #### D QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20 SOLUTION:5p3 =5 x4= 20 Option 'E' #### E QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 1/2 hours B)20 1/7 hours C)20 1/3 hours D)20 3/2 hours E)20 1/4 hours SOLUTION:1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 * 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours Answer: A #### A QUESTION:For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? options: A)(-3)^2 B)2 C)3 D)4 E)5 SOLUTION:Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4 Step 2, For each number: subtract the Mean and square the result = (1-4)^2=(-3)^2 (2-4)^2=(-2)^2 (3-4)^2 =(-1)^2 (4-4)^2=(.0)^2 (5-4)^2=(1)^2 Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options. Hence A #### A QUESTION:Pipe A can fill a tank in 2 hr, pipe B in 4hr and pipe C in 8hr. If all the pipes are open in how many hours will tank be filled? options: A)1hr 27min B)2hr 19min C)3hr 14min D)3hr E)5hr 45min SOLUTION:Part filled by (A+B+C) in 1hour = 1/2 + 1/4 + 1/8 = 7/8 All the 3 pipes together will fill the tank in 1hour 27min Answer is A #### A QUESTION:A man purchased 3 blankets @ Rs.100 each, 4 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)600 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 A #### A QUESTION:Divide Rs. 1300 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)346 B)368 C)375 D)337 E)325 SOLUTION:A+B+C = 1300 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1300 => 325 Answer:E #### E QUESTION:In case N is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)O and P E)T and U SOLUTION:O and P should serve on A ANSWER:D #### D QUESTION:The ratio of spinsters to cats is 2 to 7. If there are 40 more cats than spinsters, how many spinsters are there? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Let 2x be the number of spinsters. Then 7x is the number of cats. 7x-2x=40 x=8 and the number of spinsters is 2(8)=16. The answer is B. #### B QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters? options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n SOLUTION:C is the answer. To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra. Given - tank was already 1/3 full. - When n ltr added, it became 5/9 So 1/3 + n = 5/9 n = 5/9 - 3/9 n = 2/9 capacity of the tank is full fraction . i.e. 1 i.e. 9/9 so the question is 9/9 is how much times n = 9/9 = 1 = xn so x = 9/2 and total = 9/2n #### C QUESTION:22.085 × 0.001 = ? options: A)0.22085 B)2.2085 C)0.022085 D)0.0022085 E)None of these SOLUTION:22.085 × 0.001 = ? or,? = 0.022085 Answer C #### C QUESTION:In my core I have 5 But 500 stand in the beginning and the end of mine. I also include the first letter and the first number to make me complete. I am the name of a King. Who am I? options: A)Johny B)Jacky C)Ricky D)David E)Alex SOLUTION:D I am DAVID. At the core I have 5 If we talk in roman numeric system, 5 = V Similarly, 500 stands in the beginning and end 500 = D I also include the first letter i.e. A and the first number i.e. I (in roman numeric system) All of them combine to form DAVID. #### D QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3750 C)Rs. 3840 D)Rs. 3900 E)None SOLUTION:EXPLANATION Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5b/2 x 15x + 2y = 4000 15x + 2 x 5/2 x= 4000 20x = 4000 x = 200. So, y = 172 = 500. Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. Answer D #### D QUESTION:An article is bought for Rs.1300 and sold for Rs.1250, find the loss percent? options: A)3 11/13% B)3 2/9% C)3 5/3% D)3 2/3% E)3 7/3% SOLUTION:1300 ---- 50 50 ---- ? => 3 11/13% Answer: A #### A QUESTION:3640 ÷ 14 × 16 + 340 = ? options: A)0.7 B)3525 C)4480 D)None of these E)Cannot be determined SOLUTION:Solution Given exp. = 260 × 16 + 340 = 4160 + 340 = 4500. Answer D #### D QUESTION:A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number M is options: A)74 B)M=75 C)M=175 D)M=680 E)690 SOLUTION:I solved this question by plugging in numbers from the answer choices. A.) 74 Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5. B.) 75 I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7. 15-7 = 8 so I know the correct answer isB #### B QUESTION:A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze? options: A)1298 B)1228 C)1210 D)1782 E)1762 SOLUTION:π (232 – 122) = 1210 Answer:C #### C QUESTION:Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed? options: A)1050 B)25200 C)32400 D)5800 E)6800 SOLUTION:Number of ways of selecting (4 consonants out of 6) and (2 vowels out of 3) = 6C4 * 3C2 = 6C2 * 3C1 = 6*5 *3 2*1 = 15*3= 45 Number of groups, each having 4 consonants and 2 vowels= 45. Each group consists of 6 letters. Number of ways of arranging 6 letters among themselves = 6! = (6*5*4*3*2*1)= 720 Therefore, Required number of words= 45*720= 32400 ANSWER:C #### C QUESTION:Jacob brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%? options: A)27 B)276 C)500 D)267 E)234 SOLUTION:Let the C.P. be Rs. x. Then, 20% of x = 1100 20/100 * x = 1100 => x = 5500 C.P. = Rs. 5500, expenditure on repairs = 10% Actual price = Rs. (100 * 5500)/110 = Rs. 5000 Expenditures on repairs = (5500 - 5000) = Rs. 500. Answer: C #### C QUESTION:If X = the product of three distinct prime numbers, how many factors does X have besides 1 and itself? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:Since X has 3 distinct prime factors, X has a total of 2^3 = 8 factors. Besides 1 and itself, X has 6 factors. The answer is A. #### A QUESTION:Two trains running in opposite directions cross a man standing on the platform in 20 seconds and 18 seconds respectively and they cross each other in 19 seconds. The ratio of their speeds is: options: A)1 : 1 B)3 : 2 C)3 : 8 D)3 : 25 E)3 : 4 SOLUTION:Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 20 x meters, and length of the second train = 18 y meters. (20 x + 15 y) / (x + y) = 19 ==> 20 x + 18 y = 19 x + 19 y ==> x = y ==> x/y = 1/1 Answer: Option A #### A QUESTION:Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent? options: A)705 B)655 C)656 D)657 E)658 SOLUTION:total cost 940 940*25/100=235 so the cut in amount is 235 the less amount to be spend is 940-235=705 ANSWER:A #### A QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? options: A)1 mins B)3 mins C)8 mins D)6 mins E)4 mins SOLUTION:D = 25 * 60 + 1500 = 3000 m T = 3000/60 * 18/5 = 180 sec = 3 mins Answer: B #### B QUESTION:The capacity of a tank of dimensions (8m x 6m x 2.5m)is options: A)120 litres B)1200 litres C)12000 litres D)120000 litres E)None of these SOLUTION:Explanation: capacity of atank =volume of tank = (8 x 100 x 6 x 100 x 2.5 x 100)/1000 litres = 120000 litres Answer: D #### D QUESTION:On day one, a store sold 125 bags. On each of the next d days, the company sold 83 bags. If the average daily sales of bags over this time period (including day one) is 90 bags, what is the value of d? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:125 + 83d = 90(d+1). 7d = 35. d = 5. The answer is B. #### B QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number? options: A)150 B)125 C)140 D)180 E)200 SOLUTION:3x+4x = 420 x=60== 3x=180 ANSWER D #### D QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)227 B)268 C)240 D)889 E)232 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer:C #### C QUESTION:Among the answers given below, which is nearly equal to √7? options: A)2.3 B)1.9 C)2.6 D)2.5 E)3.0 SOLUTION:2.6 is nearly equal to the square root of 7 2.6*2.6=6.76 2.5*2.5=6.25 difference 7 - 6.76=0.24 7 - 6.25=0.75 Since 0.24 is lesser of both, 2.6 is closer. Answer is C #### C QUESTION:16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work? options: A)26.7 days B)77 days C)20 days D)88 days E)44 days SOLUTION:16 * 25 = 15 * x => x = 26.7 days Answer: A #### A QUESTION:A tank is filled in SIX hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank? options: A)56 hours B)28 hours C)55 hours D)66 hours E)21 hours SOLUTION:1/A + 1/B + 1/C = 1/6 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/6 => (1 + 2 + 4)/2B = 1/6 => 2B/7 = 6 => B = 21 hours. Answer: E #### E QUESTION:If n is a positive integer, then n(n+1)(n+2) is even without any condition options: A)divisible by 3 only when n is odd B)divisible by 4 whenever n is even C)odd whenever n is odd D)even only when n is odd E)even only when n is even SOLUTION:n*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 6,7&8) B #### B QUESTION:An office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible? options: A)18 B)24 C)30 D)45 E)60 SOLUTION:First let's consider the small notebooks. There are 5 ways to choose notebooks of the same color. The number of ways to choose four notebooks with different colors is 5C4=5. There are 10 different packages we can make with the small notebooks. We can use the same process to find 10 different packages with medium and large notebooks. The total number of different packages is 30. The answer is C. #### C QUESTION:Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ? options: A)500 B)600 C)450 D)550 E)None of these SOLUTION:Explanation: Let the lent at 5% be 'A' (A x 5 x 1)/100 + [(1500 - A)x 6 x 1]/100 = 85 5A/100 + 90 – 6A/100 = 85 A/100 = 5 => A = 500 ANSWER IS A #### A QUESTION:Five carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if four of the carpenters work together at their respective rates ? options: A)11/15 B)3/5 C)11/30 D)47/75 E)5/9 SOLUTION:Farmer A, B, C, and D A's rate: 1/3 job/hour B's rate: 1/4 job/hour C's rate: 1/5 job/hour D's rate: 1/7 job/hour By intuition we know that the three fastest farmers are A B and C. As such (1/3 + 1/4 + 1/5)*(4/5) = ? 47/75 or (D) #### D QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)50 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer E, 50 cans #### E QUESTION:#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6? options: A)–108 B)–44 C)10 D)16 E)18.25 SOLUTION:#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer. #### E QUESTION:A jogger running at 9 km/hr along side a railway track is 180 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)89 B)20 C)36 D)88 E)30 SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 180 + 120 = 300 m. Time taken = 300/10 = 30 sec. Answer: Option E #### E QUESTION:The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle? options: A)1 : 96 B)1 : 48 C)1 : 84 D)1 : 68 E)None of these SOLUTION:Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96. ANSWER:A #### A QUESTION:In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 20% of the total number of children in the camp. How many more boys must she bring to make that happen? options: A)35. B)45. C)40. D)30. E)25. SOLUTION:Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls. Now here 90% are Boys and 10% are Girls. Now question is asking about how many boys do we need to add, to make the girls percentage to or 20%.. If we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it. Now boys are 80% and girls are 20%. ( out of 100 students = 80 boys + 20 girls ). IMO option A is correct. #### A QUESTION:Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.72000 after completion of one year. What will be Jose's share of profit? options: A)20000 B)10000 C)25000 D)34000 E)40000 SOLUTION:SoL = ~s- So Anju’s share = [5/9] x 72000 = 40000 E #### E QUESTION:1.5, 2.3, 3.1, 3.9, ..? options: A)0.6 B)0.8 C)0.4 D)0.24 E)0.15 SOLUTION:1.5+0.8=2.3 2.3+0.8=3.1 3.1+0.8=3.9 3.9+0.8=4.7 ANSWER:B #### B QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y? options: A)3/2 B)2 C)4/3 D)4 E)9/2 SOLUTION:Its simple equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4. Thus, correct ans is E #### E QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? options: A)3 B)5 C)4 D)2 E)6 SOLUTION:A rate = 1/8 B rate = 1/24 (A+B) rate = (1/8)+(1/24) = 1/6 A & B finish the work in 6days correct option is E #### E QUESTION:If 75 percent of a class answered the first question on a certain test correctly, 30 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? options: A)25% B)(8) 20% C)30% D)50% E)65% SOLUTION:I didn't understand how to connect 20 percent with the whole equation. Why 20 is out of the percentile diagram (circles) but inside of 100? 20% appeared in the exam; however did not answer Question AQuestion B correctly So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose I am doing it this way: Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both. Now, 100 - [(75 - x) + x + (30 - x)] = 20 .......... values are in percent x = 20 - 100 + 105 x = 25 Ans: A #### A QUESTION:If an average hard drive had a capacity of 0.7 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)768 D)1024 E)7168 SOLUTION:0.7*2^10=0.7*1024=716.8 The answer is E. #### E QUESTION:Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 5 days before the completion of the work. How long did the work last? options: A)6 B)7 C)8 D)8 1/9 E)10 SOLUTION:Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains Then if Ben had to leave 5 days before the completion, this means that Carla had to work alone for these 5 days in which she completed 1/3 of the job. Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 7/15 3/20 (t) = 7/15 ---> t = 3 1/9 Therefore, these 3 1/9 days worked plus the 5 days that Carla had to work by herself add to 8 1/9 days Answer: D #### D QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)20 D)21.1 E)23 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 190 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)19 D)33 E)25 SOLUTION:C 19rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 Thus our anniversary falls on the 19rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### C QUESTION:4y - 4x = xy and x ≠ 0. If x and y are integers, which of the following could equal y? options: A)2 B)1 C)0 D)5 E)6 SOLUTION:Plug in the answer choices in the equation from the question stem. A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE B) y = 1 >>> 2 - x = 2x >>> Same, POE C) y = 0 >>> -x = 0 >>> x can not equal 0 D) y = -1 >>> 8 - 4x = 4x >>> Holds true for x = 1, no need to check E. This is the answer. Answer A #### A QUESTION:At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 30 other employees of Company K, how many employees does Company K have? options: A) 160 B) 120 C) 190 D) 200 E) 400 SOLUTION:Let the total number of employees in the company be x % of secretaries = 15% % of salespeople = 60% % of of employees other than secretaries and salespeople = 100 - 75 = 25% But this number is given as 30 so 25% of x = 30 x = 120 Therefore there a total of 120 employees in the company K Correct answer - B #### B QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)*100}=4% Answer is A. #### A QUESTION:How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? options: A)482 B)226 C)276 D)266 E)181 SOLUTION:Explanation: 20000(11/10)4 - 20000(6/5)2 = 482 Answer: A #### A QUESTION:If 24 men can do a piece of work in 25 hours, in how many hours will 15 men do it ? options: A)40 hours B)45 hours C)50 hours D)55 hours E)60 hours SOLUTION:Let the required number of hours be x. Then, Less men, More hours (Indirect Proportion) 15 : 24 : : 25 : x<=>(15 x x) =(24 x 25)<=>(24 x 25)/15 = 40 Hence, 15 men can do it in 60 hours Answer is A. #### A QUESTION:Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected. options: A)2/35 B)2/3 C)7/35 D)1/7 E)7/5 SOLUTION:Let A be the event that Ram is selected and B is the event that Ravi is selected. P(A) = 5/7 P(B) = 1/5 Let C be the event that both are selected. P(C) = P(A) x P(B) as A and B are independent events: = 5/7 x 1/5 = 1/7 ANSWER:D #### D QUESTION:3^b + 3^b + 3^b = options: A)7^b B)7^(b + 1) C)7^(7b) D)3^(b + 1) E)49^B SOLUTION:Easy one. 3*3^b = 3^(b+1) Ans. D #### D QUESTION:Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is: options: A)30% B)100/3% C)35% D)44% E)None of these SOLUTION:Explanation : C.P. of 6 articles = Rs. 5 => C.P. of 1 article = Rs. 5/6 S.P. of 5 articles = Rs. 6 => S.P. of 1 article = Rs. 6/5 Profit earned per article = 6/5 - 5/6 = 11/30 % Profit = 11/30∗6/5∗100% = 44% Answer : D #### D QUESTION:A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used options: A)12 months B)10 months C)14 months D)16 months E)None of these SOLUTION:Explanation : B received 2/3 of the profit => A : B = 1 : 2 Let the total capital = x Then A's capital = x/4 B's capital = x – x/4 = 3x/4 Assume B's money was used for b months Then A:B = (x/4)*15 : (3x/4)*b = 1 : 2 => 15/4 : 3b/4 = 1 : 2 => 15 : 3b = 1 : 2 => 5 : b = 1 : 2 => 5/b = 1/ 2 => b = 5*2 = 10. Answer : Option B #### B QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? options: A)13680 B)13885 C)14005 D)14280 E)14680 SOLUTION:dana borrows 6000 and returns 2% per month. so returns 120 per month. and 1440 per year. so dana owes 6000-1440=4560 per year. after 3 years she will owe 13680. Ans (A) #### A QUESTION:What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-99)*(50-100)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:If n = 20! + 15, then n is divisible by which of the following? I. 15 II. 17 III. 19 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:15 divides 20! so 15 also divides 20! + 15. 17 and 19 divide 20! so they do not divide 20! + 15. The answer is A. #### A QUESTION:If a^x = b^y, then options: A)log a/b= x/y B)log a/ log b = x/y C)log a/ log b = y/x D)log b/a = x/y E)log b/a = y/x SOLUTION:a^x = b^y => log a^x = log b^y => x log a = y log b => log a/ log b = y/x ANSWER:C #### C QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000? options: A)81000 B)81027 C)81089 D)81027 E)28939 SOLUTION:64000* 9/8 * 9/8 = 81000 Answer: A #### A QUESTION:What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”? options: A)5 B)7 C)49 D)20 E)25 SOLUTION:The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum). C #### C QUESTION:If n is the product of 3 consecutive integers, which of the following must be true about n? I. n is a multiple of 2 II. n is a multiple of 3 III. n is a multiple of 4 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:n is the product of 3 consecutive integers. So, according to the rule, n must be divisible by 3, 2 and 1 So, we already know that statements I and II must be true. Do we need to check statement III? No. Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D. #### D QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 3*20000/5=12000 ANSWER:E #### E QUESTION:Solve for x if (log2)(1-x/2)=x-2. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(log2)(1-x/2)=x-2 or,log2-(x/2)log2=x-2 or,2log2-xlog2=2x-4 or,log4+4=2x+xlog2 or,4.60=2.3x i.e.x=2. ANSWER:B #### B QUESTION:what is the smallest integer that is multiple of 7, 12 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 7, 12 and 20 which is 420 #### E QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)35 SOLUTION:Speed of the train relative to man = (63 - 3) km/hr = 60 km/hr =(60 x(5/18)) m/sec =50/3 m/sec. Therefore Time taken to pass the man =(500 x(3/50))sec = 30 sec. Answer :B #### B QUESTION:The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is ? options: A)96 litres B)98 litres C)100 litres D)102 litres E)None SOLUTION:Answer Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12 Average = ( 110 x 7 + 86 x 5 ) / 12 =(1200 / 12 = 100 liters Correct Option: C #### C QUESTION:A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,750 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week? options: A)25% B)30% C)35% D)40% E)45% SOLUTION:E for me. Let managers comminsion rate be M. m*5000+ 2*0.05*5000=2750 5000*m=2250 m=45/100=45% #### E QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double? options: A)1/3 B)1/6 C)1/12 D)1/24 E)1/36 SOLUTION:ways you can get double - 6...as each dice showing any number from 1 to 6... total ways = 6∗6=36.6∗6=36.. P=6/36=1/6 ANSWER: B #### B QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40 SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35 P(at least one graduate) = 1- 1/35 = 34/35 The answer is D. #### D QUESTION:A retailer buys 100 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)175 C)212 D)218 E)220 SOLUTION:let the market price of each pen be $1 then, Cost Price of 100 pens = $ 36 Selling Price of 100 pens =99% of $100=$ 99 profit %=((63*100)/36) %=175% Answer B #### B QUESTION:a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers Q was deleted? options: A) a B) b C) c D) d E) e SOLUTION:a+b+c+d+e => 1+2+3+4+5=15 Q=20%*15= 3 =>C #### C QUESTION:A merchant sells an item at a 20% discount, but still makes a gross profit of 25 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount? options: A)20% B)40% C)56.25% D)60% E)75% SOLUTION:original SP = X Cost =C current selling price = .8x ( 20% discount) .8x = 1.5C (25% profit) x= 1.25/.8 *C x= 12.5/8 C Original selling price is 1.5625C which is 56.25% profit Answer C #### C QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:The workforce of Company Samsung is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers? options: A)180 B)170 C)160 D)150 E)145 SOLUTION:let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added 06x/(0.4x +20) = 50/100 or 60x = 50*( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125 total worker = 125+20= 145 E #### E QUESTION:A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction T of the cookies that were placed in the other tins were placed in the green tin? options: A)15/2 B)9/4 C)5/9 D)7/5 E)9/7 SOLUTION:Blue tin or red tin: 2/3 (N) Red tin: (1/3)N Blue tin: (1/4)N What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin) # of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12 # of cookies in red and green tin = N/3 + 5N/12 = 9N/12 Fraction T= 5N/12 * 12/9N = 5/9 (C) #### C QUESTION:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $20 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year? options: A) $752 B) $755 C) $765 D) $773 E) $775 SOLUTION:= (750*6+ 770 *20)/26 = 765 Answer is C. Posted from my mobile device #### C QUESTION:A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? options: A)4 : 3 B)9:2 C)18:20 D)1:4 E)18:4 SOLUTION:A: B =24000 : 18000 = 8 : 6 = 4 : 3 ANSWER:A #### A QUESTION:Average age of students of an adult school is 46 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students. options: A)1200 B)120 C)360 D)168 E)None of these SOLUTION:Explanation : Let the original no. of students be x. According to situation, 46x + 120*32 = (x + 120)36 ⇒ x = 48 So, Required no. of students after joining the new students = x + 120 = 168. Answer : D #### D QUESTION:Find the product of the local value and absolute value of 8 in 564823 options: A)1600 B)6400 C)16000 D)12000 E)18000 SOLUTION:Explanation: Place value = Local value Face value = Absolute value The place value of 8 in 564823 is 8 x 100 = 800 The face value of 8 in 564823 is nothing but 8. => 800*8=6400 Answer: Option B #### B QUESTION:Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set? options: A) 87 B) 89 C) 90 D) 92 E) 95 SOLUTION:Set X = {11, 13, 17,............., 83, 89, 97} Set Y = {10, 20, 30,..............., 70, 80, 90} Combining two sets, say Set Z Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97} Range = Max Value - Min Value Range (Z) = 97 - 10 = 87 OA A is the answer. #### A QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)2.3 B)2.5 C)3.5 D)3.6 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:If Z = 52 and ACT = 48, then BAT will be equal to options: A)33 B)88 C)77 D)46 E)99 SOLUTION:Explanation: In the given code, A = 2, B = 4, C = 6,.... , Z = 52. So, ACT = 2 + 6 + 40 = 48 and BAT = 4 + 2 + 40 = 46 Answer: D) 46 #### D QUESTION:Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b? options: A)5 B)6 C)11 D)16 E)19 SOLUTION:The number of possible permutation without 2 in the first digit is 4X4X3X2X1=96 ways. The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways. 18c1/96c1 = 18/96= 3/16= > a+b=19. ANSWER:E #### E QUESTION:The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by? options: A)Rs.70 B)Rs.75 C)Rs.50 D)Rs.60 E)None of these SOLUTION:2C + 3T = 1300 --- (1) 3C + 3T = 1200 --- (2) Subtracting 2nd from 1st, we get -C + T = 100 => T - C = 100 ANSWER:E #### E QUESTION:The area of a circle is increased by 300%. By what percent has the diameter of the circle increased? options: A) 400% B) 200% C) 300% D) 100% E) 800% SOLUTION:The area of the circle is increased by 300%, thus the area is increased 4 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 2 times (diameter increase 2 times = area increase 4 times), which is increase by 100%. Answer: D. #### D QUESTION:A man divides $8600 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive? options: A)A)$200 B)B)$1000 C)C)$800 D)D)$1011.76 E)E)$400 SOLUTION:Let the share of each nephews be $X. Then, share of each daughter=$4X, share of each son= $5X. So, 4*4X+4*4X+2*X=8600 16X+16X+2X=8600 34X=8600, X=252.94. Daughter receives four times of nephew so 4 * 252.94 = 1011.76. So Each Daughter receives $800. answer is option D) $1011.76. #### D QUESTION:A person travels equal distances with speeds of 5km/hr, 10km/hr, 15km/hr. and takes a total time of 11minutes. Find the total distance ? options: A)1km B)1500mts C)1600mts D)2km E)1250mts SOLUTION:Let the each distance be x km total distance = 3x then total time, (x/5)+(x/10)+(x/15) = 11/60 x=0.5 total distance = 3*0.5 = 1.5km = 1500meters correct option is B #### B QUESTION:What is the measure of the angle Y made by the diagonals of the any adjacent sides of a cube. options: A)30 B)45 C)60 D)75 E)90 SOLUTION:C.. 60 degrees All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.C #### C QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 24th of September 1990? options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday SOLUTION:19th September 1987: Saturday 1988: Monday (due to leap year) 1989: Tuesday 1990: Wednesday Hence 24th September was a Monday. The answer is A. #### A QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)70 E)58 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70. Thus D is the correct answer choice #### D QUESTION:In a dairy farm, 50 cows eat 50 bags of husk in 50 days. In how many days one cow will eat one bag of husk ? options: A)34 days B)40 days C)46 days D)50 days E)None of these SOLUTION:Explanation: Less Cows, More days (Indirect Proportion) Less bags, Less days (Direct Proportion) [Cows1 50 Bags 50 1]::50:x =>x∗50∗1=50∗1∗50 =>x=50 Option D #### D QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? options: A)267 B)766 C)810 D)868 E)812 SOLUTION:12 men 120 acres 36 days 54 men ? 54 days 120 * 54/12 * 54/36 10 * 54 * 3/2 54 * 15 = 810 Answer:C #### C QUESTION:If a trader sold two cars each at Rs. 325475 and gains 10% on the first and loses 10% on the second, then his profit or loss percent on the whole is? options: A)1.44% B)1.74% C)1.84% D)1.47% E)1.00% SOLUTION:SP of each car is Rs. 325475, he gains 10% on first car and losses 10% on second car. In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (10)(10)/100 % = 1.00% Answer:E #### E QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-4)(x+9)(2X+5) = 0? options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2 SOLUTION:x = -2.5 Prob =1/12 Answer - A #### A QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)None of these SOLUTION:Explanation : Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer : Option C #### C QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8 SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 5(5/11) min. ANSWER:D #### D QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place. options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours SOLUTION:1/5+2/8 + 3/x = 1 x =20 hours. ANSWER =D #### D QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)12:17 C)17:12 D)21:32 E)15:19 SOLUTION:Here capital is not the same. Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =(20000×6+15000×6) Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio =(30000×4+50000×4) Suresh : Kiran =(20000×6+15000×6) :(30000×4+50000×4) =(20×6+15×6):(30×4+50×4) =(20×3+15×3):(30×2:50×2) =105:160 =21:32 Answer is D. #### D QUESTION:The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)6535 B)6532 C)6725 D)6874 E)6972 SOLUTION:C 6725 CP = SP * (100/(100 + profit%)) = 8339(100/124) = Rs. 6725 #### C QUESTION:We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy? options: A)A)36 B)B)90 C)C)40 D)D)42 E)E)44 SOLUTION:Let B be the number of blue hats and let G be the number of green hats. B+G=85. B=85-G. 6B+7G=600. 6(85-G)+7G=600. 510-6G+7G=600. G=600-510=90. The answer is B. #### B QUESTION:If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:The fourth proportional to 5, 8, 15 is options: A)18 B)19 C)20 D)24 E)None SOLUTION:Sol. Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : : 15 : x ⇔ 5x = (8x15) ⇔ x = (8x15) / 5 = 24. Answer D #### D QUESTION:Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate? options: A) 3 B) 6 C) 7.2 D) 5 E) 9 SOLUTION:Answer is D. x/x+36=1/5 x=9 14-9=5 #### D QUESTION:Find the simple interest on Rs. 73,000 at 16 2/3% per year for 9 months. options: A)7500 B)6500 C)8125 D)9125 E)None of them SOLUTION:P = Rs.73000,R = 50/3% p.a and T = 9/12 years = 3/4years. Simple Interest = (P*R*T)/100 = Rs.(73,000*(50/3)*(3/4)*(1/100))= Rs.9125 Answer is D. #### D QUESTION:What least number must be subtracted from 9679 so that the remaining number is divisible by 15? options: A)3 B)1 C)16 D)4 E)15 SOLUTION:On dividing 9679 by 15, we get remainder = 4. Required number be subtracted = 4 ANSWER:D #### D QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)20/9 hours E)30/43 hours SOLUTION:Speed downstream = 20 + 7 = 27 kmph. Time required to cover 60 km downstream = d/s = 60/27 = 20/9 hours. Answer: D #### D QUESTION:If each side of a square is increased by 20%, find the percentage change in its area? options: A)40% B)42% C)46% D)44% E)38% SOLUTION:let each side of the square be a , then area = a x a New side = 120a / 100 = 6a / 5 New area =(6a x 6a) / (5 x 5) = (36a²/25) increased area== (36a²/25) - a² Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44% answer :D #### D QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)200 B)220 C)240 D)250 E)260 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: Option C #### C QUESTION:The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:A water tank is three-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely? options: A)6 min B)8 min C)7 min D)9 min E)1 min SOLUTION:The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15 Since the rate is negative, the tank will be emptied. A full tank would take 15 minutes to empty. Since the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes The answer is D. #### D QUESTION:The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? options: A)2197 B)1267 C)1750 D)2267 E)1262 SOLUTION:Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000] = (4000 * 11/10 * 11/10 - 4000) = Rs. 840. Sum = (420 * 100)/(3 * 8) = Rs. 1750 Answer:C #### C QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 15 and 16. The larger of the two numbers is: options: A)338 B)278 C)322 D)368 E)121 SOLUTION:Clearly, the numbers are (23 * 15) and (23 * 16). Larger number = (23 * 16) = 368. Answer: D #### D QUESTION:A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? options: A)27 B)29 C)40 D)89 E)22 SOLUTION:1/8 - 1/x = 1/10 x = 40 Answer: C #### C QUESTION:The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is: options: A)20 B)30 C)48 D)58 E)68 SOLUTION:Explanation: Let the three parts be A, B, C. Then, A : B = 2 : 3 and B : C = 5 : 8 =5*3/5 : 8*3/5 =3: 24/5 A : B : C = 2 : 3 : 24/5=10:15:24 B = 98* 15/49 =30. Answer IS B #### B QUESTION:Of the science books in a certain supply room, 50 are on botany, 60 are on zoology, 90 are on physics. 40 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? options: A)81 B)159 C)309 D)285 E)324 SOLUTION:First, you can take all 50 Botany books, all 60 zoology books and all 40 geology books because you're sure to never pick 80 of them. There are still 90 on physics and 110 on chemistry The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry. Minimum number of books picked to reach 80 in the same science should be : 50 + 60 + 40 + 79 +79 + 1 = 309 C #### C QUESTION:If (2/3)^n=(3/2)^3, what is the value of n? options: A)-3 B)-2 C)-1 D)0 E)1 SOLUTION:(2/3)^n = (3/2)^3 = (2/3)^-3 n = -3 (Answer = A) #### A QUESTION:If a + b = y and a - b = z , then 3ab = can someone explain! options: A)(3y^2 - 3z^2)/4 B)(3z^2 - 3y^2)/4 C)3y+3z/2 D)3y - 3z/2 E)3y^2 - 3z^2/2 SOLUTION:plugging numbers is quite fast in this case: Let a=1 b=2 Then; y= 1+2=> 3 and z= 1-2=> -1 Question asks 3ab=......... As our number 3ab= 3*1*2=6 now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need. Hence: Ans is A. #### A QUESTION:9.7 , 9.7 , 9.9 , 9.9 , 10.0 , 10.1 , 10.2 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.25 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90% B)85% C)80% D)75% E)70% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.25; 10+0.25} = {9.75; 10.25}. From the 8 listed numbers, 5 are within this range so 5/8=75%. Answer: D. #### D QUESTION:There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need to remove so that only 96% of the apples are green? options: A)40 B)8 C)15 D)25 E)50 SOLUTION:98−x/100−x=96100 Or, 9800−100x=9600−96x Or, 200=4x Or, x=50 ANSWER:E #### E QUESTION:Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is: options: A)3776 B)1284.2 C)8400 D)1666.6 E)1671.8 SOLUTION:Ratio of their shares = 1000: 5000= 1:5 Deepak's share = 2000 * 5/6 = Rs. 1666.6. Answer: D #### D QUESTION:What is the unit digit of (6!*3! / 3!*4!)? options: A)5 B)6 C)0 D)3 E)4 SOLUTION:(6!*3! /3!*4!) =(6! / 4!) =5*6 =30 Units digit of the above product will be equal to 0 Answer C #### C <<<Examples ends QUESTION:The sum of the squares of three number is 138,while the sum of their products taken two at a time is 131. their sum is : options: A)20 B)30 C)40 D)None of these E)Cannot be determined SOLUTION:Solution Let the numbers be a,b and c then, a 2 + b 2+ c 2 = 138 and (ab + b c + ac) = 131. (a + b+ c)2 = a 2 + b 2 + c 2 + 2(ab + b c + ca) = 138 + 2 * 131 = 400 . ⇒ (a + b + c) = 400/20= 20 Answer A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:One card is drawn from a pack of 52 cards. What is the probability that the card drawn is not a face card? options: A)4/15 B)5/17 C)9/13 D)3/13 E)7/15 SOLUTION:Out of 52 cards there will be 16 face cards are there. probability of getting not a face card = 36/52 = 9/13 Answer is C #### C QUESTION:there r 5 papers Ratio of marks obtained in each subject is 6:7:8:9:10. Total marks obtained is 60%. 50% is pass marks. In how many subjects did he get above 50%. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Total marks in 5 papers = 60% (i.e., 60*5 = 300) 6x+ 7x+ 8x+ 9x+ 10x =60/100(500) Put x= 8 for solving, 6x= 48; 7x = 56; 8x = 64 ; 9x = 72; 10x = 80 Marks are 6:7:8:9:10 = 48+56+64+72+80 = 300 So, 4 subjects he got 50% above ANSWER:D #### D QUESTION:If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there? options: A)22896 B)25423 C)26980 D)24698 E)24360 SOLUTION:Code consists of 3 digits and no digit is repeated. First digit of the code can have 30 possibilities Second digit can have 29 possibilities Third digit can have 28 possibilities Total number of possible codes = 30*29*28 = 24360 Answer: E #### E QUESTION:If k is a non-negative integer and 15^k is a divisor of 823,435 then 5^k - k^5 = options: A)0 B)1 C)35 D)120 E)245 SOLUTION:8+2+3+4+3+5 = 25, so this number is not divisible by 3 and thus not divisible by 15. Therefore, k=0 5^k - k^5 =1-0=1 The answer is B. #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.27 C)Rs.51.79 D)Rs.51.8 E)Rs.51.93 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs.51.25. Answer: A #### A QUESTION:Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 23 years. Father's age when Ayesha's brother was born = (29 + 3) years = 32 years. Required difference = (32 - 23) years = 9 years. Answer: Option E #### E QUESTION:If y = ||x – 3| – 2|, for how many values of x is y = 5? options: A)2 B)1 C)3 D)4 E)5 SOLUTION:y = ||x – 3| – 2| can be 4 only and only when X-3= +/-7. so there are 2 values of X Answer : A #### A QUESTION:If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n? options: A)10 B)12 C)15 D)18 E)20 SOLUTION:There are 10 numbers divisible by 2 There are 5 numbers divisible by 4 There are 2 numbers divisible by 8 There is 1 number divisible by 16. Hence the total number of 2’s in 20! are 10+5+2+1=18 ANSWER:D #### D QUESTION:For which of the following functions does f(−z)=−f(z) for all real number values of x? options: A)z^8−z^4 B)z^5/(z^2+1) C)z^5/z^7 D)z^9/(z^5+1) E)z^8 SOLUTION:all even root cannot be matched eliminated put z=2 f(−z)=(−2)^5/(−2^)2+1=−32/5, and −f(z)=−2^5/2^2+1=−32/5, for a match. ANSWER: B #### B QUESTION:A man can row upstream at 10kmph and downstream at 18 kmph. The speed of the stream is options: A)2.5 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(18 -10) kmph = 4 kmph. Answer B #### B QUESTION:In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can? options: A)52 B)56 C)60 D)64 E)68 SOLUTION:Let C be the capacity of the can. (5/8)*(C-20)+20=(3/4)*C 5C-100+160=6C C=60 The answer is C. #### C QUESTION:What was the day of the week on, 18th July, 1776? options: A)Thursday B)Wednesday C)Monday D)Saturday E)SUNDAY SOLUTION:16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776) Counting of odd days : 1600 years have 0 odd day. 100 years have 5 odd days. 75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days. 1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day. Jan Feb Mar Apr May Jun Jul 31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days) Total number of odd days = (0 + 4) = 4. Required day was 'Thursday'. Answer:A #### A QUESTION:A jogger running at 9 km/hr along side a railway track is 180 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)89 B)20 C)36 D)88 E)30 SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 180 + 120 = 300 m. Time taken = 300/10 = 30 sec. Answer: Option E #### E QUESTION:The average height of 35 boys in a class was calculated as 185cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).? options: A)178.27 cm B)183.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 185 cm. Wrong total height of 35 boys = 185 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 185 cm - (166 cm - 106 cm)/35 =185 cm - 60 /35 cm = 185 cm - 1.71 cm = 183.29 cm. Answer: B #### B QUESTION:P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}? options: A){6, 12} B){6, 15} C){21,28} D){9, 15} E){15, 24} SOLUTION:p/q= d=p/q+7 d= .75 q d= .6(q+7) we get d = 21 and q = 28. Answer = C. #### C QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)12 B)45 C)77 D)88 E)51 SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer: B #### B QUESTION:If d<0, which of the following represents a positive number? options: A)d|d| B)|d|d C)|d|/d D)-d|d| E)d/ |d| SOLUTION:Answer : D #### D QUESTION:A bicyclist's wheel has a circumference of 6 meters. if the bicyclist covers 180 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour. To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.=180/6*5 =6 Answer (E) #### E QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:Today Joelle opened an interest-bearing savings account and deposited $10,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account? options: A)$12025 B)$11075 C)$11025 D)$11095 E)$11015 SOLUTION:Interest for 1st year =10000*5/100 = 500 Interest for 2nd year = 10500 *5/100 = 525 Total =10000+500+525 = 11025 Answer : C #### C QUESTION:6x + 2y = -4 4x + y = 1 In the system of equations above, what is the value of x? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:6x + 2y = -4 can be written as 3x + y = -2 Let's subtract the second equation from this equation. -x = -3 x = 3 The answer is C. #### C QUESTION:if log 5 = 0.69897, the number of digits in 5128 is options: A)90 B)39 C)88 D)28 E)11 SOLUTION:Explanation: log(5128) = 128log(5) = 128 × 0.69897 ≈ 89.46 ie, its characteristic = 89 Hence, number of digits in 2128 = 89+1 = 90 Answer: Option A #### A QUESTION:Find the value of (1-(1/3))(1-(1/4))(1-(1/5))….(1-(1/100)). options: A)1/50 B)3/50 C)4/50 D)6/50 E)9/50 SOLUTION:Answer is A. #### A QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle? I. 4 II. 12 III. 24 options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only SOLUTION:Answer = A. I, II, and III With dimensions of only 2 sides given (for a triangle), this becomes an open ended question Any area is possible out of the three #### A QUESTION:Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(a + y) / t B)2(a + t) / ay C)2ayt / (a + y) D)2(a + y + t) / ay E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for a 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:What is 30% of 210? options: A)61 B)63 C)65 D)67 E)69 SOLUTION:X/210 = 30/100 100X = 210X30 X =(210X30)/100 X =6300/100 = 63 ANSWER = B = 63 #### B QUESTION:597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred’s and ten’s places are respectively: options: A)3 and 6 B)7 and 9 C)2 and 6 D)4 and 7 E)None SOLUTION:Solution : Let the given number be 597xy6. Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3 And, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0 => y=x+3 27+x+y) =>(27+x+x+3) =>(30+2x) => x = 3 and y = 6. Answer A #### A QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 10 years? options: A)3 : 2 B)1 : 3 C)2 : 3 D)1 : 5 E)2 : 1 SOLUTION:Explanation : Simple Interest = PRT/100 Here Principal(P) and Rate of Interest (R) are constants Hence, Simple Interest ∝ T Required Ratio = Simple Interest for 2 years/Simple Interest for 10 years =T1/T2 =2/10 =1/5 =1:5 Answer : Option D #### D QUESTION:If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a eight-percent vinegar solution, what was the concentration of the original solution? options: A)9.3% B)17.3% C)26.67% D)35.5% E)41.3% SOLUTION:Let X be the quantity of non-vinegar in the strong vinegar solution Thus vinegar quantity will be 12 - X When 50 ounces of water were added the percentage of vinegar becomes 8%, thus (12 - X)/62 = 8/100 From this equation X = 7.04 Answer (12-7.04)/12 = 41.3% ANSWER:E #### E QUESTION:A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? options: A)4 : 3 B)9:2 C)18:20 D)1:4 E)18:4 SOLUTION:A: B =24000 : 18000 = 8 : 6 = 4 : 3 ANSWER:A #### A QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)58 km/hr SOLUTION:Speed of the train relative to man = 125/10 m/sec = 25/2 m/sec. 2 = 25/2 x 18/5 km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 x = 50 km/hr. Option B #### B QUESTION:While working alone at their respective constant rates, server J uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files? options: A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr SOLUTION:Server J processes 480/4 files per hour = 120 per hour Server Y processes 180/8 files per hour = 60 per hour Total files processed per hour when J and Y work together = 120+60 per hour = 180 files per hour 480/180 = 2 2/3 hours=C #### C QUESTION:A certain list of 100 data has an average (arithmetic mean) of 8 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 106 data with standard deviation less than d? options: A)-8 and 0 B)0 and 0 C)0 and 8 D)0 and 16 E)8 and 8 SOLUTION:Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 8 and 8 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. Answer: E. #### E QUESTION:There are 3 classes having 20, 24 and 30 students respectively having average marks in an examination as 20,25 and 30 respectively. The three classes are represented by A, B and C and you have the following information about the three classes. a. In class A highest score is 22 and lowest score is 18 b. In class B highest score is 31 and lowest score is 23 c. In class C highest score is 33 and lowest score is 26. options: A)can't be determined in both cases B)definite decrease in both cases C)definite increase in both cases D)will remain constant in both cases E)will remain constant in both cases21 SOLUTION:Ans: B Explanation: Class A average is 20. And their range is 18 to 22 Class B average is 25. And their range is 23 to 31 Class A average is 30. And their range is 26 to 33 If 5 students transferred from A to B, A's average cannot be determined but B's average comes down as the highest score of A is less than lowest score of B. If 5 students transferred from B to C, C's average cannot be determined the B's range fo marks and C's range of marks are overlapping. Answer:A #### A QUESTION:A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 5 hours. During that time, the faster car traveled 2/3 of the distance XY. How long would it take the slower car to travel the distance XY? options: A)6 hours B)8 hours C)10 hours D)12 hours E)15 hours SOLUTION:If one car travelled 2/3, then the other car must have travelled only 1/3, as they are meeting after 5 hours in a certain point. So: (1/3)XY= 4*y --> It took the car 5 hours to travel 1/3 of the distance at a constant speed y. So if we solve this last equation: XY= 3*5*y= 15*y --> It will take this car 15 hours in total to reach its final destination. Answer: E #### E QUESTION:Rectangular tile each of size 60cm by 56cm must be laid horizontally on a rectangular floor of size 560cm by 240cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: options: A)50 B)54 C)47 D)40 E)45 SOLUTION:Area of tile = 60*56 = 3360 Area of floor = 560*240 = 134400 No of tiles = 134400/3360 = 40 So, the no of tile = 40 ANSWER:D #### D QUESTION:In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is: options: A)24 B)26 C)42 D)46 E)48 SOLUTION:Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2. Sum of digits = x + (x + 2) = 2x + 2. (11x + 2)(2x + 2) = 144 22x2 + 26x - 140 = 0 11x2 + 13x - 70 = 0 (x - 2)(11x + 35) = 0 x = 2. Hence, required number = 11x + 2 = 24. Answer:A #### A QUESTION:Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If they are 85 km apart both 3 and 6 hours after start, then find the distance between the two stations. options: A)255km B)210km C)220km D)180km E)200km SOLUTION:In first 3 hours T1 travels R km and T2 travels S km. After 6 hours they traveled R+S+85+ 85 2(R+S ) = R+S +170 R+S = 170 Hence distance between XY is R+S+ 85 = 170 +85 =255 Answer : A #### A QUESTION:5 3 -2 -5 -3 2....What is the sum of first thirty number sequence? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 => 50-50=0. ANSWER:A #### A QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)8 B)10 C)12 D)14 E)15 SOLUTION:Number of ways in which one can travel from P to R =3×4=12 Answer: Option C #### C QUESTION:A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos? options: A)2 films and 6 photos B)5 films and 6 photos C)5 films and 14 photos D)6 films and 4 photos E)6 films and 28 photos SOLUTION:1st photo = 0.50 Subsequent = 0.50*0.6=0.3 Price of 1 full film=0.50+0.3*35=11 Price of 2 full film = 11*2=22 24-22=2 2=0.5+0.3x x=5 24--->2 full films and 1+5=6 photos Answer: A #### A QUESTION:The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 3 years? options: A)5100 B)4096 C)5200 D)5400 E)5500 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 8000 × 80/100 × 80/100 x 80/100= 4096 Answer : B #### B QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125 options: A)134 B)154 C)166 D)178 E)189 SOLUTION:28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C #### C QUESTION:If E is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of E? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:E = 30! 8 E = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 So we have a total of 14 three's ... Therefore the maximum value of K can be 14 (C) #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 --> 2x = 20 --> x = 10. --> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. Answer : C. #### C QUESTION:A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 80 percent of the drive from the center, what percent of the round-trip has the technician completed? options: A)5% B)75% C)25% D)40% E)50% SOLUTION:The complete round trip consists of driving to the service center and then back home again. So, once the technician drives to the service center he/she has already competed 50% of the entire trip. Since the technician completes a portion of the trip back home,the correct answer must be greater than 50% Only one answer choice works. Answer: B #### B QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? options: A)12 min B)17 min C)19 min D)11 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 6 - 1 = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min. Answer: A #### A QUESTION:Minute hand overlaps hour hand in 65 mins. In how many days it will gain 1440 hours ? options: A)58.384 days B)59.384 days C)57.384 days D)69.384 days E)55.384 days SOLUTION:In this problem , it has considered that 65 mins = 1hr so mins has increased by 5 mins so multiply 5*24=120 mins extra , That is now per day it adds 2hr extra so divide 1440/26=59.384 days ANSWER:B #### B QUESTION:Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat? options: A)5! B)8! C)9! D)12! E)11! SOLUTION:Ans.(B) Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways #### B QUESTION:Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 75 km more than the other. What is the distance between the two stations? options: A)540 km B)675 km C)276 km D)178 km E)176 km SOLUTION:Explanation: Let us assume that trains meet after 'x' hours Distance = speed * Time Distance traveled by two trains = 20x km and 25x km resp. As one train travels 75km more than the other, 25x – 20x = 75 5x = 75 x = 15 hours As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr Therefore, total distance = 45*15 = 675 km. ANSWER: B #### B QUESTION:Zaya purchase 13 jars in a store then she returned 10 jars to store .Now how many jars she had? options: A)A)5 B)B)11 C)C)19 D)D)3 E)E)4 SOLUTION:13-10=3. Answer is D #### D QUESTION:If 2994 ÷ 14.5 = 171, then 29.94 ÷ 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.2 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ] = 171/10 = 17.1 Answer is A. #### A QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded? options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :- letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..) Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get IDAATRE ANSWER:D #### D QUESTION:There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ? options: A)9:6 B)3:2 C)118:126 D)193:122 E)201:132 SOLUTION:m=portion of milk in solution m=(4/7+2/3+3/5)/3➡193/315 315-193=122 122/315=portion of water in solution ratio of milk to water=193/122 ANSWER:D #### D QUESTION:What is the leastvalue of x. So that 23x57 is divisible by 3? options: A)3 B)4 C)1 D)5 E)6 SOLUTION:The sum of the digits of the number is divisible by 3, then the number is divisible by3. 2 + 3 + x + 5 + 7 = 17 + x Least value of x may be 1 Therefore 17 + 1 = 18 is divisible by 3. C #### C QUESTION:A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage? options: A)116% B)166.66% C)60% D)100% E)150% SOLUTION:Explanation: Let the cost price of 1 litre pure milk be Re.1, then {6 litres(milk)->cp=Rs.6, 2 litres(water)->cp=Rs.0}->cp=Rs.6 only and 8 litre mixture ->SP -> 8 x 2 = Rs.16 Profit %= [16/6 -6]x100=100/6=166.66% ANSWER IS B #### B QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2 SOLUTION:42/360 * 22/7 * 12 * 12 = 52.8 m2 Answer: C #### C QUESTION:What is the units digit of (3^5)(4^13)? options: A)2 B)4 C)6 D)7 E)8 SOLUTION:-> The ones place of (~3)^n repeats after 4 times like 39713. The ones place of (~4)^n repeats after 2 times like 464. Then, 3^5=3^4*1+13^1., 4^13=4^2*6+1=4^1=~4 which is (3^5)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is A. #### A QUESTION:If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour? options: A)17/140 B)29/180 C)26/143 D)1/5 E)39/121 SOLUTION:50 apprentices can finish the job in 4 hours,thus: 10 apprentices can finish the job in 4*5 = 20 hours; In 1 hour 10 apprentices can finish 1/20 of the job. 30 journeymen can finish the same job in 4,5 hours,thus: 15 journeymen can finish the job in 7*2 = 14 hours; In 1 hour 15 journeymen can finish 1/14 of the job. Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job. Answer: A #### A QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)120% B)190% C)100 percent D)200% E)101% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)95 SOLUTION:number of handshakes = 10C2= 10*9/2 = 45 ANSWER:B #### B QUESTION:A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |Y|<3? options: A)1/7 B)3/7 C)2/5 D)3/11 E)4/7 SOLUTION:|X||X| can take 7 values. To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x ⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases = 3/7 B #### B QUESTION:There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly then what is the probability that neither blue nor green? options: A)2/21 B)3/31 C)4/17 D)3/19 E)probability=8/21 SOLUTION:Total number of balls = (8 + 7 + 6) = 21 Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red. Therefore, n(E) = 8. P(E) = 8/21. #### E QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 5 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 5 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 8 a.m. Answer: C #### C QUESTION:A car covers a distance of 630 km in 6 ½ hours. Find its speed? options: A)105 kmph B)176 kmph C)298 kmph D)186 kmph E)268 kmph SOLUTION:630/6 = 105 kmph Answer:A #### A QUESTION:What is value of (P + Q)/(P - Q) if P/Q = 7 ? options: A)1/3 B)2/3 C)4/3 D)5/3 E)None of these SOLUTION:Explanation: (P + Q)/(P - Q) = (P/Q+1)/(P/Q - 1) = (7 +1)/(7 - 1) = 4/3. Answer: C #### C QUESTION:In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different Y sets can be produced by this process? options: A) 41 B) 89 C) 125 D) 243 E) 512 SOLUTION:Case 1: 1 used envelope => 1 way Case 2: 2 used envelopes - 4-1-0: Choose 4 from 5 cards: 5 ways - 3-2-0: Choose 3 from 5 cards: 10 ways Case 3: All envelopes used - 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways - 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15 Total Y: 1+5+10+10+15=41 => Answer: A #### A QUESTION:How many terminating zeroes T does 200! have? options: A) 40 B) 48 C) 49 D) 55 E) 64 SOLUTION:You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C #### C QUESTION:Goldenrod and No Hope are in a horse race with 6 contestants. How many different L arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race? options: A) 720 B) 360 C) 120 D) 24 E) 21 SOLUTION:no hope finishing before goldenrod= 1/2 of the times therefore the different L arrangements are 1/2* 6! = 360 = B #### B QUESTION:If, 1 * 3 * 5 = 16 3 * 5 * 7 = 38 Then find, 15 * 17 * 19 =? options: A)89 B)49 C)68 D)38 E)338 SOLUTION:E 338 (19 * 17) + 15 = 338 #### E QUESTION:Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.60? options: A)426 B)430 C)443 D)470 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones. Having 7.6$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.6 $ left. so we buy 1 pack of 50 for 1$. We now have 0.6$ left, so we buy 20 individual envelopes. If we add up the numbers, we get 400+50+20=470 envelopes. Answer D #### D QUESTION:40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:Let x be the amount of liquid Q to be added. (3/8)*40 + x = (6/11)*(40+x) 1320 + 88x = 1920 + 48x 40x = 600 x = 15 The answer is E. #### E QUESTION:Find value of x from given equation 2x + 1 = -17 options: A)-8 B)-9 C)-7 D)7 E)6 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:In how many ways can six members be selected from a group of ten members? options: A)10C6 B)10C8 C)10C4 D)10C3 E)10C1 SOLUTION:Six members can be selected from ten members in 10C6 = 10C4 ways. Answer: B #### B QUESTION:Which is the middle even number between 6 and 14? options: A)10 B)6 C)8 D)14 E)26 SOLUTION:6+x = 14-x 2 x = 8 X = 4 Now 6+x = 10 ANSWER:A #### A QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 972 sq m, then what is the breadth of the rectangular plot? options: A)16 B)17 C)18 D)19 E)14 SOLUTION:Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 972 3b2 = 972 b2 = 324 b = 18 m. Answer: Option C #### C QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton? options: A)330 B)300 C)252 D)225 E)210 SOLUTION:Baker Ram is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5. To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210. Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210. #### E QUESTION:Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour? options: A)a) 66.67-x B)b) 40-x C)c) 80-2x D)d) 120-x E)e) 40-x/2 SOLUTION:Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same. Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of: R = (100 mi)/(1.5) = 66.67 mph That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars. One of the speeds is x, and let's call the other y. We want y. x + y = 66.67 y = 66.67 - x Answer =(A) #### A QUESTION:The present ages of three persons in proportions 5 : 6 : 4. Five years ago, the sum of their ages was 60. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)25,30,20 D)18, 24, 32 E)None of these SOLUTION:Explanation: Let their present ages be 5x, 6x and 4x years respectively. Then, (5x - 5) + (6x - 5) + (4x - 5) = 60 15x-15 = 60 x = 5 Their present ages are 5x = 25 years, 6x = 30 years and 4x = 20 years respectively. Answer: C #### C QUESTION:A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)300 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 =350 B #### B QUESTION:A wildlife preserve is being planned for 6,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population? options: A) 340 B) 330 C) 670 D) 310 E) 300 SOLUTION:Number of rhinos = 6000 Watering area = 10,000 acres Number of rhino to increase by 10 percent ,then number of rhino = 6600 Grazing area for a rhino = 100 Total grazing area for 6600 rhinos= 6600 * 100 = 6,60,000 Total area required for the wildlife preserve = 6,60,000 + 10,000 = 6,70,000 = 670 * 1000 Answer C #### C QUESTION:8^100 is divisible by 17. Find the remainder? options: A)10 B)12 C)16 D)18 E)20 SOLUTION:This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1. So divide 100 by 16 and find the remainder. Remainder = 4 Therefore, 100 = (16 × 6) + 4 Now this problem can be written as 810017 = 816×6+417 = (816)6×8417 Now this problem simply boils down to (1)6×8417 = 8417 84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16. C #### C QUESTION:(A% of 2B + B% of A) is equal to ? options: A)A% of B B)B% of A C)3% of AB D)AB% of 3 E)None SOLUTION:Answer A% of 2B + B% of A =2AB/100 + AB/100 = 23AB/100 = 3% of AB Correct Option: C #### C QUESTION:If 3 women can color 180 m long cloth in 2 days, then 5 women can color 300 m long cloth in? options: A)2 days B)3 days C)5 days D)1 day E)4 days SOLUTION:The length of cloth painted by one woman in one day = 180/ 3× 2 = 30 m No. of days required to paint 300 m cloth by 5 women = 300/ 5 × 30 = 2 days Answer : A #### A QUESTION:Mixture A is 30 percent alcohol, and mixture B is 60 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 40 percent alcohol, approximately how many gallons of mixture A are in the mixture? options: A)0.8 B)0.7 C)0.6 D)0.5 E)0.4 SOLUTION:(60-50)/(50-30) = Qa/Qb 10/20= Qa/Qb 1/2 = Qa/Qb Qa = (1/6) * 4 = 4/6 = 1/2 = 0.50 Answer : D #### D QUESTION:The sale price sarees listed for Rs.200 after successive discount is 20% and 5% is? options: A)187 B)169 C)152 D)178 E)175 SOLUTION:200*(80/100)*(95/100) = 152 Answer:C #### C QUESTION:In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden. What is the length of the garden? options: A)22 B)24 C)26 D)28 E)30 SOLUTION:Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length Also, 3 meter is left from all sides of the boundary of the garden. Hence, length of the garden = (11 × 2) + 3 + 3 = 28 meter Answer is D. #### D QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is? options: A)8118 B)8127 C)8618 D)8436 E)8128 SOLUTION:A = 7500(26/25)3 = 8436 Answer: D #### D QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2000 B)2781 C)2278 D)2081 E)2721 SOLUTION:Explanation: (10*10)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer: A #### A QUESTION:For 1rs 6p interest wat will be for 1000rs? options: A)45Rs B)50Rs C)40Rs D)30Rs E)60Rs SOLUTION:For 1rs , 4p interest for 1000rs, x x= 1000/1 * 6p ==> 6000 paise To express in rs, 6000/100 = 60rs ANSWER:E #### E QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 6? options: A)1/4 B)5/36 C)2/11 D)3/13 E)1/5 SOLUTION:n(S) = 6*6 = 36 E = {(1,5),(2,4),(3,3),(4,2),(5,1)} Probability = 5/36 Answer is B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)40 B)41 C)48 D)67 E)45 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: Option C #### C QUESTION:The speeds of 3 trains in the ratio 10:15:20. The ratio between time taken by them to travel the same distance is? options: A)6:4:3 B)1:2:3 C)4:8:9 D)6:5:2 E)4:8:7 SOLUTION:Ratio of time taken is = 1/10 : 1/15 : 1/20 = 6:4:3 Answer is A #### A QUESTION:The difference between simple interest and C.I. at the same rate for Rs.5000 for 2 years in Rs.72. The rate of interest is? options: A)11 B)12 C)77 D)85 E)65 SOLUTION:5000 = 72(100/R)2 5 R2 = 720 => R = 12.Answer:B #### B QUESTION:What is the remainder when 1014*1047*1050*1053 is divided by 33? options: A)3 B)6 C)30 D)21 E)18 SOLUTION:OA is 'C'. OE: take the remainder from each of 1044/33, 1047/33 and so on.. 1014/33 gives remainder = 24 1047/33 gives remainder = 24 1050/33 gives remainder = 27 1053/33 gives remainder = 30 the net remainder is the product of above individual remainders. i.e = 24*24*27*30 break them into pairs 24*24/33 gives remainder 15 and 27*30/33 gives remainder 18 so 15*18/33 gives remainder 6. B #### B QUESTION:A garrison of 150 men has provisions for 31 days. At the end of 16 days, a reinforcement arrives, and it is now found that the provisions will last only for 5 days more. What is the reinforcement? options: A)150 B)450 C)400 D)600 E)300 SOLUTION:150 ---- 31 150 ---- 15 x -----5 x*5 = 150*15 x = 450 150 ------- 300 Answer: E #### E QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ? options: A)95 B)110 C)20 D)None of these E)Cannot be determined SOLUTION:Solution 2/5of 350 - 4/7of 210 = 20. Answer C #### C QUESTION:The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to: options: A)0.04 B)0.004 C)0.4 D)0.0004 E)None of them SOLUTION:Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is A #### A QUESTION:When n is divided by 48, the remainder is 6. What is the remainder when 4n is divided by 8? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 48) 4n = 4(6) =24, which leaves a remainder of 0 when divided by 8. Answer A #### A QUESTION:probability that guy1 will succesfully hit a shot is 2/3. probabilty of guy2 succesfully hitting a shot is 2/3. if they shoot two shots each, what is the probability that they have equal number of hits? options: A)9/27 B)10/27 C)11/27 D)12/27 E)11/26 SOLUTION:(1/3*1/3)[guy1]*(1/3*1/3)[guy2] for 1 hit each: (4 ways) (2/3*1/3)*(2/3*1/3), (2/3*1/3)*(1/3*2/3), (1/3*2/3)*(2/3*1/3), (1/3*2/3)*(1/3*2/3) for 2 hits each:(1 way) (2/3*2/3)*(2/3*2/3) Add all these cases, you will get answer as 11/27. ANSWER:C #### C QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6 SOLUTION:Explanation: 40*(48/100) = 19.2 --- 64 ? --- 12 => Rs.3.6 Answer: D #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent? options: A)75% B)67% C)29% D)55% E)45% SOLUTION:600 --- 400 100 --- ? => 67% Answer: B #### B QUESTION:Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 7 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them? options: A)22 km B)40 km C)65 km D)18 km E)16 km SOLUTION:Distance = Relative Speed * Time = (7 + 3) * 4 = 40 km [ They are travelling in the opposite direction, relative speed = sum of the speeds]. Answer: B #### B QUESTION:The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)80 kg B)85 kg C)90 kg D)100 kg E)110 kg SOLUTION:Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. B) #### B QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:How many ONE letter words are formed using the letters of the word WALK? options: A)1 B)16 C)7 D)4 E)2 SOLUTION:The number of letters in the given word is 4. The number of ONE letter words that can be formed using these four letters is 4P1=4*1=4 Answer:D #### D QUESTION:A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 12 multiples of 14, how many multiples of 7 are there in Q? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Halfway between the multiples of 14, there will be another multiple of 7. The total number of multiples of 7 is 12+11 = 23. The answer is D. #### D QUESTION:Which of the following is closer to √0.8+√0.05? options: A)0.5 B)0.7 C)0.9 D)1.1 E)1.2 SOLUTION:√0.8+√0.05=approximately √0.81+√0.04=0.9+0.2=1.1. Hence, the correct answer is D. #### D QUESTION:A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is options: A)8 years B)2 years C)7 years D)8 years E)5 years SOLUTION:Let's Son age is x, then Father age is x+22. => 3(x+3) = (x+22+3) => 3x+9 = x+25 => 2x = 16 years = 8 YEARS Answer: D #### D QUESTION:A can work four times as fast as B. Together they can finish a job in 12 days. In how many days can A complete the job alone? options: A)14 B)15 C)16 D)17 E)18 SOLUTION:B's rate is x and A's rate is 4x. x + 4x = 1/12 x = 1/60 A's rate is 4x = 1/15 A can complete the job in 15 days. The answer is B. #### B QUESTION:The positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true? I. c > a II. c = a III. c < a options: A)I only B)II only C)III only D)I and II only E)II and III only SOLUTION:Let q = 10% then l = 100/11 % let b = 100 then a = 110 after increasing a by l and decreasing b yq we get c= 108 therefore c<a C it is answer #### C QUESTION:What is the SI on Rs.8000 from August 6th to Dec 30th at 5% per annum rate of interest? options: A)Rs 100 B)Rs 120 C)Rs 140 D)Rs 160 E)Rs 200 SOLUTION:Number of days from August 6th to December 30th = 146 days ( we don’t count the given day) Simple Interest= PTR 100 = 8000 x 146 365 x 5 100 = Rs 160 D #### D QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was? options: A)16 years B)14 years C)18 years D)19 years E)15 years SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38 => x = 19 Son's age 5 years back = (19 - 5) = 14 years. Answer: B #### B QUESTION:A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? options: A)158 m B)150 m C)110 m D)130 m E)157 m SOLUTION:Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 => y = x/15 (x + 100)/25 = x/15 => x = 150 m. Answer: B #### B QUESTION:85 80 25 70 55 25 35 ? ? options: A)10 25 B)25 85 C)35 25 D)85 35 E)25 75 SOLUTION:85-5=80 again 25 80-10=70 70-15=55 again 25 55-20=35 35-25=10 again 25 then answer is 10 ,25 ANSWER:A #### A QUESTION:If (x + 1) times (2x + 1) is an odd integer, then x must be options: A)an odd integer B)an even integer C)a prime number D)a composite number E)a negative integer SOLUTION:(x + 1) times (2x + 1) means (x + 1) * (2x + 1).. (x + 1)*(2x + 1)= 2x^2+3x+1... for 2x^2+3x+1 to be odd, 3x+1 should be odd.. hence 3x should be even, which further leads to x as even.. so x is even integer.. ANSWER:B #### B QUESTION:Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 41 pages per hour. If Tom starts reading a novel at 3:20, and Jan begins reading an identical copy of the same book at 4:26, at what time will they be reading the same page? options: A)6:26 B)6:56 C)7:26 D)7:56 E)8:26 SOLUTION:Since Tom reads an average of 1 page every 2 minutes, Tom will read 33 pages in the first 66 minutes. Jan can catch Tom at a rate of 11 pages per hour, so it will take 3 hours to catch Tom. The answer is C. #### C QUESTION:A wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face? options: A)52.9% B)55.4% C)58.3% D)61.7% E)64.5% SOLUTION:There are a total of 9*9*9 = 729 cubes. All the exterior cubes will have at least one face painted red. The interior is formed by 7*7*7 = 343 cubes. The number of cubes with at least one side painted red is 729 - 343 = 386 cubes The probability that a cube has at least one side painted red is 386/729 which is about 52.9% The answer is A. #### A QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:A firm has 3 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.) options: A)42 B)46 C)50 D)54 E)58 SOLUTION:The number of ways to form a group of 3 is 8C3 = 56 The number of groups with no senior partner is 5C3 = 10 The number of groups with at least one senior partner is 56-10 = 46 The answer is B. #### B QUESTION:In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are finance majors? options: A)3 B)5 C)8 D)11 E)17 SOLUTION:pqrs = 1365 = 3* 5 *7 * 13 Since 1< p < q < r < s, the number of students who are finance majors is q = 5. The answer is B. #### B QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,700 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Price in 96 = 22000 Price decrease each year = 2.5/100*22000 = 550 Price in 97 = 22000 - 550 Price in 98 = 22000 - 2*550 Price in 99 = 22000 - 3*550 Price in 00 = 22000 - 4*550 Price in 01 = 22000 - 5*550 Price in 02 = 22000 - 6*550 = 18700 Investment in the car = 1000 Net price of the car in 02 = 18700 + 1000 = $19700 Correct Option: B #### B QUESTION:An oblong piece of ground measures 19m 2.5dm by 12m 5dm. From the centre of each side a path 2m wide goes across to the centre of the opposite side. Find the cost of paving these paths at the rate of rs.1.32 per sq m? options: A)Rs. 43.6 B)Rs. 78.65 C)Rs 54.75 D)Rs. 344 E)Rs. 34.4 SOLUTION:Area of path horizontal=20*192.5=3850 dm^2 Area of path vertical=20*125=2500 dm^2 Since center path is covered twice so total area=(3850+2500)-(20*20)=5950 dm^2 total cost=1.32*59.5 m^2=78.54 ANSWER:B #### B QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is: options: A)51:52 B)52:53 C)51:53 D)52:55 E)53:54 SOLUTION:Explanation: Let C.P. of the article be Rs. x. Then, required ratio = 104% of x / 106% of x = 104/106 = 52/53 = 52:53 ANSWER IS B #### B QUESTION:A solution of 60 ounces of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar? options: A)20 ounces B)80 ounces C)100 ounces D)120 ounces E)180 ounces SOLUTION:20% sugar in 60 oz solution; Sugar = 60*20/100 = 12 oz Water = 60-12 = 48 oz Now; let's add "x" oz of water in the solution; Total solution = 60+x oz Sugar = 12 oz.(Sugar's amount will not change as we are not adding or subtracting sugar) 12 = (60+x) * 5/100 60+x = 240 x = 240 - 60 = 180 oz Answer: "E" #### E <<<Examples ends QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)364 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 120 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school? options: A)30 B)50 C)70 D)80 E)90 SOLUTION:Let x be the number of new boarders. The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10. 120 / (120+x) = 4/5 x = 30 The answer is A. #### A QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)106 C)110 D)120 E)130 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes? options: A)6 min B)12 min C)10 min D)15 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 11 - 1 = 10 rounds per hour. Time taken to complete one round at this speed = 1/10 hr = 6 min. A #### A QUESTION:If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5+a^6)? options: A)-14 B)-4 C)-1 D)4 E)14 SOLUTION:if a = -1, then putting values in equation = -[ (-1)^2 + (-1)^3 + (-1^4) + (-1^5)+(-1^6) ] = -[ 1 - 1 + 1 - 1 + 1] = -1 Answer = C = -1 #### C QUESTION:-64*29+468=? options: A)1430 B)1302 C)-2801 D)-1388 E)None of these SOLUTION:=> -64*(30-1)+468; => -(64*30)+64+468; => -1920+532=-1388. Correct Option: D #### D QUESTION:If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is: options: A)8 B)9 C)12 D)14 E)13 SOLUTION:Let the numbers be x and y Then x2-y2=39 And x-y=3 We get x+y=13 Solving x-y=3, x+y=13 X=8, y=5 Larger number 8 ANSWER A 8 #### A QUESTION:If every 2 out of 3 readymade shirts need alterations in the sleeves, and every 4 out of 5 need it in the body, how many alterations will be required for 60 shirts ? options: A)88 B)123 C)133 D)143 E)153 SOLUTION:no.of Alteration required in 1 shirt is (2/3)+(4/5)+(3/4)=133/60 for 60 shirts it will 60*(133/60)=133 ANSWER:C #### C QUESTION:A boy has thirteen trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)186 ways B)177 ways C)188 ways D)195 ways E)189 ways SOLUTION:The boy can select one trouser in thirteen ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 13 * 15 = 195 ways. Answer:D #### D QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number? options: A)A)3/7 B)B)5/8 C)C)6 D)D)6/7 E)E)5/12 SOLUTION:Let the two numbers be x and y. 60/100 * x + y = 5/4y => 3/5 x = 1/4 y => x/y = 5/12 E) #### E QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second? options: A)1234 B)1567 C)1349 D)1456 E)1356 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1997 has to be the ring finger Answer is (D) #### D QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)88% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,11 = 11/100 x= 80*11/100 x= 8.8 8.8/10 = 0.88 = 88%, Answer C #### C QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)11% B)25% C)87% D)19% E)12% SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book? options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20 SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations: m + p + c = 20 (since 4/5 of the 25 spots are full of books) m = 2p p = 4 + c From that, you can use Substitution to get everything down to one variable. c = p - 4 m = 2p p = p Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf. With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M? options: A)59 B)49 C)58 D)113 E)131 SOLUTION:You have 6 digits: 3, 4, 5, 6, 7, 8 Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other. The first digit (hundreds digit) of both numbers should be consecutive integers Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options? Try and make a pair with (4** and 5**). Make the 4** number as large as possible and make the 5** number as small as possible. 487 and 536 (difference is 49) or Try and make a pair with (6** and 7**). Make the 6** number as large as possible and make the 7** number as small as possible. We get 685 and 734 (difference is 49) B #### B QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B #### B QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $27. What is the cost of the carpet, in dollars per square yard? (1 square yard = 6 square feet) options: A)xy/297 B)11xy/3 C)3xy/11 D)297/(xy) E)162/(xy) SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 6. The price per square yard is 27 / (xy/6) = 162/(xy). The answer is E. #### E QUESTION:In the quadrilateral PQRS d=10 cm, h1=4.6 cm and h2=2.3 cm. Find the area options: A)21 B)22 C)23 D)34.5 E)25 SOLUTION:area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona) so 1/2*10*(4.6+2.3)=34.5 ANSWER:D #### D QUESTION:If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board? options: A)1136 B)1268 C)1244 D)1296 E)1308 SOLUTION:Here m = 9, n = 9 Hence, number of rectangles that can be formed = mC2 × nC2 = 9C2 × 9C2 = (9C2)^2 = 36^2 =1296 Ans-D #### D QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? options: A)508 B)500 C)800 D)570 E)503 SOLUTION:We can select one boy from 20 boys in 20 ways. We select one girl from 25 girls in 25 ways We select a boy and girl in 20 * 25 ways i.e., = 500 ways. Answer:B #### B QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b? options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given. SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2. Answer: A. #### A QUESTION:The average salary of all the workers in a workshop is $1000. The average salary of 5 technicians is $5000 and the average salary of the rest is $500. The total number of workers in the shop is? options: A)25 B)20 C)15 D)30 E)18 SOLUTION:Let the total number of workers be x 1000x = 5000*5 + 500(x-5) x = 25 Answer is A #### A QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 9:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train? options: A)12:30 B)1:00 C)1:30 D)2:00 E)2:30 SOLUTION:In thirty minutes the first train travels 35 km. The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h. The second train will catch the first train in 35/10 = 3.5 hours, so at 1:00 pm. The answer is B. #### B QUESTION:Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price? $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Taking the prices of products in ascending order(already arranged) $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 we see that median value is the 6th value as there in total 11 values given Arithmetic mean = total/number of entries = 1428/11 =129.8181 We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit Correct Answer - B #### B QUESTION:There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)108 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand. #### C QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years, The age of the 15th student is options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Explanation: Age of the 15th student = [15 * 15 - (14 * 7 + 16 * 7)] = 15 years. Answer: E #### E QUESTION:Concentrated pineapple juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated pineapple juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? . options: A)20 B)30 C)50 D)80 E)100 SOLUTION:150 employees 80 are full-time 100 have worked at company X for at least a year 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? 150-80=70 employees not full time 70-20= 50 employees not full time who worked over a year 100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year ANSWER:C #### C QUESTION:Tough and Tricky questions: Absolute Values. If |a| = 1/5 and |b| = 2/3, which of the following CANNOT be the result of a + b? options: A)13/15 B)-13/15 C)-7/15 D)7/15 E)7/5 SOLUTION:|a| = 1/5 Absolute value of 'a' can have two values = 1/5 and -(1/5) |b| = 2/3 Absolute value of 'b' can have two values = 2/3 and -(2/3) Now different combinations of a + b are as follows: a + b = (1/5) + (2/3) = 13/15 - a - b = -(1/5) - (2/3) = -13/15 a - b = (1/5) - (2/3) = -(7/15) -a + b = -(1/5) + (2/3) = 7/15 Cross verifying with the given options, left over option is E. #### E QUESTION:Find the value of y from the given equation. 9^y = 3^12, what is y? options: A)3 B)5 C)7 D)8 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2 SOLUTION:Solution Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 Answer A #### A QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)5 B)4 C)6 D)8 E)3 SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4%.Answer:B #### B QUESTION:If 7^t is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of t? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:So the question just means that we have to find all the multiples t of 7 between 1 to 100 So there are 14 multiples of 7 ( 7 - 98) But 49 and 98 contain two 7's as factors so we have to add 14 + 2 = 16 E #### E QUESTION:An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)267 B)180 C)287 D)177 E)911 SOLUTION:Angle traced by the hour hand in 6 hours =(360/12)*6 Answer: B #### B QUESTION:In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight ? options: A)3 hours B)2.4 hours C)1.4 hours D)1 hour E)None of these SOLUTION:Explanation: Let the duration of the flight be x hours. Then 600x−600x+12=200600x−12002x+1=200x(2x+1)=32x2+x−3=0=>(2x+3)(x−1)=0 Neglecting the negative value for x we get x = 1 Answer: D #### D QUESTION:If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book. options: A)23777 B)69667 C)26976 D)2697 E)1079 SOLUTION:Explanation: Number of digits used in 1 digit numbers = 1*9 = 9 Number of digits used in 2 digit numbers = 2*90 = 180 Number of digits used in 3 digit numbers = 3*900 = 2700 Number of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320 Hence, number of pages with 4 digit number = 320/4 = 80 Total number of pages = 1079 ANSWER: E #### E QUESTION:If w is a positive integer, then 3^w + 3^(w +1) = options: A)4^a B)3^a − 1 C)3^(2a) + 1 D)3^a*(a − 1) E)4(3^w) SOLUTION:3^w + 3^(w +1) = 3^w + (3^w * 3^1) = 3^w (1 + 3) = 3^w(4) Ans. E) 4(3^w) #### E QUESTION:A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5% options: A)Rs 6.56 B)Rs 9.56 C)Rs 10.56 D)Rs 11.56 E)None of these SOLUTION:Explanation: 80 : 5 = 105 : x x= (5×105/80) = Rs 6.56 Option A #### A QUESTION:A train is 485 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length options: A)20 seconds B)30 seconds C)40 seconds D)50 seconds E)None of these SOLUTION:Explanation: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 485+140 = 625 meter Time = Distance/speed =625∗2/25=50seconds Option D #### D QUESTION:The probability that a man will be alive for 10more yrs is 3/4 & the probability that his wife will alive for 10 more yrs is 1/5. The probability that none of them will be alive for 10 more yrs, is options: A)1/2 B)1 C)2/3 D)1/5 E)2 SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/5 Ans.(D) #### D QUESTION:How many seconds does a train 110 meters long, traveling at 54 km/h, take to completely cross a bridge of 160 meters in length? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:54 km/h = 54000/3600 = 15 m/s Time = 270 / 15 = 18 seconds The answer is A. #### A QUESTION:One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)9:4 C)5:6 D)5:0 E)2:4 SOLUTION:Explanation: 45 * 5/18 = 10 25:20 => 5:4 Answer: Option A #### A QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 13*0 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:A two digit number reversed and multiplied by 4 is 3 more than the original digit. what is the digit? options: A)61 B)62 C)63 D)64 E)66 SOLUTION:If no is xy , then 10x+y = 4*(10y+x)-3= 40y +4x-3 6x-39y +3 =0 2x-13y +1 =0 13 y =2x+1 when y=1, x=6 so number is 61. ANSWER:A #### A QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)24 B)66 C)55 D)88 E)61 SOLUTION:(15*18)/12 = 24 Answer:A #### A QUESTION:P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings? options: A)1:8 B)1:6 C)2:1 D)1:1 E)1:7 SOLUTION:Ratio of investments of P and Q is 2 : 5 Total salary claimed by P = 12 * 5000 = Rs. 60000 Total profit = Rs. 2 lakhs. Profit is to be shared = Rs. 140000 Share of P = (2/7) * 140000 = Rs. 400000 Share of Q = Rs. 100000 Total earnings of P = (60000 + 40000) = Rs. 100000 Ratio of their earnings = 1:1 Answer:D #### D QUESTION:The successive discounts 20% and 15% are equal to a single discount of? options: A)43% B)72% C)32% D)44% E)29% SOLUTION:C 32% Let the CP of an article be Rs. 100 Given that successive discounts are 20% and 15%. SP = 85% of 80% of 100 = (85/100)(80/100)(100) => SP = Rs. 68 Clearly, single discount is 32%. #### C QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 54 km/hr? options: A)2.5 B)2.9 C)6.67 D)2.8 E)2.1 SOLUTION:Speed = 54 * 5/18 = 15 m/sec Time taken = 100/15 = 6.67 sec. Answer:C #### C QUESTION:A 270m long train running at the speed of 120kmph crosses another train running in opposite direction at the speed of 80kmph in 9 second. What is the length of the other train? options: A)150m B)230m C)290m D)310m E)420m SOLUTION:Relative speed = 120+80 = 200*5/18 = 500/9 m/s Let the length of the other train be x meters x+270/9 = 500/9 x = 230m Answer is B #### B QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B QUESTION:The mean of 50 observations was 41. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)35.2 B)36.1 C)36.5 D)41.5 E)None SOLUTION:Sol. Therefore correct sum = ( 41 × 50 + 48 – 23) = 2075. Therefore correct mean = 2075 / 50 = 41.5. Answer D #### D QUESTION:The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? options: A)76 B)88 C)66 D)55 E)35 SOLUTION:Area of a triangle = r * s Where r is the inradius and s is the semi perimeter of the triangle. Area of triangle = 2.5 * 28/2 = 35 cm2 Answer:E #### E QUESTION:A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule? options: A)18 B)81 C)56 D)72 E)24 SOLUTION:IMO 'E' is the answer. Matches will be in multiples of 5x+4. The answer that satisfies this condition is E #### E QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean m. 72 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.6 years and the standard deviation is 2.6 years, what percent of the distribution has more than 10.2 years as a shelf’s average life? options: A)17% B)16% C)15% D)14% E)13% SOLUTION:Average = 7.6 SD = 2.6 7.6 - 2.6 < 72% of distribution < 7.6 + 2.6 5.0 < 72% of distribution < 10.2 28% is outside this range. Given: Distribution is symmetric. So 14% of distribution is less than 5.0 and the other 14% of distribution is greater than 10.2. Answer: D #### D QUESTION:The editor of an anthology of short stories will select authors from a pool of 12 authors, of which 5 are female. If the anthology is to include the work of 7 authors of which at least 2 are female, in how many ways can the editor select the authors? options: A)734 B)745 C)756 D)767 E)778 SOLUTION:12C7 = 792 The number of ways to select 7 males is 7C7 = 1 The number of ways to select 6 males and 1 female is 7C6*5C1 = 35 792 - 1 - 35 = 756 The answer is C. #### C QUESTION:Jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ? options: A)5 B)10 C)22 D)25 E)30 SOLUTION:Let's TEST Answer C: 22 seashells... With 22 seashells, Jamie would have 22(20) =440 cents. This would allow him to buy 8 books for 440 cents total, so this is the correct answer. C #### C QUESTION:In 120 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: options: A)24 m B)25 m C)22.5 m D)9 m E)12 m SOLUTION:Distance covered by B in 9 sec. = 120/45 x 9 m = 24 m. A beats B by 24 metres. Answer: Option A #### A QUESTION:If n is a natural number, then 6n^2 + 6n is always divisible by? options: A)6 only B)6 and 12 C)12 only D)18 only E)20 only SOLUTION:6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Answer is B #### B QUESTION:The difference between a number and its two-fifth is 510. What is 10% of that number ? options: A)33 B)85 C)37 D)27 E)28 SOLUTION:Explanation: Let the number be x. Then, . 10 % 0f 850 = 85. Answer: B) 85 #### B QUESTION:The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? options: A)4 years B)8 years C)6 years D)5 years E)1 years SOLUTION:Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 => x = 4. Age of youngest child = x = 4 years. Answer: A #### A QUESTION:Set A = {1, 2, 3, 4, 5, 6, q} Which of the following possible values for q would cause Set A to have the smallest standard deviation? options: A) 1 B) 2.5 C) 3 D) 3.5 E) 7 SOLUTION:I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice. Answer D. #### D QUESTION:2^2*3^3*2^2*3^6 = options: A)3^5*2^5 B)2^9*3^4 C)2^4*3^9 D)5^8 E)6^10 SOLUTION:2^2*3^3*2^2*3^6 = A) 3^5*2^5 B) 2^9*3^4 C) 2^4*3^9 D) 5^8 E) 6^10 If the base is same, powers are added so that follows C) 2^4*3^9. Hence the answer is C #### C QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)99 B)277 C)48 D)99 E)22 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer:C #### C QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number? options: A)7 B)9 C)11 D)13 E)15 SOLUTION:Let the three numbers be x, x+2, and x+4. 3x = 2(x+4) + 3 x = 11 and then the third number is x+4 = 15. The answer is E. #### E QUESTION:The maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is options: A)91 B)81 C)1001 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 891 and 810. ‹=› 81. Answer B #### B QUESTION:A cube of side one meter length is cut into small cubes of side 5 cm each. How many such small cubes can be obtained? options: A)2878 B)8000 C)1000 D)2997 E)2701 SOLUTION:Along one edge, the number of small cubes that can be cut = 100/5 = 20 Along each edge 5 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 20 * 20 * 20 = 8000 Answer: B #### B QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:Find 283/1983×100 options: A)14.29 B)14.21 C)14.22 D)14.27 E)14.23 SOLUTION:Never start finding common factors. Adjust the denominator to 2000. So we are introducing an error of 17 which is 171983=1117171983=1117 th of the denominator. 283002000=14.15283002000=14.15 But this answer is slightly less than actual answer. Now 14.1511714.15117 = 0.12 approximately. Adding 0.12 to 14.25 gives 14.27. Option B is correct. #### B QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0 options: A)-1 B)1 C)2 D)3 E)4 SOLUTION:a = 3, b = 5, c = 2 x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6 x1 = (-5 + 1)/6 = -4/6 = -2/3 x2 = (-5 - 1)/6 = -6/6 = -1 A #### A QUESTION:The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by? options: A)33 1/3% B)33 1/8% C)33 6/3% D)33 8/3% E)31 1/3% SOLUTION:100 75 ------- 75 ------- 25 100 ------ ? => 33 1/3% Answer: A #### A QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)100 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer C, 50 cans #### C QUESTION:Find the average of all numbers between 2 and 63 which are divisible by 5 options: A)15 B)20 C)25 D)32.5 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60)/12=390/12=32.5 Answer: Option D #### D QUESTION:The area of a triangle is with base 3m and height 4m? options: A)4 m2 B)6 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 3 * 4 = 6 m2 Answer: B #### B QUESTION:A certain list of 100 data has an average (arithmetic mean) of 8 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 106 data with standard deviation less than d? options: A)-8 and 0 B)0 and 0 C)0 and 8 D)0 and 16 E)8 and 8 SOLUTION:Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 8 and 8 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. Answer: E. #### E QUESTION:If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? options: A)100 B)10 C)0.01 D)0.0001 E)0.0001 SOLUTION:Given that 100 microns = 1 decimeter =10,000 angstroms So, 1 micron = 10,000/100 =100 Answer : A #### A QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/6. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)25. B)24. C)23. D)20. E)16. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 6,5 and 10 Lets take LCM of three balls 6,5 and 10 = 30. The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS. Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls. IMO option E is correct. #### E QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings? options: A)Rs.3600 B)Rs.3629 C)Rs.3279 D)Rs.3629 E)Rs.3283 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 18000 => x = 3600 Savings = Income - expenditure = 5x - 4x = x So, savings =Rs.3600. Answer: A #### A QUESTION:H.C.F. of 513, 1134 and 1215 is options: A)27 B)21 C)76 D)42 E)33 SOLUTION:H.C.F. of 513, 1134 and 1215 = 3 × 3 × 3 = 27 Answer: Option A #### A QUESTION:3 workers transfer a tool weighing 120kg in 12 seconds. How many men are required to transfer it in 9 seconds? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:We have, M1D1H1 = M2D2H2 3*120*12 = M2*120*9 M2 = 3*120*12/120*9 = 4 ANSWER:A #### A QUESTION:Diesel costs Rs.4 per lit and petrol costs 4.63 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol. options: A)9 months B)5 months C)6 months D)3 months E)2 months SOLUTION:Explanation : =>In the First Month the price of the diesel would be 4*110/100 = 4.4 =>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84 which is higher than the price of the petrol! Answer : E #### E QUESTION:If 4 men working 10 hours a day earn Rs. 1000 per week, then 9 men working 6 hours a day will earn how much per week? options: A)Rs 840 B)Rs 1350 C)Rs 1620 D)Rs 1680 E)None of these SOLUTION:Explanation : (Men 4:9) : (Hrs/Day 10:6) :: 1000 : x hence 4 * 10 *x = 9 * 6 * 1000 or x = 9*6*1000/ 4*10 = 1350 Answer : B #### B QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:2*6=12.Answer is B. #### B QUESTION:In an examination 60% failed in Math and 40% failed in French. If 10% failed in both. What % of students passed in both. options: A)25% B)15% C)20% D)30% E)10% SOLUTION:Passed in Math = 100 - 60 = 40% Passed in French = 100 - 40 = 60% Students who passed Math or French = 100 -10 = 90% Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-90 =10% ANSWER:E #### E QUESTION:What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 6), (x, 6)? options: A)64 B)81 C)125 D)196 E)225 SOLUTION:To find the area of a square, knowing the length of one side is sufficient. From the coordinates given, we can see that one side equals 14. The area is 14*14 = 196. The answer is D. #### D QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(6900*6)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? options: A)700 B)666 C)600 D)400 E)800 SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C #### C QUESTION:In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1? options: A)25 B)45 C)55 D)70 E)30 SOLUTION:Day 1&2 = 80; Only Day 1&2 (80-20) = 60, Day 2&3 = 70; Only Day 2&3 (70-20) = 50, Only Day 1 = 175 - (60+50+20) = 45 Answer:B #### B QUESTION:Which of the following is NOT the sum of the squares of two integers? options: A)36 B)37 C)65 D)146 E)147 SOLUTION:List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. (A) 36 - 9+25. NO. (B) 37 - 1+36. NO. (C) 65 - 1+64. NO. (D) 146 - 25+121. NO. (E) - must be the answer. ANSWER:E #### E QUESTION:An article is bought for Rs.700 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 8/3% C)28 4/7% D)35 1/3% E)32 1/3% SOLUTION:700 ---- 200 100 ---- ? => 28 4/7% Answer: C #### C QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ? options: A)87 B)95 C)99 D)100 E)103 SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: C. #### C QUESTION:A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? options: A)4 : 3 B)9:2 C)18:20 D)1:4 E)18:4 SOLUTION:A: B =24000 : 18000 = 8 : 6 = 4 : 3 ANSWER:A #### A QUESTION:An investment compounds annually at an interest rate of 33.34% What is the smallest investment period by which time the investment will more than triple in value? options: A)1 B)2 C)3 D)5 E)4 SOLUTION:Assume initial amount is x Annual Interest is 34.1% so after 1 year the amount will become x * (100+33.34)/100 => x*4/3 now we need to find n for x * (4/3)^n = 3x or in other words n = 4 E #### E QUESTION:In an encryption code 'PLAYS' is written as '{:SUD' when encoded and 'SLEEP' is written as 'D:RR{' when encoded. How is ''SLAPPY" written in that encryption code? options: A)D:S{{U B)SLAPPY C){RUDD: D){:SUU{ E)U{{S:D SOLUTION:D = S : = L S = A P = { P = { Y = U Correct Answer: A #### A QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is? options: A)12 B)14 C)15 D)19 E)10 SOLUTION:Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank. 1/x + 1/(x - 5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x- 15)(x - 3) = 0 => x = 15. Answer:C #### C QUESTION:In how many different ways can change be provided for a one dollar bill using pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents), if at least two of each type of coin must be included? options: A)0 B)6 C)8 D)10 E)15 SOLUTION:I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any other coins. We cannot have all four coins represented if we have four quarters. Case I does not allow any ways. II. Case II = Three Quarters (75 cents) This does not allow for two each of the other coins. Case II does not allow any ways. III. Case III = Two Quarters (50 cents) This allows for 2-3 dimes. Subcase 1 = 2 Q, 3 D (80 cents) (2 ways) we could have 2-3 nickels Subcase 2 = 2 Q, 2 D (70 cents) (4 ways) we could have 2-5 nickels Case III allows for a total of 6 ways There's no other case, because we have to have at least two quarters and two dimes. The total over the cases equals Total = 0 + 0+ 6 =6 ways. OA =(B) #### B QUESTION:The entire contents of a full sack of flour can be used to make 15 cupcakes and 10 pizzas. The same full sack of flour can be used to make 7 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made? options: A)10 B)21 1/2 C)18 3/4 D)19 E)19 1/4 SOLUTION:15x+10y=7x+14y x=1/2y. Answer B #### B QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1055 B)1065 C)1070 D)1075 E)1080 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 A #### A QUESTION:In 1 hour, a boat goes 5 km along the stream and 9 km against the stream. The speed of the boat in still water (in km/hr) is : options: A)3 km/hr. B)2 km/hr. C)7 km/hr. D)8 km/hr. E)5 km/hr. SOLUTION:Speed in still water = 1/2(9 + 5) km/hr = 7 km/hr. ANSWER :C #### C QUESTION:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there. It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week). We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat). => 3* odd is again odd. 2 * age of students is always even. So final equation is even +odd = odd. Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer A. #### A QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:The length of a rectangle is twice its breadth. If its length is decreased by 4 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle. options: A)10/3cm B)20/3cm C)20cm D)16cm E)14cm SOLUTION:Explanation: Let breadth = x. Then, length = 2x. Then, (2x - 4) (x + 5) - 2x * x = 75 => 6x - 25 = 75 => x =20/3. Length of the rectangle = 20/3 cm. Answer: Option B #### B QUESTION:The area of a circle is increased by 300%. By what percent has the radius of the circle increased? options: A) 400% B) 200% C) 100% D) 600% E) 800% SOLUTION:The area of the circle is increased by 300%, thus the area is increased 4 times. The area of a circle it proportional to the square of the radius (area=πr^2), therefore the radius must increase 2 times (diameter increase 2 times = area increase 4 times), which is increase by 100%. Answer: C #### C QUESTION:What is the difference between the local value of 1 and 2 in the number 2124? options: A)70 B)75 C)20 D)80 E)60 SOLUTION:Explanation: 100 – 20 = 80 Answer: D #### D QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 3 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? options: A)1/24 B)1/8 C)1/4 D)1/3 E)3/8 SOLUTION:I hope you are familiar with basic probability fundas - Let's say you have just ONE letter and TWO envelopes ONE of which is correctly addressed and the other addressed incorrectly. What's the probability of putting the Letter in the correctly addressed envelope - To answer this question - we see IN HOW MANY WAYS can the letter be put into the envelope - you could put it (assuming you don't know which envelope is which) in either of the two - so in total you have TWO ways of shoving the letter in. However, there's only ONE way in which it can go into the correctly addressed envelope - so 1/2 is the prob of putting in correct envelope. This is easy. Now in our current problem - let's say we have just ONE letter but FOUR envelopes. Only one of these envelopes has the address corresponding to the letter. The remaining three envelopes are incorrectly addressed. So the probability that you will put the letter correctly is 1/4. Right? What happens if i ask you the reverse question? what is the prob for putting it in the incorrect envelope. Suddenly you have three envs that are incorrect so you can put the letter incorrectly with a prob of 3/4. Right? The whole problem can be broken down into Four Events that will fulfill the requirement of the question Event 1 - E1 We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the first letter goes into the correct envelope) we have the remaining THREE Letters and THREE envelopes. Event 2 - E2 Let's take letter number 2 now - what is the probability that it LANDS in the INCORRECT envelope. Again by the same logic as above - there are 3 envelopes remaining out of which ONLY ONE has the correct address for LETTER number 2. The remaining 2 have INCORRECT address and LETTER NUMBER 2 could go in either of these 2 to meet our condition. Thus the probability of this event is 2/3 So till now what we have done is - we have calculated the prob of shoving Letter number 1 in correct env -- 1/4 we have calculated the prob of shoving Letter number 2 in INcorrect env --- 2/3 Event 3 - E3 Now let's take letter number 3 - again according to question we want to shove this in the WRONG envelope. There are 2 remaining envelopes and hence the prob of shoving this in the wrong env (or equally in the RIght env) is 1/2. Finally we come to event E4 - the Letter number 4. This has only one way of going in so its probability of being put into the WRONG envelope is 1. ok so we can see that our grand event is actually a combination of FOUR EVENTS happening - each with a probability of its own. So to calculate the total probability of the Grand Event itself we just multiply the individual probabilities since each event happens INDEPENDENTLY of each other Egrand = 1/4 * 2/3 * 1/2 * 1/1 = 1/12 However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result. If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 and worked thru the remaining letters, we could have equally well started out with letter L2 or L3 or L4. Thus since each of these events ARE MUTUALLY EXCLUSIVE, meaning THEY CAN NEVER HAPPEN ALL THE SAME TIME BUT ONLY ONE LETTER AT A TIME, to calculate the TOTAL PROBABILITY of we will add the individual probabilities 1/12 + 1/12 + 1/12 + 1/12 which works out to 1/8. B #### B QUESTION:A gold mine has 5% depletion rate. i.e. after each year of mining, the miners extract 5/100 of the mine's ore. If the current quantity of the gold reserves of the mine is currently estimated at 2 tons, how much gold would the miners be able extract over the next 4 years? options: A)0.400 tons B)0.200 tons C)0.175 tons D)0.160 tons E)0.185 tons SOLUTION:X is the quantity of gold reserves of the mine After a year of mining the quantity of gold left would be X1=X-5/100X i.e. X1=95/100X Same thing for X2, X3, X4, respectively representing the quantity of gold left after 2, 3, 4 years of mining. So we have: X1=95/100 X X2=95/100 X1 X3=95/100 X2 X4=95/100 X3 By multiplying both ends of the equations we get: X1*X2*X3*X4 = (95/100)^4 X*X1*X2*X3 Simplification leaves us with: X4 = (95/100)^4 X X4 is the quantity of gold left after four years of mining. So the cumulative quantity of gold (Q4) which has been extracted after 4 years is: Q4= X-X4=X-(95/100)^4X i.e. Q4 = X (1-(95/100)^4) In this case, given X was: X=2 tons So Q4 = 2 * (1-(95/100)^4) = 2 * (1-81450625/10^8) =2 * 18549375/10^8 = 0.1854 tons round to Q4=0.185 ton Answer E. #### E QUESTION:Marie has 248 $ in her account of the bank. She has to buy presents for her 7 children and wants to distribute the money fairly. How much he will once have the money shared fairly? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(248$ / 7children) = 35.42 Took the lowest number = 35 * 7 children = $245 $248 - $245 = staying $3 Correct option: C) 3$ #### C QUESTION:In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can? options: A)65 B)44 C)86 D)29 E)26 SOLUTION:Let the capacity of the can be T litres. Quantity of milk in the mixture before adding milk = 4/9 (T - 8) After adding milk, quantity of milk in the mixture = 6/11 T. 6T/11 - 8 = 4/9(T - 8) 10T = 792 - 352 => T = 44. Answer: B #### B QUESTION:What is the remainder when 1274 * 1275 * 1277 *1285 is divided by 12? options: A) 0 B) 6 C) 11 D) 9 E) 7 SOLUTION:1271*1275*1277*1285 = (1272 - 2)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1) Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-2)(3)(-7)(1) = 42. Thus the question becomes: what is the remainder upon division of 42 by 12? The answer to this question is 6. Answer: B #### B QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:If u r genius solve it:- 70 * 17 = 11 60 * 16 = 15 50 * 15 = ? options: A)2 B)12 C)6 D)8 E)10 SOLUTION:Logic: 70*17=1190=1+1+9+0=11 60*16=960=9+6+0=15 50*15=750=7+5+0=? Answer : B #### B QUESTION:A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture? options: A)1 kgs B)3 kgs C)5 kgs D)6 kgs E)None of these SOLUTION:Explanation : If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg. We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg. Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C. Step 1: Find out the ratio Qa:Qc using alligation rule. Qa/Qc=(30−25)/(25−20)=1/1. Step 2: Find out the ratio Qb:Qc using alligation rule. Qb/Qc=30−25/(25−24)=5/1. Step 3: Qc is found by adding the value of Qc in step 1 and step 2 =1+1=2. Therefore, the required ratio =1:5:2. If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture. Answer : C #### C QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age 10 years back was: options: A)10 years. B)14 years. C)17 years. D)16 years. E)12 years. SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22 Son's age 10 years back (22 - 10) = 12 years. ANSWER :E #### E QUESTION:A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done? options: A)572 B)672 C)472 D)372 E)None SOLUTION:Solution: 10C5: when both are not included. 10C4: when one of them is included. Number of ways = 10C5 +10C4+ 10C4 = 672 Answer: Option B #### B QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-2)(x+1)(2X+5) = 0? options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2 SOLUTION:x = -1 Prob = 1/12 Answer -A #### A QUESTION:A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)11 sec C)88 sec D)33.33 sec E)10 sec SOLUTION:Speed = 54 * 5/18 = 15 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 1/15 = 33.33 sec Answer: D #### D QUESTION:X is an even number and Y is a positive odd number. Which of the following expressions cannot be even? options: A)(XY)^Y B)X^3Y^3 C)X^3 D)XY E)Y^2 SOLUTION:If x is even, let x = 0 and see what happens. A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE) B. 0³Y³ = 0 (EVEN - ELIMINATE) C. 0³ = 0 (EVEN - ELIMINATE) D. (0)Y = 0 (EVEN - ELIMINATE) E. Y² Answer:E #### E QUESTION:Y and Z start a business with Rs.3000 and Rs.6000 respectively. How should they share their profits at the end of one year? options: A)4:1 B)1:3 C)1:4 D)1:5 E)1:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by Y and Z = 3000 : 6000 => 1:2 . Answer:E #### E QUESTION:There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 36, then find the smaller number? options: A)25 B)66 C)77 D)60 E)44 SOLUTION:Let the two positive numbers be 5x and 8x respectively. 8x - 5x = 36 3x = 36 => x = 12 => Smaller number = 5x = 60. Answer: D #### D QUESTION:A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used options: A)12 months B)10 months C)14 months D)16 months E)None of these SOLUTION:Explanation : B received 2/3 of the profit => A : B = 1 : 2 Let the total capital = x Then A's capital = x/4 B's capital = x – x/4 = 3x/4 Assume B's money was used for b months Then A:B = (x/4)*15 : (3x/4)*b = 1 : 2 => 15/4 : 3b/4 = 1 : 2 => 15 : 3b = 1 : 2 => 5 : b = 1 : 2 => 5/b = 1/ 2 => b = 5*2 = 10. Answer : Option B #### B QUESTION:In a recent head-to-head run-off election, 10,000 absentee ballets were cast. 2/3 of the absentee ballets were thrown out and 2/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000 SOLUTION:1/3 * 3/5 (total absentee votes) = 1/5 (total votes)=1/5*10000=2000 Answer is A #### A QUESTION:What will come in place of the x in the following Number series? 1, 2, 12, 7, 23, 12, 34, x options: A)14 B)15 C)16 D)17 E)18 SOLUTION:There are two series here 1, 12, 23, 34, ... (Increase by 11) 2, 7, 12, ... (Increase by 5) Hence, next term is 12 + 5 = 17 Correct Answer Choice is D #### D <<<Examples ends QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A set of numbers has the property that for any number t in the set,t+3 is in the set. If -1 is in the set, which of the following must also be in the set? I. 2 II. 5 III. 7 options: A)II only B)I only C)I,II only D)II,III only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+3 must be there. if -1 is the starting element the sequence is as follows. S ={-1,2,5,8,11....} if -1 is not the starting element the sequence is as follows S = {...-4,-1,2,5,8,11...} By observing the above two sequences we can say that 2,5 must be there in set S. Answer : C #### C QUESTION:It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? options: A)8:50 a.m B)5:50 a.m C)7:50 a.m D)6:50 a.m E)7:00 a.m SOLUTION:The time it takes Kannan to get to work: time to walk to car park + time to drive 10 + 110 = 120 minutes = 2 hours Kannan needs to get out of the house 2 hours before 9:00 am at 9:00 - 2:00 = 7:00 a.m correct answer E #### E QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water options: A)6.8km/hr B)54km/hr C)90km/hr D)3.8km/hr E)7.9km/hr SOLUTION:still in water=1/2(98+10)km/hr =54km/hr correct option is :B #### B QUESTION:If the selling price of 8 articles is same as the cost price of 10 articles. Find the gain or loss percentage? options: A)25% B)45% C)35% D)65% E)55% SOLUTION:Let the C.P of each article be Re 1. Then, S.P of 8 articles = C.P of 10 articles = Rs. 10 Now, C.P of 8 articles = Rs. 8, S.p of 8 articles = Rs 10 Gain = Rs ( 10 - 8 ) = Rs 2. Gain% = ( 2/8 × 100 ) % = 25% Answer : A #### A QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)2200 miles. B)2300 miles. C)1900 miles. D)2500 miles. E)2100 miles. SOLUTION:E 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 #### E QUESTION:A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4 options: A)II,III only B)I only C)I,III only D)II only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+4 must be there. if -3 is the starting element the sequence is as follows. S ={-3,1,5,9....} if -3 is not the starting element the sequence is as follows S = {...-7,-3,1,5,9...} By observing the above two sequences we can say that 9 must be there in set S. Answer : B #### B QUESTION:The perimeter of one face of a cube is 40 cm. Its volume will be: options: A)125cm3 B)400cm3 C)250cm3 D)1000cm3 E)None of these SOLUTION:Explanation: Edge of cude = 40/4 = 10 cm Volume = a*a*a = 10*10*10 = 1000 cm cube Option D #### D QUESTION:If P = Q/R, -1 < R < 0 and 4 < Q, which of the following is correct? options: A)P > 4. B)0 < P <4. C)-4 < P < 0. D)P < -4. E)P < -20. SOLUTION:Q is +veR is -ve Eliminate AB For min. value max. numerator and minimize dinominator take Q=4.1P=-0.9 P=4.1/-0.9 P<-4 Ans D #### D QUESTION:The largest 4 digit number exactly divisible by 88 is? options: A)9930 B)9936 C)9944 D)9952 E)9960 SOLUTION:Largest 4-digit number = 9999 88) 9999 (113 88 ---- 119 88 ---- 319 264 --- 55 --- Required number = (9999 - 55) = 9944. C) #### C QUESTION:Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together? options: A)6 B)7 C)7.5 D)8 E)9 SOLUTION:Each day, Molly can do 1/15 of the task. Each day, Sandy can do 1/10 of the task. Each day, they can do 1/15 + 1/10 = 1/6 of the task. The task will be completed in 6 days. The answer is A. #### A QUESTION:In the xy-coordinate system, what is the slope of the line that goes through point (2, 4) and is equidistant from the two points P = (9, 3) and Q = (5, 9)? options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:First, get the middle coordinate between (9,3) and (5,9). x = 9 + (5-9)/2 = 7 y = 3 + (9-3)/2 = 6 Second, get the slope of (7,6) and (2,4). m = 6-4 / 7-2 = 2/5 = 0.4 Answer: D #### D QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)196 E)200 SOLUTION:185 Answer is B #### B QUESTION:A person X working alone can complete a work in 5 days. A person Y completes the same amount of work in 10 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:The fraction of work completed in two days is 2/5 + 2/10 + 2/30 = 20/30 The fraction of work remaining is 1 - 20/30 = 10/30 The number of days required for Z is 10 days. The answer is E. #### E QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)22 B)25 C)66 D)77 E)91 SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000 options: A)3336,1667 B)3339,1667 C)3333,1666 D)3333,1668 E)3333,1669 SOLUTION:they invested in the ratio 1:2 a's share =1/3*5000=1666 b's share=2/3*5000=3333 ANSWER:C #### C QUESTION:If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it? options: A)22 B)38 C)60 D)88 E)90 SOLUTION:Explanation: Let the required no of hours be x. Then Less men , More hours (Indirect Proportion) \inline \fn_jvn \therefore 10:36 ::25:x \inline \fn_jvn \Leftrightarrow (10 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{10}=90 Hence, 10 men can do it in 90 hours. Answer: E) 90 #### E QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:If you roll a fair-sided die twice, what is the probability of getting a double (5,5)? options: A)1/24 B)1/36 C)1/12 D)1/18 E)1/3! SOLUTION:total no. in two dice (1,1) ,(2,2) .....(6,) Total number of events= 6*6 Total events of getting same pair(5,5) = 6 Probability= 6/6*6= 1/6=1/3! E #### E QUESTION:65 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? options: A)64 B)128 C)151 D)216 E)256 SOLUTION:65 small cube will make a large cube with 4 cubes in each line i.e. Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line. Total number of small cubes in new cube = 6^3 = 216 Extra cube required = 216 - 65 = 151 Hence, C is the answer. #### C QUESTION:Today is Monday. After 61 days, it will be: options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)sunday SOLUTION:EXPLANATION Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer B #### B QUESTION:The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. what is the principal sum options: A)124.05 B)124.09 C)124.04 D)124.06 E)124.02 SOLUTION:Explanation: Compound Interest on P at 10% for 2 years when interest is compounded half-yearly = Simple Interest on P at 10% for 2 years = Given that difference between compound interest and simple interest = 124.05 Answer:A #### A QUESTION:A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n? options: A)8/7 B)8 C)9/8 D)7 E)5 SOLUTION:Say each floor worker is paid $x, then the manager is paid $xn. Total salary would be 9x+xn and we are told that it equals to 9xn: 9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9 n = 9/8 Answer: C #### C QUESTION:Thomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer? options: A)10 B)14 C)19 D)21 E)25 SOLUTION:The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5 The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0 Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5 The % of profit in selling a single computer=(4545.5/45454.5)*100=10% Answer:A #### A QUESTION:What is the sum of natural numbers between 50 and 100 options: A)4800 B)4860 C)3825 D)5500 E)5550 SOLUTION:a = first number l = last number Sn = n/2[a + l] between 50 and 100 numbers = 51 => 100 - 50 = 50 + 1 = 51 Sn = 51/2 × 150 = 51 × 75 = 3825 Answer : C #### C QUESTION:The average age of students in section A of 122 students is 28 years and the average age of students in section B of 180 students is 35 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)25years E)32years SOLUTION:The required average = (122*28+180*35)/122+180 = 32 years Answer is E #### E QUESTION:The average of 10 numbers is calculated as 5. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:10 * 5 + 36 – 26 = 60/10 = 6 ANSWER:E #### E QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)5.14 SOLUTION:Time taken by First tank Fill 1/2 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank =12 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours Answer: option E #### E QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9 Probability to become a secretary = (9/10 * 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick? options: A)5, 12, and 8 kg B)6, 12, and 8 kg C)7, 12, and 8 kg D)8, 12, and 8 kg E)None SOLUTION:Solution: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2x+2, respectively. So x+2x+x+2=26 4x=24 x=6 Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively. Answer B #### B QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)19% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer: C #### C QUESTION:If w<0, which of the following must be true? options: A)–100 < w < 100 B)w ≤ –1 C)w ≤ 1 D)w^2 ≥ 1/4 E)–100 < w < 0 SOLUTION:w is a negative number. A. –100 < w < 100w can be a negative number less than -100 B. w ≤ –1w can be a fraction, in which case it would be greater than -1 C. w ≤ 1must be true since 1 is positive and w is negative D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5 E. –100 < w < 0w can be a negative number less than -100=C #### C QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)76 m B)178 m C)225 m D)187 m E)176 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x)= 750 => x = 225 m. Answer: C #### C QUESTION:Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment? options: A)1200 B)3000 C)1000 D)3600 E)2400 SOLUTION:Let the additional invested amount for 8% interest be x; Equation will be; 2400+0.05*2400+x+0.08x = 2400+x+0.08(2400+x) 0.05*2400+0.08x = 0.06x+0.08*2400 0.02x = 2400(0.08-0.05) x = 2400*0.03/0.02 = 3600 Ans:D #### D QUESTION:A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg? options: A)s.7.7 B)s.7.4 C)s.7.5 D)s.7.1 E)s.7.9 SOLUTION:100*(20/100) = 20 --- 10 ? --- 1 => Rs.2 300 --- 80 ? --- 2 => Rs.7.5 Answer:C #### C QUESTION:In a certain code language, '3a, 2b, 7c' means 'Truth is Eternal'; '7c, 9a, 8b, 3a' means 'Enmity is not Eternal' and '9a, 4d, 2b, 8b' means 'Truth does not perish'. Which of the following means 'enmity' in that language ? options: A)3 B)9 C)8 D)6 E)2 SOLUTION:Explanation: Justification: In the second and third statements, the common code is '9a' and the common word is 'not'. So, '9a' means 'not'. In the first and second statements, the common codes are '7c' and '3a' and the common words are 'is' and 'Eternal'. So, in the second statement, '8b' means 'enmity'. Answer: C) 8b #### C QUESTION:A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 1/2 days. How many more days are required to complete the remaining work if they work together? options: A)3 (5/18) B)3 (5/16) C)3 (5/11) D)4 (21/22) E)3 (5/21) SOLUTION:A can do 1/10 of the work in a day. B can do 1/12 of the work in a 1 day. Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60 They take 60/11 days to complete the work together. Given that they already worked for 1/2 days. The number of days required to complete remaining work => 60/11 - 1/2 = 109/22 = 4 (21/22) days. Answer:D #### D QUESTION:The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? options: A)27 B)30 C)31 D)33 E)34 SOLUTION:The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 A #### A QUESTION:Pipe A can fill the tank in 30 minutes and pipe B in 20min and pipe C can empty the tank in 90 minutes. How long it will take to fill the tank if three of the pipes are operating together? options: A)10.55 B)12.0 C)13.1 D)13.85 E)15.2 SOLUTION:Pipe A fills 1/30th of the tank in a minute and pipe B, 1/20th. Pipe C empties in 90min (1/30)+(1/20)-(1/90)=(1/x) 13/180=1/x => x=180/13 => x=13.85 minutes Answer: D #### D QUESTION:what is the smallest integer that is multiple of 7, 12 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 7, 12 and 20 which is 420 #### E QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0 SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant). In options B , if you put x = -5, you get -ve value for y co-ordinate. Answer must be (B) #### B QUESTION:Calculate the HCF of 64, 318, 250 options: A)6 B)5 C)4 D)3 E)2 SOLUTION:Explanation: Lets solve this question by factorization method. 64=2 x 2 x 2 x 2 x 2 x 2, 318=2 × 3 × 53, 250=2 × 5 × 5 × 5 So HCF will be minimum term present in all three, i.e. 2×32=18 Answer: Option E #### E QUESTION:If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is: options: A)Rs. 182 B)Rs. 190 C)Rs. 196 D)Rs. 204 E)Rs. 210 SOLUTION:Explanation: Given ratio =1/2:2/3:3/4=6:8:9 1st part = Rs. 782*6/23=Rs. 204 Answer is D #### D QUESTION:If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was options: A)Rs 1.56 B)Rs 2.40 C)RS 3.00 D)Rs 3.80 E)Rs 4.20 SOLUTION:first 1/5 mile costs = 1.00 remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14, hence 14*0.20=2.80 total fare = 2.80 + 1.00 =3.80 ANSWER:D #### D QUESTION:A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 40 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost? options: A)40 B)33 C)50 D)51 E)52 SOLUTION:Yes, ensure that you understand the relation thoroughly! Cost per liter = K * Fraction of Spirit 40 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 20 cents. Fraction of spirit is 1/2. 20 = K * (1/2) K = 40 Cost per liter = 40 * (1/3) (1 part spirit, 2 parts water) Cost for 3 liters = 40 * (1/3) * 3 = 40 cents A. 40 cents #### A QUESTION:Lionel left his house and walked towards Walt's house, 48 miles away. Four hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt? options: A)12 B)16 C)20 D)24 E)28 SOLUTION:In the first 4 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=4*3=12 miles. So, the distance between him and Walt was 48-12=36 miles when Walt left his house. Now, their combined rate to cover this distance was 3+6=9 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=36/9=4 hours. Total time that Lionel was walking is 4+4=8 hours, which means that he covered in that time interval distance=rate*time=3*8=24 miles. Answer: D. #### D QUESTION:A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A options: A)26.2 km B)25.7 km C)23.2 km D)26.67 km E)None of these SOLUTION:Explanation: Distance travelled by each of them is to be made equal. => Distance travelled walking = Distance covered cycling. Let after 4 hours of walking, A walk for x hours more before B catches up with him. => Distance = Speed * Time (4+x)4 = 10x x = 8/3 Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67 ANSWER: D #### D QUESTION:A train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train? options: A)322 B)324 C)326 D)328 E)330 SOLUTION:Length = Speed * time Speed = L/T S = 2000/25 S = 80 M/Sec Speed= 80*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 324 Kmph Answer: B #### B QUESTION:A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is: options: A)19m B)17m C)15m D)16m E)20m SOLUTION:rectangular area = l × b = 120 and perimeter = 2(l+b) = 46 l+b = 23 (l-b)power2 - 4lb = (23)power2 - 4 × 120 = (529-480) = 49 = l-b = 7 l+b = 23, l-b = 7, we get l = 15, b = 8 Diagonal = √152+82 √225+64 => √289 = 17m Answer is B. #### B QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am SOLUTION:In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours. Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am. Answer: D #### D QUESTION:A train 280 m long passed a pole in 28 sec. How long will it take to pass a platform 660 m long? options: A)52 B)94 C)71 D)68 E)88 SOLUTION:Speed = 280/28 = 10 m/sec. Required time = (280 + 660)/10 = 94 sec. Answer: B #### B QUESTION:How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet) options: A)37×260^2 B)36×260^2 C)36×270^2 D)10^2×26^3 E)10^3×26^2 SOLUTION:We are given that License plate could be either of the form DDLLL or DDDLL Now, every D could be filled in 10 ways and every L could be filled in 26 ways. or Number of ways for DDLLL = 10 * 10 * 26 * 26 * 26 --(1) Number of ways for DDDLL = 10 *10*10*26*26 --(2) Total ways = (1) + (2) = \(36×260^2\) Answer s B. #### B QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:How many odd 4-digit positive integers W that are multiples of 5 can be formed without using the digit 3? options: A)648 B)729 C)900 D)1296 E)3240 SOLUTION:I choose A. Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded) Possible n° of 2nd digit: 9 (3 is excluded) Possible n° of 3rd digit: 9 (3 is excluded) Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0) So, W=8*9*9*1=648 (A) #### A QUESTION:Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes? options: A) 911 B) 100 C) 101 D) 160 E) 785 SOLUTION:Let's take the approach that uses the answer choices to eliminate wasted time. 32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt. Looking at the answers it is clear...we can only choose (D) THE CORRECT ANSWER IS D. #### D QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Explanation : If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29 If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29 If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27 Hence ,the common number is only 23 so it will be answer. Answer : A #### A QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)8 B)10 C)12 D)11 E)15 SOLUTION:Speed = 120/10 = 12 m/sec speed of the second train = 120/5 = 8 m/sec relative speed = 12+8 = 20 m/sec Req time = 120+120/20 = 12 sec ANSWER C #### C QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: options: A)27% B)87% C)15% D)66% E)88% SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900. Face value = Rs. (50 x 20) = Rs. 1000. Dividend = Rs. 27 x 1000 = Rs. 135. 2 100 Interest obtained = 135 x 100 % = 15% 900 View Answer Discuss in Forum Answer: C #### C QUESTION:Three distinct single-digit numbers. A,B,C are in GP. If abs(x) for real x is the absolute value of x(x if x is +ve or 0 and -x if x is -ve), then the number of different possible values of abs(A+B+C) is options: A)5 B)6 C)3 D)4 E)7 SOLUTION:A,B,C may be (1,2,4) & (4,2,1) (1,3,9) & (9,3,1) (2,4,8) & (8,4,2) (4,6,9) & (9,6,4) find abs(A+B+C) for these 8 GPs 7,13,15,19 So,we get 4 different values ANSWER:D #### D QUESTION:A scuba diver descends at a rate of 32 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 6400feet below the sea level..how long will he take to reach the ship? options: A)200 minutes B)240 minutes C)220 minutes D)210 minutes E)77 minutes SOLUTION:Time taken to reach = 6400/32= 200 minutes ANSWER:A #### A QUESTION:If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is? options: A)22 B)65 C)78 D)33 E)25 SOLUTION:Given that, cost price of 50 article is equal to selling price of 40 articles. Let cost price of one article = Rs. 1 Selling price of 40 articles = Rs. 50 But Cost price of 40 articles = Rs. 40 Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25% Answer:E #### E QUESTION:A beats B by 50m in a race of 500m ,then B beats by C by 25m in a race of 500m.Find the distance by which A beats C in a race of 400? options: A)55m B)56m C)57m D)58m E)59m SOLUTION:A beats B in 500m race by 50m so,for every 10 m race A beat B by 1m.. So,in 400 m race A beat B by 40m In a case of B & C, B beats C by 25m in 500m race.. So,B beats C by 1m in 20 m race Now,in a 400m race B beats C by 18m.. In a 400m race, A beats B by 40m & B beats C by 18m.. So,A beats C by 58m ANSWER:D #### D QUESTION:Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose? options: A)1.25% B)2.1% C)2.25% D)2.65% E)3% SOLUTION:Generally in such cases, there is always loss. So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss. Loss% = Common loss and gain% 2 = x 2 10 10 Therefore, here common loss and gain % = 15% Hence, Loss% = 15 2 = 2.25% C #### C QUESTION:For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z? options: A)(n/m)% B)(m × n)% C)(100 / [m × n]) % D)(100 × m/n)% E)(100 × n/m)% SOLUTION:x is n% of y MEANS x= (n/100 )* y------------------------eq1 z is m% of y MEANS z= (m/100 )* y------------------------eq2 Find equation of xz substitute value of y from 2nd equation into Ist equation so x= (n/100)*(100z/m) so x= (n/m)z or x= (100n/m)z/100 so answer E is 100n/m %.E #### E QUESTION:24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24 v1 + v2 = 25 p1 = 4v1 p2 = v2/5 4v1 + v2/5 = 24 v1 + v2 = 25 4v2 - v2/5 = 76 19v2/5 = 76 => v2 = 20 => v1 = 5 => p1 = 20 Answer - D #### D QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 14 x = 2 Mini’s age = 8 years And Minakshi’s age = 6 years Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7 ANSWER:C #### C QUESTION:If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1, then what is the value of abc/def ? options: A) 27/4 B) 27/8 C) 3/4 D) 3/2 E) 1/4 SOLUTION:Say a = 2. Then: a/b = 1/3 --> b = 6; b/c = 2 --> c = 3; c/d = 1/2 --> d = 6; d/e = 3 --> e = 2; e/f = 1 --> f = 2. abc/def = (2*6*3)/(6*2*2) = 3/2. Answer: D. #### D QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? options: A)5760 lr B)6000 lr C)6500 lr D)4000 lr E)4500 lr SOLUTION:1/x - 1/6 = -1/8 x = 24 hrs 24 * 60 * 4 = 5760 ANSWER A #### A QUESTION:Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 7 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them? options: A)22 km B)40 km C)65 km D)18 km E)16 km SOLUTION:Distance = Relative Speed * Time = (7 + 3) * 4 = 40 km [ They are travelling in the opposite direction, relative speed = sum of the speeds]. Answer: B #### B QUESTION:If the tens digit of positive integer x is 6 and the tens digit of positive integer y is 6, how many possible values of the tens digit of 2(x+y) can there be? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 60 + p and 60 + q respectively. 2(60+p+60+q)= 240 + 2(p + q). 2(p+q) can range from 0 up to a maximum value of 36 when p=q=9. Then the tens and ones digits of 2(x+y) can range from 40 up to 76. There can be 4 possibilities for the tens digit. The answer is C. #### C QUESTION:If x^2=3x+2, then x^3 = ? options: A)3x+2 B)6x+2 C)11x+6 D)8x-3 E)5x+4 SOLUTION:x^2 = 3x+2 x^3 = x*x^2 = x*(3x+2) = 3x^2 + 2x = 3(3x+2)+2x = 11x+6 The answer is C. #### C QUESTION:Sonika bought a V.C.R. at the list price of 18,700. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R. options: A)20,196 B)19,780 C)19,680 D)19,380 E)None of these SOLUTION:Sol. List price of V.C.R. =18,700 Rate of sales tax = 8% ∴ Sales tax = 8% of 18,700 = 8⁄100 × 18700 = 1496 So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,700 + 1496 = 20,196. Answer A #### A QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)2.3 B)2.5 C)3.5 D)3.6 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C *100 =50% Answer A #### A QUESTION:A 6000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)36 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (3,000 by that net inflow to get the minutes) - 36 min. Answer E. #### E QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)34 SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER:A #### A QUESTION:Find the area of a parallelogram with base 20 cm and height 10 cm? options: A)287 cm2 B)887 cm2 C)200 cm2 D)250 cm2 E)668 cm2 SOLUTION:Area of a parallelogram = base * height = 20 * 10 = 200 cm2 Answer: C #### C QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:Let x be the number of cars and let y be the number of cars parked illegally. 4%*x = 20%*y y/x = 1/5 = 20% The answer is A. #### A QUESTION:A, B and C enter into a partnership. They invest Rs. 70,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years? options: A)21 : 32 : 4 B)21 : 26 : 4 C)21: 12 : 1 D)21: 16 : 28 E)none SOLUTION:Sol. A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) =252 : 192 : 336 = 21: 16 : 28 Answer D #### D QUESTION:A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? options: A)4 min B)8 min C)9 min D)6 min E)1 min SOLUTION:S = 600/40 = 15 mps S = 3600/15 = 240 sec = 4 min Answer:A #### A QUESTION:A store sells four different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:4C2=6. The answer is B. #### B QUESTION:Sum of the squares of three numbers is 363 and the sum of their products taken two at a time is 131. Find the sum? options: A)20 B)22 C)25 D)27 E)29 SOLUTION:(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 363 + 2* 131 a + b + c = √625 = 25 C #### C QUESTION:If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d. The sum of A + B = (10c+d)+(10d+c)=11(c+d). The only answer that is a multiple of 11 is 44. The answer is D. #### D QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is options: A)3 months B)4 months C)6 months D)8 months E)10 months SOLUTION:Solution S.I on Rs. 1600 = T.D on Rs. 1680. Rs.1600 is the P.W of Rs.1680. Rs.80 is S.I on Rs.1600 at 15%. Time = (100x80 / 600x15) = 1/3 year = 4 months. Answer B #### B QUESTION:9823 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)3377 E)None of these SOLUTION:Answer x = 13200 - 9823 = 3377 Option: D #### D QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more men joined them. How many days will they take to complete the remaining work? options: A)3days B)4days C)2days D)8days E)5days SOLUTION:1 man's 1 day work = 1/108 12 men's 6 days work = 6/9 = 2/3 remaining work = 1 – 2/3 = 1/3 18 men's 1 days work = 18/108 = 1/6 1/6 work is done by them in 1 day therefore, 1/3 work is done by them in 6/3 = 2 days. ANSWER C 2days #### C QUESTION:P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in --- days if all of them are working together. options: A)2 B)3 3⁄7 C)4 ¼ D)5 E)5 ¼ SOLUTION:Explanation : Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/6 Work done by R in 1 day = 1/12 Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24 => Working together, they will complete the work in 24/7 days = 3 3⁄7 days Answer : Option B #### B QUESTION:If n = 2.0254 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n? options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0046 E) 0.0153 SOLUTION:n*=2.03 n*-n=2.03-2.0254 0.0046 Answer: D #### D QUESTION:A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box? options: A)5 m B)6 m C)4 m D)7 m E)8 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is: options: A)89.25 km/hr. B)77 km/hr. C)90.25 km/hr. D)94.25 km/hr. E)96.25 km/hr. SOLUTION:Let the speed of two bullet trains be 7x and 8x km/hr. Then, 8x = (440/5) = 88 x = (88/8) = 11 Hence, speed of first bullet train = (7 x 11) km/hr = 77 km/hr. B #### B QUESTION:The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number? options: A)A)9 B)B)10 C)C)12 D)D)7 E)E)13 SOLUTION:The total of twelve numbers = 12X7 = 84 The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74 So, the middle number is (84 - 74 ) = 10 B #### B QUESTION:The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 3: 00 p.m., at what time were there 32 million bacteria in the dish? options: A)6: 00 p.m. B)9: 00 p.m. C)6: 00 a.m. D)8: 00 a.m. E)10: 00 a.m. SOLUTION:Given: The number of bacteria in a petri dish increased by 50 percent every 2 hours There were 108 million bacteria in the dish at 2: 00 p.m Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours. Required: At what time were there 32 million bacteria in the dish? Assume that there were n intervals of 2 hours between 32 million and 108 million. 32 * (1.5)^n = 108 (3/2)^n = 108/32 = 27/8 = (3/2)^3 Hence n = 3 intervals. Each interval was of 2 hours. Therefore, the number of hours = 6 Subtracting 6 hours from 3 PM, we get 9 AM as the answer. Option B #### B QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 40 miles per gallon, and from Town B to Town C, the car averaged 50 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)42.85 B)40 C)35 D)41 E)39 SOLUTION:step 1) took LCM of 40 and 50.. came as 200. step 2) 200 distance between B to C... do 200/50 hence 4 gallons used step 3) twice distance.. hence 200*2= 400... do as above.. 400/40= 10 gallons used step 4) total gallons.. 4+10= 14 gallons step ) total miles= 200+400= 600 miles hence.. average of whole journey = 600/14 which comes to 42.85 Answer : A #### A QUESTION:If there are 200 questions in a 3 hr examination. Among these questions are 10 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? options: A)17.14286 min B)62 min C)70.1346 min D)74 min E)76.1346 min SOLUTION:x=time for type B prolems 2x=time for type A problem total time=3hrs=180min 190x+10*2x=180 x=180/210 x=0.72 time taken for type A problem=10*2*0.857143=17.14286min ANSWER:A #### A QUESTION:Find the value of 72515 x 9999 = m? options: A)345434667 B)246465757 C)465767867 D)725077485 E)645354643 SOLUTION:72515 x 9999 = 72515 x (10000 - 1) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 D #### D QUESTION:One of the following numbers can be marked out as the odd one out. can you find which one? 1) 680986879 2) 716089780 3) 820670987 4) 932967879 options: A)The odd number is 680986879 B)The odd number is 820670987 C)The odd number is 716089780 D)The odd number is 932967879 E)None SOLUTION:Correct Answer : B if you add up the first three digits of all the numbers, it adds up to 14 except for second option 820670987 #### B QUESTION:The sum of three integers A, B and C is 60. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C? options: A)40 B)45 C)35 D)50 E)55 SOLUTION:A is one third of the sum of B and C.. or A=1/3(B+C)... But A+B+C=60 so 1/3(B+C)+B+C=60 4(B+C)/3= 60 B+C =60*3/4 = 45 A=60-45=15 2)B is one fifth of the sum of A and C or B=1/5(A+C)... But A+B+C=60 so 1/5(A+C)+A+C=60 A+C=60*5/6=50 but A=15, so C=50-15=35 Answer :C #### C QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence? options: A)−164 B)0 C)16 D)32 E)64 SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term) sum of 64 terms = 32 ANSWER:D #### D QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:9 B)8:7 C)8:1 D)8:2 E)8:8 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8 : 7 Answer:B #### B QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? options: A)26 B)39 C)42 D)65 E)156 SOLUTION:Here 156 has three two's two three's and one 13 rest of them must be in w so w= 13*3*4 = 156 Answer: E #### E QUESTION:Find the value of (85 + 32/113) × 113 options: A)9263 B)9244 C)9636 D)9623 E)9637 SOLUTION:=(85 + 32/113) × 113 =(9605 + 32)/113× 113 =9637/113× 113 =9637 Answer is E. #### E QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides? options: A)3 B)6 C)5 D)9 E)1 SOLUTION:S = (1 + 2 + 7)/2 = 5 Answer:C #### C QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000 SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager. Average company salary * Number of employees = Total company salary >>> $80,000 * 10 = $800,000 Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000) >>> $800,000 - $300,000 - $240,000 = $260,000. The correct answer is C. #### C QUESTION:Find the value of 3 + 2 • (8 – 3) options: A)(a) 25 B)(b) 13 C)(c) 17 D)(d) 24 E)(e) 15 SOLUTION:3 + 2 • (8 – 3) = 3 + 2 (5) = 3 + 2 × 5 = 3 + 10 = 13 Answer: (D) #### D QUESTION:If G = 775 × 778 × 781, what is the remainder when G is divided by 14? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:G 775/14 leaves a remainder 5 778/14 leaves a remainder 8 781/14 leaves a remainder 11 5*8*11 =440 So the remainder will be the remainder of 440/14 which is 6 Ans A #### A QUESTION:Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 16, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates? options: A) 4/11 B) 1/2 C) 15/22 D) 144/17 E) 11/4 SOLUTION:P1 takes 12 hrs Rate for P2P3 together = 1/16 + 1/18 = 17/144 Therefore they take 144/17 Ratio = 144/17 = D #### D QUESTION:In a school the number of girls is 30% the number of boys. Find the number of boys as a percentage of girls? options: A)112% B)12% C)333% D)150% E)16% SOLUTION:It is given that in a school the number of girls is 30% the number of boys. If boys=10 girls=3 We are asked for the number of boys as a percentage of girls b/g=10/3=10 1/3=3.333=333% Answer is C #### C QUESTION:If x = 1- 3t and y = 2t - 3, then for what value of t does x = y? options: A) 5/2 B) 3/2 C) 2/3 D) 4/5 E) 0 SOLUTION:We are given x = 1 – 3t and y = 2t – 3, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 3t for x and 2t – 3 for y in the equation x = y. This gives us: 1 – 3t = 2t – 3 4 = 5t 4/5 = t The answer is D. #### D QUESTION:A certain elevator has a safe weight limit of 1950 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 190 pounds and the average weight of the others being 200 pounds? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Lets assume there are 2X people. Half of them have average weight of 190 and other half has 200. Maximum Weight is = 1950 So 190*X + 200*X = 1950 => 390X = 1950 => X is approximately equal to 5. So total people is 2*5 = 10 Answer D. #### D QUESTION:What is the total surface area in square meters of a rectangular solid whose length is 9 meters, width is 8 meters, and depth is 5 meters? options: A)152 m2 B)162 m2 C)180 m2 D)300 m2 E)314 m2 SOLUTION:Surface Area of a cuboid = 2(lb+bh+lh) = 2(9*8+8*5+9*5)=2(72+40+45)=2*157=314 m2 Answer : E #### E QUESTION:The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? options: A)3:4 B)3:0 C)3:1 D)7:3 E)3:7 SOLUTION:Let the present ages of A and B be 4.5x and 3x years respectively. Then, (4.5x - 4)/(3x + 4) = 1/1 1.5x = 8 => x = 5.33 Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: D #### D QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true? options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9 SOLUTION:x^2−x=k => x^2−x - k = 0 For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative. b^2-4ac ≥0 => 1- 4*1*(-k) ≥0 =>1 + 4k ≥0 => k ≥ -14 Answer A #### A QUESTION:If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office? options: A)38 B)27 C)24 D)19 E)17 SOLUTION:Explanation: Let t be his usual time to reach his office and v be his usual speed. v = d/t ……….(d is the distance Ajay travels while going to his office) vt = d At v1 = 4v/5 ; t1 = t + 6 4v/5 = d/(t + 6) 4v/5* (t + 6) = d 4v/5* (t + 6) = vt On solving we get, t = 24 minutes ANSWER:C #### C QUESTION:In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is: options: A)2 B)4 C)7 D)12 E)15 SOLUTION:Sol. Speed in still water = 1/2 (9+5) kmph = 7 kmph. Answer C #### C QUESTION:A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting? options: A)200 B)250 C)350 D)800 E)830 SOLUTION:science books sold = 2x × 0.2 = 0.4x science books unsold = 2x – 0.4x = 1.6x art books sold = 5x × 0.2 = x art books unsold = 5x – x = 4x total books unsold = 1.6x + 4x = 5.6x 5.6x = 2240 x = 400 2x science = 800 D #### D QUESTION:The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway? options: A)2 feet per second B)2.5 feet per second C)3 feet per second D)4 feet per second E)5 feet per second SOLUTION:I get E. Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d. So we get two equations: 3t=d-120 6t=d Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met. So, Bill's average rate of movement Q is: He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds. (240+60)/(20+40)= 5 ft/sec=E #### E QUESTION:A bag contains 50 black balls and 10 white balls. One ball is drawn at random. What is the probability that the ball is white? options: A)1 B)1/6 C)1/3 D)1/2 E)None of these SOLUTION:Explanation: Total cases = 50 + 10 = 60 Favourable cases = 10 So probability = 10/60 = 1/6 Answer: B #### B QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)9% B)4% C)6% D)3% E)5% SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer:B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)210m B)240m C)963m D)874m E)578m SOLUTION:Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B)240m #### B QUESTION:In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.64.50 per Kg? options: A)3 : 1 B)3 : 2 C)4 : 3 D)5 : 3 E)None SOLUTION:Required ratio = 750 : 250 = 3 : 1 Answer A #### A QUESTION:10, 20, 12, 24, 16, 32, ? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:E 24 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted? options: A)3 B)6 C)2 D)12 E)27 SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black. But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2. Answer: C. #### C QUESTION:Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely? options: A)15 sec B)19 sec C)12 sec D)10 sec E)11 sec SOLUTION:Explanation: D = 250 m + 250 m = 500 m RS = 80 + 40 = 120 * 5/18 = 100/3 T = 500 * 3/100 = 15 sec Answer: Option A #### A QUESTION:Diesel costs Rs.4 per lit and petrol costs 4.63 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol. options: A)9 months B)5 months C)6 months D)3 months E)2 months SOLUTION:Explanation : =>In the First Month the price of the diesel would be 4*110/100 = 4.4 =>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84 which is higher than the price of the petrol! Answer : E #### E <<<Examples ends QUESTION:How many 3-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same? options: A)1236 B)504 C)4096 D)4608 E)6561 SOLUTION:First digit.. 9 posibilities Second digit, 8 possibilities third digit, 7 possibilities 9*8*7 = 504. B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A project scheduled to be carried out over a single fiscal year has a budget of $12,000, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,540. By how much was the project over its budget? options: A) $380 B) $540 C) $1,050 D) $1,380 E) $1,430 SOLUTION:Difficulty level: 600 Each month's budget = 12000/12 = 1000 Budget for 4 months = 4*1000 = 4000 Actual amount spent = 4540 Amount spent over the budget = 4540 - 4000 = 540 Answer (B), Regards, #### B QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5 SOLUTION:We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10. # of different approximations are possible. Approach #1: 2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200); 2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107 Answer: C. Approach #2: 2*5=10 3*17=~50 (actually more than 50); 7*13=~100 (actually less than 100); 11*19=~200 (actually more than 200) 2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107. Answer: C. #### C QUESTION:A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x? options: A)7 B)8 C)9 D)6 E)5 SOLUTION:(3+11+7+9+15+13+8+19+17+21+14+x)/12 =12 ⇒(137+x)/12=12 ⇒137+x=144 ⇒x=144−137=7 Answer is A. #### A QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%? options: A)20% B)28% C)29% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 86 2/3 SP1 = 86 SP1 = 129 100 --- 29 => 29% Answer:C #### C QUESTION:If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place. options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours SOLUTION:1/5+2/8 + 3/x = 1 x =20 hours. ANSWER =D #### D QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/9 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)11/30 B)29/60 C)17/30 D)13/18 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/2*1/3=x/6 Platinum card unspent limit is= x-1/9x=8/9x So if gold card balance is transferred then the rest unspent will be 8/9x-x/6=13/18x So the ans is D #### D QUESTION:A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is: options: A)35.55 km/hr B)36 km/hr C)71 km/hr D)71.11 km/hr E)70 km/hr SOLUTION:Total time taken =((160/64)+(160/80))hrs=9/2hrs. Average speed =(320 x2/9)km/hr= 71.11 km/hr. ANSWER D #### D QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 4*5*6*7*8=6720. ANS:A #### A QUESTION:Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is? options: A)3/7 B)3/2 C)3/1 D)3/9 E)3/4 SOLUTION:Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. Answer:B #### B QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible? options: A)270 B)252 C)272 D)292 E)285 SOLUTION:number of astronauts with previous experience = 7 Remaining =9 we need to pick exactly one from the first group and 2 from the second group (7C1)*(9C2) =7*36= 252 Answer : B #### B QUESTION:Five pieces of wood have an average length of 126cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood? options: A)a) 90 B)b) 105 C)c) 110 D)d) 130 E)e) 140 SOLUTION:B. 105 sum of all lengths of all 5 pieces of wood = 126 * 5 = 630 3rd piece (sorted in increasing length) length = 140 (median) for sum of first 2 wood length to become max, last two should be least. let 4th, 5th wood also have length 140 each. total of last 3 = 140 * 3 = 420 sum of first 2 = 630 - 420 = 210 each of these 2 will have length 210/2 = 105 Aswer B #### B QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 6 years will be options: A)2 : 3 B)7 : 11 C)5 : 4 D)4 : 5 E)11 : 9 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 28 x = 4 Mini’s age = 16 years And Minakshi’s age = 12 years Ratio of their ages after 8 years = (16 + 6) : (12 + 6) = 22 : 18 = 11 : 9 ANSWER:E #### E QUESTION:It is required to seat 7 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)86,288 B)86,214 C)86,400 D)86,328 E)86,368 SOLUTION:Total number of candidates = 6 + 5 = 11. In the row of 11 positions, the even places are 2nd, 4th, 6th,8th,10th. Now, number of even places = 5. Number of girls to occupy the even places = 5. Even places can be filled = P (5, 5) ways. Number of boys = 6. The remaining 6 places can be filled by 6 boys = P (6, 6) ways By the fundamental principle of counting: The required number of seating arrangements P(5, 5) x P(6, 6) = 5! x 6! = 120 x 720 = 86,400 ANSWER:C #### C QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2. options: A)29 B)27 C)28 D)24 E)21 SOLUTION:(4)^11x (7)^5 x (11)^2 = (2 x 2)^11 x (7)^5 x (11)^2 = 2^11 x 2^11 x7^5x 11^2 = 2^22 x 7^5 x11^2 Total number of prime factors = (22 + 5 + 2) = 29. Answer is A. #### A QUESTION:A container has a capacity of 20 gallons and is full of spirit. 5 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 5 times. Find how much spirit is left in the resulting mixture finally? options: A)(257/525) gallons B)1.5552 gallons C)1.5 gallons D)1.25 gallons E)None of these SOLUTION:There is a direct formula to calculate such repetition: Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n where n is number of times mixing done: Left QTY / 20 = (20 -5)^5 / 20^5 Left QTY = 20 (15/20)^5 Left QTY = 20 ( 3/5 )^5 Left QTY = 1.5552 Answer is B #### B QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: options: A)14 B)67 C)56 D)89 E)34 SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer:A #### A QUESTION:There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division? options: A)22 B)35 C)37 D)20 E)75 SOLUTION:D 20 29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30 = 20. #### D QUESTION:A train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds. What is the length of the train (in meters)? options: A)190 B)200 C)210 D)220 E)230 SOLUTION:Let the length of the train be x meters. The speed of the train is x / 15. Then, x + 140 = 25*(x / 15) 10x = 2100 x = 210 meters The answer is C. #### C QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ? options: A)4/17 B)4/18 C)4/76 D)4/13 E)4/29 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer: D #### D QUESTION:If p is the product of the integers from 1 to 38, inclusive, what is the greatest integer k for which 3^k is a factor of p? options: A)13 B)15 C)17 D)19 E)21 SOLUTION:38! has 3, 6, 9,....30, 33, 36 as factors, which are 12 multiples of 3. We need to add 5 more to these 12 because of 9, 18, 27, and 36. The greatest integer of k is 17. The answer is C. #### C QUESTION:Pipe A can fill a tank in 2 hr, pipe B in 4hr and pipe C in 8hr. If all the pipes are open in how many hours will tank be filled? options: A)1hr 27min B)2hr 19min C)3hr 14min D)3hr E)5hr 45min SOLUTION:Part filled by (A+B+C) in 1hour = 1/2 + 1/4 + 1/8 = 7/8 All the 3 pipes together will fill the tank in 1hour 27min Answer is A #### A QUESTION:Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 42 minutes. The waste pipe can empty the full cistern in? options: A)8 min B)7 min C)5 min D)9 min E)4 min SOLUTION:1/10 + 1/15 - 1/x = 1/42 x = 7 Answer: B #### B QUESTION:How many seconds does a train 110 meters long, traveling at 54 km/h, take to completely cross a bridge of 160 meters in length? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:54 km/h = 54000/3600 = 15 m/s Time = 270 / 15 = 18 seconds The answer is A. #### A QUESTION:The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L? options: A)5 B)4 C)1/2 D)1/5 E)1/8 SOLUTION:If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5. The answer is D. #### D QUESTION:How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)24 sec B)30 sec C)27 sec D)28 sec E)29 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 400 * 3/50 = 24 sec. Answer:A #### A QUESTION:At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes? options: A)2150 B)2600 C)3120 D)1500 E)1895 SOLUTION:Winner votes = 100-30 = 70 polled votes = [(100*1000)/2*70-100]+100 = 2600 Answer is B #### B QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? options: A)45 B)33 1/3 C)27 D)16 2/3 E)15 SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x: 1.5/x = 1/20 x = 30 Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution. Answer is A. #### A QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? options: A)1000 B)817 C)278 D)268 E)280 SOLUTION:2 * 22/7 * 1.75 * x = 11000 x = 1000 Answer: A #### A QUESTION:We are given the positive numbers a,b,c, which form an arithmetic progresion in the given order. We know that a+b+c=9. The numbers a+1,b+1,c+3 form a geometric progression in the given order. Find c. options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Solution: Since a,b,c form an arithmetic progression, c=b+d=a+2d and a+b+c=a+a+d+a+2d=3a+3d=9, so a+d=b=3 and a+c=6=>c=6−a. Since a+1,b+1,c+3 form a geometric progression, we have (b+1)2=(a+1)(c+3), or 16=(a+1)(6−a+3)=(a+1)(9−a) 16=9a+9−a2−a a2−8a+7=0, therefore a=7 or a=1. But if a=7, c=6−a=6−7=−1<0 and by definition c is positive, so a=7 is not a solution. Therefore a=1 and c=6−a=6−1=5. Answer A #### A QUESTION:A group of people,dogs, and birds has seventy legs, thirty heads, and twenty tails. How many cats are among this group? (Assume all birds have two legs and a tail.) options: A)0 B)5 C)13 D)15 E)20 SOLUTION:Write P, C, and B for the number of people, dogs, and birds respectively, so that we have 2P + 4C + 2B = 70, P + C + B = 30,C + B = 20: Comparing the last two equations we obtain P = 10, and the first equation simplifies to 4C + 2B = 50, or 2C + B = 25. Therefore, C = (2C + B) -(C + B) = 25- 5 = 5 correct answer B #### B QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)165 B)771 C)245 D)177 E)121 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer: C #### C QUESTION:The average age of 29 students in a group is 15 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years? options: A)31 B)36 C)29 D)53 E)57 SOLUTION:age of the teacher=(29*16-29*15) =29 years. ANSWER:C #### C QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? options: A)120cc B)360cc C)450cc D)589C E)478cc SOLUTION:Explanation: r1 = x r2 = 3x Π * x2 * h = 40 Π9 x2h = 40 * 9 = 360cc Answer: B #### B QUESTION:What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9? options: A)397 B)401 C)403 D)405 E)399 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=405. Answer: D. #### D QUESTION:If the simple interest on Rs.3100 amount to Rs. 632.40 in 2 Years, What is the rate percent? options: A)11.2% B)10.2% C)12.2% D)13.2% E)18.2% SOLUTION:$632.40 = (3100*2*R)/100 R = 10.2% Answer: B #### B QUESTION:Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: options: A)7/8 B)1/8 C)1/3 D)1/5 E)1/9 SOLUTION:Original share of 1 person =1/6 New share of 1 person =1/5 Increase =1/5 - 1/6 =1/30 Required fraction = (1/30)/(1/6)=1/5 Answer is D. #### D QUESTION:A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color? options: A)50 B)8 C)60 D)42 E)32 SOLUTION:in the first case the lady takes up 32 red colour then he takes up 24 y (cause he should take up pair) then he takes up 1y+1blue then 2blue(cause to make sure he has a pair of each color in hand) 32+24+2+2=60 ANSWER:C #### C QUESTION:A group of five people are weighed with the results as follows (in pounds): 135, 140, 165, 178, 199. If the weight of the heaviest person is increased by 9 pounds, which of the following statements best describes the change in the mean and the median of the weights? options: A) The mean and the median will remain unchanged. B) The mean will remain unchanged but the median will increase. C) The mean will increase but the median will remain unchanged. D) The mean and the median will increase by the same amount. E) The mean and the median will increase by different amounts. SOLUTION:Old set = {135, 140, 165, 178, 199}. New set = {135, 140, 165, 178, 208} --> the median (middle term) will remain the same and the mean will increase. Answer: C. #### C QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:In a apartment, 70% of the people speak English, 10% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi? options: A)1/3 B)2/3 C)2/5 D)1/2 E)2/9 SOLUTION:P (E) = 70 / 100 = 3 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E ∩ H) = 30 / 100 = 3 / 10 P (E or H) = P (E U H) = P (E) + P (H) - P (E ∩ H) = (7 / 10) + (1 / 10) - (3 / 10) = 3 / 10 = 1/2 D #### D QUESTION:How many cubes of 5cm edge can be cut out of a cube of 20cm edge options: A)36 B)64 C)216 D)484 E)None of these SOLUTION:Explanation: number of cubes=(20 x 20 x 20) / (5 x 5 x 5) = 64 Answer: B #### B QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:If x is divisible by 2 and 7, which of the following must divide evenly into x? I. 60 II. 32 III. 14 options: A)I,II only B)I,III only C)I only D)III only E)II only SOLUTION:If x is divisible by 2,7 means it will be = or > 14, 28,42 etc... That are not divisible by 60, 32. So, the answer is D #### D QUESTION:The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ? options: A)20 years B)21 years C)22 years D)34 years E)24 years SOLUTION:The average age of the 5 members is 20 years => The sum of the ages of the 5 members is 20*5 = 100 years Once the new member joins, the average age becomes 24 years. Let the age of the new member be x. Then (110+x)/6 = 24 => x = 34 years Answer D #### D QUESTION:If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is? options: A)A)15 B)B)10 C)C)14 D)D)12 E)E)11 SOLUTION:2 * 22/7 * 14 * x = 880 => x = 10 ANSWER:B #### B QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book? options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20 SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations: m + p + c = 20 (since 4/5 of the 25 spots are full of books) m = 2p p = 4 + c From that, you can use Substitution to get everything down to one variable. c = p - 4 m = 2p p = p Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf. With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E QUESTION:X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 8. What is the value of Z? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2. X + 3Y + 3Z = 5Y + 8 Z+2+3Z+3+3Z = 5Z+5+8 2Z = 8 Z = 4 The answer is C. #### C QUESTION:If c is 20% of a and 10% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 200% SOLUTION:Answer = E 20a/100 = 10b/100 b = 20a/10 = 200a/100 = 200% #### E QUESTION:Alex age after 13years will be 10 times his age 10years back. What is the present age of Alex? options: A)15 B)13 C)20 D)21 E)26 SOLUTION:Let Alex's present age be x Alex's age after 17 years = x+17 Alex's age 10 years back = x-10 x+17= 10(x-10) x = 13 Rajeev's present age = 13 years Answer is B #### B QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160 SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 8*12=96 five-minute intervals, thus total of 96*30 tickets were sold. Say x student and 3x regular tickets were sold, then x+3x=96*30 --> x=24*30 and 3x=3*(24*30)=24*90. Therefore, the total revenue from ticket sales that day was 24*30*6+24*90*10=$25,920. Answer: B. #### B QUESTION:Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries? options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140 SOLUTION:Probability of basket = 3/5 Probability of no basket = 2/5 Required probability=3* 3/5*2/5*2/5 =36/125 A is the answer . #### A QUESTION:J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to options: A)22 B)14 C)6 D)8 E)16 SOLUTION:Given J > P J + P = 7, only options are (6, 1), (5, 2), (4, 3) From the given options, If J = 4 the P = 3. Times taken by them = 244+243=14 Answer:B #### B QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)9 D)2 E)9 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:A certain kind of necklace is made from 9 gold, 6 blue, and 3 white beads. What is the maximum number of these necklaces that can be made from 36 beads of each color ? options: A)8 B)4 C)6 D)5 E)4 SOLUTION:Atleast 9 gold breads are needed to make a necklace, so irrespective of the combinations of blue and white beads, the number of necklaces that can be formed will be 36/9 =4 Answer:- E #### E QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 300 m long platform in 26 sec. What is the length of the goods train? options: A)382 B)782 C)278 D)270 E)220 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 300)/26 = 20 x = 220 m. Answer: E #### E QUESTION:A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 980gm. for a kg.His gain is …%. options: A)2.04% B)5.36% C)4.26% D)6.26% E)7.26% SOLUTION:His percentage gain is 100*20/980 as he is gaining 20 units for his purchase of 980 units. so 2.04%..ANSWER:A #### A QUESTION:Of the 800 employees of Company X, 90 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 60 percent ? options: A)200 B)160 C)112 D)80 E)600 SOLUTION:The # oflong-termemployees is 90%*800=720. After y of them retire new # oflong-termemployees would become 720-y. Total # of employees would become 800-y. We want 720-y to be 60% of 800-y --> 720-y=(800 -y)*60% --> y = 600. Answer: E. #### E QUESTION:A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |Y|<3? options: A)1/7 B)3/7 C)2/5 D)3/11 E)4/7 SOLUTION:|X||X| can take 7 values. To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x ⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases = 3/7 B #### B QUESTION:Set R has a mean of 12 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){15, 16} B){3, 4} C){6, 7} D){5, 6} E){11, 13} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 12,the values (11,13) are closer than others. Hence Answer : E #### E QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice? options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7 SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2*(1/2)^2 = 2/4 =0.5. The answer is, therefore, (A). #### A QUESTION:AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 16.0 grams 4:00 P.M. x grams 7:00 P.M. 20.4 grams Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.? options: A)12.0 B)18.1 C)12.2 D)12.3 E)18.0 SOLUTION:The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours. Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm: Fractional increase from 1 PM to 4 PM = X / 16.0 Fractional increase from 4 PM to 7 PM = 20.4 / X X \ 16 = 20.4 \ X X^2 = 20.4 * 16 X = 18 answer : E #### E QUESTION:What distance will be covered by a bus moving at 126 kmph in 10 seconds? options: A)287 B)600 C)350 D)276 E)207 SOLUTION:126 kmph = 126 * 5/18 = 35 mps D = Speed * time = 35 * 10 = 350 m. Answer:C #### C QUESTION:Rahul take a loan of sum Rs.550.This is to be repaid in two equal annual installments. If the rate of interest be 20% compounded annually,then find the value of each installment? options: A)360 B)420 C)230 D)540 E)610 SOLUTION:Let the value of each installment be Rs.x [x/(1+(20/100))]+[x/(1+(20/100))2]=550 (100x/120)+(10000x/14400)=550 (5x/6)+(25x/36)=550 x=360 Option A #### A QUESTION:In a mixed college 160 students are there in one class. Out of this 160 students 3/5 students are girls. How many boys are there ? options: A)A)40 B)B)64 C)C)80 D)D)120 E)E)140 SOLUTION:Total Number of Students :160 Total Girls : 160*3/5 =96 Total Boys : 160-96= 64 Answer is B #### B QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is? options: A)39yr B)42yr C)45yr D)32yr E)50yr SOLUTION:Let B's present age = x years Then A's present age = x+9 years x+9+10 = 2(x-10) x + 19 = 2x - 20 x = 39years Answer is A #### A QUESTION:Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible? options: A)10 B)25 C)126 D)252 E)630 SOLUTION:With 10 players, the process of figuring out how many groups of 5 can be formed is pretty straight-forward.... 10C5 = 10!/(5!5!) = 256 possible groups of 5 Once forming that first group of 5, the remaining 5 players would all be placed on the second team by default. The 'twist' is that the two teams of 5 can "show up" in either order: For example, if we call the two teams of 5 players: A,B,C,D,E and F,G,H,I,J ABCDE vs. FGHIJ is the SAME match-up as.... FGHIJ vs. ABCDE So we are NOT allowed to count that matchup twice. This means we have to divide the 256 by 2. Final Answer:C #### C QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 11000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)14 B)21 C)22 D)23 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (10000 × 7) + 6000 ( x – 7) ‹=› 2000x = 28000 ‹=› x = 14. Answer A #### A QUESTION:Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 7 meters, and the interior of tank B has a height of 7 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? options: A)70% B)80% C)100% D)120% E)125% SOLUTION:The radius of tank A is 7/(2*pi). The capacity of tank A is 10*pi*49 / (4*pi^2) = 245 / (2*pi) The radius of tank B is 10 / (2*pi). The capacity of tank B is 7*pi*100 / (4*pi^2) = 350 / (2*pi) Tank A / Tank B = 245/350 = 7/10 = 70% The answer is A. #### A QUESTION:A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,700 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Price in 96 = 22000 Price decrease each year = 2.5/100*22000 = 550 Price in 97 = 22000 - 550 Price in 98 = 22000 - 2*550 Price in 99 = 22000 - 3*550 Price in 00 = 22000 - 4*550 Price in 01 = 22000 - 5*550 Price in 02 = 22000 - 6*550 = 18700 Investment in the car = 1000 Net price of the car in 02 = 18700 + 1000 = $19700 Correct Option: B #### B QUESTION:Lisa earns a profit of $3 on each ribbon that she sells, and $5 on each bracelet. If at the end of the day Lisa has earned $120 and she has sold at least 10 pieces of each item. At least how many bracelets she has sold? options: A)2 B)5 C)9 D)12 E)15 SOLUTION:Since Lisa has sold at least 10 pieces for each item, let us say Lisa sells (10 + r) number of ribbons and (10 + b) number of bracelets, her profit for the day = 3(10 + r) + 5(10 + b) => 3(10 + r) + 5(10 + b) = 120 => 30 + 3r + 50 + 5b = 120 => 3r + 5b = 120 - 30 - 50 = 40 => 5b = 40 - 3r => b = 8 - (3/5)r To minimize b, we need to maximize r and it will be a multiple of 5. r = 5, b = 8 - (3/5)5 = 5 r = 10, b = 8 - (3/5)10 = 2 Beyond that b will become -ve. So Lisa has sold at least 10 + 2 = 12 bracelets. Answer: D #### D QUESTION:If x, y, and z are positive integers and x = 4y = 7z, then the least possible value of x + y + z is options: A)33 B)40 C)49 D)39 E)84 SOLUTION:x + y + z = x/4 + x + x/7 = (7 + 28 + 4 )x/28 =39x/28 39 is not divisible by 28, so for least value, x = 28 Answer - D #### D QUESTION:Find the unit digit in the product 274*318*577*313 options: A)5 B)2 C)10 D)26 E)89 SOLUTION:Explanation: Required digit=Unit digit is in(4*8*7*3)=2 Answer B #### B QUESTION:If the cost price is 96% of the selling price, then what is the profit percent? options: A)4.17% B)5% C)6.12% D)3.25% E)5.75% SOLUTION:Let S.P. = $100 C.P. = $96 Profit = $4 Profit% = 4/96 * 100 = 25/6 = 4.17% Answer is A #### A QUESTION:How many keystrokes are needed to type numbers from 1 to 1000? options: A)2704 B)2890 C)2893 D)3001 E)None of these SOLUTION:1-9 9 digits 10-99 There are 90 2-digit numbers (90)(2) = 180 digits 100-999 There are 900 3-digit numbers (900)(3) = 2700 digits 1000 4 digits 9 + 180 + 2700 + 4 = 2893 Answer: C #### C QUESTION:There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3 options: A)I B)II C)III D)II &III E)I &II SOLUTION:Name T = full pool U fills a pool in a days ==> 1 day U fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c 1 day (U+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (U+Y+Z) together fill: T ==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==>d = abc/(ab+bc+ca) d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3 B #### B QUESTION:The average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results? options: A)30 B)25 C)48 D)50 E)None SOLUTION:Answer Sum of 85 result = sum of 20 result + sum of 65 result. = 20 x 65 + 65 x 20 = 2600 Correct Option: A #### A QUESTION:A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 4, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit? options: A)23/24 B)31/36 C)55/64 D)65/81 E)75/121 SOLUTION:P(no even digits) = 2/3*2/3*2/3*2/3 = 16/81 P(at least one even digit) = 1 - 16/81 = 65/81 The answer is D. #### D QUESTION:The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Also note here the relevance of 'K must be less than 400'. 21K is 180n (a multiple of 180). 180n = 2^2 * 3^2 * 5 * n = 3*7*K n must have a 7 at least. K must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60. So K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 60*7 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 60*2 or 60*3*2 or 60*5 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has. Answer (C) #### C QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 6:30:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 150 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)1200 B)1300 C)1500 D)1800 E)1900 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 6:30:90 Initial soap:alcohol = 6/30 =6:30 after doubled soap:alcohol =2* 6/30 = 12/30=12:30 Initial soap:water = 6/90=6:90 after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360 After soap: alcohol:water --> 12:30:360 given alcohol 150 cubic centimeter. ratio is 60:150:1800 (12:30:360) For 150 cubic centimeter of Alcohol ---1800 cu cm water is required. Answer-D #### D QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group? options: A)87 B)67 C)23 D)75 E)25 SOLUTION:Let the initial number of members in the group be n. Initial total weight of all the members in the group = n(48) From the data, 48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23 Therefore there were 23 members in the group initially. Answer: C #### C QUESTION:8, 24, 12, 36, 18, 54, (....) options: A)72 B)68 C)108 D)27 E)86 SOLUTION:8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 Answer is D. #### D QUESTION:Set Q consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set Q, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:A = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of Q = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0. What is the difference between the two greatest possible values of x? Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. options: A)124 B)241 C)394 D)421 E)842 SOLUTION:Ratio of a:b:c= 2:4:1 Two possible greatest single digit values for b are 8 and 4 if b is 8, then x= 482 if b is 4, then x= 241 difference= 482-241= 241 B is the answer #### B QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)40 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:M = {-6, -5, -4, -3, -2} T = {-3, -2, -1, 0, 1, 2, 3, 4} If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative? options: A)0 B)1/3 C)2/5 D)1/2 E)3/5 SOLUTION:We will have a negative product only if 1, 2, 3, or 4 are selected from set T. P(negative product) = 4/8 = 1/2 The answer is D. #### D QUESTION:John bought 9.25m of cloth for $397.75. Find the cost price per metre. options: A)46 B)47 C)58 D)56 E)43 SOLUTION:Cloth bought by John = 9.25 m Cost of 9.25 m = $397.75 Cost per metre = 397.75 ÷ 9.25 The cost of the cloth per metre = $ 43 Answers: E #### E QUESTION:A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount? options: A)21% B)25% C)69% D)31% E)12% SOLUTION:Let the price be 100. The price becomes 140 after a 40% markup. Now a discount of 20% on 140. Profit=112-100 12% answer E #### E QUESTION:Find the area, diameter = 12m. options: A)113.00 square meter B)113.04 square meter C)113.08 square meter D)113.24 square meter E)113.43 square meter SOLUTION:Diameter = 12 meter. Radius = diameter/2. = 12/2. = 6 meter. Area of a circle = πr2. Here, pi (π) = 3.14 meter, radius (r) = 6. Area of a circle = 3.14 × 6 × 6.. = 3.14 × 36. = 113.04 square meter or 113.04 m2. ANSWER : B #### B QUESTION:The total marks obtained by a student in Mathematics and Physics is 80 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)30 C)25 D)50 E)None of these. SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 80 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (80 + 20) / 2 = 50. ANSWER:D #### D QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 616 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 616 ⇒ y[12/10 + 1] = 616 ⇒ 22y/10 = 616 ⇒ 22y = 6160 ⇒ y = 6160/22 = 560/2 = Rs.280 B #### B QUESTION:The speeds of 3 trains in the ratio 10:15:20. The ratio between time taken by them to travel the same distance is? options: A)6:4:3 B)1:2:3 C)4:8:9 D)6:5:2 E)4:8:7 SOLUTION:Ratio of time taken is = 1/10 : 1/15 : 1/20 = 6:4:3 Answer is A #### A QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C QUESTION:The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream? options: A)5 kmph B)67 kmph C)22 kmph D)88 kmph E)12 kmph SOLUTION:Speed of the boat in still water = (60+70)/2 = 65 kmph. Speed of the stream = (70-60)/2 = 5 kmph. Answer:A #### A QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire? options: A)2 B)8 C)7 D)3 E)10 SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 72,000 m : C is the circumference C = 3 meters #### D QUESTION:If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be options: A)(1.5)^4 B)(1.05)^5 C)(1.05)^4 D)1 + (0.05)^4 E)1 + 4(0.05) SOLUTION:In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of . We'd have.... Answer :B #### B QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction? options: A)5hours B)40hours C)8hours D)20hours E)30hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 40 =20 hours Answer is D #### D QUESTION:10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them. options: A)1628.4 B)1534 C)1492 D)240 E)None of these SOLUTION:Solution: Let average expenditure of 10 people be x. then, 10x = 20*5+5*(x+4); Or, 10x = 20*5+5x+20; Or, x = 24; So, total money spent = 24*10 = Rs. 240. Answer: Option D #### D QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:If the productivity of a brigade grows by 40% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade? options: A)1.51 B)0.82 C)1.2 D)1.21 E)1.44 SOLUTION:B = 10-men brigade p = increase in the productivity = 40% Solution: B x p = B x 1.4 = 1.4B -------> the productivity of 11 men brigade 1.4B x p = 1.4B x 1.1 = 1.51B -----> the productivity of 12 men brigade The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.51B/B = 1.51 A #### A QUESTION:A dragon has 100 heads. A soldier can cut off 15, 17, 20 or 5 heads, respectively with one blow of his sword. In each of these cases, 24, 2, 14, 17 new heads grow on its shoulders. If all heads are cut off, the dragon dies. Can the dragon ever die? options: A)61 B)3 C)5 D)6 E)1 SOLUTION:Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die. Answer:B #### B QUESTION:A man can do a job in 5 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? options: A)6.3 B)6.9 C)3.5 D)6.1 E)6.2 SOLUTION:1 day work of the three persons = (1/5 + 1/20 + 1/25) = 29/100 So, all three together will complete the work in 100/29 = 3.5 days. Answer:C #### C QUESTION:The average of 35 students in a class is 17 years. The average age of 25 students is 15. What is the average age of remaining 10 students? options: A)26 years B)27 years C)28 years D)29 years E)30 years SOLUTION:Sum of the ages of 14 students = (17 * 35) - (15 * 21) = 595 - 315 = 280 Required average = (280/10) = 28 years. Answer:C #### C QUESTION:Which of the following number is divisible by 24 ? options: A)3100000 B)3115832 C)3115800 D)3125832 E)3125834 SOLUTION:31214 is not divisible by 3 and 8 => 31214 is not divisible 24 61212 is not divisible by 8 though it is divisible by 3 => 61212 is not divisible 24 512216 is not divisible by 3 though it is divisible by 8 => 512216 is not divisible 24 3125832 is divisible by 3 and 8 => 3125832 is divisible 24 D) #### D QUESTION:A monkey starts climbing up a tree of 20 feet tall. Each hour it hops 3 feet and slips back 2 feet. How long monkey will take to reach the top of the tree? options: A)16 hours. B)19 hours. C)12 hours. D)18 hours. E)13 hours. SOLUTION:The monkey hops 3 feet and slips down 2 feet. So for the first hour it climb 1 feet. Then for 2 hours 2 feet. Continuing the same till 17 hours, the monkey might have reached 17 feet. In 18th hour monkey hops 3 feet and reach the 20 feet. Hence the answer is 18 hours. Answer D #### D QUESTION:There are 40 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)6 B)12 C)20 D)24 E)27 SOLUTION:40*2/3 *3/4= 20 Answer: C #### C QUESTION:A milk man has 30 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is: options: A)20% B)25% C)33.33% D)35% E)None of these SOLUTION:Explanation: when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 30 liters of milk. Therefore, profit percentage = 35 %. Answer: D #### D QUESTION:Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture? options: A)1 : 9 B)1 by 5 C)1 : 7 D)1 : 3 E)1 : 1 SOLUTION:Selling price of the mixture = 70 and profit = 20% Cost price of the mixture = 70×100120=70×5670×100120=70×56 By applying alligation rule: So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5 Answer:B #### B QUESTION:A train 120 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)443 m B)354 m C)450 m D)380 m E)250 m SOLUTION:D 350 D = 72 * 5/18 = 25 = 500 – 120 = 380 #### D QUESTION:WHEN A PERSON SELLS TWO ITEMS $1656 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURS A LOSS OR GAIN OF: options: A)no loss no gain B)20 % profit C)4% loss D)2% profit E)2% loss. SOLUTION:The 2 items are sold at 1656 each , one at a profit of 20% and the other at a loss of 20% So the original rates of the items are 1380 and 2070 respectively So the total he spend for those 2 items is 3450 but he ended up in selling them with (1656*2) 3312 So the loss is 3450 - 3312 = 138 The loss percentage is (138/3450) *100 = 4% loss - Answer C #### C QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 4 years hence? options: A)22 B)77 C)70 D)68 E)71 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 4 years, their ages will be 44 and 24. Sum of their ages = 44 + 24 = 68. Answer: D #### D QUESTION:If the population of a certain country increases at the rate of 1 person every 60 seconds, by how many persons does the population increase in 2 Hours? options: A)120 B)80 C)100 D)150 E)140 SOLUTION:Answer = 1 * 120(2 hour = 120 minutes)= 120 Answer = A #### A QUESTION:How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? options: A)15 kg B)18 kg C)20 kg D)24 kg E)None of these SOLUTION:Here, cost price of mixture = 100×100/100+25 = 32 paise ∴q1q2=32−24/42−32=810=45 and hence q1 = 4⁄5 × 25 = 20 kg Answer C #### C QUESTION:Calculate the largest 6 digit number which is exactly divisible by 99? options: A)999991 B)999965 C)999912 D)999936 E)999930 SOLUTION:Largest 4 digit number is 999999 After doing 999999 ÷ 96 we get remainder 55 Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 ANSWER : D #### D QUESTION:The first three terms of a proportion are 3, 9 and 12. The fourth term is? options: A)22 B)28 C)27 D)36 E)88 SOLUTION:(9*12)/3 = 36 Answer:D #### D QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$11,000 B)$50,000 C)$16,500 D)$ 6,600 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 2200 less between 3 people(x-(2200*3))/3 Set both eq. equal to each other. 16,500 Answer C) #### C QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money? options: A)1489 B)6845 C)2598 D)1875 E)2600 SOLUTION:P = 75(100/20)5 => P = 1875 Answer: D #### D QUESTION:The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog? options: A)12 B)24 C)30 D)48 E)120 SOLUTION:We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together. Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!*2=48. Answer: D #### D QUESTION:The product of two numbers a and b equals one-quarter their average. What is a in terms of b? options: A)a= b/(8b-1) B)a= b/(7b-1) C)a= b/(8b) D)a= b/(8b-4) E)a= 2b/(8b-1) SOLUTION:a*b = ( a+b)/8 8ab =a+b a= b/(8b-1) ANSWER:A #### A QUESTION:An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Going down = 16 m Going Up = 8 --> Total = 24 Going down = 8 --> Total = 32 Going Up = 4 --> Total = 36 Going down = 4 --> Total = 40 Going up = 2 --> Total = 42 Going down = 2 --> Total = 44 Going up = 1 --> Total = 45 Going down = 1 --> Total = 46 Going up = 0.5 --> Total = 46.5 (Caught) No of going downs = 5 .. ANSWER:A #### A QUESTION:If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:0.[u]225[/u = 0.225225225..... Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5. Answer E #### E QUESTION:If x > y and y > z, which of the following represents the greatest number W? options: A) x − z B) x − y C) y − x D) z − y E) z − x SOLUTION:Because x>y>z thus W=x- z wil lbe greatest Ans: A #### A QUESTION:There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)675 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 10C2 Number of ways of selecting 2 non fiction books = 6C2 10C2 * 6C2 = 45 * 15 = 675 Answer: C #### C QUESTION:A merchant marks his wares 40% more than the real price and allows 20% discount. His profit is: options: A)20% B)18% C)16% D)12% E)None of these SOLUTION:Let the CP = 100 Rs. Mark Price = 140 Discount = 20% Selling price 80/100 × 140 Hence profit = 12% Answer: D. #### D <<<Examples ends QUESTION:In 110 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: options: A)20 m B)25 m C)22 m D)9 m E)12 m SOLUTION:Distance covered by B in 9 sec. = 110/45 x 9 m = 22 m. A beats B by 20 metres. Answer: Option C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If 4a = 16b and 9b = 14c, Find a:b:c? options: A)52:13:7 B)13:7:52 C)7:13:52 D)64:14:9 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (9b = 14c ==> b/c = 14/9) ==> a:b = 16:4 and b:c = 14:9 a:b:c = 64:14:9 Answer: Option D #### D QUESTION:85% of a number is added to 24, the result is the same number. Find the number? options: A)28 B)288 C)279 D)160 E)232 SOLUTION:(85/100) * X + 24 = X 3X = 480 X = 160 Answer:D #### D QUESTION:Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is? options: A)7 1/2 sec B)2 sec C)3 sec D)5 sec E)7 sec SOLUTION:70 + 50 = 120 * 5/18 = 100/3 mps D = 150 + 100 = 250 m T = 250 * 3/100 = 15/2 = 7 ½ sec ANSWER A #### A QUESTION:A wildlife preserve is being planned for 6,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population? options: A) 340 B) 330 C) 670 D) 310 E) 300 SOLUTION:Number of rhinos = 6000 Watering area = 10,000 acres Number of rhino to increase by 10 percent ,then number of rhino = 6600 Grazing area for a rhino = 100 Total grazing area for 6600 rhinos= 6600 * 100 = 6,60,000 Total area required for the wildlife preserve = 6,60,000 + 10,000 = 6,70,000 = 670 * 1000 Answer C #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is? options: A)11 B)72 C)36 D)99 E)27 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240)/12 => x = 20 Speed of each train = 20 m/sec. = 20 * 18/5 =72 km/hr. Answer: B #### B QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 60 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school? options: A)12 B)15 C)20 D)24 E)30 SOLUTION:Let x be the number of new boarders. The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10. 60 / (60+x) = 4/5 x = 15 The answer is B. #### B QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 616 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 616 ⇒ y[12/10 + 1] = 616 ⇒ 22y/10 = 616 ⇒ 22y = 6160 ⇒ y = 6160/22 = 560/2 = Rs.280 B #### B QUESTION:Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat? options: A)5! B)8! C)9! D)12! E)11! SOLUTION:Ans.(B) Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways #### B QUESTION:There are 5 physics books and 1 chemistry book on shelf P and 3 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student? options: A)1/42 B)1/36 C)1/30 D)1/24 E)1/18 SOLUTION:P(a chemistry book is moved to shelf Q) = 1/6 P(a chemistry book is then chosen from shelf Q) = 1/4 P(the student takes a chemistry book) = 1/6 * 1/4 = 1/24 The answer is D. #### D QUESTION:A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings? options: A)12 B)13 C)46 D)37 E)26 SOLUTION:16x + 85 = 17(x + 3) x = 34 + 3 = 37 Answer: D #### D QUESTION:Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 72 kmph and 90 kmph. In how much time will the trains cross each other? options: A)80/8 B)80/9 C)80/5 D)80/3 E)80/1 SOLUTION:Relative speed = (72 + 90)* 5/18 = 9* 5 = 45 mps. The time required = d/s = (100 + 100 + 200)/45 = 400/45 = 80/9 sec. Answer: B #### B QUESTION:A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters, at 10 meters per minute. However, the toy train is defective and it now produces only two different tunes at random. What is the probability that the toy train produces 3 music tunes of the same type (1 in _____ ) ? options: A)3 B)9 C)8 D)4 E)5 SOLUTION:1/2^3=1/8 but here der r two types of tone and we need to find the odds of d train of two tones to form 3 tones consequently so 2*1/8= 1/4 so ans is 4 ANSWER:D #### D QUESTION:If the speed of a man is 54 km per hour, then what is the distance traveled by him in 25 seconds ? options: A)275m B)360m C)375m D)420 m E)440 m SOLUTION:The distance traveled in 25 sec = 54*(5/18) *25 =375m ANSWER:C #### C QUESTION:What is the minimum value of |x-4| + |x+8| + |x-5| ? options: A)-13 B)13 C)5 D)7 E)8 SOLUTION:A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative. |x-4| >= 0 --> Minimum occurs at x = 4 |x+8| >= 0 --> Minimum occurs at x = -8 |x-5| >= 0 --> Minimum occurs at x = 5 x = -8 --> Result = 12 + 0 + 13 = 25. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9. x = 4 --> Result = 0 + 12 + 1 = 13 x = 5 --> Result = 1 + 13 + 0 = 14 x = 8 --> Result = 4 + 16 + 3 = 23 So minimum value of the expression occurs at x = 4 and the resultant value = 13 Answer: B #### B QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled 3 min--------1/30 parts x min--------- 1 part(full) x=90 min =1 hour 30 min ANSWER:C #### C QUESTION:In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other? options: A)24 B)48 C)56 D)72 E)96 SOLUTION:These 5 people can be arranged in 5! ways. These are the total number of ways you get. Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!. Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72 ANSWER:D #### D QUESTION:The average of first 10 odd numbers is? options: A)22 B)10 C)98 D)66 E)88 SOLUTION:Sum of 10 odd no. = 100 Average = 100/10 = 10 Answer:B #### B QUESTION:A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is: options: A)130 B)360 C)500 D)540 E)580 SOLUTION:L = 800 m S = 78kmph = 65/3 mps Time to pass tunnel = 1min = 60 sec t.f (800+X)/(60) = (65/3) =500 ANSWER:C #### C QUESTION:A polling company reports that there is a 50% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z? options: A)11 B)10 C)6 D)4 E)5 SOLUTION:50% - Candidate Elected 100%-60% = 40% - Candidate doesnotsigh Bill X 50% - Candidate randomly chooses between two bills. These are multiplicative: 50% x 40% x 50% 0.5 x 0.4 x 0.5 = 0.10 = 10% Answer (B) #### B QUESTION:What is the equation of a circle of radius 5 units centered at (3, 2)? options: A)x^2 + y^2 + 6x – 4y = 23 B)x^2 + y^2 - 6x + 4y = 23 C)x^2 + y^2 + 6x + 4y = 23 D)x^2 + y^2 - 6x – 4y = - 12 E)x^2 + y^2 - 6x – 4y = 12 SOLUTION:the equation of a circle with center at (a,b) and radius R is (X-a)^2+(Y-b)^2=R^2 => answer = (X-3)^2+(Y-2)^2=5^2 solving,,we get the equation in answer choice E. #### E QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary options: A)42,000 B)43,000 C)44,000 D)45,000 E)46,000 SOLUTION:as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned) Rest amounts are in the form of greater than or lesser than , Hence C $45000 answer is D #### D QUESTION:In how many ways can the letters of word INTELLIGENT be arranged such that all the vowels as well as all the Consonants always appear together? options: A)9! B)5!*4! C)5!*5! D)5!*4!*2! E)4!*7!*2! SOLUTION:Since all the vowels and consonants have to be together there can only be there are 4! way to order the vowels and 7! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2. So 4!7!2! (E) #### E QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5*a1 + 7*b1 = t 5*a2 + 7*b2 = t 5*(a1 - a2) = 7*(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:Lisa plays a dice game in which she rolls two, fair, six-sided dice two times. If her second roll matches her first roll, she wins. What is the probability that she wins if her first roll was 10? options: A)1/6 B)5/36 C)1/9 D)1/12 E)1/18 SOLUTION:There are 3 ways to roll a 10 with two six-sided dice: 4 and 6, 6 and 4, 5 and 5. You only count 5 and 5 once. There are 6*6=36 ways to roll two six-sided dice. Thus the probability of rolling a 10 is 3/36 = 1/12. D #### D QUESTION:Find the invalid no.from the following series 9, 16, 21, 28, 33, 37 options: A)13 B)18 C)40 D)37 E)25 SOLUTION:The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 37 is wrong. Answer : D #### D QUESTION:If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q options: A)1 B)3 C)5 D)7 E)9 SOLUTION:3/7 = 0.428571... (a repeating pattern one digit long) B #### B QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides? options: A)2 B)7 C)5 D)3 E)4 SOLUTION:S = (1 + 1 + 2)/2 = 2 Answer: A #### A QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it? options: A)23 days B)16 days C)11 days D)24 days E)35 days SOLUTION:D 24 days 2c = ¼ + 1/6 – 1/3 = 1/12 c = 1/24 => 24 days #### D QUESTION:The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 60 percent, then the value of T decreases by what percent? options: A)25% B)33 ¹/₃% C)50% D)66 ²/₃% E)75% SOLUTION:We can assign numbers: lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T) Now increasing S by 50% gives S=4, K remains constant, so T = 2 (6/2=3) decrease in T= 1, percent decrease in T = (1/4)*100 = 25% Answer A #### A QUESTION:If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars? options: A)3⁄20 B)11⁄60 C)9⁄40 D)1⁄5 E)2⁄15 SOLUTION:Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car. Half of them are men, and the other half are women, more precisely 60. It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total. Answer E #### E QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-7 < x < 3 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -7 < x < 3 - no because x can be between 3 < x < 7 E. none of the above. Answer: E #### E QUESTION:Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? options: A)10liters B)15liters C)20liters D)18liters E)22liters SOLUTION:Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters Let x liters of pure milk be added. Then, 0.5/(10+x) = 2/100 2x = 30 x=15 liters Answer is B #### B QUESTION:There are 7 couples. If they will sit 14 chairs in a row such that each couple sits side by side, how many possible cases are there? options: A)120 B)240 C)1,200 D)2,460 E)654120 SOLUTION:Tie the couples. Then we have 5 persons that have to be arranged in 4 places. 4! ways. Now the couples can change position with each other. 2! ways. 7! * (2!)^7=5040 *128 = 645120 Answer is E. #### E QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ? options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points SOLUTION:A: B = 80 : 75, A : C = 80 : 65. B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5 Therfore ,In a game of 60, B can give C 8 points. Answer is E. #### E QUESTION:835, 734, 642, 751, 853, 981, 532 options: A)751 B)853 C)981 D)532 E)None of these SOLUTION:Solution In each number except 751,the difference of third and first digit is the middle one. Answer A #### A QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 34, what is the minimum possible range in scores of the three test-takers? options: A)a 17 B)b) 34 C)c) 35 D)d) 45 E)e) 80 SOLUTION:It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have: A- 0 and 17 B- 0 and 28 C- 0 and 35 therefore the minimum range is 34, it cant be any lower however you play with the numbers. B #### B QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is options: A)11 B)15 C)6 D)8 E)76 SOLUTION:Explanation: Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A) 11 #### A QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:Which of the following can be expressed as a terminating decimal? options: A)1/25 + 1/35 B)1/225 + 1/1,250 C)1/11,000 + 1/13,000 D)1/75 + 1/35 E)1/125 + 1/8 SOLUTION:In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first. A. 1/25 + 1/35 = 12/175 = 12/25*1/7 1/7 does is not a terminating decimal. E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000 This is a terminating decimal and our answer. Correct Option: E #### E QUESTION:There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? options: A)941,1009 B)991,1001 C)991,1009 D)791,1009 E)931,1009 SOLUTION:999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a2-b2=(a+b)(a-b) =(1000+9)*(1000-9) = (1009)*(991) Given that number of cats is less than number if mice. So number of cats is 991 and number of mice were 1009 Answer C #### C QUESTION:Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is options: A)2 : 3 B)4 : 3 C)6 : 7 D)9 : 16 E)None SOLUTION:Sol. Let us name the trains as A and B. Then, (A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3. Answer B #### B QUESTION:A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water? options: A)22 B)37 C)32 D)27 E)18 SOLUTION:US = 25 DS = 39 M = (39 + 25)/2 = 32 Answer:C #### C QUESTION:If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b = options: A) −48 B) −2 C) 2 D) −7 E) 48 SOLUTION:a(a + 7) = 18 and b(b + 7) = 18 => a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively => a+b = -7 Ans: D #### D QUESTION:The area of a triangle is with base 18m and height 6m? options: A)88 m2 B)10 m2 C)66 m2 D)54 m2 E)31 m2 SOLUTION:1/2 * 18 * 6 = 54 m2 Answer: D #### D QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence? I. w-6,x-6,y-6,z-6 II. 5w,2x,3y,5z III. 5w,5x,5y,5z options: A)II and III B)III only C)I and III D)I and II E)II only SOLUTION:lets look at the three choices... I. w-6,x-6,y-6,z-6 since the difference is constant, it is an arithmetic sequence... II. 5w,2x,3y,5z since the difference is not constant, it is not an arithmetic sequence III. 5w,5x,5y,5z since the difference is constant it is an arithmetic sequence... Answer is A) #### A QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)288 B)200 C)279 D)992 E)208 SOLUTION:(800*3*3)/100 = 72 920 + 72 = 992 Answer: D #### D QUESTION:4, 6, 12, 14, 28, 30, ? options: A)32 B)64 C)62 D)60 E)52 SOLUTION:The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60 Answer : D. #### D QUESTION:The overall age of X and Y is 19 year greater than the overall age of Y and Z. Z is how many decades younger that X? options: A)11 B)15 C)12 D)19 E)20 SOLUTION:D 19 (X + Y) – (Y + Z) = 19 X – Z = 19 #### D QUESTION:what is the least number by which 15,625 must be divided to get a number perfect square options: A)21 B)25 C)24 D)40 E)45 SOLUTION:15,625/25=625 625=(25)^2 Ans-25 ANSWER:B #### B QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)1 B)7 C)3 D)8 E)5 SOLUTION:40*(40/100) = 16 --- 64 ? --- 12 => Rs.3 Answer: D #### D QUESTION:Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is options: A)42 B)36 C)28 D)20 E)24 SOLUTION:Explanation: Distance covered = 120+120 = 240 m Time = 12 s Let the speed of each train = v. Then relative speed = v+v = 2v 2v = distance/time = 240/12 = 20 m/s Speed of each train = v = 20/2 = 10 m/s = 10×36/10 km/hr = 36 km/hr Answer: Option B #### B QUESTION:A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere interest rate is increased by 8%, it would amount to bow mucb ? options: A)Rs 990 B)Rs 995 C)Rs 997 D)Rs 992 E)Rs 999 SOLUTION:S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _ . R = ((100 x 120)/(800*3) ) % = 5%. New rate = (5 + 3)% = 8%. New S.l. = Rs. (800*8*3)/100 = Rs. 192. :. New amount = Rs.(800+192) = Rs. 992 Answer is D. #### D QUESTION:The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Four pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ? options: A) 5 B) 12 C) 24 D) 32 E) 120 SOLUTION:CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!. But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2. The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 5. Answer: option A #### A QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 10 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 50 will be in team A 50 will be in team B The larger diff is 70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10. Answer choice C #### C QUESTION:If N = 2^0.15 and N^b = 8, b must equal options: A)3/80 B)3/5 C)20 D)5/3 E)80/3 SOLUTION:15/100 = 3/20 N = 2 ^ 3/20 N^b = 2^3 (2^3/20)^b = 2^3 b = 20 Answer: C #### C QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. #### C QUESTION:The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. what is the principal sum options: A)124.05 B)124.09 C)124.04 D)124.06 E)124.02 SOLUTION:Explanation: Compound Interest on P at 10% for 2 years when interest is compounded half-yearly = Simple Interest on P at 10% for 2 years = Given that difference between compound interest and simple interest = 124.05 Answer:A #### A QUESTION:There are 680 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)425 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 680. Hence 3x + 5x = 680 Solve for x 8x = 680 x = 85 Number of boys 3x = 3 × 85 = 255 Number of girls 5x = 5 × 85 = 425 A #### A QUESTION:If 0 < a < b and k = (2a + 8b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 10 D)k > 10 E)k > 11 SOLUTION:Here's another approach: k = (2a + 8b)/b = 2a/b + 8b/b = 2(a/b) + 8 Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2. So, we get k = (some number less than 2) + 8 From here, we can see that k must be less than 10 Answer: C #### C QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit? options: A)2777 B)2999 C)2799 D)2781 E)10500 SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 24500 * 3/7 = Rs. 10500.Answer: E #### E QUESTION:A can run 3 Kms in 3 min 18 sec and B can run same distance in 3 min 40 sec, then by how much distance A can beat B? options: A)300 m B)220 m C)280 m D)195 m E)295 m SOLUTION:Distance travelled=3000m Time taken by A=3 m 18 s Time taken by B=3 m 40 sec=220 sec speed of B=3000m/220 s=150/11 m/s Difference between time of A and B=22 sec when time will be 3 m 18 s A will have travelled 3000m but B need 22 sec more to finish. Distance travelled by B in 22 sec=(150/11)*22=300 m Hence, A beat B by 300 m ANSWER:A #### A QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100 x 3000)/(12500 x 4)% = 6% answer :D #### D QUESTION:A high school had 1200 students enrolled in 2003 and 1500 students in 2006. If the student population P ; grows as a linear function of time t, where t is the number of years after 2003. a) How many students will be enrolled in the school in 2010? options: A)1800 B)1900 C)1700 D)1500 E)1600 SOLUTION:a) The given information may be written as ordered pairs (t , P). The year 2003 correspond to t = 0 and the year 2006 corresponds to t = 3, hence the 2 ordered pairs (0, 1200) and (3, 1500) Since the population grows linearly with the time t, we use the two ordered pairs to find the slope m of the graph of P as follows m = (1500 - 1200) / (6 - 3) = 100 students / year The slope m = 100 means that the students population grows by 100 students every year. From 2003 to 2010 there are 7 years and the students population in 2010 will be P(2010) = P(2003) + 7 * 100 = 1200 + 700 = 1900 students Answer B #### B QUESTION:The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 16000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is options: A)Rs. 7000 B)Rs. 8000 C)Rs. 8500 D)Rs. 9000 E)None SOLUTION:Answer Average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = Rs. 9000 Correct Option: D #### D QUESTION:Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? options: A)54 B)59 C)63 D)71 E)62 SOLUTION:Total = 70 Thrower = 46 Rest = 70 - 46 = 24 Left Handed = 24/3 = 8 Right handed = 16 If all Thrower are right handed then total right handed is 46 + 16 = 62 so E. 62 is the right answer #### E QUESTION:A coin is weighted so that the probability of heads on any flip is 0.2, while the probability of tails is 0.8. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 B)(0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2 C)(0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2 D)(0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.2 Probability of Tail, P(T) = 0.8 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2*(0.2)^3*(0.8)^2 1 Tail and 4 Heads, Probability = 5C1*(0.2)^4*(0.8)^2 0 Tail and 5 Heads, Probability = (0.2)^5 Required Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 Answer: option A #### A QUESTION:In certain code 'TWICE' is written as '34$5δ' and 'WEARS' is written as '4δ29%'. How is 'SEAT' written in that code? options: A)22 B)23 C)697 D)66P E)82 SOLUTION:Answer: Option B #### B QUESTION:A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A? options: A)2: 7 B)2: 0 C)2: 4 D)2: 3 E)2: 1 SOLUTION:80* 7: x* 3 = 1:1 1/2 560: 3x = 2: 3 x = 280.Answer:D #### D QUESTION:The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? options: A)81 : 121 B)81 : 127 C)81 : 191 D)81 : 161 E)81 : 182 SOLUTION:Explanation: Ratio of the sides = ³√729 : ³√1331 = 9 : 11 Ratio of surface areas = 92 : 112 = 81 : 121 Answer: Option A #### A QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price? options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 140 % ------> 560 (140 * 4 = 560) Selling price = Rs.560/- A #### A QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)14355 B)15432 C)17576 D)18543 E)16878 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:John bought 9.25m of cloth for $397.75. Find the cost price per metre. options: A)46 B)47 C)58 D)56 E)43 SOLUTION:Cloth bought by John = 9.25 m Cost of 9.25 m = $397.75 Cost per metre = 397.75 ÷ 9.25 The cost of the cloth per metre = $ 43 Answers: E #### E QUESTION:A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running? options: A)2 1/7 hours B)2 1/2 hours C)2 7/2 hours D)4 1/2 hours E)2 1/5 hours SOLUTION:Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours. Answer:B #### B QUESTION:Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east? options: A)3.625 B)3 C)4.5 D)4 E)3.5 SOLUTION:Set up two R x T =D cases. 1. 1/12 km/ min x T = 2.75 from which T= 33 mins. We know total journey time now is 51 +33 =84. The rate is the same ie 1/12km/min. set up second R x T =D case. 1/12 km/min x 84 = 7 km Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5 E. #### E QUESTION:The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles? options: A)4329 B)2799 C)4312 D)2799 E)2712 SOLUTION:Let the radii of the smaller and the larger circles be s m and l m respectively. 2∏s = 264 and 2∏l = 352 s = 264/2∏ and l = 352/2∏ Difference between the areas = ∏l2 - ∏s2 = ∏{1762/∏2 - 1322/∏2} = 1762/∏ - 1322/∏ = (176 - 132)(176 + 132)/∏ = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m Answer: C #### C QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist? options: A)6 B)9 C)36 D)120 E)144 SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places Second Place, Physics Book - in 4 ways Third Place, Math Book - in 2 ways (only 2 books left) Fourth Place, Physics - in 2 ways (only 2 Physics book left) Rest two places can be arranged in one way only. Total no of ways = 4*3*3*2*2*1*1 = 144 ways E #### E QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 30¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)66 E)49.5 SOLUTION:Total price of six cans = 6*36.5 = 219 Total price of 4 cans = 4*30 = 120 Total rice of two cans = 219 - 120 = 99 Average price of two cans = 99/2 = 49.5 c Another way to do it is this: Assume that the four leftover cans were of 30c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 2*36.5 + 4*6.5 = 99 Avg cost of the two cans = 99/2 = 49.5c Answer (E) #### E QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)6620 B)9278 C)2782 D)5772 E)5286 SOLUTION:A = 20000(11/10)3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ? options: A)5/6 B)5/9 C)5/3 D)5/0 E)5/1 SOLUTION:No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways. Thus 6 * 5 * 4 = 120 favourable cases. The total cases are 6 * 6 * 6 = 216. The probability = 120/216 = 5/9. Answer: B #### B QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red? options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15 SOLUTION:P(Both are red), =6C213C2=6C213C2 =5/26 C #### C QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)2 months B)7 months C)8 months D)10 months E)12 months SOLUTION:Explanation: 7 * 8 : 9 * x = 8:9 => x= 7 months ANSWER:B #### B QUESTION:A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? options: A)8 B)12 C)15 D)21 E)27 SOLUTION:As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain: A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15 B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12 A+B=15+12=27 Answer: E. #### E QUESTION:Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 4 = f(3x – 6) options: A)3 B)4 C)6 D)7 E)13 SOLUTION:Answer = A = 3 f(x) = 3x – 5 2*[f(x)] – 4 = f(3x – 6) 2(3x-5) -4 = 3 (3x-6) - 5 6x - 14 = 9x - 23 x = 3 #### A QUESTION:Sonika deposited Rs.4500 which amounted to Rs.8400 after 2 years at simple interest. Had the interest been 4% more. She would get how much? options: A)9680 B)8790 C)8760 D)9020 E)5000 SOLUTION:(4500*2*4)/100 = 360 8400 -------- 8760 Answer: C #### C QUESTION:Find the average of all numbers between 2 and 63 which are divisible by 5 options: A)15 B)20 C)25 D)32.5 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60)/12=390/12=32.5 Answer: Option D #### D QUESTION:Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time? options: A)9 B)8 C)10 D)8.5 E)21 SOLUTION:63/3=21 Answer : E #### E QUESTION:4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)4 days B)6 days C)7 days D)9 days E)1 days SOLUTION:1 women's 1 day work = 1/28 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/28 + 10/140) = 1/4 5 women and 10 children will complete the work in 4 days. Answer: A #### A QUESTION:The number which exceeds 16% of it by 63 is : options: A)75 B)52 C)58 D)60 E)62 SOLUTION:Solution Solution Let the number be x. x-16% of x =63 x-16/100x =63 x-4/25x=63 21/25x=63 x=(63x25/21)= 75 Answer A #### A QUESTION:A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour? options: A)7 km/hr B)7.2 km/hr C)7.4 km/hr D)7.8 km/hr E)8.9 km/hr SOLUTION:Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B #### B QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points T is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points T is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:Median H of price of the car is 52,000. which could be the median of the other two. 35000, 44000, x, y, 57000. options: A)38000 B)47000 C)48000 D)51,000 E)56,000 SOLUTION:Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits H is 56,000.E #### E QUESTION:A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(13 -8) kmph = 2.5 kmph. Answer A #### A QUESTION:If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream options: A)1.5kmph B)0.5kmph C)0.4kmph D)1.6kmph E)2.5kmph SOLUTION:Speed upstream = 32/4 = 8 kmph Speed down stream = 72/8 = 9 kmph Speed of stream = ½ (9-8) = 0.5kmph ANSWER:B #### B QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(6900*6)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble? options: A)134 B)167 C)125 D)113 E)111 SOLUTION:C lb : reverse the calculations: So 48.75 ÷ 0.75 = 65, 65 ÷ 0.8 = 81.25 and 81.25 ÷ 0.65 = 125. #### C QUESTION:In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y? options: A)6 B)3 C)4 D)5 E)7 SOLUTION:lets start from z, as per the question stem z + 5 + 7 = 16 -->> z= 4 similarly, y + 4 + 5 = 7 --> y = -2 similarly,, x + -2 + 4 = 5 --> x = 3 hence , x-y = 3+2 = 5 ANSWER:D #### D QUESTION:A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap? options: A)7203 B)2403 C)3603 D)4803 E)5803 SOLUTION:LCM of 16, 20, 25, 45 = 3600 1 * 3600 + 3 = 3603 not divisible by 21 2 * 3600 + 3 = 7203 is divisible by 21 ANSWER:A #### A QUESTION:Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.870? options: A)Rs.700 B)Rs.780 C)Rs.750 D)Rs.1000 E)None of these SOLUTION:Explanation: 870 = P [1 + (5*16/5)/100] P= 750 Answer: Option C #### C QUESTION:Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) options: A)8/3 B)3/8 C)8/5 D)12/5 E)5/3 SOLUTION:Distance traveled by Eddy = 540 km Time taken by Eddy = 3 hours Average speed of Eddy = 540/3 = 180 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 180/75 = 12/5 Answer D #### D QUESTION:The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.8,517 for a cell phone, then what was the cost price of the cell phone? options: A)Rs.5,845 B)Rs.6,750 C)Rs.5,700 D)Rs.6,925 E)None of these SOLUTION:Explanation: 123% of CP =SP Therefore, CP = Rs.8,517x100/123 = Rs.6925 Answer: Option D #### D QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 130*4=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn? options: A) 188 B) 258 C) 376 D) 470 E) 517 SOLUTION:consider 5x acres of land used for bean consider 2x acres of land used for wheat consider 4x acres of land used for corn Total given is 1034 acres 11x =1034 x = 94 land used for corn Y= 4 * 94 = 376 correct option - C #### C QUESTION:At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.50. What is the price of 2 doughnuts? options: A)$ 0.55 B)$ 1.00 C)$ 1.10 D)$ 1.30 E)$ 1.50 SOLUTION:3D + C = 2.25......(1) 2D + C = 1.5........(2) (1) - (2) --> D = 0.75 --> 2D = 1.5 Answer: E #### E QUESTION:Due to construction, the speed limit along an 9-mile section of highway is reduced from 45 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 5.61 B)B) 3.42 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 9 miles stretch = 9*60/45 = 9*4/3 = 12 New time in minutes to cross 9 miles stretch = 9*60/35 = 9*12/7 = 15.42 Time difference = 3.42 Ans:B #### B QUESTION:Smitty Farm picks 9866 cherries a day. If Smitty distributes their apples evenly across 9 different retail shops, how many cherries would remain with him. options: A)1 cherry B)7 cherry C)2 cherry D)4 cherry E)5 cherry SOLUTION:This is equivalent to finding the first number that is divisible by 9 that occurs before 9,866. In order to divide the sum in 9 parts, the amount must be divisible by 9 Divisibility rule of 9: The sum of the digits must be divisible by 9 Sum of digits of 9+8+6+6 = 29. If we add 7, then it is divisible by 9. Hence, we need to add 7 to this number for it to be divisible by 9 Correct Option : B #### B QUESTION:A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h? options: A)42 km/h B)46 km/h C)50 km/h D)54 km/h E)58 km/h SOLUTION:speed = distance / time = (130 + 320)/30 = 450/30 (m/s) * 3600/1000 = 54 km/h The answer is D. #### D QUESTION:6) A marketing firm determined that , of 180 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap? options: A)a) 15 B)b) 20 C)c) 30 D)d) 10 E)e) 45 SOLUTION:100 = At least one of Soap A or B Both brands = x Brand B = 3x => 60 + x + 3x = 100 => 4x = 40 => x = 10 Answer - D #### D QUESTION:A student chose a number, multiplied it by 3, then subtracted 220 from the result and got 110. What was the number he chose? options: A)90 B)100 C)110 D)120 E)130 SOLUTION:Let x be the number he chose, then 3⋅x−220=110 3x=330 x=110 correct answer C #### C QUESTION:what is the integer among the following that represents a sum of 3 consecutive even integers? options: A)200 B)303 C)400 D)554 E)588 SOLUTION:Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers) Divisibility of 3: Sum of the digits of the number must be divisible by 3 Divisibility of 2: Unit digit of the number must be divisible by 2 A. 200NOT A MULTIPLE OF 3 SO RULED OUT B. 303NOT A MULTIPLE OF 2 SO RULED OUT C. 400NOT A MULTIPLE OF 3 SO RULED OUT D. 554NOT A MULTIPLE OF 3 SO RULED OUT E. 588A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!! #### E QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination. options: A)15 B)21 C)17 D)19 E)21 SOLUTION:Total Money = Rs. 10350. Let 50 rupees note was X. Then 500 rupees note = 36 - X Now, 50*X + 500 * (36 - X) = 10350 50X + 18000 - 500X = 10350 - 450X = - 7650 X = 17. No. of 50 rupees note = 17. Answer: Option C #### C QUESTION:The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares options: A)22 cm B)24 cm C)26 cm D)28 cm E)None of these SOLUTION:Explanation: We know perimeter of square = 4(side) So Side of first square = 40/4 = 10 cm Side of second square = 32/4 = 8 cm Area of third Square = 10*10 - 8*8 = 36 cm So side of third square = 6 [because area of square = side*side] Perimeter = 4*Side = 4*6 = 24 cm Option B #### B QUESTION:Bradley owns x video game cartridges. If Bradley’s total is one-third the total owned by James and four times the total owned by Charles, how many video game cartridges do the three of them own altogether, in terms of x? options: A)(16/3)x B)(17/14)x C)(13/4)x D)(19/12)x E)(17/4)x SOLUTION:x = Bradley’s total 3x = James’s total (1/4)x = Charles’s total Add each total x + 3x+ (1/4)x = 4x + (1/4)x = = (17/4)x Answer : E #### E QUESTION:In a school the number of girls is 30% the number of boys. Find the number of boys as a percentage of girls? options: A)112% B)12% C)333% D)150% E)16% SOLUTION:It is given that in a school the number of girls is 30% the number of boys. If boys=10 girls=3 We are asked for the number of boys as a percentage of girls b/g=10/3=10 1/3=3.333=333% Answer is C #### C QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour? options: A)A)5 B)B)10 C)C)20 D)D)30 E)E)40 SOLUTION:Explanation: T = 15/45 * 60 = 20 Answer: Option C #### C QUESTION:A candidate got 35% of the votes and lost to the rival by 1350 votes. How many votes were cast? options: A)4000 B)4500 C)5000 D)5500 E)6000 SOLUTION:35%-----------L 65%-----------W ------------------ 30% = 1350 10% = 450 100% of the votes = 4500 Answer: B #### B QUESTION:Virat buys an old car for Rs. 50000 and spends Rs. 6000 on its repairs. If he sells the scooter for Rs. 70000, his gain percent is: options: A)25% B)11 (1/9) % C)12 (2/3) % D)12% E)None of these SOLUTION:Explanation: C.P. = Rs. (50000 + 6000) = Rs. 56000 S.P. = Rs. 70000. Gain% = ( (14000 / 56000) * 100 ) % = 25% ANSWER A #### A QUESTION:One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number? options: A)4 B)6 C)0 D)9 E)19 SOLUTION:Answer: Option D x/2 – x/3 = 6 => x =6 3 + 6 = 9 #### D QUESTION:A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? options: A)5 B)6 C)21 D)8 E)9 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [385 * 3/55] sec = 21 sec Answer: C #### C QUESTION:The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot? options: A)14 M B)20 M C)18 M D)12 M E)15 M SOLUTION:LB = 460 M2 LET BREATH = B L = B * (100 + 15)/100 = 115B/100 FROM THESE 115B/100 * B = 460 B2 = 46000/115 = 400 B = ROOT OF 400 = 20 M ANSWER B #### B QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)214 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 64x X = 3.57 60 * 3.57 = 214 km ANSWER:B #### B QUESTION:A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? options: A)15 1/3 days B)13 1/3 days C)19 1/3 days D)11 1/3 days E)12 1/3 days SOLUTION:B 13 1/3 days 5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days #### B <<<Examples ends QUESTION:What percent of a day is 15 hours? options: A)37×1/2% B)16×1/2% C)18×2/3% D)22×1/2% E)None SOLUTION:Solution Required percentage = (15/24×100)% = (75 / 2)%. = 37×1/2%. Answer A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Tough and Tricky questions: Absolute Values. If |a| = 1/5 and |b| = 2/3, which of the following CANNOT be the result of a + b? options: A)13/15 B)-13/15 C)-7/15 D)7/15 E)7/5 SOLUTION:|a| = 1/5 Absolute value of 'a' can have two values = 1/5 and -(1/5) |b| = 2/3 Absolute value of 'b' can have two values = 2/3 and -(2/3) Now different combinations of a + b are as follows: a + b = (1/5) + (2/3) = 13/15 - a - b = -(1/5) - (2/3) = -13/15 a - b = (1/5) - (2/3) = -(7/15) -a + b = -(1/5) + (2/3) = 7/15 Cross verifying with the given options, left over option is E. #### E QUESTION:A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day at 1 mile faster than 2nd day for same hours. How many miles in total did she walk? options: A)63 B)44 C)58 D)60 E)62 SOLUTION:First day - 18 miles with 3 miles per hours then total - 6 hours for that day Second day - 4 miles per hour and 5 hours - 20 miles Third day - 5 miles per hour and 5 hours - 25 miles Total 18+20+25 = 63 Answer: option A. #### A QUESTION:There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female? options: A)75 B)100 C)125 D)175 E)225 SOLUTION:female = x Male = 750-x x/2 + 750-x/4 = 1/3* (750)= 250 x= 250 x/2 = 125 is supposed to be the answer ANSWER:C #### C QUESTION:If m and n are positive integers, and m=2n and k=9m, then - options: A)k is a factor of m. B)2m is a factor of k. C)3m is a factor of k/2. D)m/2 is a factor of k. E)k is a factor of m/2. SOLUTION:m=2n --> m is even. k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k. Answer: D. #### D QUESTION:E and F have a data plan which gives them 200 GB every month. If E uses 7 GB every 9 days and F uses 5 GB every 4 days, how many GB will be unused after a 30 day month? Answer in fractions. options: A)365/6 B)73/6 C)35/6 D)835/6 E)200/6 SOLUTION:Number of GB that E uses every day: 7/9 Number of GB that F uses every day: 5/4 Number of GB that E and F use every day: 7/9+5/4=73/36 Number of GB that E and F use in 30 days: 30x(73/36)=365/6 Number of GB remaining: 200-365/6=835/6 Answer is D #### D QUESTION:John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish? options: A) 24 B) 34.8 C) 37.8 D) 40 E) 84 SOLUTION:The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p: 0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40. Answer: D. #### D QUESTION:Let S be the set of values which can be written as the sum of 5 consecutive perfect squares. What is the smallest element of S which is divisible by 17? options: A)255 B)355 C)522 D)355 E)664 SOLUTION:Each element of S can be written in the form (x- 2)2 + (x - 1)2 + x2 + (x + 1)2 + (x + 2)2 = x2 + 2x2 + 2 + 2x2 + 8 = 5x2 + 10 = 5(x2 + 2) where x is some positive integer with x 3. By iterating over values of x, we observe that when x = 7, x2 + 2 = 51 = 3 * 17; no smaller value of x exists which satisfies the problem statement. Hence, the solution is 5(x2 + 2) = 5 *51 = 255 correct answer A #### A QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer? options: A)55 B)25 C)85 D)45 E)35 SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer. Therefore 0+1+3+4+5+6+7+9=35 Answer is E #### E QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution? options: A)62.0 B)65.25 C)68.75 D)70.15 E)72.35 SOLUTION:SOL: Lets assume that 46L of sol1 was mixed with 10L of sol2. Alcohol in Sol1: 46*3/4 = 34.5L Alcohol in Sol2: 10*2/5 = 4L Total Alcohol in the mixed solution of 56L = 34.5 + 4 = 38.5L Alcohol concentration in the new sol: (38.5/56)*100 = 68.75% ANSWER:C #### C QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:How many multiples of 5 are there between 5 to 95? options: A)9 B)18 C)17 D)16 E)15 SOLUTION:As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the unit’s place). So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. Answer C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A QUESTION:If f(x)= 5x^3- 4x+8 and g(y)= 6y-4, then g(f(x)) = options: A)11x^2+4x+4 B)11x^2-12x+44 C)30x^3-24x+44 D)30x^3+4x+4 E)30x^3-12x+44 SOLUTION:g(f(x)) = 6(f(x)) -4 = 6(5x^3- 4x+8) - 4 = 30x^3-24x+44 =>C #### C QUESTION:Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 9 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)32/9 C)15/4 D)10/3 E)17/5 SOLUTION:Rate(1)=1/6 Rate(2)=1/9 Combined = 5/18 Work done in 2 days=5/9 Work left = 4/9 Rate * Time = Work left 1/8 * Time = 4/9 Time=32/9 B #### B QUESTION:Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE? options: A)1/15 B)1/14 C)1/12 D)1/13 E)1/17 SOLUTION:Explanation : Let two digit number that Shiwani thought be 'xy', where x and y are single digit number. Therefore, 10x+y=p(x+y)+3, where p is a natural number p=10x+y−3x+y. Also, y+x>3. Possible values of x and y for which p is a natural number are :- (x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9), (x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null), (x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4) There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits. Probability that Devesh thought of the same number as Shiwani = 1/14 Answer : B #### B QUESTION:How many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:250/15 = 16 (plus remainder) so there are 16 multiples of 15 250/14 = 17 (plus remainder) so there are 17 multiples of 14 We need to subtract 1 because 15*14 is a multiple of both so it was counted twice. The total is 16+17-1 = 32 The answer is C. #### C QUESTION:Find the greatest number that will divide 48, 210 and 136 leaving 4, 12 and 4 as remainders respectively options: A)19 B)17 C)13 D)22 E)21 SOLUTION:Explanation: Answer will be HCF of (48-4, 210-12, 136-4) HCF of (44, 198, 132) = 22 Option D #### D QUESTION:Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit options: A)Rs. 8510 B)Rs. 8620 C)Rs. 8730 D)Rs. 8820 E)None of these SOLUTION:Explanation: =>(8000×(1+5/100)2) =>8000×21/20×21/20 =>8820 Option D #### D QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done? options: A)144 B)180 C)192 D)360 E)None of these SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options. Task 2 can be assigned to 3 or 4 So, there are only 2 options for task 2. So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6. = 2 × 3 × 4 × 3 × 2 × 1 = 144 Answer A #### A QUESTION:The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy? options: A)7 B)9 C)11 D)13 E)14 SOLUTION:Explanation: 3x + 5x + 7x = 45 x =3 3x = 9 B) #### B QUESTION:A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent? options: A)33 1/8 % B)33 7/3 % C)50 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 24. If he buys 6 a rupee, his CP = 4 He selling at 4 a rupee, his SP = 6 Profit = SP - CP = 6 - 4 = 2 Profit Percent = 2/4 * 100 = 50 % Answer: C #### C QUESTION:there r 5 papers Ratio of marks obtained in each subject is 6:7:8:9:10. Total marks obtained is 60%. 50% is pass marks. In how many subjects did he get above 50%. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Total marks in 5 papers = 60% (i.e., 60*5 = 300) 6x+ 7x+ 8x+ 9x+ 10x =60/100(500) Put x= 8 for solving, 6x= 48; 7x = 56; 8x = 64 ; 9x = 72; 10x = 80 Marks are 6:7:8:9:10 = 48+56+64+72+80 = 300 So, 4 subjects he got 50% above ANSWER:D #### D QUESTION:A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction T of the cookies that were placed in the other tins were placed in the green tin? options: A)15/2 B)9/4 C)5/9 D)7/5 E)9/7 SOLUTION:Blue tin or red tin: 2/3 (N) Red tin: (1/3)N Blue tin: (1/4)N What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin) # of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12 # of cookies in red and green tin = N/3 + 5N/12 = 9N/12 Fraction T= 5N/12 * 12/9N = 5/9 (C) #### C QUESTION:What is the HCF of 2/3, 5/9 and 6/5 options: A)1/45 B)2/45 C)4/15 D)8/45 E)9/45 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 5, 6)/(LCM of 3, 9, 5) = 1/45 Answer: Option A #### A QUESTION:Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 asquotient and the 15 as remainder? options: A)1245 B)1567 C)1678 D)1335 E)1635 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Large number = 270+1365 = 1635 E #### E QUESTION:The ages of Rahul and Madhan differ by 16 years. Six years ago, Madhan’s age was thrice as that of Rahul’s,find their present ages options: A)14 years, 30 years B)12 years, 28 years C)16 years, 34 years D)18 years, 38 years E)none of these SOLUTION:Let Rahul’s age = x years So, Madhan’s age = ( x + 16 )years Also, 3(x - 6) = x + 16 - 6 or, x = 14 Rahul’s age = 14 years And, Madhan’s age 14 + 16 = 30 years ANSWER:A #### A QUESTION:The average of first 13 even numbers is? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Sum of 13 even numbers = 13 * 14 = 110 Average = 182/13 = 14 ANSWER:E #### E QUESTION:The ratio 3 : 5 expressed as a percent equals options: A)60% B)40% C)80% D)125% E)None SOLUTION:Solution 3 : 5 = 3/ 5 = (3 / 5 x 100)%. = 60 %. Answer A #### A QUESTION:If (1 – 1.5)N = 1, then N = options: A) −400 B) −140 C) −2 D) 4 E) 400 SOLUTION:(1 – 1.5)N = 1 Simplify to get: -0.5N = 1 Rewrite as (-1/2)N = 1 Multiply both sides by -2 to get: N = -2 Answer: C #### C QUESTION:45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:45 workers * 8 hours / 30 meters = x * 6 / 55 x = 110 total workers 110 - 45 = 65 new workers The answer is D. #### D QUESTION:In a certain neighborhood, there are half as many beige houses as white houses, and 3 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses? options: A)4:1 B)3:5 C)2:3 D)1:3 E)1:4 SOLUTION:The ratio of beige:white:brown = 3:6:2 The answer is C. #### C QUESTION:Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit? options: A)5.8% B)5.5% C)5.6% D)2.6% E)5.3% SOLUTION:C.P. of 1 toy = 375/12 = Rs. 31.25 S.P of 1 toy = Rs. 33 Profit = 1.75/31.25 * 100 = 28/5 = 5.6% Answer: C #### C QUESTION:A store reduced the price of all items in the store by 9% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? options: A)80.0 B)80.9 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 9% price becomes = 0.91 *100 = $ 91 after the final reduction of 10% price becomes = 0.9* 91 = $ 81.9 price of all items on second day is 81.9% of price on first day correct answer option E #### E QUESTION:A horse chases a pony 8 hours after the pony runs. Horse takes 12 hours to reach the pony. If the average speed of the horse is 320 kmph, what s the average speed of the pony? options: A)182kmph B)192kmph C)193kmph D)196kmph E)190kmph SOLUTION:pony take 20 hours and horse take 12 hours...then Distance chased by them is 320*12.so speed of pony is (320*12)/20=192kmph. ANSWER IS B #### B QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)17 Kmph B)78 Kmph C)72 Kmph D)18 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer: C #### C QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was? options: A)160000 B)228788 C)266891 D)267689 E)127791 SOLUTION:X * (105/100) * (105/100) * (105/100) = 185220 X = 185220/1.157625 X = 160000 Answer:A #### A QUESTION:If the set S is composed of the following numbers {99, 100, 100, 105, 106, 115, 124}, which of the following is largest? options: A)The average (arithmetic mean) of set S B)The median of set S C)The mode of set S D)The range of set S E)The standard deviation of set S SOLUTION:A) 99, 100, 100, 105, 106, 115, 124 = 749 and its mean is 749/7 = 107. B) The list is of 7 numbers and median is 105. C) Mode is number of repetition of a number in the list , here it is 100. D) Range = Max value - min value = 124 -99 = 25. E) SD = square root of (sum of ( mean of series - number)^2 ) / n => < 100 IMO option A is correct answer.. #### A QUESTION:A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)227 B)266 C)230 D)500 E)271 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 48 = 50/3 3(x + 300) = 2400 è x = 500m. Answer: D #### D QUESTION:In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time. options: A)10 hours B)12 hours C)14 hours D)16 hours E)None of these SOLUTION:Explanation : speed of the boat = 6 km/hr Speed downstream = (6+2) = 8 km/hr Speed upstream = (6-2) = 4 km/hr Distance travelled downstream = Distance travelled upstream = 32 km Total time taken = Time taken downstream + Time taken upstream = (32/8) + (32/4) = (32/8) + (64/8) = (96/8) = 12 hr. Answer : Option B #### B QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)7508 C)7528 D)7527 E)7232 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 Answer:A #### A QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 11? options: A)44 B)88 C)45 D)176 E)352 SOLUTION:Solution: sequence of 11 lets say sequence is 11n, 11(n+1), 11(n+2), 11(n+3), 11(n+4) so range is 11n+44-11n = 44 if we put the different values of n we will get different but the range will be multiple of 44 and only 45 is not multiple of 44 Answer : C #### C QUESTION:A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different W arrangements of plays can be run, if the same play can’t be run more than once? options: A)24 B)125 C)243 D)504 E)729 SOLUTION:Number of W ways to choose the first play: 9 Second play: 8 Third:7 9*8*7= 504.D #### D QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 7*1+1 (7*1+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol? options: A) 7/2 B) 5 C) 20/3 D) 8 E) 300/17 SOLUTION:20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents. If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters. According to the statement; 20+x = 32% of (100+x) OR 20+x=(100+x)8/25 500+25x=800+8x 17x=300 x=300/17 Ans:E #### E QUESTION:There are two sections C and D of a class, consisting of 18 and 22 students respectively. If the average weight of sections C is 20 kg and that of sections D is 18 kg. Find the average weight of the whole class options: A)18.7 B)18.8 C)18.9 D)19.9 E)None SOLUTION:Solution Total weight of(18+22)Students = (18x20+22x18)Kg = 756 kg. Average weight of the whole class = (756 /40 ) = 18.90. Answer C #### C QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)100/3% loss C)50/3% profit D)100/3% loss E)200/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss ANSWER IS A #### A QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 620 m long? options: A)86 B)89 C)277 D)278 E)291 SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 620)/10 = 86 sec. Answer: A #### A QUESTION:A man has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)37 B)38 C)60 D)90 E)28 SOLUTION:Let number of notes of each denomination be x. Then, x + 5x + 10x = 320 16x = 320 x = 20. Hence, total number of notes = 3x = 60. Answer:C #### C QUESTION:A fruit seller had some apples. He sells 35% and still has 6500 apples. Originally, he had ? options: A)650apples B)600 apples C)772 apples D)700 apples E)None SOLUTION:Answer ∵ 65% of N = 800 ∴ N = (650 x 100)/65 = 1000 Correct Option: E #### E QUESTION:A grocer buys apples for 63¢ per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price? options: A)66¢ B)70¢ C)75¢ D)77¢ E)84¢ SOLUTION:for making calculation simple let us consider he buys 10 pounds @ 63/pound=630¢ in total . 10% apples lost...means 9 pounds left. further he wants 20% profit on 630 ¢ means he wants to earn 756¢ sales price should be 756/9==¢ 84 ANSWER:E #### E QUESTION:Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ? options: A)689 B)569 C)123 D)512 E)456 SOLUTION:Explanation: Let total number of children be x Then, x x1/8X=x/2*16,x=64 Number of notebooks =1/8x^2=(1/8*64*64)=512 Answer:D #### D QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C QUESTION:A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)120 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (9 - 8) = 1 km/hr. Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m. .'. Distance between the criminal and policeman = (265 - 50) m = 215 m. Answer : E #### E QUESTION:Find the option to replace the question mark in the series below 5 ? 15 75 525 4725 options: A)2 B)6 C)7 D)5 E)8 SOLUTION:ol: 5 x 1 = 5 5 x 3 = 15 15 x 5 = 75 75 x 7 = 525 525 x 9 = 4725 So ? = 5 Answer:D #### D QUESTION:It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn options: A)16 B)45 C)36 D)20 E)90 SOLUTION:1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min.. only A and B are left.. if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins.. ans 20 D #### D QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 190 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)19 D)33 E)25 SOLUTION:C 19rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 Thus our anniversary falls on the 19rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### C QUESTION:A certain bacteria colony doubles in size every day for 25 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit? options: A)6.33 B)7.5 C)10 D)15 E)24 SOLUTION:If there is one bacteria colony, then it will reach the limit of its habitat in 25 days. If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 24 times. Answer: E. Similar questions to practice: Hope it helps. #### E QUESTION:Subtracting 10% from X is the same as multiplying X by what number? options: A)80% B)90% C)10% D)50% E)60% SOLUTION:Explanation: X - (10/100) X = X * ? ? = 90% ANSWER IS B #### B QUESTION:There are 8 people and 5 chairs. In how many different ways people can occupy the chairs? options: A)1640 B)1650 C)1660 D)1670 E)1680 SOLUTION:number of ways = 8*7*6*5 = 1680 Answer is E #### E QUESTION:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be options: A)45 min B)60 min C)55 min D)70 min E)80 min SOLUTION:Time = 50/60 hr = 5/6hr Speed = 48mph distance = S*T = 48 * 5/6 = 40km time = 40/60hr = 2/3hr New speed = 40* 3/2 kmph = 60kmph Answer : B. #### B QUESTION:A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? options: A)Rs. 105 and Rs. 6 B)Rs. 216 and Rs. 12 C)Rs. 210 and Rs. 12 D)Rs. 210 and Rs. 6 E)None SOLUTION:Explanatory Answers Let half of the full basic fare be Rs. X. Therefore, full basic fare is Rs. 2X. Let the reservation charge be Rs. Y per ticket. Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge) 2X + Y = 216 --- (1) The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y. Hence, 3X + 2Y = 327 --- (2) Solving (1) and (2) we get, X = 105 and Y = 6 Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6 Answer D #### D QUESTION:In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 6 consecutive days in Rwanda? options: A)4/7 B)3/7 C)15/64 D)4/28 E)28/135 SOLUTION:using Binomial. theorem nCr (p)^r (q)^n-r 6C4 (1/2)^4 (1/2)^r which is 15/64 Answer is C. #### C QUESTION:City A to city B, Andrew drove for 1hr at 46 mph and for 3 hours at 60 mph. What was the average speed for the whole trip? options: A)56.5 B)57.5 C)61 D)61.5 E)62.5 SOLUTION:The total distance is 1×46+3×60=226 And the total time is 4 hours. Hence, Average Speed=(Total Distance/Total Time) =226/4=56.5 A #### A QUESTION:Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 30ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:If each side is 120 feet..then total perimeter is 150*4=600 poles every 20 feet hence no of poles= 600/20=30 ANSWER:B #### B QUESTION:What is the difference between local value & face value of 9 in the numeral 65793? options: A)8453 B)8956 C)8991 D)9890 E)10000 SOLUTION:(Local value of 9) - (Face value of 9) = (9000 - 9) = 8991 C #### C QUESTION:Two representatives must be selected from each of two groups of students. One group consists of two men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ? options: A)1/6 B)1/4 C)5/9 D)1/3 E)1/2 SOLUTION:Group 1: 2 Men and 1 Woman Group 2: 1 Men and 2 Woman Need: 2 Men and 2 women Case 1: 2 Men from Group 1 and 2 women from group 2 - 2C2*2C2 = 1 ways Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 2*1*1*2 = 4 ways Total Favorable cases = 1+4 = 5 Total Possible ways of selecting students 2 from each group = 3C2*3C2 = 3*3 = 9 Probability = 5/9 Answer : Option C #### C QUESTION:If 9^y = 3^14, what is y? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:9^y = 3^2y = 3^14 2y=14 y = 7 The answer is E. #### E QUESTION:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 140800, how many purple chips were selected? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:140800 = 1*5^2*8^3*11 The factors of 8 must come from the purple point value, so there are 3 purple chips. The answer is C. #### C QUESTION:When 2/3 of the garments in the shipment were inspected, 28 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 90 percent of the garments in the shipment pass? options: A)10 B)9 C)13 D)7 E)5 SOLUTION:B = 9 2/3x= 30 x=45 for 90% approval we need 41 garments approved. already approved = 28 we need 13 more. Answer : C #### C QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)10years B)12 years C)5 years D)3 years E)24 years SOLUTION:Explanation: 9261 = 8000(21/20)N (21/20)3 = (21/20)N => N = 3 years Answer:D #### D QUESTION:Two goods trains each 375 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)40 B)45 C)48 D)51 E)36 SOLUTION:Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 375 + 375 = 750 m. Required time = 750 * 6/125 = 36 sec. Answer: Option E #### E QUESTION:What is the place value of 0 in the numeral 2074? options: A)0 B)1 C)2 D)5 E)6 SOLUTION:Note : The place value of zero (0) is always 0. It may hold any place in a number, its value is always 0. A #### A QUESTION:Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together? options: A)17 1/7 B)17 1/9 C)17 1/2 D)17 1/7 E)17 1/5 SOLUTION:1/30 + 1/40 = 7/120 120/7 = 17 1/7 days Answer: A #### A QUESTION:It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)142 B)144 C)3680 D)3280 E)3680 SOLUTION:Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th . Now, number of even places = 3. Number of girls to occupy the even places = 3. Even places can be filled = P (3, 3) ways. Number of boys = 4. The remaining 4 places can be filled by 4 boys = P (4, 4) ways By the fundamental principle of counting: The required number of seating arrangements P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144 ANSWER:B #### B QUESTION:John bought 9.25m of cloth for $425.50. Find the cost price per metre. options: A)46 B)47 C)58 D)56 E)54 SOLUTION:Cloth bought by John = 9.25 m Cost of 9.25 m = $425.50 Cost per metre = 425.50 ÷ 9.25 The cost of the cloth per metre = $ 46 Answers: A #### A QUESTION:A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit? options: A)$10 B)$16 C)$20 D)$24 E)$25 SOLUTION:Let P be the original price paid by the retailer. 1.25*P = 100 P = 80 The profit is $20. The answer is C. #### C QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)25 SOLUTION:Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER IS A #### A QUESTION:A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 63 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents? options: A)14 B)45 C)54 D)65 E)81 SOLUTION:Just check the answers and reverse the numbers until you get 63. 81 - 18 = 63 Answer E #### E QUESTION:A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in --- proportion. options: A)6:10:5 B)5:10:6 C)10:5:6 D)10:6:5 E)5:6:10 SOLUTION:Initial investment capital ratio of A and B = 3 : 5 Let initial capital of A and B be 3x and 5x respectively. Amount that C invested after 6 months =5x (since it is equal to B's investment) Ratio in which profit should be distributed after 1 year =3x×12:5x×12:5x×6 =3×12:5×12:5×6 =3×2:5×2:5 =6:10:5 Answer is A. #### A QUESTION:The value of x + x(xx) when x = 2 is: options: A)10 B)18 C)16 D)64 E)36 SOLUTION:x + x(xx) Put the value of x = 2 in the above expression we get, 2 + 2(22) = 2 + 2(2 × 2) = 2 + 2(4) = 2 + 8 = 10CORRECT ANSWER : A #### A QUESTION:Computer completes the first iteration in 10 seconds and then the following iterations are completed in 7 seconds as constants are already loaded. What is the maximum number of completed iterations under 5 minutes? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:b must be an integer as it is the number of completed iterations at a rate of 7sec/iteration 10 + 7b =5*60 7b = 290 b= 41 The total number of iterations --> 41+1 = 42 and 43rd iteration will be completed at 304seconds which is above 5 minutes ANSWER: B #### B QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job? options: A)4 days B)6 days C)8 days D)2 days E)9 days SOLUTION:Sandy can do 1/6 of the job each day. Molly can do 1/12 of the job each day. The combined rate is 1/6 + 1/12 = 1/4 of the job each day. The job will take 4 days. The answer is A. #### A QUESTION:What is the smallest possible common multiple of three integers, all larger than 22? options: A)27. B)54. C)846. D)19,656. E)23 SOLUTION:The Least common positive multiple would be for the immediate least number(s) after 22 i.e 22. Since nowhere is it stated that the three integers must be different, the integers could be 22,22 and 22... leading to least possible positive common multiple to be 22. Answer E. #### E QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$11,000 B)$50,000 C)$16,500 D)$ 6,600 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 2200 less between 3 people(x-(2200*3))/3 Set both eq. equal to each other. 16,500 Answer C) #### C QUESTION:The area of an isosceles trapezoid with sides of length 5 and bases of length 6 and 12 is? options: A)44 B)42 C)40 D)38 E)36 SOLUTION:Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 12 will be divided into 3 parts= 6, 3 and 3 (Making one square and two right triangles) For the right triangle, height will be= (5^2-3^2)^1/2= 4 And the area of trapezoid = 1/2 (B1+B2)H= 1/2*18*4= 36 E #### E QUESTION:The divisor is 12, the quotient is 4 and the remainder is 1. What is the dividend? options: A)48 B)49 C)96 D)97 E)72 SOLUTION:D = d * Q + R D = 12 * 4 + 1 D = 48 + 1 D = 49 Answer: B #### B QUESTION:If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is? options: A)20:15:15 B)20:15:10 C)20:15:12 D)20:15:11 E)20:15:13 SOLUTION:6A = 8B = 10 C A:B:C = 1/6:1/8:1/10 = 20:15:12.Answer: C #### C QUESTION:Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment? options: A)1200 B)3000 C)1000 D)3600 E)2400 SOLUTION:Let the additional invested amount for 8% interest be x; Equation will be; 2400+0.05*2400+x+0.08x = 2400+x+0.06(2400+x) 0.05*2400+0.08x = 0.06x+0.06*2400 0.02x = 2400(0.06-0.05) x = 2400*0.01/0.02 = 1200 Ans: "A" #### A QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6 SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2 Answer:B #### B QUESTION:find out the probability to get 1Rs coin head, 2Rs coin Tail and 5Rs coin head?? options: A)1/2 B)1/8 C)1/16 D)1/4 E)None of these SOLUTION:1Rs coin head=1/2 2Rs coin Tail=1/2 5Rs coin head=1/2 =(1/2)*(1/2)*(1/2) =1/8 ANSWER:B #### B QUESTION:On a ranch, a rancher can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 4 attempts? options: A)3/4 B)5/8 C)7/8 D)11/16 E)15/16 SOLUTION:P(missing all 4)=(1/2)^4=1/16 P(success on at least one attempt)=1-1/16=15/16 The answer is E. #### E QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible? options: A)30 B)42 C)120 D)360 E)720 SOLUTION:5 people ,7 seats, only 2 can drive if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways since any one can drive total ways = 24 *2= 48 ways 4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways 48*15=720 ANSWER:E #### E QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:According to the 2001 census,the population growth rate of Lucknow is going to be an increasing AP with first year's rate as 5% and common difference as 5% but simultaneously the migration,rate is an increasing GP with first term as 1% and common ratio of 2.If the population on 31 december 2000 is 1 million,thn find in which year will Lucknow witness its first fall in population? options: A)2006 B)2007 C)2005 D)2008 E)2009 SOLUTION:population growth rate according to the problem year 1 = 5% year 2 = 10% year 3 = 15% year 4 = 20% year 5 = 25% year 6 = 30% population decrease due to migration year 1 = 1% year 2 = 2% year 3 = 4% year 4 = 8% year 5 = 16% year 6 = 32% Thus, the first fall would happen in year 2006 ANSWER:A #### A QUESTION:AB +BA ___ 101 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)10 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. only 10 fits in.. C #### C QUESTION:8k8 + k88 -------- 1,6w6 If k and w represent non-zero digits within the integers above, what is w? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16w6 Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and w=6. Answer: A. #### A QUESTION:A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work? options: A)6 B)5 C)5.5 D)7 E)8 SOLUTION:B's 10 day's work = ( 1 x 10 ) = 2 . 15 3 Remaining work = ( 1 - 2 ) = 1 . 3 3 Now, 1 work is done by A in 1 day. 18 Therefore 1 work is done by A in ( 18 x 1 ) = 6 days. #### A QUESTION:In climbing a round pole of 80 meters height, a monkey climbs 5 meters in a minute and slips 2 meters in the alternate minute. To get to the top of the pole, the monkey would take : options: A)51 minutes B)54 minutes C)58 minutes D)61 minutes E)63 minutes SOLUTION:a monkey climbs 5 meters in one min & slips 2m in other min. therefore the monkey reach 3meters in 2min 3m=2min 25*3m=25*2min - >75m=50min hence the remaining 5m jumps the monkey in 1min to reach original height so 51 min ANSWER:A #### A QUESTION:Jenna rode her bike to school at 5 kph, but rode home at 15 kph. What was her average speed traveling to and from school? options: A)5 kph B)7 kph C)10 kph D)13 kph E)15 kph SOLUTION:(5 kph +15 kph)/2 =10 kph Correct answer is: C #### C QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:If the rectangular screen of a computer monitor is designed to have a length of x inches, a perimeter of P inches and an area of A square inches, which of these equations must be true? options: A)x^2 + Px + A = 0 B)x^2 - Px - 2A = 0 C)2x^2 + Px + 2A = 0 D)2x^2 - Px - 2A = 0 E)2x^2 - Px + 2A = 0 SOLUTION:Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0. Now, assume: Length =x = 1 inchand width = 1 inch; Perimeter =P = 4 inches; Area =A = 1 square inches. Plug the values of x, P, and A into the answer choices: only for E 2x^2 - Px + 2A = 2 - 4 + 2 = 0. Answer: E. #### E QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs. 7500 B)Rs. 9000 C)Rs. 9500 D)Rs. 10,000 E)None of these SOLUTION:Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs. 7500. ANSWER IS A #### A QUESTION:A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? options: A)A)452000 B)B)200000 C)C)800000 D)D)500000 E)E)652000 SOLUTION:3 children got = 3*15% = 45% wife got = 30% orphan house = 5% total = 45+30+5 = 80% remaining = 100-80 = 20% 20% = 40000 100% = 40000*100/20 = $200000 Answer is B #### B QUESTION:The ratio 2 : 3 expressed as a percent equals options: A)12.5% B)40% C)67% D)125% E)None SOLUTION:Solution 2 : 3 = 2/ 3 = (2 / 3 x 100)%. = 66.6 %. Answer C #### C QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.899] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ? options: A)0 B)1 C)27 D)54 E)0 SOLUTION:K=[lCM of 80 and 45] * (any integer) however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer for value of k(60) * any integer unit value will be always zero . E #### E QUESTION:A 140 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? options: A)35 B)20 C)47 D)36 E)40 SOLUTION:1: 2/5 = 5: 2 2/7 * 140 =40 Answer:E #### E QUESTION:Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? options: A)10liters B)15liters C)20liters D)18liters E)22liters SOLUTION:Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters Let x liters of pure milk be added. Then, 0.5/(10+x) = 2/100 2x = 30 x=15 liters Answer is B #### B QUESTION:The largest 4 digit number exactly divisible by 88 is? options: A)9930 B)9936 C)9944 D)9952 E)9960 SOLUTION:Largest 4-digit number = 9999 88) 9999 (113 88 ---- 119 88 ---- 319 264 --- 55 --- Required number = (9999 - 55) = 9944. C) #### C QUESTION:A train 130 m long crosses a platform with a speed of 70 kmph in 20 sec; find the length of the platform? options: A)150 B)145 C)165 D)162 E)152 SOLUTION:D = 130 + x T = 20 S = 130+x/15 * 18/5 = 70 kmph. => (130+x) * 18 = 5250 => 130 + x = 292 => x= 162 m Answer: D #### D QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field? options: A)120 sq. m B)140 sq. m C)125 sq. m D)130 sq. m E)110 sq. m SOLUTION:Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m Area = 15 x 8 =120 sq. m ANSWER:A #### A QUESTION:What is the sum of all four digit integers formed using the digits 3 ,4 ,5 and 6 (repetition is allowed) options: A)1279874 B)1279872 C)1279875 D)1279876 E)1279870 SOLUTION:n = 4 * 4 * 4 * 4 = 256 <x> = (6666 + 3333) / 2 = 4999.5 Sum = number of integers x average value n * <x> = 256 * 4999.5 = 1279872 answer = B #### B QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 * 58 = Rs. 2784. Answer:A #### A QUESTION:In how many W ways can 5 people from a group of 6 people be seated around a circular table options: A)56 B)80 C)100 D)120 E)144 SOLUTION:W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner) = 6 * 4! = 6 * 24 = 144 Answer - E #### E QUESTION:The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year? options: A)12300 B)12350 C)12000 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 120/100 = 12000 C #### C QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.3 x = 4.8 Alternate solution: Try to backsolve. Initial volume = 4.8 After one hour --> (1/4)4.8 = 1.2 After two hours --> (1/4)1.2 = 0.3 Answer: C #### C QUESTION:A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)22 B)71 C)54 D)77 E)99 SOLUTION:S = 240/16 * 18/5 = 54 kmph Answer: C #### C QUESTION:Of the 70 electronics components that a factory must manufacture, 90 percent would be most e¢ ciently manufactured by Machine A and the remaining 10 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 70 components. If 50 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently? options: A) 30 B) 32 C) 42 D) 35 E) 36 SOLUTION:A can manufacture 90 % of 70 efficiently, which is 63. B can manufacure 10 % of 70 efficiently, which is 7. Now 50 % of 70 are produced by A. This means 35 parts. Since A can produce 63 efficiently, all 35 are produced efficiently. Rest (35) is produced by B, which can produce max. 7 parts efficiently. Hence parts that were produced efficiently = 7+35 = 42. (C). #### C QUESTION:A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? options: A)42 B)70 C)140 D)165 E)225 SOLUTION:1 of 5 will be chosen for the math 2 of 10 will be chosen for the computer None of the 3 chosen people can be in more than one departments. We can choose any of the 5 candidates for the math dep., which gives as 5 selections. We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /2!*8!= (9*10) / 2 = 90 / 2 = 45. We are multiplying our individual selections: 5*45 = 225 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans E #### E QUESTION:A searchlight on top of the watchtower makes 4 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds? options: A)5/6 B)4/5 C)3/4 D)2/3 E)1/2 SOLUTION:The searchlight completes one revolution every 15 seconds. The probability that the man's area will be lit up is 5/15=1/3. The probability that he will stay in the dark is 1-1/3=2/3 The answer is D. #### D QUESTION:In how many ways can the letters of the word REPORT be arranged? options: A)1206 B)360 C)2520 D)3000 E)3478 SOLUTION:REPORT has 6 words, but R is repeated two times. Thus ways = 6! / 2! = 360 ways B #### B <<<Examples ends QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 26,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,22,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 26,000 = Rs. 1,22,000 ANSWER:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1000 per sq.metre. options: A)Rs. 15,000 B)Rs. 15,500 C)Rs. 15,600 D)Rs. 20,625 E)None SOLUTION:Solution Area of the floor = (5.5 x 3.75)m² = 20.635m ² Cost of paying = Rs. (1000 x 20.625) = Rs.20625. Answer D #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer:A #### A QUESTION:The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet? options: A)12a.m B)10a.m C)19a.m D)76a.m E)37a.m SOLUTION:D = 110 – 20 = 90 RS = 20 + 25 = 45 T = 90/45 = 2 hours 8 a.m. + 2 = 10 a.m. Answer: B #### B QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7 SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144. Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520. P = favorable/total = 2520/144 = 35/2. Answer: B. #### B QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)16 km/hr B)17 km/hr C)60 km/hr D)15 km/hr E)19 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer: C #### C QUESTION:If -5 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy? options: A)-42 < xy < 30 B)-42 < xy < 24 C)-28 < xy < 18 D)-24 < xy < 21 E)-24 < xy < 24 SOLUTION:The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-5)*(-6)=30. Therefore -42 < xy < 30. Answer: A. #### A QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? options: A)35 B)36 C)37 D)43 E)39 SOLUTION:James worked for 41 hours hence he earned 40*x+5*2x=50x dollars; We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours. Answer: D. #### D QUESTION:Bradley owns x video game cartridges. If Bradley’s total is one-third the total owned by James and four times the total owned by Charles, how many video game cartridges do the three of them own altogether, in terms of x? options: A)(16/3)x B)(17/14)x C)(13/4)x D)(19/12)x E)(17/4)x SOLUTION:x = Bradley’s total 3x = James’s total (1/4)x = Charles’s total Add each total x + 3x+ (1/4)x = 4x + (1/4)x = = (17/4)x Answer : E #### E QUESTION:The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ? options: A)31 kg B)63 kg C)61 kg D)62 kg E)91 kg SOLUTION:let c=coach's avg. weight original total weight=(30 friends)(30 kg avge)=900kg (900+3c)/(30+3)=33 kg avg. c=63 kg Answer B #### B QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)255 B)267 C)225 D)277 E)211 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m. Answer:C #### C QUESTION:A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work? options: A)4 days B)2 days C)6 days D)8 days E)9 days SOLUTION:C 6 days 4/10 + 9/x = 1 => x = 15 1/10 + 1/15 = 1/6 => 6 days #### C QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is? options: A)Rs.24028 B)Rs.24000 C)Rs.24003 D)Rs.24029 E)Rs.24029 SOLUTION:Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs.24000 Answer: B #### B QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest .What is the rate of interest ? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:Solution S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100x3000/12500x4) = 6 %. Answer D #### D QUESTION:The speed of light is approximately 93 * 10^5 miles per second. This approximate speed is how many miles per hour? options: A) 3,35 * 10^8 B)70 * 10^7 C) 11 * 10^8 D) 16 * 10^8 E) 70 * 10^8 SOLUTION:The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be. (.93*10^5)*3600 = (.93*10^5)*(3.6*10^3) = some number*10^8... The key is realizing that thesome numberhas to be bigger thatn .93(because .93*3.6), and the only answer that fits that is A #### A QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)2% C)1% D)6% E)7% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\ Rate = (100 * 3000) / (12500 * 4) = 6% Answer: D #### D QUESTION:Adidas company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks? options: A) 16 B) 64 C) 256 D) 576 E) 4096 SOLUTION:MAGOOSHOFFICIAL SOLUTION: Adidas company has four empty trucks that will head out in the morning, all four to the same destination. Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices. N = 4*4*4*4 = 16*16 = 256 Answer = (C) #### C QUESTION:Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age? options: A)12 years B)13 years C)15 years D)14 years E)18 years SOLUTION:Let MTomy's present age be 'x' years. x+ 16 = 3(x- 4) => 2x = 28 => x = 14 years. D #### D QUESTION:R campers fished for 2 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour? options: A)2m + n(R-m) B)(2m + n(R-m))/3 C)(2m + n(m-R))/3 D)(2m + n)/2 E)(2m + n)/R SOLUTION:m of the campers caught 2 fish apiece in 2 hours --> total fish caught by m campers = 2m; The rest caught a combined total of n fish. Total fish caught in 2 hours = 2m+n --> per hour (2m+n)/2. Answer: D. #### D QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by? options: A)33 1/3% B)33 1/8% C)33 6/3% D)33 8/3% E)31 1/3% SOLUTION:100 75 ------- 75 ------- 25 100 ------ ? => 33 1/3% Answer: A #### A QUESTION:If 2m + n = 7 and m + 2n = 5, then (2m + n)/2 = options: A) 1 B) 7/2 C) 17/5 D) 18/5 E) 4 SOLUTION:2*(m+2m = 5) equals 2m+4n=10 2m+4n=10 - 2m + n= 7 = 3n=3 Therefore n = 1 Plug and solve... 2m + 1 = 7 2m=6 m=3 (6+1)/2= 7/2 B #### B QUESTION:Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ? options: A)2 B)5 C)15 D)20 E)25 SOLUTION:Audery and Ferris collective Work rate: 1/4 + 1/3 = 7/12 Collective work Time = 12/7 = 1.7 Hrs Job Was actually done in = 2 (Includes breaks) Breaks = Actual time taken - Collective work time = 2 - 1.7 = .3 Hrs = 1/2 so ferrais took 6 breaks =.3/6=.06 hrs = 5 m so Answer is B) 10 mins #### B QUESTION:The third proportional to 2 and 6 is? options: A)18 B)17 C)14 D)15 E)13 SOLUTION:(6*6)/2 = 18 Answer:A #### A QUESTION:The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers? options: A)87 B)42 C)78 D)76 E)26 SOLUTION:5x 6x 2x 50 25 100 250x + 150x + 200x = 4200 600x = 4200 x = 7 => 6x =42 Answer: B #### B QUESTION:Remainder of (6^17+17^6)/7= ? options: A)2 B)1 C)0 D)3 E)4 SOLUTION:6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7 17^6/7 = (2*7+3)^6/7 = 3^6/7 = 27^2/7 =(4*7-1)^2/7 =(-1)^2/7 = 1/7 so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0 ANSWER:C #### C QUESTION:Myra drove at an average speed of 30 miles per hour for the first 30 miles of a trip & then at an average speed of 60 miles/hr for the remaining 30 miles of the trip. If she made no stops during the trip what was her average speed in miles/hr for the entire trip? options: A)The average speed is 35 miles per hour. B)The average speed is 40 miles per hour. C)The average speed is 55 miles per hour. D)The average speed is 66 miles per hour. E)The average speed is 45 miles per hour. SOLUTION:Here, distance for which Myra traveled at the two speeds is same. Average Speed = 2ab/(a+b) = 2*30*60/(30 + 60) = 40 mph Answer (B) #### B QUESTION:A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)224 E)E)302 SOLUTION:If x is the original number of employees, then after 13% reduction in employees number is .87x but we are given .87x = 181 x = 208 So the original number of employees is 208 Correct Answer - B #### B QUESTION:Cara picked a number of pears, each of which she sold, canned, or poached. If she canned 40 percent more than she poached, and she poached 80 percent less than she sold. If there were a total of 111 pears, then how many pears did she sell? options: A)69 B)72 C)75 D)78 E)81 SOLUTION:Let x be the amount of pears that she sold. Then she poached 0.2x. Then she canned 1.4*0.2x=0.28x. The total amount of pears is x+0.2x+0.28x=1.48x The fraction of pears that she sold is 1/1.48=100/148=25/37. The number of pears she sold is (25/37)*111=75. The answer is C. #### C QUESTION:An empty pool being filled with water at a constant rate takes 8hours to fill to 4/5 of its capacity.how much more time will it take to finish filling the pool? options: A)5hr 30min B)5hr 20min C)4hr 48min D)3 hr 12min E)5hr 40 min SOLUTION:As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill. To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed). Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 5 hours 40 minutes. Answer: E. #### E QUESTION:If a dozen of oranges cost $5, what would be the cost of 10 oranges? options: A)3.56 B)4.16 C)4.86 D)5.1 E)5.2 SOLUTION:The cost of one orange=5/12=0.416 The cost of ten oranges= 0.416x10= $ 4.16 Answer: B #### B QUESTION:A division of a company consists of five men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)2/5 B)2/7 C)2/9 D)2/11 E)2/13 SOLUTION:Total number of ways to select 2 members = 10C2 = 45 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/45 = 2/9 The answer is C. #### C QUESTION:18 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. options: A)190 B)153 C)210 D)220 E)230 SOLUTION:1st person will shake hand with 17 people 2nd person will shake hand with 16 people 3rd person will shake hand with 15 people ...... total no. of handshakes = 17+...+3+2+1 = 17*(17+1)/2 = 153 or, if there are n persons then no. of shakehands = nC2 = 18C2 = 153 ANSWER:B #### B QUESTION:A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number? options: A)297 B)187 C)278 D)200 E)267 SOLUTION:25 + 25 = 50 25% ------ 50 100% ----- ? => 200 Answer:D #### D QUESTION:The average of first 18 even numbers is? options: A)19 B)18 C)16 D)11 E)17 SOLUTION:Sum of 18 even numbers = 18 * 19 = 342 Average = 342/18 = 19 Answer:A #### A QUESTION:If the price has fallen by 20% what percent of its consumption be: increased so that the expenditure may be the same as before? options: A)A)11% B)B)10% C)1/9 % D)1/11 % E)1/4% SOLUTION:100 – 20 = 80 80------20 100------? => 1/4% ANSWER:E #### E QUESTION:Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat? options: A)3! B)8! C)11! D)12! E)14! SOLUTION:Ans.(A) Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways #### A QUESTION:A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks? options: A)60 B)80 C)100 D)120 E)140 SOLUTION:The dealer earns a profit of $2 per paperback and $3 per hardback. If all 160 books were paperbacks, the dealer would earn a profit of $320. Since the actual profit was $400, the dealer must have sold 80 hardbacks. Then the number of paperbacks sold was 160-80 = 80. The answer is B. #### B QUESTION:Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms? options: A) 6 B) 4.8 C) 2.5 D) 2 E) 1 SOLUTION:Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms? (A) 6 (B) 4.8 (C) 2.5 (D) 2 (E) 1 If A is the answer, then the question means that the concentration of water the newt day became 96%. Out of 12 kilograms 98%, or 11.76 kilograms was water and 0.24 kilograms was non-water. The next day, after some water evaporated, oranges became 96% water and 4% of non-water, so the next day 0.24 kilograms of non-water composed 4% of oranges, which means that the new weight of the oranges was x*0.04=0.24 --> x=6 kilograms. Answer: A. #### A QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? options: A)8/35 B)34/35 C)27/35 D)21/32 E)33/35 SOLUTION:Solution: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)*P(B) = 2/5 * 4/7 = 8/35 ANSWER IS A #### A QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 14 years? options: A)30 B)34 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 14 years = (20 + 14) years =34 years. Answer : B #### B QUESTION:By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c? options: A)22388 B)38000 C)27888 D)27288 E)28112 SOLUTION:Explanation: CP + CP/8 = 45000 CP = 40000 SP = 40000*(95/100) = 38000 Answer: B #### B QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.? options: A)50 kmph B)58 kmph C)62 kmph D)65 kmph E)75 kmph SOLUTION:Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph. Speed of goods train = (112 - 50) kmph = 62 kmph. Answer : C. #### C QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:Sandy leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Sandy's house. The distance between their homes is 52 kilometers, Sandy's walking speed is 6 km/h, and Ed's walking speed is 4 km/h. How many kilometers will Sandy walk before she meets Ed? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Sandy walks 12 km in the first two hours so there are 40 km remaining. When Ed starts walking, they complete a total of 10 km per hour. They will meet four hours after Ed starts walking. Since Sandy walks for 6 hours, she walks 36 km. The answer is D. #### D QUESTION:A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ? options: A)650 meter B)555 meter C)500 meter D)458 meter E)None of these SOLUTION:Explanation: Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time =>800+x=65/3∗60 =>800+x=20∗65=1300 =>x=1300−800=500 So the length of the tunnel is 500 meters. Option C #### C QUESTION:Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations R are there for the children? options: A)240 B)480 C)720 D)1440 E)3600 SOLUTION:MAGOOSHOFFICIAL SOLUTION: First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats? X X X _ _ _ _ _ X X X _ _ _ _ _ X X X _ _ _ _ _ X X X _ _ _ _ _ X X X There are five different “three in a row” locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B — just those two orders. This means the total number of configurations for these three children is 5*2 = 10. Now, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats — that’s a permutation of the 4 items —- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats. Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations R of 24*10 = 240. Answer = A #### A QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other? options: A)1:2 B)2:1 C)1:3 D)3:1 E)1:4 SOLUTION:root (b):root(a) 2:1 ANSWER:B #### B QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number? options: A)9 B)11 C)17 D)13 E)15 SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7. Given (x + 1) + (x + 7) = 28 => 2x + 8 = 28 => x = 10 The third number = x + 3 = 10 + 3 = 13. Answer: D #### D QUESTION:If the population of a certain country increases at the rate of 1 person every 60 seconds, by how many persons does the population increase in 2 Hours? options: A)120 B)80 C)100 D)150 E)140 SOLUTION:Answer = 1 * 120(2 hour = 120 minutes)= 120 Answer = A #### A QUESTION:A computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed to the final retail price. options: A)$1,000 B)$960 C)$240 D)$200 E)$150 SOLUTION:Cost price=1000 Profit=20% =20% of 1000=200 selling price=CP+ Profit SP=1200 a Discount of 20% to employees means 20% off on 1200 so 20% of 1200= 240 so a employee thinks he saved 240.. Answer: C #### C QUESTION:The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? options: A)165 B)161 C)162 D)163 E)164 SOLUTION:To minimize one quantity maximize other. 164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165. Answer: A. #### A QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 The total amount of Fuel paid by the company during the given period is approximately what percent of the total amount of salary paid during this period? options: A)A)0.5% B)B)1% C)C)1.25% D)D)3% E)E)4% SOLUTION:Required percentage = (288 + 342 + 324 + 336 + 420) = [ 17 x 100 ] % 1710 ~= 1%. Answer : B #### B QUESTION:A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class? options: A)45 B)40 C)35 D)30 E)50 SOLUTION:Explanation: Let the total number of students = x The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks. But total increase in the marks = 1/2×x=x/2 Hence we can write as x/2=20 ⇒x=20 x 2=40 Answer: Option B #### B QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is: options: A)8% B)6% C)9% D)10% E)11% SOLUTION:Rs 1552 income = Rs 128 By investing Rs 97 income = 128/1552*97 = Rs 8 Divdend = 8% ANSWER A #### A QUESTION:Calculate the sum of first 89 natural numbers. options: A)2017 B)2647 C)2147 D)2045 E)4005 SOLUTION:Solution We know that(1+2+3+.....+89) = n(n+1)/2 Therefore (1+2+3+....+89) =(89×90 / 2) = 4005. Answer E #### E QUESTION:A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by : options: A)7 only B)13 only C)11 only D)1001 only E)1003 only SOLUTION:256256 = 256 x 1001; 678678 = 678 x 1001, etc. So, any number of this form is divisible by 1001 ANSWER:D #### D QUESTION:Jenna rode her bike to school at 5 kph, but rode home at 15 kph. What was her average speed traveling to and from school? options: A)5 kph B)7 kph C)10 kph D)13 kph E)15 kph SOLUTION:(5 kph +15 kph)/2 =10 kph Correct answer is: C #### C QUESTION:The average age of a class of 23 students is 22 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? options: A)40 B)41 C)46 D)42 E)49 SOLUTION:Total age of all students =23×22 Total age of all students + Age of the teacher =24×23 Age of the teacher =24×23−23×22=23(24−22)=23×2=46 Answer is C. #### C QUESTION:log3 N+log12 N what is 3 digit number N that will be whole number options: A)6291 B)7292 C)1728 D)1929 E)1727 SOLUTION:No of values N can take is 1 12^3=1728 ANSWER:C #### C QUESTION:How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane? options: A)03 B)4 C)5 D)1 E)7 SOLUTION:You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines. AB , AC BA , BC CA , CB There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB. The lines are: AB, BC and AC ; 3 lines only. So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important. Answer:A #### A QUESTION:A work can be finished in 15 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is options: A)4:3 B)3:4 C)2:3 D)3:2 E)5:4 SOLUTION:Work done by 20 women in 1 day = 1/15 Work done by 1 woman in 1 day = 1/(15×20) Work done by 16 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×16) Ratio of the capacity of a man and woman =1/(15×16) : 1/(15×20) = 1/16 : 1/20 = 1/4 :1/5 = 5:4 Answer is E. #### E QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)G.C.D.=0.18 D)0.2 E)0.21 SOLUTION:Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer: Option C #### C QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots? options: A)4/M B)4M C)900M D)M/900 E)M/4 SOLUTION:The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours. The answer is E. #### E QUESTION:Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is: options: A)173 m B)200 m C)273 m D)300 m E)None of these SOLUTION:xplanation: Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, <ACB = 30º and <ADB = 45º. AB/AC=tan30 Answer: C #### C QUESTION:2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 20 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A? options: A)15 km/hr B)16 km/hr C)17 km/hr D)18 km/hr E)None of these SOLUTION:Explanation : Total distance covered by B=20*6=120kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=120/8=15 km/hr Answer : A #### A QUESTION:Sonika bought a V.C.R. at the list price of 18,900. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R. options: A)20,412 B)19,780 C)19,680 D)19,380 E)None of these SOLUTION:Sol. List price of V.C.R. =18,900 Rate of sales tax = 8% ∴ Sales tax = 8% of 18,900 = 8⁄100 × 18500 = 1512 So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,900 + 1512 = 20,412. Answer A #### A QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale? options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these SOLUTION:Let the original price be x and sale be of y units. Then, the revenue collected initially = x × y Now, new price = 0.8x, new sale = 1.8y Then, new revenue collected = 1.44xy % increase in revenue = 0.44xy/xy×100 = 44% increase Answer A #### A QUESTION:How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/6!? options: A)2 B)3 C)5 D)6 E)9 SOLUTION:7! = 720 1/1000 < 1/720< 1/100 0.001 < 1/720 < 0.01 So 1/720 has 2 leading zeros Answer: A #### A QUESTION:A group of people,dogs, and birds has seventy legs, thirty heads, and twenty tails. How many cats are among this group? (Assume all birds have two legs and a tail.) options: A)0 B)5 C)13 D)15 E)20 SOLUTION:Write P, C, and B for the number of people, dogs, and birds respectively, so that we have 2P + 4C + 2B = 70, P + C + B = 30,C + B = 20: Comparing the last two equations we obtain P = 10, and the first equation simplifies to 4C + 2B = 50, or 2C + B = 25. Therefore, C = (2C + B) -(C + B) = 25- 5 = 5 correct answer B #### B QUESTION:John deposited $10,000 to open a new savings account that earned 2 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened? options: A)$10,100.25 B)$10,101.50 C)$10,200.75 D)$10,201.00 E)$10,400.35 SOLUTION:2 percent annual interest compounded quarterly --> 0.5% in 3 moths. For the first 3 moths interest was 0.5% of $10,000, so $50; For the next 3 moths interest was 0.5% of $10,000,plus0.25 earned on previous interest of $100, so $50+$0.25=$50.25; Total interest for 6 months was $50+$50.25=$100.25, hence balance after 6 months was $10,000+ $100.25=$10,100.25. Answer: A. #### A QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 20 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)80. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (20gray+50other) 90gray+40other Answer:D #### D QUESTION:The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 360 m, its area is? options: A)180 B)882 C)277 D)261 E)281 SOLUTION:5x + 12x + 13x = 360 => x = 12 a = 60, b = 144, c = 156 S = (60 + 144 + 156)/2 = 180 Answer: A #### A QUESTION:Solve below question 2x + 1 = -17 options: A)-8 B)-9 C)9 D)8 E)-7 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie? options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9 SOLUTION:There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9 Answer: E #### E QUESTION:A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color? options: A)50 B)8 C)60 D)42 E)32 SOLUTION:in the first case the lady takes up 32 red colour then he takes up 24 y (cause he should take up pair) then he takes up 1y+1blue then 2blue(cause to make sure he has a pair of each color in hand) 32+24+2+2=60 ANSWER:C #### C QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5 of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students. options: A)200 B)210 C)220 D)230 E)240 SOLUTION:210 ANSWER:B #### B QUESTION:There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle. When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left. So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left. Finally, they woke up the 7th thief and this time the diamonds were divided equally. How many diamonds did they steal in total? options: A)2397 B)2401 C)2411 D)2423 E)None of the above SOLUTION:We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60. Answer B #### B QUESTION:If xy > 0, which of the following must be negative? options: A)-x/y B)xy C)x/y D)2xy E)2x/y SOLUTION:- / + = - Answer : A #### A QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit? options: A)s.2323 B)s.2380 C)s.2329 D)s.2660 E)s.2312 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 7790 * 14/41 = Rs.2660. Answer: D #### D QUESTION:Which of the following will give a non-integer on taking cube root? options: A)–64 B)–1 C)8 D)9 E)27 SOLUTION:all except 9, square root of 9 is 3 which is an integer but cube root is not an integer so answer is D #### D QUESTION:During a certain two-week period, 75 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 2/3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period? options: A)5 A B)10 A C)15 A D)18 A E)25 A SOLUTION:Movies: 75 % comedies. 25 % remaining genre. Now in this 25 %, there are only 2 categories. Action movies and Drama Movies. If Action = x; Drama movies = 2x/3. Total 5x/3. 5x/3 = 25; x = 15 Action movies: 15 % Drama movies: 10 % we can say that out of 100 z,: comedies: 75 z action: 15 z drama: 10 z Now action movies were A This means: A = 15 z. z = A/ 15 Comedies: 75 z = 75 * (A/15) 5 A A is the answer. #### A QUESTION:Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 55% nuts, what percent of the combined mixture is dried fruit? options: A)8.5% B)11.7% C)14.2% D)17.6% E)20.5% SOLUTION:55% is 25%-points above 30% and 5%-points below 60%. So the ratio of Sue's mix to Jane's mix is 1:5. 1/6*70% = 11.7% The answer is B. #### B QUESTION:How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed options: A)5040 B)1254 C)4510 D)1203 E)4510 SOLUTION:'LOGARITHMS' contains 10 different letters Required number of words = Number of arrangements of 100 letters taking 4 at a time = 10P4 = 10 * 9 * 8 * 7 = 5040 Ans: A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 B)240 C)288 D)267 E)211 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 24)m = 360 m. Let the length of the platform be x meters. Then, (x + 360)/36 = 15 ==> x + 360 = 540 ==> x = 180 m.Answer: A #### A QUESTION:If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there? options: A)22896 B)25423 C)26980 D)24698 E)24360 SOLUTION:Code consists of 3 digits and no digit is repeated. First digit of the code can have 30 possibilities Second digit can have 29 possibilities Third digit can have 28 possibilities Total number of possible codes = 30*29*28 = 24360 Answer: E #### E QUESTION:The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km? options: A)300 B)400 C)250 D)350 E)450 SOLUTION:50 kmph consumption is 1 lt/hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance. 1 lt costs $30 so 8 lt costs $240 extra expenses for 1 hr - $20 8 hrs - $160 total expense - $240 + $160= $400 Answer : B #### B QUESTION:The area of a triangle is with base 4m and height 6m? options: A)11 m2 B)10 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 4 * 6 = 12 m2 Answer: E #### E QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 6 rows or 4 rows or 8 rows, then no tree will be left. Find the least number of trees required options: A)24 B)60 C)28 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(6,4,8) = 24 Answer: A #### A QUESTION:A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 60% above the original cost per share of stock, then interns of m for how many dollars was each share sold? options: A)a) 2m/300 B)b) m/300 C)c) 5m/900 D)d) m/300 + 50 E)e) 350/m SOLUTION:Let Cost of 300 shares be $ 3000 So, Cost of 1 shares be $ 10 =>m/300 Selling price per share = (100+60)/100 * m/300 Or, Selling price per share = 5/3 * m/300 => 5m/900 Hence answer will be (C) #### C QUESTION:How many Books each of Volume 100 meter cube can be packed into a crate of volume 3000 meter cube? options: A)50 B)cannot be determined C)150 D)300 E)350 SOLUTION:Gud question with a simple concept. In geo if we want to insert one shape into another we need to know the dimensions of the two shapes. In above with volume given , we can come up with different shapes, so we cant know the answer For ex :3000 m3 can be 300*10 or 30*100 or just 3000*1 we don't know , so we cant calculate Answer : B #### B QUESTION:A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen? options: A)119 B)1,200 C)3,240 D)3,600 E)14,400 SOLUTION:To meet the conditions we can have only 2 cases: 2 officers and 3 civilians: C25∗C39=840 3 officers and 2 civilians: C35∗C29=360 Total: 840+360=1,200. Answer: B. #### B QUESTION:The ratio 3 : 5 expressed as a percent equals options: A)60% B)40% C)80% D)125% E)None SOLUTION:Solution 3 : 5 = 3/ 5 = (3 / 5 x 100)%. = 60 %. Answer A #### A QUESTION:In a business Ram invests Rs.60,000. After 6 months his uncle invests Rs.40,000. After one year they got a profit of Rs.12,000. Then uncle gets his share as options: A)Rs.2500 B)Rs.2000 C)Rs.1000 D)Rs.3000 E)Rs.4000 SOLUTION:ram=60,000(12months) uncle=(40000)(6months) 60000*12 : 40000*6 3 : 1 uncle share= (1/3+1)(12000)=3000 ANSWER:D #### D QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point. options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10) SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A #### A QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3% SOLUTION:Let 100 is the enrollment in 1990. Enrollment in 1980= 83.3 % increase= (Increase from 1980 to 1990)/Enrollment in 1983 =>16.7*100/83.3 =20% ANSWER:C #### C QUESTION:If a and b are positive integers of C such that a/b=2.86, which of the following must be a divisor of a? options: A)10 B)B.13 C)18 D)26 E)50 SOLUTION:The prompt gives us a couple of facts to work with: 1) A and B are positive INTEGERS 2) A/B = 2.86 We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in). The simplest place to start is with... A = 286 B = 100 286/100 = 2.86 These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)... A = 143 B = 50 143/50 = 2.86 There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A.... Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices. Final Answer: B #### B QUESTION:Each factor of 230 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42? options: A)1/16 B)5/42 C)1/8 D)3/16 E)1/4 SOLUTION:210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below); 42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself; So, the probability is 2/16=3/16. Answer: D #### D QUESTION:John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him? options: A)10 B)67 C)32 D)44 E)55 SOLUTION:75-20=55. Answer is E #### E QUESTION:In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 28 more than twice the number of heads => 2(d + 2c) = 28 + 2(c + d) => d + 2c = 14 + c + d => 2c = 14 + c => c = 14 i.e., total number of cows = 14 Answer is B. #### B QUESTION:For any non-zero a and b that satisfy |ab| = ab and |C| = -c |b - 4| + |ab - b| = ? options: A)a) ab - 4 B)b) b - 2b + 4 C)c) ab + 4 D)d) 2b - ab - 4a E)e) 4 - ab SOLUTION:|a| = -a Suggests that 'a' is Negative |ab| = ab Suggests that 'ab' is Positive 'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative But since 'a' is Negative therefore 'b' is Negative too. Since b is negative so |b - 4| = -b+4 Since ab is Positive and b is Negative so |ab - b| = ab - b i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4 Answer: Option B #### B QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0 SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant). In options B , if you put x = -5, you get -ve value for y co-ordinate. Answer must be (B) #### B QUESTION:By selling a house for Rs.45000, it was found that 1/2 of the outlay was gained, what ought the selling to price to have been in order to have lost 2 p.c? options: A)38020 B)38000 C)38028 D)29400 E)38192 SOLUTION:CP + CP/2 = 45000 CP = 30000 SP = 30000*(98/100) =29400 Answer:D #### D QUESTION:The average age 15 girls of a class is 15 years. Out of these, the average age of 12 girls is 13 years and that of the other 3 girls is 14 years. The age of the 15th girl is? options: A)35 B)30 C)31 D)28 E)27 SOLUTION:Age of the 15th girl = 15*15 - (12*13+3*14) = 225-198 = 27 years Answer is E #### E QUESTION:Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? options: A)21 B)16 C)16 D)28 E)12 SOLUTION:Speed Ratio = 1:7/6 = 6:7 Time Ratio = 7:6 1 -------- 7 4 --------- ? è 28 m Answer: D #### D QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer: B #### B QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? options: A)336 B)425 C)275 D)235 E)689 SOLUTION:B 425 (68 ÷ 16) × 100 #### B QUESTION:If x + | x | = 0, which of the following must be true? options: A)x > 0 B)x≥0 C)x < 0 D)x≤0 E)x = 0 SOLUTION:Manipulate the equations: x + | x | = 0 |x| = -x -x > 0 OR -x = 0 This means x could be 0 or x is less than 0. D. x≤0 E. x=0 Answer: D #### D QUESTION:A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share? options: A)8239 B)2900 C)2000 D)2393 E)2009 SOLUTION:Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively. Then, 4x - 3x = 1000 => x = 1000. B's share = Rs. 2x = 2 * 1000 = Rs. 2000. Answer: C #### C QUESTION:Two goods trains each 375 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)40 B)45 C)48 D)51 E)36 SOLUTION:Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 375 + 375 = 750 m. Required time = 750 * 6/125 = 36 sec. Answer: Option E #### E QUESTION:Income and expenditure of a person are in the ratio 4 : 3. If the income of the person is Rs. 20000, then find his savings? options: A)Rs.3600 B)Rs.3603 C)Rs.3639 D)Rs.3632 E)Rs.5000 SOLUTION:Let the income and the expenditure of the person be Rs. 4x and Rs. 3x respectively. Income, 4x = 20000 => x = 5000 Savings = Income - expenditure = 4x - 3x = x So, savings = Rs.5000 Answer: E #### E QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left? options: A)400 B)991 C)881 D)771 E)551 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A #### A QUESTION:By selling 50 mangoes, a shopkeeper gains the price of 10 mangoes. His gain per cent is options: A)25% B)35% C)20% D)23% E)30% SOLUTION:Suppose S.P of 50 mangoes = Rs 50 Therefore, Gain = Rs 10 => C.P = Rs 40 Gain % = 10/40 x 100 = 25% Gain = 25% ANSWER:A #### A QUESTION:The remainder obtained when a prime number greater than 4 is divided by 4 is options: A)a) 1 or 3 B)b) 1 or 5 C)c) 3 or 5 D)d) 4 or 5 E)e) 5 SOLUTION:The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 4, i.e. 7 and 5: 7/4 = 1 + remainder of 3 5 / 4 = 1 + remainder of 1 This is already sufficient to see that answer choice a) is correct. A #### A QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long? options: A)65sec B)70sec C)74sec D)80sec E)85sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 500)/10 = 74 sec. Answer:C #### C QUESTION:The greatest ratio out of 2:1, 5:8, 3:2, 8:9 and 8:5 is? options: A)2:1 B)3:2 C)5:8 D)8:5 E)8:9 SOLUTION:2/1=2 5/8=0.625 3/2=1.5 8/9=0.888 8/5=1.6 ANSWER:A #### A QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)288 B)200 C)279 D)992 E)208 SOLUTION:(800*3*3)/100 = 72 920 + 72 = 992 Answer: D #### D QUESTION:Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? options: A)654 B)655 C)656 D)588 E)658 SOLUTION:total cost 840 840*30/100=252 so the cut in amount is 252 the less amount to be spend is 840-252=588 ANSWER:D #### D QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)95 SOLUTION:number of handshakes = 10C2= 10*9/2 = 45 ANSWER:B #### B QUESTION:In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different Y sets can be produced by this process? options: A) 41 B) 89 C) 125 D) 243 E) 512 SOLUTION:Case 1: 1 used envelope => 1 way Case 2: 2 used envelopes - 4-1-0: Choose 4 from 5 cards: 5 ways - 3-2-0: Choose 3 from 5 cards: 10 ways Case 3: All envelopes used - 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways - 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15 Total Y: 1+5+10+10+15=41 => Answer: A #### A QUESTION:Two trains 150 meters and 180 meters long are running in the same direction with speeds of 102 km/hr, 66km/hr. In how much time will the first train cross the second options: A)37 sec B)22 sec C)27 sec D)35 sec E)33 sec SOLUTION:Explanation: Relative speed of the trains = (102 - 66) km/hr = 36 km/hr = (36× 5/18) m/sec = 10 m/sec. Time taken by the trains to cross each other = Time taken to cover (150 + 180) m at 10 m /sec = (330/10) sec = 33 sec. Answer: Option E #### E QUESTION:Find the next term in series - 25, 37, 49, 61, ? options: A)71 B)72 C)73 D)74 E)75 SOLUTION:Series is Increased by 12. 25 +12 =37 37 +12 =49 49 +12 =61 61 +12 =73 ANSWER:C #### C QUESTION:Find the value of 72519 x 9999 = m. options: A)233243413 B)354545451 C)343435451 D)565656767 E)725117481 SOLUTION:72519 x 9999 = 72519 x (10000 - 1) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 E #### E QUESTION:In how many W ways can 5 people from a group of 6 people be seated around a circular table options: A)56 B)80 C)100 D)120 E)144 SOLUTION:W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner) = 6 * 4! = 6 * 24 = 144 Answer - E #### E <<<Examples ends QUESTION:The fourth proportional to 5, 8, 15 is options: A)18 B)19 C)20 D)24 E)None SOLUTION:Sol. Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : : 15 : x ⇔ 5x = (8x15) ⇔ x = (8x15) / 5 = 24. Answer D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 35% impurities to the product. Find the net profit percentage of the dealer? options: A)44% B)40% C)68.75% D)56.25% E)36% SOLUTION:The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight. It means that he is selling $4 worth of product for $5. The dealer then further added 35% impurities to the product. It means that he is selling $5 worth of product for $6.75. So his profit is $6.75-$4 = $2 and his profit percent is (2.75/4)*100 = 68.75% Answer:- C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train? options: A)200 metres B)180 metres C)324 metres D)228 metres E)150 metres SOLUTION:Speed= 60 x 5/18 m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9 m = 200 m. Option A #### A QUESTION:How many terminating zeroes T does 200! have? options: A) 40 B) 48 C) 49 D) 55 E) 64 SOLUTION:You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C #### C QUESTION:If q and r are even integers, which of the following is an odd integer? options: A)qr + 2 B)q(r − 1) C)q(q + 5) D)3q + 4r E)(q + 3)(r − 1) SOLUTION:If q and r are even integers, then: A. qr + 2: even + even = even B. q(r − 1): even(odd) = even C. q(q + 5): even(odd) = even D. 3q + 4r: even + even = even E. (q + 3)(r − 1): (odd)(odd) = odd. Answer is E. #### E QUESTION:Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them? options: A)5/7 B)5/3 C)5/1 D)5/6 E)5/2 SOLUTION:P(at least one graduate) = 1 - P(no graduates) = 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6 Answer: D #### D QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:A rectangular garden is to be twice as long as it is wide. If 150 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:ALTERNATE APPROACH Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations. Given Perimeter is 150 So, 2 ( L + B ) = 150 Or, L + B = 75 Now use the answer options ( Given Length ; Breath will be half the length) (A) 40 L = 40 ; B = 20 L + b = 60 (B) 50 L = 50 ; B = 25 L + b = 75 (C) 60 L = 60; B = 30 L + b = 90 (D) 70 L = 70; B = 35 L + b = 105 (E) 80 L = 80; B = 40 L + b = 120 Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (B) #### B QUESTION:In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun? options: A)67 kg. B)68 kg. C)69 kg. D)Data inadequate E)None of these SOLUTION:EXPLANATION Let Arun’s weight by X kg. According to Arun, 65 < X < 72 According to Arun’s brother, 60 < X < 70. According to Arun’s mother, X <= 68 The values satisfying all the above conditions are 66, 67 and 68. Required Average =( 66 + 67 + 68 /3 )= (201/3) = 67 kg Answer A #### A QUESTION:The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)6535 B)6532 C)6725 D)6874 E)6972 SOLUTION:C 6725 CP = SP * (100/(100 + profit%)) = 8339(100/124) = Rs. 6725 #### C QUESTION:Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm. options: A)227 B)299 C)300 D)161 E)212 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (22 + 18) * (15) = 300 cm2 Answer: C #### C QUESTION:Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $18.00, how many discounted tickets did he buy? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:Let x be the number of tickets he bought at $2 per ticket. then 2 x + (10-x)1.6 = 18 0.4x = 2 => x = 5 discounted tickets = 10 -x = 5 Ans : C #### C QUESTION:What is the lowest possible common multiple M of 2 distinct integers, each greater than 329? options: A)330·331 B)330^2 C)33·331 D)660 E)330 SOLUTION:Lowest possible common multiple M of 2 distinct integers will have to be multiple of the number greater than 329...which 330.. so one number will be 330...another one will be 660.. Ans is D. #### D QUESTION:How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 options: A)5 B)6 C)7 D)8 E)None of these SOLUTION:Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 -> 9 (X) 2343 -> 12 (/) 3474 -> 18 (X) 4131 -> 9 (X) 5286 ->21 (/) 5340 -> 12 (/) 6336 -> 18 (X) 7347 -> 21 (/) 8115 -> 15 (/) 9276 -> 24 (/) Required number of numbers = 6. ANSWER IS B #### B QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(13 -8) kmph = 2.5 kmph. Answer A #### A QUESTION:Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:Set A: {1, 3, 4, 6, 9, 12, 16} If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 4? options: A)3/14 B)2/7 C)9/14 D)5/7 E)1/35 SOLUTION:using probability you can solve: 3/7*2/6*1/5=1/35. Ans E #### E QUESTION:6% of customers that enter a store on any given day must not pay tax. If 1000 people shop every day, how many people pay taxes in the store every week options: A)6500 B)6580 C)7200 D)7120 E)6800 SOLUTION:6% of customers do not pay taxes. 6/100 * 1000 customers do not pay taxes. 6/100 * 1000 = 60 Therefore 1000 - 60 customers do pay taxes. 1000 - 60 = 940 940 * 7 days per week = 6580 B) #### B QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture? options: A)1 : 9 B)1 by 5 C)1 : 7 D)1 : 3 E)1 : 1 SOLUTION:Selling price of the mixture = 70 and profit = 20% Cost price of the mixture = 70×100120=70×5670×100120=70×56 By applying alligation rule: So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5 Answer:B #### B QUESTION:There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season? options: A)A)55% B)B)60% C)C)80% D)D)72% E)E)70% SOLUTION:There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 30% chance that Federer will not play at all in the whole season We can also infer that there is 70% chance that Federer will play. Answer E #### E QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)21% C)21.33% D)22.109% E)23% SOLUTION:Lets say the indicated weight is x for $10 but the trader actually get 1.1x for $10 now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1 so profit % = (12.1-10)/ 10 = 0.21 = 21% ANSWER:B #### B QUESTION:What is the Compound Interest on Rs.7000 at 8.5% p.a. compounded half-yearly for 5 years. options: A)3616.5 B)3613.5 C)3313.5 D)3616.5 E)3113.5 SOLUTION:Compound interest : A = P(1 + r/n)nt A = 10,613.50 C.I. >> 10,613.50 - 7000 >> Rs. 3613.5 Answer:B #### B QUESTION:12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points? options: A)990 B)495 C)1980 D)none E)Cannot be determined SOLUTION:Explanation : For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals. Answer : B #### B QUESTION:In how many ways can the integer 120 be expressed as a product of two different positive integers? options: A)10 B)8 C)5 D)4 E)2 SOLUTION:120=(2^3)*3*5 Since 120 is not a perfect square, no of ways=5 Answer C #### C QUESTION:Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%. options: A)429.3 B)270 C)177 D)166 E)111 SOLUTION:Explanation: Cost of each share = (20 + 2.5% of 20) = Rs.20.5 Therefore, number of shares = 8800/20.5 = 429.3 ANSWER:A #### A QUESTION:Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side? options: A)20,25 B)21,25 C)27,23 D)28,25 E)30,25 SOLUTION:Let the two parallel sides of the trapezium be a cm and b cm. Then, a-b = 4 ------ (1) And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2) Solving 1 and 2, we get: a=27,b=23 So, the two parallel sides are 27 cm and 23 cm. C #### C QUESTION:It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold Calculate the break even point if the price he charges for 1 hotdog is $1.50 options: A)140 B)150 C)160 D)170 E)180 SOLUTION:Let x be the number of hotdogs sold Let C be the cost of buying and selling x hotdogs Let R be the revenue made for selling x hotdogs R = selling price of 1 hotdog × number of hotdogs sold R = 1.50x C = fixed cost + variable cost variable cost = fee charged for 1 hotdog × number of hotdogs sold variable cost = 1x C = 75 + 1x R = C 1.50x = 75 + 1x 1.50x - 1x = 75 + 1x - 1x 0.5x = 75 x = 150 since 0.5 × 150 = 75 The break even point is to sell 150 hotdogs. Answer B #### B QUESTION:If (x^2 + 1)y=4, which of the following is not a possible value for y? options: A)3/2 B)2 C)4/3 D)4 E)9/2 SOLUTION:Its simple equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4. Thus, correct ans is E #### E QUESTION:A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office? options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h SOLUTION:u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27 \inline \Rightarrow 1.5k = 27 \inline \Rightarrow k=18km/h E #### E QUESTION:A rectangular courtyard 3.78 metres long and 2.25 metres wide is to be paved exactly with square title, all of the same size. What is the largest size of the tile which could be used for the purpose ? options: A)11 cms B)21 cms C)42 cms D)None of these E)46 cms SOLUTION:Solution Largest size of the tile = H.C.F. of 378 cm an= 21 cm = 525 cm. Answer B #### B QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these SOLUTION:Explanation: Let their ages be x and (x + 24) years. 5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11. Their present ages are 35 years and 11 years Option D #### D QUESTION:A batsman makes a score of 100 runs in the 17th inning and thus increases his averages by 5. What is his average after 17th inning? options: A)39 B)35 C)20 D)40.5 E)41.5 SOLUTION:let the average after 16th inning =x then total run after 16th inning=16x then total run after 17th inning=16x+100 then average run after 17th inning=(16x+100)/17 (16x+100)/17=x+5 = > 16x+100 = 17x+85 => x =15 x=15; average after 17th inning =15+5=20 ANSWER:C #### C QUESTION:A toy train started on a 12-feet loop trail at a rate of 4 feet per minute. One minute afterwards, a toy scooter from the same starting point on the loop trail at 6 feet per minute. What is the shortest time that the scooter would take on the trail in order to catch up with the train? options: A)4 minutes B)3 minutes C)2 minutes D)1 minutes E)0.8 minutes SOLUTION:we don't need to assume here the direction.we need to find which will take less time so there are 2 cases 1)both moving in same direction...then time would be 2 minutes 2)both moving in opp direction then time would be 0.8 minutes as we need the shortest time it would be the second case Answer:E #### E QUESTION:A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is? options: A)13 B)21 C)77 D)88 E)11 SOLUTION:20 15 5 25 20 8 500 + 300 + 40 = 840/40 = 21' Answer: B #### B QUESTION:Two cars are driving toward each other. The first car is traveling at a speed of 100 km/h, which is 20% slower than the second car's speed. If the distance between the cars is 1125 km, how many hours will it take until the two cars meet? options: A)4 B)4.5 C)4.8 D)5 E)5.5 SOLUTION:The speed of the first car is 100 km/h. The speed of the second car is 100 / 0.8 = 125 km/h. The two cars complete a total of 225 km each hour. The time it takes the cars to meet is 1125 / 225 = 5 hours. The answer is D. #### D QUESTION:Hiralal gave a loan of Rs. 20 to Ramlal and recovered it at the rate of Rs 3.50 for eight months, commencing from the end of 1st month. What is the effective rate of simple interest? options: A)60% B)80% C)20% D)90% E)none SOLUTION:Explanation: Principal = Rs 20 Amount = Rs 3.50 x 8 = Rs 28 Interest = Rs 28 - Rs 20 = Rs 8 Time = 8 months = 8/12 years 8 = 20×8×r/12×100 r = 12×100/20 = 60% p.a. Answer A #### A QUESTION:We made a down payment of $80 and borrowed the balance on a new cello which cost $500. The balance with interest was paid in 23 monthly payments of $19 each and a final payment of $4. The amount of interest paid was what percent of the amount borrowed? options: A)3.5% B)4% C)4.5% D)5% E)5.5% SOLUTION:We borrowed $420. To pay back this loan, we paid 23*$19 + $4=$441. The interest was $441-$420=$21. The percentage was $21/$420=0.05=5%. The answer is D. #### D QUESTION:What is the smallest integer k for which 64^k > 4^16? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:64^k > 4^16 4^(3k) > 4^16 3k > 16 k = 6 The answer is C. #### C QUESTION:A and B invests Rs.4000 and Rs.6000 in a business. After 4 months, A withdraws three-fourth of his capital and 4 months later, B withdraws half of his capital. In what ratio should they share the profits at the end of the year? options: A)2:5 B)3:5 C)4:5 D)3:7 E)5:7 SOLUTION:A : B (4000*4)+(1000*8) : (6000*8)+(3000*4) 24000 : 60000 2 : 5 Answer: A #### A QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)15% B)25% C)115% D)75% E)55% SOLUTION:Explanation: SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer: B #### B QUESTION:If the price of petrol increases by 30, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? options: A)25% B)23% C)16.67% D)33.33% E)None of these SOLUTION:Explanation : let us assume before increase the petrol will be Rs. 100. After increase it will be Rs (100+30) i.e 130. Now, his consumption should be reduced to :- =(130−100)/130 ∗ 100. Hence, the consumption should be reduced to 23%. Answer : B #### B QUESTION:A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by : options: A)7 only B)13 only C)11 only D)1001 only E)1003 only SOLUTION:256256 = 256 x 1001; 678678 = 678 x 1001, etc. So, any number of this form is divisible by 1001 ANSWER:D #### D QUESTION:How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together. options: A)17280 B)4320 C)720 D)80 E)None of thsee SOLUTION:Explanation: word SIGNATURE contains total 9 letters. There are four vowels in this word, I, A, U and E Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now So total letter are 6. 6 letters can be arranged in 6! ways = 720 ways Vowels can be arranged in themselves in 4! ways = 24 ways Required number of ways = 720*24 = 17280 Option A #### A QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd? options: A)45 B)50 C)30 D)60 E)55 SOLUTION:90 numbers between - 10 and 100 Out of which half would be even, half odd. Number of odd unit digit number = 45. correct option is A #### A QUESTION:Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 res. The ratio in which these two mixtures be mixed to get a new mixture containing milk and a water in the ratio 9:4? options: A)2:8 B)2:1 C)2:2 D)2:3` E)2:7 SOLUTION:Step (i) : Let C.P. of milk be Re.1 Given ratio of mixture in A = 8:5  Milk in 1 lit mixture in A = 8/13 lit  C.P of 1 lit mixture in A = Rs. 8/13 Ratio of Mixture in B = 5:2  milk in 1 litre mixture in B – 5/7 lit  C.P of 1 lit mixture in B = Rs. 5/7 Ratio of new mixture = 9:4  milk in 1 lit mixture = 9/13 C.P of 1 lit mixture = Rs/ 9/13 (Mean price) Step (ii) : By the rule of allegation, i. C.P of 1 liter of mixture in A =8/13 ii. C.P of 1 liter of mixture in B = 5/7 iii. Mean price (p) = 9/13 iv. d – m = 9/13 – 5-7 = 2/91 v. m – c = 9/13 – 8/13 = 1/13  Required ratio = 2/91 : 1/13 = 2:7 Answer:E #### E QUESTION:The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size? options: A)6 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Side of smallest cube = L.C.M of 5,10,20 = 20cm Volume of the cube = (20 x 20 x 20)cm3 = 8000 cm3 Volume of the block= (5 x 10 x 20) cm3 = 1000 cm3 Number of blocks = (8000/1000) = 8 Answer: B #### B QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ? options: A)13500 B)10500 C)9423 D)8500 E)None of these SOLUTION:Explanation: Simran : Nanda =(50000×36):(80000×30)=(50000×36):(80000×30) =3:4=3:4. Simran's share = Rs. (24500×37)(24500×37) = Rs. 10500. ANSWER IS B #### B QUESTION:A student scored an average of 65 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics? options: A)86 B)165 C)76 D)125 E)26 SOLUTION:Given M + P + C = 65 * 3 = 195 --- (1) M + P = 90 * 2 = 180 --- (2) P + C = 70 * 2 = 140 --- (3) Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry. P = (2) + (3) - (1) = 180 + 140 - 195 = 125 Answer:D #### D QUESTION:The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area? options: A)197 B)240 C)279 D)268 E)269 SOLUTION:4a = 68 => a = 17 172 – 82 = 152 1/2 * 16 * 30 = 240 Answer:B #### B QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. options: A)1200 B)1400 C)2660 D)1600 E)1800 SOLUTION:A is a working member and for that, he receive 5% of the profit = 5% of 7400 = 5*7400/100 = 370 Remaining amount = 7400-370 = 7030 Ratio of their investments = 6500*6 : 8400*5 : 10000*3 = 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20 = 13 : 14 : 10 Share of B in the profit = 7030 * (14/37) = 190*14 = 2660 Answer is C #### C QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is options: A)35 B)37 C)38 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 8) years. (x+8+10)=2(x—10) hence x=38. Present age of B = 38 years Answer: Option C #### C QUESTION:Ayush was born two years after his father's marriage. His mother is five years younger than his father but 25 years older than Ayush who is 10 years old. At what age did the father get married ? options: A)28years B)29years C)30years D)31years E)32years SOLUTION:Explanation: Ayush's present age = 10 years. His mother's present age = (10 + 25) years = 35 years. Ayush's father's present age = (35+ 5) years = 40 years. Ayush's father's age at the time of Ayush's birth = (40 - 10) years = 30 years. Therefore Ayush's father's age at the time of marriage = (30 - 2) years = 28 years. Answer: A) 28 year #### A QUESTION:Sum of the numbers from 1 to 25 is options: A)210 B)325 C)320 D)105 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 25. So S20=25×26/2=325 Correct Option: B #### B QUESTION:The LCM and HCF of two numbers are 100 and 10 respectively. Find the larger of the two numbers if their sum is 110. options: A)100 B)12 C)35 D)466 E)56 SOLUTION:There are 2 approaches in solving this. Methode 1. HCF * LCM = The Actual Number. 100* 10= 1000 So the answer which we are looking for has to be a factor of 1000. So among the options shortlist the answers by eliminating those numbers which is not divisible by 1000. and then take the highest number as the answer as the question asks abt the highest number. answer is A #### A QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.30000? options: A)6620 B)3277 C)2688 D)2998 E)9930 SOLUTION:A = 30000(11/10)3 = 39930 = 30000 ---------- 9930 Answer:E #### E QUESTION:The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is? options: A)2:6 B)2:3 C)4:5 D)2:1 E)2:4 SOLUTION:Let the ratio be k : 1. Then, k * 16.3 + 1 * 15.4 = (k + 1) * 15.8 = (16.3 - 15.8)k = (15.8 - 15.4) = k = 0.4/0.5 = 4/5 Required ratio = 4/5 : 1 = 4:5. Answer:C #### C QUESTION:72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand? options: A)Rs. 3.23 B)Rs. 5.11 C)Rs. 5.51 D)Rs. 7.22 E)None SOLUTION:Explanation : The best way to solve this question is to multiply the alternatives by 72 and find which one gives the middle three digits 96.7. To cut time, you can choose to multiply 72 by integer values only, e.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504. It must be remembered that the decimal part of the answer will be multiplied by 72 and the actual answer will increase . Let us now roughly multiply the decimal values of the options also by 72, e.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2 and 72 × 0.5 = 36. So, option (1) will yield (216 + 14) = 230 (approximately), option(2) will yield (360 + 7) = 367 (approximately), option(3) will yield (360 + 36) = 396 (approximately), and option(4) will yield (504 + 14) = 528 (approximately). Of these only option (3) satisfies our requirement of 2nd and 3rd digits being 96. Answer : C #### C QUESTION:In a party attended by 13 persons, each clinch their glass with every other. How many glass clinches? options: A)51 B)52 C)78 D)54 E)55 SOLUTION:Total no. of person = 11 Total no. of glass clinches = n(n-1)/2 =13*12/2 = 78 ANSWER:C #### C QUESTION:If (x + 1)^2 = 144, which of the following could be the value of 2x? options: A)–26 B)–13 C)–10 D)12 E)-21 SOLUTION:You can also get to the answer by backsolving using answer choices Starting with choice B = -13 (x + 1)^2 = 144 (-13 + 1)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -13 will result in 144 in the equation so x must be -11, Then 2x = 2 * -13 = -26 Answer: A #### A QUESTION:In the new budget, the price of rice rose by 20%. By how much percent must a common man reduce his consumption so that his expenditure on it does not increase? options: A)16.66% B)17% C)15.8% D)12% E)None of these SOLUTION:Explanation : Solution: reduction in consumption = [r/(100+r) * 100]% = (20/120 * 100) = 16.66% Answer : A #### A QUESTION:A bat is bought for Rs.400 and sold at a gain of 30% find its selling price? options: A)s.460/- B)s.480/- C)s.500/- D)s.520/- E)s.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 130 % ------> 520 (130 * 4 = 520) Selling price = Rs.520/- Option 'D' #### D QUESTION:12 buckets of water fill a tank when the capacity of each bucket is 49 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 7 litres? options: A)39 B)84 C)80 D)82 E)86 SOLUTION:Capacity of the tank = (12 × 49) litre Number of buckets required of capacity of each bucket is 17 litre = 12×49/7=12×7=84 Answer is B #### B QUESTION:With out any halt a train travels a certain distance with an average speed of 66 km ph , and with halts it covers the same distance at an average speed of 33 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ? options: A)48 min. B)12min. C)60min. D)18min. E)19min. SOLUTION:With halt in 1 hour the train travels 60km With out halt for traveling same distance it take 66/33= 2/1 = 120 minutes :. 60 minutes is the halting time per hour ANSWER:C #### C QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree. From the diagram, (36−x)2=x2+122(36−x)2=x2+122 ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144 ⇒72x=1296−144⇒72x=1296−144 ⇒x=16 Answer:A #### A QUESTION:A can do a piece of work 20 days. B can do work in 35 days. In how many days they will complete the work together? options: A)15 days B)16.32 days C)12.72 days D)17 days E)18 days SOLUTION:LCM = 140, Ratio= 20:35=4:7 No of days= 140/(4+7) = 90/5 = 12.72 days ANSWER:C #### C QUESTION:There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)320 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence 3x + 5x = 600 Solve for x 8x = 600 x = 75 Number of boys 3x = 3 × 75 = 225 Number of girls 5x = 5 × 75 = 375 C #### C QUESTION:A man can row upstream at 10 kmph and downstream at 20 kmph, and then find the speed of the man in still water? options: A)11 B)77 C)25 D)88 E)34 SOLUTION:US = 20 DS = 30 M = (30 + 20)/2 = 25 Answer:C #### C QUESTION:A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%? options: A)7 B)6 C)5 D)9 E)8 SOLUTION:C 5 C.P. of 6 toffees = $ 1 S.P. of 6 toffees = 120% of $ 1 = $ 6/5 For $ 6/5, toffees sold = 6. For $ 1. Toffees sold = 6 * 5/6 = 5 #### C QUESTION:12.5 * 6.2 * 8.8 = ? options: A)352 B)435 C)224 D)682 E)742 SOLUTION:D 682 ? = 12.5 * 6.2 * 8.8 = 682 #### D QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero? options: A)472392 B)648421 C)720756 D)729951 E)810364 SOLUTION:All six digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 9 ways. And, fourth digit can be filled in 9 ways. And, fifth digit can be filled in 9 ways. And, sixth digit can be filled in 8 ways. Total ways = 9*9*9*9*9*8 = 472392 Hence option (A). #### A QUESTION:If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is options: A)5 km/hr B)4 km/hr C)2 km/hr D)1 km/hr E)None of these SOLUTION:Explanation: Rate upstream = (15/3) kmph Rate downstream (21/3) kmph = 7 kmph. Speed of stream (1/2)(7 - 5)kmph = 1 kmph Answer: D #### D QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? options: A)1227 B)2088 C)26788 D)8112 E)1871 SOLUTION:A = 7500(26/25)2 = 8112 Answer: D #### D QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)214 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 64x X = 3.57 60 * 3.57 = 214 km ANSWER:B #### B QUESTION:In 120 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: options: A)24 m B)25 m C)22.5 m D)9 m E)12 m SOLUTION:Distance covered by B in 9 sec. = 120/45 x 9 m = 24 m. A beats B by 24 metres. Answer: Option A #### A QUESTION:A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color? options: A)24/78 B)24/709 C)24/76 D)24/71 E)24/72 SOLUTION:Explanation: Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 2 marbles are drawn from 13 marbles at random. Therefore, n(S) = 13C2 = 78 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 24/78 ANSWER:A #### A QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 8 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 5 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 8 days; So for 4 days, it will be = 8 x 5 / 4 = 10 So, 10-5 = 5 Answer A #### A QUESTION:A jogger running at 9 km/hr along side a railway track is 180 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)89 B)20 C)36 D)88 E)30 SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 180 + 120 = 300 m. Time taken = 300/10 = 30 sec. Answer: Option E #### E QUESTION:The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. options: A)42cm B)44cm C)46cm D)48cm E)49cm SOLUTION:Explanation: Side of first square = (80/4) = 20 cm; Side of second square = (64/4)cm = 16 cm. Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2. Side of third square = (144)(1/2) cm = 12 cm. Required perimeter = (12 x 4) cm = 48 cm. Answer: Option D #### D QUESTION:In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:The total number of books the students borrowed is 20*2=40. The students who borrowed zero, one, or two books borrowed 8*1+3*2=14 books. The 7 students who borrowed at least three books borrowed 40-14=26 books. If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books. The answer is A. #### A QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 6 years ago? options: A)152460 B)214560 C)131632 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^6 Answer is C #### C QUESTION:Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction? options: A)Rs.21.60 B)Rs.21.68 C)Rs.21.18 D)Rs.21.98 E)Rs.21.29 SOLUTION:Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000 He lend the same amount for C.I at 6% p.a. for two years. => Siddharth's income = C.I - S.I = p[1 + r/ 100]n - p - pnr/100 = p{ [1 + r/ 100]2 - 1 - nr/100 = 6,000{ [1 + 6/100]2 - 1 - 12/100} = 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12) = 6,000 (0.0036) = 6 * 3.6 = Rs.21.60 Answer: A #### A QUESTION:Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM? options: A)40 km B)45 km C)60 km D)65 km E)70 km SOLUTION:Let the distance travelled by x km. Then, x - x = 2 10 15 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60 kmph. = 12 kmph. 5 C #### C QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 30¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)66 E)49.5 SOLUTION:Total price of six cans = 6*36.5 = 219 Total price of 4 cans = 4*30 = 120 Total rice of two cans = 219 - 120 = 99 Average price of two cans = 99/2 = 49.5 c Another way to do it is this: Assume that the four leftover cans were of 30c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 2*36.5 + 4*6.5 = 99 Avg cost of the two cans = 99/2 = 49.5c Answer (E) #### E QUESTION:On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.5, what is the probability that Malachi will return home at the end of the day on the following Monday? options: A)0.008 B)0.125 C)0.128 D)0.512 E)0.64 SOLUTION:Re-phrasing the question: What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain Probability of rain = 0.5 Therefore, probability of no rain = 0.5 0.5*0.5*0.5 = 0.125 Hence B #### B QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 3*20000/5=12000 ANSWER:E #### E QUESTION:In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted? options: A)72% B)47% C)42% D)34% E)28% SOLUTION:Town A is 40%, therefore town B must be 60% Town A registered voters:0.70∗0.40=0.28 Town B registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent ANSWER:B #### B QUESTION:A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced? options: A)1:3 B)1:2 C)2:3 D)2:1 E)3:1 SOLUTION:From the wording in the prompt, we're essentially mixing two liquids: Liquid X is 40% concentrate Liquid Y is 25% concentrate We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra: X = # of ounces of liquid X Y = # of ounces of liquid Y (.4X + .25Y) / (X + Y) = .35 .4X + .25Y = .35X + .35Y .05X = .1Y 5X = 10Y From here, you have to be CAREFUL to answer the question that is ASKED. 5X = 10Y Y/X = 5/10 = 1/2 ANSWER:B #### B QUESTION:If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips? options: A)1/4 B)1/8 C)1/2 D)1/16 E)1/32 SOLUTION:(1/2) * (1/2) * (1/2) * (1/2) = 1/16 Answer: D #### D QUESTION:The value of (10^9-10^2)/(10^7-10^3) is closest to which of the following? options: A)1 B)10 C)10^2 D)10^3 E)10^4 SOLUTION:Because the question asks for what value isclosestthe question invites approximation. Let's look at the numerator: 10^9 - 10^2 10^9 is HUGE compared to 10^2. So 10^9 - 10^2 is very close to 10^9 itself. (Just as 100 - 0.0001 is very close to 100 itself). Likewise, 10^7 is HUGE compared to 10^3. So 10^7 - 10^3 is very close to 10^7. So we have: 10^9/10^7 or 10^(9-7) = 10^2. Choose C. #### C QUESTION:If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x? options: A)-1 B)2 C)1 D)-2 E)0 SOLUTION:If we solve the question, we get x=-2. Option: D #### D QUESTION:The area of an isosceles trapezoid with sides of length 5 and bases of length 10 and 16 is? options: A)48 B)40 C)52 D)54 E)58 SOLUTION:Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 16 will be divided into 3 parts= 10, 3 and 3 (Making one square and two right triangles) For the right triangle, height will be= (5^2-3^2)^1/2= 4 And the area of trapezoid = 1/2 (B1+B2)H= 1/2*26*4= 52 C is the answer #### C QUESTION:A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)29 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 180, so from 2003 to 2005 it increased by (180-140)/140=40/140=2/7=~29%. Answer: E. #### E QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 11000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)14 B)21 C)22 D)23 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (10000 × 7) + 6000 ( x – 7) ‹=› 2000x = 28000 ‹=› x = 14. Answer A #### A QUESTION:Which of the following is a prime number ? options: A)33 B)81 C)97 D)93 E)none SOLUTION:Clearly, 97 is a prime number #### C QUESTION:What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each? options: A)$3.36 B)$6.85 C)$8.46 D)$10.08 E)$12.46 SOLUTION:Answer = E 2 * 2.49 + 4 * 1.87 = 2 (2.50 - 0.01) + 4 (2.00 - 0.13) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46 #### E QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 seconds. What is the length of the fast train? options: A)23 m B)23 (2/9)m C)38 (8/9)m D)29 m E)28 m SOLUTION:Relative speed = (40 - 20) km/hr = (20 x(5/18))m/sec = (50/9)m/sec. Therefore Length of faster train = ((50/9) x 7) m = (350/9)m = 38 (8/9) m. C #### C QUESTION:Find the circumference and area of radius 13 cm. options: A)124 cm² B)531 cm² C)354 cm² D)584 cm² E)594 cm² SOLUTION:Area of circle = πr² = 22/7 × 13 × 13 cm² = 531 cm² ANSWER:B #### B QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20 SOLUTION:Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(30-10) = 10 kmph => Rate in still water = 1/2(30+10) = 20 kmph Option E #### E QUESTION:A ladies hostel had provision of food for 200 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is: options: A)28.97 B)28.0 C)28.47 D)27.47 E)29.47 SOLUTION:Explanation : After 10 days : 200 women had food for 25 days. Suppose 175 women had food for x days. Now, Less women, More days (Indirect Proportion) 175 : 200 :: 25 : x => 175 x x = 200 x 25 => x = 200 x 25 / 175 => x =28.47 Answer : C #### C QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:If d is the mean of x, y, and z, what is the mean of x + 5, y + 5, z + 5 ? options: A)d B)3d C)15d D)d + 5 E)d + 15 SOLUTION:If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. SD will not change. If we increase or decrease each term in a set by the same percent (multiply by a constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent. So in our case mean will increase by 5 as we are adding 5 to each term in a set --> Mean =d + 5. Answer: D. #### D QUESTION:Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology? options: A)30 B)90 C)120 D)168 E)188 SOLUTION:I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168 Using your analysis: We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168 = 232 So, in the image we know that the number of students in the zone with the black boundary = 232 Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize) And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w Since the total number of students = 400, we can write: 232 +b+w= 400 Or,b+w= 400 - 232 = 168 That is,b= 168 -w So, the maximum value ofbwill happen forw= 0 This is how we get, the maximum value ofb= 168 D #### D QUESTION:Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. options: A)z=3x B)x=3z C)y=2x D)x=2y E)y=3x SOLUTION:Rovert Travelled for x,y and for z min. Total Time : x + y + z Which is equal to : 3y Equating both sides we get x+y+z = 3y => x+z =2y ........ Eqn 1 Looking out at options D Says x =2y Using it in Eqn 1 2y + z = 2y => Z = 0 mins, Which I guess is not possible. The Ans isD #### D QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle? options: A)19 cm2 B)30 cm2 C)17 cm2 D)18 cm2 E)12 cm2 SOLUTION:The circumference of the circle is equal to the permeter of the rectangle. Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5 => x = 1 Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2 Answer:B #### B QUESTION:John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam four years ago? options: A)2 B)4 C)6 D)8 E)16 SOLUTION:j= 3s after 6 years j +6 = 2(s+6) j= 2s+6 2s +6 = 3s s= 6 four years ago s= 6-4= 2 A is the answer #### A QUESTION:If x and y are perfect squares, then which five of the following is not necessarily a perfect square? options: A)x^2 B)xy C)4x D)x+y E)x^5 SOLUTION:If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square. Answer: A. #### A QUESTION:If -5 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy? options: A)-42 < xy < 30 B)-42 < xy < 24 C)-28 < xy < 18 D)-24 < xy < 21 E)-24 < xy < 24 SOLUTION:The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-5)*(-6)=30. Therefore -42 < xy < 30. Answer: A. #### A QUESTION:Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ? options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1 SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4. Actually B is the right answer. #### B QUESTION:Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds? options: A)186 B)130 C)180 D)181 E)120 SOLUTION:LCM of 9, 12, 15 and 18 is 180 LCM=180 ANSWER:C #### C QUESTION:The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 19,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263. What is the difference between the areas of Russia and China? options: A)5,476,811 kilometers squared B)9,500,148 kilometers squared C)9,843,123 kilometers squared D)1,878,965 kilometers squared E)4,787,900 kilometers squared SOLUTION:he difference between the areas of Russia and China is given by 19,098,242 - 9,598,094 = 9,500,148 kilometers squared correct answer B #### B QUESTION:Worker A takes 12 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? options: A)40 days B)40/9 days C)39/9 days D)30/9 days E)20/3 days SOLUTION:A's one hour work = 1/12. B's one hour work = 1/15. (A+B)'s one hour work = 1/12+1/15 = 9/60 = 3/20. Both A & B can finish the work in 20/3 days E #### E QUESTION:A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300m B)278m C)350m D)228m E)282m SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 36 = 50/3 3(x + 300) = 1800 è x = 300m. Answer:A #### A QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 75 and n is not prime, what is the greatest possible value of f(n)? options: A)72 B)69 C)65 D)60 E)58 SOLUTION:Since we need the largest value of f (n), we will start with the largest option. Option A: 2*2*2*2*2*2 = . This is not a product of distinct prime numbers. Hence incorrect Option B: 69 = 3*23. This is a product of distinct prime numbers. Rest all the options are smaller that 69. Correct Option: B #### B QUESTION:What will come in place of the x in the following Number series? 75, 225, x, 2025, 6075 options: A)675 B)752 C)300 D)400 E)1200 SOLUTION:(A) 25 x 3 = 75, 75 x 3 = 225 , 225 x 3 = 675, 1675 x 4 = 2025. #### A QUESTION:The girl child birth in a town is 40% of boy child birth. What is the number of boy child as a percentage of girl child birth? options: A)150% B)250% C)125% D)35% E)65% SOLUTION:The number of girl child birth in a town is 40% of boy child birth If the boy child birth=10 Girl child birth=4 We are asked to find the number of boy child birth as a percentage of girl child birth B/G=10/4=2.50=250% Answer is B #### B QUESTION:The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 422 C)Rs. 419 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2560 TD = Rs. 360 PW = F - TD = 2560 - 360 = Rs. 2200 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2200 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2160 for unexpired time =360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C #### C QUESTION:If |z|/w = 5,which of the following must be true? options: A)z = -5w B)z = 5w C)z^2 = 25w^2 D)z^2 = 25w^3 E)z^3 = 125w^3 SOLUTION:|z|/w = 5. |z| = 5w. Then z = 5w or -5w and so z^2 = 25w^2. The answer is C. #### C QUESTION:6x − 12 = 6y 5y + 5x = 10 Which of the following is the number of solutions to the system of equations shown above? options: A)More than three B)Exactly three C)Exactly two D)Exactly one E)None SOLUTION:6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 5y + 5x = 10 =>x + y = 2 -- 2 From equation 1 and 2 , we get 2x = 4 => x=2 y=0 Therefore , the given system will have Exactly one solution D #### D QUESTION:The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A options: A)A)11 B)B)12 C)C)13 D)D)14 E)E)15 SOLUTION:Explanation: Given that A+B = 11 + B + C => A – C = 11 + B – B = 11 => C is younger than A by 11 years Answer: Option A #### A QUESTION:Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers k did Carl drive each way? options: A) 350 B) 345 C) 320 D) 280 E) 240 SOLUTION:Let us backsolve here. The answer option has to be divisible by 7 to give us 1/2. Let us try k=280 km. Time taken will be 3.5 hours and 4 hours. Hence D is the answer. #### D QUESTION:One out of every 4000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch? options: A)450 B)900 C)90,000 D)1800,000 E)900,000 SOLUTION:(D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 4000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/4000 = 450/y. Solve for y and you will get the total number of chips in the batch: 1800,000. The answer is (D). #### D QUESTION:A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle? options: A)96 km B)100 km C)106 km D)116 km E)126 km SOLUTION:Distance covered in first two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in next two hours = 14 × 2 = 48 km Distance covered in first six hours 20 + 24 + 48 = 92 km Remaining distance = 8 km 92 + 8 = 100 km Answer B #### B QUESTION:A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour? options: A)(a) 60/11 B)(b) 5 C)(c) 26/5 D)(d) 27/5 E)(e) 28/5 SOLUTION:from the uphill we can find out the distance = 5*2 = 10 average speed = total distance/total time = 20/ (2+ (10/6)) = 60/11 Answer is A. #### A QUESTION:A can complete a work in 12days and B can do the same work in 8days. If A after doing 2days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4 1/2days C)6 1/2 days D)7 3/4days E)10days SOLUTION:The required answer = (12-2)*8 / 12 = 80/12 = 6 1/2days Answer is C #### C <<<Examples ends QUESTION:How many integers between 4000 and 5000 that have distinct digits and increase from left to right ? options: A)10 B)48 C)60 D)20 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 445_ --> 4 446_ --> 3 447_ --> 2 448_ --> 1 456_ --> 3 457_ --> 2 458_ --> 1 467_ --> 2 468_ --> 1 478_ --> 1 Number of integers =20 D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:There are 136 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June? options: A)15 B)11 C)12 D)13 E)14 SOLUTION:IMO 15 Take each answer choice and substract it from 136 and the divided this with 11. A #### A QUESTION:The overall age of X and Y is 19 year greater than the overall age of Y and Z. Z is how many decades younger that X? options: A)11 B)15 C)12 D)19 E)20 SOLUTION:D 19 (X + Y) – (Y + Z) = 19 X – Z = 19 #### D QUESTION:Evaluate 28% of 550 + 45% of 280 options: A)232 B)242 C)252 D)262 E)280 SOLUTION:Explanation: = (28/100) * 550 + (45/100) * 280 = 154 + 126 = 280 Answer: Option E #### E QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)11 sec C)88 sec D)33.33 sec E)10 sec SOLUTION:Speed = 54 * 5/18 = 15 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 1/15 = 33.33 sec Answer: D #### D QUESTION:Fill in the missing number: ? 14 12 11 10.5 10.25 options: A)10.1 B)10.4 C)10.2 D)10.5 E)18 SOLUTION:18 Divide each number by 2 and then add 5 to it. ANSWER E #### E QUESTION:If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is? options: A)22 B)65 C)78 D)33 E)25 SOLUTION:Given that, cost price of 50 article is equal to selling price of 40 articles. Let cost price of one article = Rs. 1 Selling price of 40 articles = Rs. 50 But Cost price of 40 articles = Rs. 40 Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25% Answer:E #### E QUESTION:There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female? options: A)75 B)100 C)125 D)175 E)225 SOLUTION:female = x Male = 750-x x/2 + 750-x/4 = 1/3* (750)= 250 x= 250 x/2 = 125 is supposed to be the answer ANSWER:C #### C QUESTION:total dinning bill of 3 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared . options: A)21.84 B)50.96 C)53.84 D)24.84 E)50.26 SOLUTION:dinner bill of 3 person = 139 + 10% tip so, 10% of 139 = (139*10)/100 = 13.9 So, the actual total amount = 139+13.9 = $ 152.9 so per head bill = 152.9/3 = $ 50.96 ANSWER:B #### B QUESTION:What is the units digit of (52^5)(37^3)(71^9)? options: A)3 B)4 C)6 D)7 E)8 SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2. The units digit of 37^3 is the units digit of 7^3 which is 3. The units digit of 71^9 is the units digit of 1^9 which is 1. The units digit of 2*3*1 is 6. The answer is C. #### C QUESTION:The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 144 metres, what is its area? options: A)1320 sq.metres B)1260 sq.metres C)1280 sq.metres D)1380 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 144 ⇒ x = 6 Area = 7 × 6 × 5 × 6 = 1260 sq.m. Answer B #### B QUESTION:In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 6 metres then what will be the area of the square so formed? options: A)Cannot be determined B)2600 cm2 C)5184 cm2 D)3025 cm2 E)None of these SOLUTION:Let the side of the square be x m. ∴ Perimeter of the square = 48 × 6 = 4x ∴ x = 72 m ∴ Area = (72)2 = 5184 m2 Answer C #### C QUESTION:Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.9 hour B)2.1 hour C)4.7 hour D)2.4 hour E)3.2 hour SOLUTION:Part filled by pipe A in 1 hour =1/8 Part filled by pipe B in 1 hour =1/4 Part filled by pipe C in 1 hour =1/24 Part filled by pipes A,B,C together in 1 hour=1/8+1/4+1/24=10/24 i.e, pipes A,B,C together can fill the tank in = 24/10 hr =2.4 hour. ANSWER:D #### D QUESTION:Concentrated grapes juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated grapes juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:Concentrated grapes juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4.... options: A)7 B)6 C)3 D)4 E)1 SOLUTION:First if we count 1223334444. they are 10 In the next term they are 20 Next they are 30 and so on So Using n(n+1)2×10≤2888 For n = 23 we get LHS as 2760. Remaining terms 128. Now in the 24th term, we have 24 1's, and next 48 terms are 2's. So next 72 terms are 3's. The 2888 term will be “3”. Answer:B #### B QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)19% B)11% C)18% D)218% E)14% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer:C #### C QUESTION:Which of the following is closest to (-7/8)^199？ options: A)-1 B)-1/2 C)0 D)1 E)2 SOLUTION:(-7/8)^4 = 2401/4096 which is already less than 2/3. For larger exponents, the expression will get closer and closer to zero. The answer is C. #### C QUESTION:The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? options: A)27 B)30 C)31 D)33 E)34 SOLUTION:The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 A #### A QUESTION:In how many different number of ways a Committee of 4person of can be selected from 4boys and 4girls such that at least 1 girl is included in the committe options: A)70 B)69 C)67 D)68 E)65 SOLUTION:1G 3B 2G 2B 3G 1B 4G =(4C1*4C3)+(4C2*4C2)+(4C3*4C1)+4C4 = (4*4)+(6*6)+(4*4)+1 = 16+36+16+1=69 Total 4M 4W 8C4=70 4C4=1 At least one girl = total - with out girl At least one girl =70-1=69 B) #### B QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:Among the members of the Malmo family, there are three times as many members who do not wear glasses as members who do. Half of the Malmo family members have blue eyes, and 4/5 of the family members who have blue eyes do not wear glasses. What percent of the Malmo family members wear glasses and do not have blue eyes? options: A)10 B)15 C)20 D)25 E)35 SOLUTION:Number in black are given and in red are calculated. Now, since x+3x=100, then x=25 and therefore =25−10=15 Answer: B. #### B QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:P = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of P = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 18 hours. If all the three pipes are opened together, then the tank will be filled in? options: A)3 9/97 hrs B)4 2/4 hrs C)3 9/17 hrs D)3 9/27 hrs E)3 9/19 hrs SOLUTION:Net part filled in 1 hour = 1/9 + 1/6 - 1/18 = 4/18 The tank will be full in 18/4 hrs, i.e., 4 2/4 hrs. Answer:B #### B QUESTION:A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? options: A)15 1/3 days B)13 1/3 days C)19 1/3 days D)11 1/3 days E)12 1/3 days SOLUTION:B 13 1/3 days 5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days #### B QUESTION:a and b are positive integers less than or equal to 9 and multiple of 4. If a and b are assembled into the seven-digit number abaabab, which of the following must be a factor of abaabab? options: A)3 B)4 C)5 D)7 E)8 SOLUTION:The last two digit of the number are ab. Both a and b are multiple of 4,thus the last two digits are divisible by 4, which makes the number abaabab divisible by 4. Thus 4 is always a factor of abaabab. Answer: B #### B QUESTION:If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)? options: A)85/365∗84/364 B)13/65∗13/64 C)1 - 85!/365! D)1 - {365!}/{280!(365^8^5)} E)1 - 85!/(365^8^5) SOLUTION:Probability(At Least 2 share a bday) = 1 - Probability(All 85 have distinct birthdays) total ways to pick 85 birthdays = 365^85 Ways to pick distinct 85 out of the 365 & distribute it to 85 people = C(365,85)*85! Hence Probability = 1−365!/280!36585 ANswer is D #### D QUESTION:Albert borrowed a total of $ 6000 from john and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)571 B)581 C)441 D)445 E)631 SOLUTION:Let x be the amount borrowed form john. So amount borrowed form Charlie = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 3*7/100*2100 = 441. C #### C QUESTION:For an upcoming charity event, a male vocalist has agreed to sing 4 out of 6 “old songs” and 2 out of 5 “new songs.” How many ways can the singer make his selection? options: A)25 B)50 C)150 D)480 E)600 SOLUTION:Number of ways the vocalist can sing "old songs" = C64=15 Number of ways the vocalist can sing "new songs" = C52=10 Therefore total number of ways the singer can make the selection = (Number of ways the vocalist can sing "old songs")*(Number of ways the vocalist can sing "new songs")= 15*10=150 Answer: C #### C QUESTION:A certain computer manufacturing firm last year produced 80 percent of its computers using parts made by its subsidiary company. If the remaining 10,000 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether? options: A)60000 B)60100 C)60500 D)50000 E)70000 SOLUTION:80% parts used of subsidary company, so 20% parts used of other companies. Now, 20% parts = 10,000 computers So, 1% parts = 10,000/20 Or, 100% parts = 50,000 computers. Hence answer is (D) #### D QUESTION:I. j; k; m; n; p II. j - 10; m; m; m; p + 15 III. j + 2; k + 1; m; n - 1; p - 2 If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation D to least standard deviation in which of the following? options: A) I, III, II B) II, I, III C) II, III, I D) III, I, II E) III, II, I SOLUTION:Range of 1st Set = (p-j) Range of 2nd Set = P+15 - j +10 = (p-j) +25 Range of 3rd Set = P -2 - j - 2 = (p-j) - 4 R2 > R1 > R3 ==> SD2 > SD1 > SD3 Since,D= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B #### B QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? options: A)25% B)33 1/3% C)50% D)66 2/3% E)75% SOLUTION:General formula for percent increase or decrease, (percent change): percent=Change/Original∗100 So, the time between maintenance checks increased by 25−20/20∗100=25 Answer: A. #### A QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary? options: A)Rs.3500 B)Rs.4000 C)Rs.4500 D)Rs.5000 E)None SOLUTION:Explanation: Let salary be Rs.x. Then, x-15% of x -30% of 85% of x = 2380 or x- 15x/100−30×85×x/100×100=2380 or 200x-30x-51x=2380×2002380×200 or 119x = 2380×2002380×200 or x 2380×200/119=4000 Correct Option: B #### B QUESTION:B @ K I 9 D © 5 2 T $ M 4 E J # U R 1 A δ K 5 W 6 % F Q 7 H P 8 Z Which of the following should come in place of the question mark(?) in the following series based on the elements in the above arrangement? K9D 2$M JUR ? options: A)δKW B)δK5 C)δ56 D)δW6 E)None of these SOLUTION:Explanation: K +6 2 +6 J +6 δ 9 +6 S +6 U +6 5 D +6 M +6 R +6 W ANSWER IS E #### E QUESTION:Line W has the equation 3x + y = 7. Which of the following lines is perpendicular to Line W? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line W as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line W? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:{3, 5, 8, y} For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y options: A)16/5, 28/3 B)4, 16/5 C)4, 16/5, 28/3 D)4, 28/3 E)3, 4, 5 SOLUTION:The set can have the following forms: 1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3 2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4 3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4 4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case. Thus the possible values are 4 and 28/3. D is the correct answer. #### D QUESTION:15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours. Then how many sugar cubes of 5 grams each, will 20 ants move in 3 hours? options: A)360 B)480 C)720 D)960 E)1000 SOLUTION:D 15 ants move 600/5=120 sugar cubes of 10 grams in 1 hour. 5 grams sugar cubes will take less time to move. Thus if weight of the sugar cube is 5 grams, 15 ants will move 120 X 10 / 5 = 240 sugar cubes in 1 hour. More ants, more sugar cubes they can move. 20 ants will move 240 X 20 / 15 = 320 sugar cubes in 1 hour Thus in 3 hours, 20 ants will move 320 X 3 = 960 sugar cubes of 5 grams. #### D QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 25,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 25,000 is made = 96,000 + 25,000 = Rs. 1,21,000 ANSWER:D #### D QUESTION:A pharmaceutical company received $2 million in royalties on the first $20 million in sales of and then $9 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales? options: A)8% B)15% C)45% D)52% E)56% SOLUTION:(9/108)/(2/20) = 30/54 = 55,5% it means that 9/108 represents only 83,3%. Therefore a decrease of 15%. Answer B #### B QUESTION:Baby Isabel plays with blocks. Each block is 3.9 inches tall. She has a collection of 32 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be? options: A)67" B)124.8" C)106" D)120" E)151.7" SOLUTION:3.9"*32=124.8". Answer is B. #### B QUESTION:A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : options: A)8/15 B)7/15 C)2 D)1/15 E)1/10 SOLUTION:A's 1 day's work =1/15 B's 1 day's work =1/20 (A + B)'s 1 day's work =(1/15+1/20)=7/60 . (A + B)'s 4 day's work =(7/60 x 4)=7/15. Therefore, Remaining work =(1 -7/15 )=8/15. Answer: Option A #### A QUESTION:The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg. What is the correct weight? options: A)58kgs B)58.85kgs C)58.9kgs D)59kgs E)59.85kgs SOLUTION:Actual total weight is (20X 58.4 - 56 + 66) = 1178 Kgs Actual average weight is 1178/20 = 58.9kgs C #### C QUESTION:The sum of the non-prime numbers between 10 and 20, non-inclusive, is options: A)60 B)75 C)90 D)105 E)120 SOLUTION:sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 * # of terms = (11 + 19)/2 * 9 = 15 *9 = 135 sum of non-prime numbers b/w 10 and 20, non inclusive ===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75 Answer: B #### B QUESTION:A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 8000. options: A)Rs. 2500 B)Rs. 8500 C)Rs. 7200 D)Rs. 8000 E)None of these SOLUTION:Explanation: A = 2B and B = 5C => A : B = 2 :1and B : C = 5 : 1 => A : B : C = 10 : 5 : 1 Ratio of capitals of A, B and C = 10 : 5 : 1 B's share = Rs.[(5/16) × 8000] = Rs. 2500 Answer: Option A #### A QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/10 * 480 =48 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 48-68 =20>>> therfore answer is 20 greater A #### A QUESTION:Find 60/42*4 options: A)14.7653 B)0.5897 C)3.6974 D)0.3571 E)1.2587 SOLUTION:Answer=60/42*4 =60/168=0.3571 Option D is correct #### D QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)4882.40 B)8082.40 C)4002.40 D)4082.40 E)9082.40 SOLUTION:Explanation: Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40 Answer: Option D #### D QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:What is the remainder when you divide 2^200+2 by 7? options: A)1 B)2 C)3 D)6 E)5 SOLUTION:answer is D. this is very similar to the 32^32^32+2 divided by 7 question. #### D QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years? options: A)587 × 108 miles B)587 × 10-12 miles C)587 × 1010 miles D)587 × 10-10 miles E)587 × 1012 miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 × 1012 miles. Answer is B. #### B QUESTION:A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:4, 6, 12, 14, 28, 30, ? options: A)32 B)64 C)62 D)60 E)52 SOLUTION:The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60 Answer : D. #### D QUESTION:If x : y = 3 : 4, find (4x + 5y) : (5x - 2y). options: A)32/7 B)13/7 C)2/7 D)32/17 E)2/17 SOLUTION:. X/Y=3/4  (4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2) =(4(3/4)+5)/(5(3/4)-2) =(3+5)/(7/4)=32/7 ANSWER A 32/7 #### A QUESTION:The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit? options: A)$3000 B)$1000 C)$2000 D)$5000 E)$6000 SOLUTION:C $2000 Let C.P. be $x. Then, (1920 - x)/x * 100 = (x - 1280)/x * 100 1920 - x = x - 1280 2x = 3200 => x = 1600 Required S.P. = 125 % of $1600 = 125/100 * 1600 = $2000. #### C QUESTION:Three seventh of a number is 12 more than 40% of that number. What will be the 10% of that number? options: A)A)148 B)B)210 C)C)21 D)D)248 E)E)258 SOLUTION:3/7 x – 40/100 x = 12 x = 35 * 12 35 * 12 * 10/100 = 42/2 = 21 ANSWER:C #### C QUESTION:There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks? options: A)5,15 B)4,15 C)5,10 D)4,10 E)5,20 SOLUTION:Assume you have locks 1-5 and keys A-E. Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum. Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D #### D QUESTION:Among the answers given below, which is nearly equal to √7? options: A)2.3 B)1.9 C)2.6 D)2.5 E)3.0 SOLUTION:2.6 is nearly equal to the square root of 7 2.6*2.6=6.76 2.5*2.5=6.25 difference 7 - 6.76=0.24 7 - 6.25=0.75 Since 0.24 is lesser of both, 2.6 is closer. Answer is C #### C QUESTION:If the positive integer x is a multiple of 1 and the positive integer y is a multiple of 7, then xy must be a multiple of which of the following? I. 7 II. 2 III. 3 options: A)II only B)I and II only C)I only D)II and III only E)I, II, and III SOLUTION:x=1a y=7b xy=7ab where a,b are integers Hence , xy will always be divisible by 7 . C is the answer. #### C QUESTION:A "word" is defined as a sequence of three dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed? options: A)3 B)5 C)6 D)8 E)9 SOLUTION:there are two ways of possibilities.. 1) all three same colour- YYY or BBB- 2 ways 2) two of one colour and one of different colour- 3!/2!-3ways.. now two /one could be Y/B or B/Y.... so 3*2=6.. total 6+2=8 ans D #### D QUESTION:A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is options: A)4/19 B)7/19 C)12/19 D)21/99 E)26/77 SOLUTION:Solution P( None is defective) = 18C2 / 22C2 = 51/77 P( at least one is defective) = (1- 51/77) = 26/77. Answer E #### E QUESTION:What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit? options: A)20(2/3)% B)20% C)21% D)22(2/3)% E)None of these SOLUTION:Explanation : Total numbers = 70 Total numbers in 1 to 70 which has 1 in the unit digit = 7 Total numbers in 1 to 70 which has 9 in the unit digit = 7 Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14 Required percentage = (14/70) × 100 = 140/7 = 20% Answer : Option B #### B QUESTION:Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ? options: A)5/6 B)5/9 C)5/3 D)5/0 E)5/1 SOLUTION:No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways. Thus 6 * 5 * 4 = 120 favourable cases. The total cases are 6 * 6 * 6 = 216. The probability = 120/216 = 5/9. Answer: B #### B QUESTION:100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads? options: A)33/100 B)41/101 C)51/101 D)87/101 E)98/101 SOLUTION:Let aa be the number of coins showing heads Then, P(A=50)=P(A=51)P(A=50)=P(A=51) ⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101 C #### C QUESTION:If x and y are non-zero integers, and 36x^4 – 4y^4 = 6x^2 + 2y^2, which of the following could be the value of x2 in terms of y? options: A)2y^2+1/6 B)2y^2+1/8 C)2y^2+1 D)2y^2 E)2y SOLUTION:36x^4 – 4y^4 = 6x^2 + 2y^2 (6x^2 + 2y^2) (6x^2 - 2y^2) = 6x^2 + 2y^2 6x^2 - 2y^2 = 1 6x^2 = 2y^2+1 x^2 = 2y^2+1/6 Answer : A #### A QUESTION:The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area? options: A)288 B)240 C)267 D)299 E)162 SOLUTION:4a = 68 => a = 17 172 – 82 = 152 1/2 * 16 * 30 = 240 Answer:B #### B QUESTION:A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap? options: A)7203 B)2403 C)3603 D)4803 E)5803 SOLUTION:LCM of 16, 20, 25, 45 = 3600 1 * 3600 + 3 = 3603 not divisible by 21 2 * 3600 + 3 = 7203 is divisible by 21 ANSWER:A #### A QUESTION:On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ? options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation: Formula: (Divisor*Quotient) + Remainder = Dividend. Soln: (56*Q)+29 = D -------(1) D%8 = R -------------(2) From equation(2), ((56*Q)+29)%8 = R. => Assume Q = 1. => (56+29)%8 = R. => 85%8 = R => 5 = R. Answer B #### B QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 30 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam. options: A)15 B)30 C)35 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 90(x - 5) 80x - (5 * 30) = 90(x - 5) 300 = 10x => x = 30 ANSWER:B #### B QUESTION:The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer? options: A)1500 B)1600 C)1750 D)1900 E)2000 SOLUTION:Let the price of basic computer be C and the price of the printer be P: C+P=$2,500. The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750. Plug this value in the first equation: C+750=$2,500 --> C=$1,750 Answer: C. #### C QUESTION:Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21 options: A)1 B)-1 C)2 D)-2 E)3 SOLUTION:B -1 19x + 19y + 17 = -19x + 19y - 21 38x = -38 => x = -1 #### B QUESTION:Mr. Hernandez, who was a resident of State X for only 9 months last year, had a taxable income of $42,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year? options: A) $900 B) $1275 C) $1200 D) $1300 E) $1060 SOLUTION:Total tax for the year = 42,500 x 4% = 1700 As stated Annual tax is prorated as per the duration of stay. Prorated Tax = 1700 (9/12) = 1275 Answer B #### B QUESTION:A certain fraction has the same ratio to 1/18, as 2/5 does to 7/9. What is this certain fraction? options: A)1/20 B)1/25 C)1/30 D)1/35 E)1/40 SOLUTION:x / (1/18) = (2/5) / (7/9) x = 2*9*1 / 18*5*7 = 1/35 The answer is D. #### D QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The distance between the nest and the ditch is 250 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 250 = 7500. D = ST 7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km) D) #### D QUESTION:If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area? options: A)120 cm2 B)187 cm2 C)178 cm2 D)189 cm2 E)176 cm2 SOLUTION:The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 10 = 120 cm2 Answer: A #### A QUESTION:The side of a square is increased by 25% then how much % does its area increases? options: A)56.75 % B)56.25 % C)53.85 % D)57.25 % E)56.21 % SOLUTION:a = 100 a2 = 10000 a = 125 a2 = 15625 ---------------- 10000 --------- 5625 100 -------? => 56.25 % Answer:B #### B QUESTION:The average age of 29 students in a group is 15 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years? options: A)31 B)36 C)29 D)53 E)57 SOLUTION:age of the teacher=(29*16-29*15) =29 years. ANSWER:C #### C QUESTION:Jerry wrote down all the positive integers that have at most 7 digits and contain only the digits 0 and 1. How many times did he write down the digit 1 ? options: A)128 B)224 C)288 D)448 E)512 SOLUTION:Jerry wrote down a total of 27 − 1 = 127 numbers (0 is missing). Add 0 to the numbers Jerry wrote. We divide the resulting 128 numbers in pairs. If x is one of the numbers Jerry wrote then we put it in pair with 1111111 − x (whose digits are also 0s and 1s). For example 1100101 is paired with 11010. In this way, we divide the numbers into 64 distinct pairs so that each number appears exactly once. Note that there are exactly 7 digits 1 in each pair. So, Jerry wrote the digit 1 exactly 64 × 7 = 448 times. correct answer D #### D QUESTION:A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle? options: A)Rs.1148 B)Rs.1160 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 82% of Rs.1400 = Rs.(82/100×1400) Rs.1148. Answer A #### A QUESTION:In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the A share of profit? options: A)10600 B)10400 C)10200 D)12200 E)14200 SOLUTION:Given A=45000 B=30000 C=22500 A:B:C= 450:300:225 As A withdrew its half of capital after 4 months,it can withdraw 22500 rupees But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost 9+4=13 months.For that 9 months, the capital for A is half of its original capital, So A= 450*4+ 225*9= 1800+2025= 3825 Similarly, B= 300*13=3900 Similarly,C= 225*13= 2925 Therefore, ratio of A:B:C= 3825: 3900 : 2925= 51:52:39 A's share=51/142(28400)=10200 ANSWER:C #### C QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2430 votes. How many votes were cast? options: A)7500 B)3388 C)8100 D)2888 E)2661 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2430 100%---------? => 8100 Answer: C #### C QUESTION:Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1235 B)1345 C)1678 D)1767 E)1647 SOLUTION:Let the smaller number be x. Then larger number = (x + 1375). x + 1375 = 6x + 15 5x = 1360 x = 272 Large number = 272+1375 = 1647 E #### E QUESTION:A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long? options: A)388 B)190 C)277 D)288 E)261 SOLUTION:L = S*T S= 1200/120 S= 10 m/Sec. Total length (D)= 1900 m T = D/S T = 1900/10 T = 190 Sec .Answer:B #### B QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)198 E)200 SOLUTION:185 Answer is B #### B QUESTION:Grace has 18 jellybeans in her pocket. She has 10 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? options: A)4 B)8 C)12 D)13 E)15 SOLUTION:The worst scenario is when she takes 10 red and 4 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. Answer: E. #### E QUESTION:Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is? options: A)17/65 B)17/29 C)17/21 D)P(EᴜP) =17/20 E)17/212 SOLUTION:n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D #### D QUESTION:A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture? options: A)12 liters B)10 liters C)4 liters D)2 liters E)3 liters SOLUTION:70 * (10/100) = 7 Wine Water 87 1/2% 12 1/2% 87 1/2% ------- 63 12 1/2% -------? => 9-7=2 ANSWER:D #### D QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 4 years hence? options: A)22 B)77 C)70 D)68 E)71 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 4 years, their ages will be 44 and 24. Sum of their ages = 44 + 24 = 68. Answer: D #### D QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(6900*6)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ? options: A)502 B)503 C)504 D)505 E)506 SOLUTION:7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3. Now,we see 3,7,11,15....2015 are in AP tn=a+(n-1)d 2015=3+(n-1)4 2015=3+4n-4 4n=2016 n=504 ANSWER:C #### C QUESTION:If x^2 + 1/x^2 = 3,what is the value of x^4 + 1/x^4 ? options: A)7 B)12 C)14 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 3 andSQUAREboth sides: (x² + 1/x²)²= 9 So, (x² + 1/x²)(x² + 1/x²) = 9 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 9 Simplify: x⁴ + 1/x⁴ = 7 Answer: A #### A QUESTION:Today is Monday. After 61 days, it will be: options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)sunday SOLUTION:EXPLANATION Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer B #### B QUESTION:How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 options: A)5 B)6 C)7 D)8 E)None of these SOLUTION:Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 -> 9 (X) 2343 -> 12 (/) 3474 -> 18 (X) 4131 -> 9 (X) 5286 ->21 (/) 5340 -> 12 (/) 6336 -> 18 (X) 7347 -> 21 (/) 8115 -> 15 (/) 9276 -> 24 (/) Required number of numbers = 6. ANSWER IS B #### B QUESTION:A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $1050? options: A)$3,000 B)$3,150 C)$4,000 D)$4,150 E)$6,000 SOLUTION:We're told that a sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $1050. Since the salesperson receives a $150 salary, the remaining $900 has to be accounted for by the 15% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales. Let's TEST Answer C: $4,000 Since 15% of $1,000 = $150 15% of $4,000 = 4($150) = $600 This is TOO HIGH (it's supposed to be $900), so we need a LOWER total sales figure. Let's TEST Answer E: $6,000 Since 15% of $1,000 = $150 15% of $6,000 = 6($150) = $900 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: E #### E QUESTION:In the city of San Durango, 60 people own cats, dogs, or rabbits. If 36 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)7 D)12 E)32 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 60 = 36 + 40 + 10 - (12) - 2x x = 7 So, answer will be C #### C QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 11? options: A)44 B)88 C)45 D)176 E)352 SOLUTION:Solution: sequence of 11 lets say sequence is 11n, 11(n+1), 11(n+2), 11(n+3), 11(n+4) so range is 11n+44-11n = 44 if we put the different values of n we will get different but the range will be multiple of 44 and only 45 is not multiple of 44 Answer : C #### C QUESTION:If a sum of money at simple interest doubles in 6 years, it will become 4 times in options: A)15years B)16years C)11years D)18years E)12years SOLUTION:Explanation: let sum =x . s.i.=x rate =(100*x)/(x*6)=50/3% now ,sum =x, s.i= 3x, rate =50/3% time =(100*3x)/(x*50/3) = 18 years Answer: D #### D QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? options: A)58 B)70 C)63 D)65 E)72 SOLUTION:1/2bh=1/2(2a+1)(2a+6) Now 4a-2=2a+6 2a=8 . a=4 Therefore, A(0,0); B(0,14); C(9,14) 1/2*9*14=63 Answer: C #### C QUESTION:Express a speed of 90 kmph in meters per second? options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps SOLUTION:90 * 5/18 = 25 mps Answer:E #### E QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 6 years hence? options: A)22 B)77 C)70 D)98 E)72 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 6 years, their ages will be 46 and 26. Sum of their ages = 46 + 26 = 72. Answer: E #### E QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec time = (360+140)/25/2 = 500*2/25 =40sec ANSWER:A #### A QUESTION:If x^2 + 1/x^2 = 9, what is the value of x^4 + 1/x^4 ? options: A)10 B)72 C)79 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 9 andSQUAREboth sides: (x² + 1/x²)²= 81 So, (x² + 1/x²)(x² + 1/x²) = 81 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 81 Simplify: x⁴ + 1/x⁴ = 79 Answer: C #### C QUESTION:In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.300 and C's share is Rs.130, what is B's capital? options: A)19878 B)12798 C)6166 D)11750 E)22073 SOLUTION:300 + 130 = 430 800 - 430 = 370 300 ---- 5000 370 ---- ? => 6166 Answer: C #### C QUESTION:A polling company reports that there is a 50% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z? options: A)11 B)10 C)6 D)4 E)5 SOLUTION:50% - Candidate Elected 100%-60% = 40% - Candidate doesnotsigh Bill X 50% - Candidate randomly chooses between two bills. These are multiplicative: 50% x 40% x 50% 0.5 x 0.4 x 0.5 = 0.10 = 10% Answer (B) #### B QUESTION:How many different eight letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R? options: A)59 B)11!/(2!*2!*2!) C)56 D)76 E)11!/(3!*2!*2!*2!) SOLUTION:E- -R We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}. We should consider two cases: 1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR. 2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56. Total = 56 + 3 = 76. Answer: D. #### D QUESTION:How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? options: A)482 B)226 C)276 D)266 E)181 SOLUTION:Explanation: 20000(11/10)4 - 20000(6/5)2 = 482 Answer: A #### A QUESTION:By selling 20 pens for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%? options: A)8.76 B)10.76 C)8.76 D)9.76 E)5.76 SOLUTION:70% --- 20 130% --- ? 70/130 * 20 = 10.76 Answer: B #### B QUESTION:Two employees X and Y are paid a total of Rs. 800 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.200.63 B)s.250.63 C)s.290.63 D)s.300.63 E)s.363.63 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 800 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 800 ⇒ y[12/10 + 1] = 800 ⇒ 22y/10 = 800 ⇒ 22y = 8000 ⇒ y = 8000/22 =Rs.363.63 E) #### E QUESTION:What percent of 60 is 90? options: A)133 1⁄3 B)150 C)60 D)33 1⁄3 E)25 SOLUTION:% of 60 is 90? = 90/60 = 3/2 = 150% Thus B is the correct answer. #### B QUESTION:If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following? options: A)m/3 B)9m C)9m^2 D)m^2/3 E)m^2/9 SOLUTION:m = 9 ^ (X-1) m = 3 ^ (2x-2) m^2 = 3 ^ (4x-4) m^2/9 = 3 ^ (4x-6) Answer E #### E QUESTION:A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit? options: A)$10 B)$16 C)$20 D)$24 E)$25 SOLUTION:Let P be the original price paid by the retailer. 1.25*P = 100 P = 80 The profit is $20. The answer is C. #### C QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet? options: A)124 sq.ft. B)120 sq.ft. C)126 sq.ft. D)129 sq.ft. E)132 sq.ft. SOLUTION:Let l = 9 ft. Then l + 2b = 37 => 2b = 37 - l = 37 - 9 = 28 => b = 28/2 = 14 ft Area = lb = 9 × 14 = 126 sq. ft. Answer is C. #### C QUESTION:In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County? options: A)200 B)210 C)216 D)224 E)235 SOLUTION:The number must be a multiple of both 8 and 7 so the answer is 224. The answer is D. #### D QUESTION:If Juan takes 16 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)16x/y B)16y/x C)x/(16y) D)16/(xy) E)xy/16 SOLUTION:This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate. Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate. We can find Juan’s rate as follows: Rate = Distance/Time = y yards/16 seconds Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have: Time = Distance/Rate Time = x yards/(y yards/16 seconds) Time = (x yards) x (16seconds/y yards) Time = 16x/y seconds Answer A. #### A QUESTION:If 6^w is a factor of (10!)^2, What is the greatest possible value of w ? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:w 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7 6= 2*3 Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D #### D QUESTION:If x is an even integer and y = 5x + 1, which of the following CANNOT be a divisor of y? options: A)11 B)31 C)21 D)41 E)30 SOLUTION:x takes even values as 2,4,6,8., y=5x+1 x is an even term so 5x must be an even term when it adds with 1 so it must be a odd integer 30 didn't follows this condition ans is E #### E QUESTION:A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)20 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 150 and and in 2005 180, so from 2003 to 2005 it increased by (180-150)/150=30/150=20%. Answer: E. #### E QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work? options: A)2 days B)76 days C)8 days D)6 days E)4 days SOLUTION:1 man's 1 day work = 1/108 12 men's 6 day's work = 1/9 * 6 = 2/3 Remaining work = 1 - 2/3 = 1/3 18 men's 1 day work = 1/108 * 18 = 1/6 1/6 work is done by them in 1 day. 1/3 work is done by them in 6 * 1/3 = 2 days. Answer: A #### A QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d? options: A)2 B)8 C)10 D)11 E)14 SOLUTION:1155 = 3 * 5 * 7 * 11 a = 11 d = 3 a - d = 8 Answer is B #### B QUESTION:Which of the following is closer to (3!+2!)+(3!-2!)? options: A)8 B)22 C)10 D)14 E)12 SOLUTION:(3!+2!)+(3!-12!)=6+2+6-2 = 12 Answer: E #### E QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is: options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 20 : 8 :: 12 : x => 8 x 20 x x = 10 x 8 x 12 => x = 10 x 8 x 12 / (8 x 20) => x = 6 Answer : C #### C QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A <<<Examples ends QUESTION:From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x) options: A)10 B)14 C)15 D)16 E)30 SOLUTION:Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)15 B)30 C)36 D)72 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 16) = (x + 8) or x = 24. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72. Answer: D #### D QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)15% B)25% C)115% D)75% E)55% SOLUTION:Explanation: SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer: B #### B QUESTION:Which of the following points is symmetric with y=x at (2,3)? options: A)(-2,-1) B)(-2,1) C)(2,1) D)(3,2) E)(-1,2) SOLUTION:We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x. (2,3) would become (3,2). Answer (D). #### D QUESTION:The present age of a father is 3 years more than three times the age of his son. Five years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father. options: A)33 B)38 C)27 D)40 E)48 SOLUTION:if the present age be x years. father's will be (3x+3)years.. so, (3x+3+5)=2(x+3)+10 or, x=8 so the fathers present age =(3x+3)=(3*8+3)years =27 years.. ANSWER : OPTION C #### C QUESTION:If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available. options: A)35 7/8 B)36 C)21 3/7 D)34 5/7 E)34 6/7 SOLUTION:Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts. If we use 8 tons of cement, then we'll get 5/7*30 = 21 3/7 tons of mixture. Answer: C. #### C QUESTION:Jake wants to invite 9 friends to his 8th birthday party. Each invitation requires 2 stamps to mail, costing 12 cents each. How much will Jake have to spend on stamps to send invitations to his 9 friends? options: A)$1.08 B)$1.41 C)$1.74 D)$1.98 E)$2.16 SOLUTION:2 stamps multiplied by 12 cents = 24 cents per invitation. 24 cents multiplied by 9 invitations = 216 cents = $2.16, hence answer : E. #### E QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is? options: A)40m2 B)45m2 C)49m2 D)51m2 E)55m2 SOLUTION:39/360 * 22/7 * 12 * 12 = 49m2 Answer:C #### C QUESTION:1/3, 1/2, 1/4, 2 1/3, 3 1/2, 4 1/4, 4 1/3, 6 1/2, ? options: A)8 1/4 B)9 1/4 C)8 1/2 D)8 1/3 E)6 1/4 SOLUTION:there are 3 series--- 1/3,2 1/3,4 1/3. 1/2,3 1/2,6 1/2. 1/4,4 1/4,? ans 8 1/4 ANSWER:A #### A QUESTION:For which of the following functions f is f(c) = f(1-c) for all c? options: A)f (c) = 1 - c B)f (c) = 1 - c^2 C)f (c) = c^2 - (1 - c)^2 D)f (c) = c^2*(1 - c)^2 E)f (x) = x/(1 - x) SOLUTION:I remember seeing this problem in a GMATprep test. I think choice D should be F(c)=(c^2) (1-c)^2. If that is true then substituting (1-c) for will give us the same function back and the answer choice is D, where the function is multiplicative #### D QUESTION:How much water must be added to 60 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)10 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 60 litres of milk = (1⁄4 × 60) litres = 15 litres. Answer C #### C QUESTION:The area of a triangle is with base 4m and height 6m? options: A)11 m2 B)10 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 4 * 6 = 12 m2 Answer: E #### E QUESTION:John had a stock of 700 books in his bookshop. He sold 50 on Monday, 82 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold? options: A)26.5% B)50% C)46.5% D)56.5% E)60% SOLUTION:Let N be the total number of books sold. Hence N = 50 + 82 + 64 + 78 + 135 = 280 Let M be the books NOT sold M = 700 - N = 700 - 280 = 420 Percentage Books not sold / total number of books = 420/700= 0.60 = 60% correct answer E #### E QUESTION:Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+30 3x + 6 = x + 30 2x = 24 \inline \therefore x = 12 \inline \therefore Middle number = x + 2 = 12+2 = 14 C #### C QUESTION:Which of the number is the odd one out? options: A)21165 B)17642 C)81002 D)52832 E)72927 SOLUTION:D 52832 All the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27. Answer is D #### D QUESTION:For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3). If 3x = –25, then x = options: A) –15 B) –2 C) -3 D) 6 E) 15 SOLUTION:(3+2)(x-3)=-25.. x-3=-5.. x=-2 B #### B QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:A train is 288 meter long is running at a speed of 29 km/hour. In what time will it pass a bridge of 101 meter length? options: A)48.29 B)50 C)26.8 D)45.29 E)30 SOLUTION:Speed = 29 Km/hr = 29*(5/18) m/sec = 145/18 m/sec Total distance = 288+101 = 389 meter Time = Distance/speed = 389 * (18/145) = 48.29 seconds. Answer: A #### A QUESTION:A given line L has an equation 3x+4y=5. Which of the following is the equation of line which is parallel to the above line? options: A) 4x + 3y = 5 B) 3x + 4y = 10 C) 3x + 5y = 5 D) 3x + 5y = 3 E) 3x – 4y = 5 SOLUTION:3x+4y=5 --- equation 1 2 lines are parallel if a1/a2 = b1/b2 ≠ c1/c2 Comparing the original line with option B 3x+4y = 10 -- equation 2 From equations 1 and 2 , we get 5=10 which is not possible Hence our answer is 3x + 4y = 10 Answer B #### B QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:The H.C.F. and L.C.M. of 0.63, 1.05 and 2.1 options: A)(i)0.20(ii)6.31 B)(i)0.21(ii)5.30 C)(i)0.21(ii)6.30 D)(i)1.21(ii)6.50 E)None of these SOLUTION:Explanation : Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10. Without decimal places, these numbers are 63, 105 and 210. Now, H.C.F. of 63, 105 and 210 is 21. H.C.F. of 0.63, 1.05 and 2.1 is 0.21. L.C.M. of 63, 105 and 210 is 630. L.C.M. of 0.63, 1.05 and 2.1 is 6.30. ANSWER IS C #### C QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 * 72 = 48 Answer: B #### B QUESTION:A train is moving at a speed of 132 km/hr. If the length of the train is 200 meters, how long will it take to cross a railway platform 295 meters long options: A)6 ½ sec B)7 ½ sec C)8 sec D)13 ½ sec E)9 sec SOLUTION:Explanation: Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec. Distance covered in passing the platform = (200 + 295) m = 495 m. Time taken =495 ×(3/110) sec =27/2 sec = 13 ½ sec Answer: Option D #### D QUESTION:The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)14 years B)17 years C)18 years D)12 years E)11 years SOLUTION:9 * 2 = 181 Answer:C #### C QUESTION:The value of x + x(xx) when x = 2 is: options: A)10 B)18 C)16 D)64 E)36 SOLUTION:x + x(xx) Put the value of x = 2 in the above expression we get, 2 + 2(22) = 2 + 2(2 × 2) = 2 + 2(4) = 2 + 8 = 10CORRECT ANSWER : A #### A QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 6 years will be options: A)2 : 3 B)7 : 11 C)5 : 4 D)4 : 5 E)11 : 9 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 28 x = 4 Mini’s age = 16 years And Minakshi’s age = 12 years Ratio of their ages after 8 years = (16 + 6) : (12 + 6) = 22 : 18 = 11 : 9 ANSWER:E #### E QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? options: A)8/35 B)34/35 C)27/35 D)21/32 E)33/35 SOLUTION:Solution: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)*P(B) = 2/5 * 4/7 = 8/35 ANSWER IS A #### A QUESTION:A triangle has sides 10, 17, and 21. A square is inscribed in the triangle. One side of the square lies on the longest side of the triangle. The other two vertices of the square touch the two shorter sides of the triangle. What is the length of the side of the square? options: A)148/29 B)168/29 C)168/26 D)158/29 E)198/29 SOLUTION:By Heron's Formula, the area, A, of a triangle with sides a, b, c is given by A = square root[s(s − a)(s − b)(s − c)], where s = ½(a + b + c) is the semi-perimeter of the triangle. Then s = ½(10 + 17 + 21) = 24, and A = 84. A square inscribed in a 10 by 17 by 21 triangle, with perpendicular dropped onto the side of length 21. Now drop a perpendicular of length h onto the side of length 21. We also have A = ½ × base × perpendicular height. Hence A = 21h/2 = 84, from which h = 8. Notice that the triangle above the square is similar to the whole triangle. (This follows because its base, the top of the square, is parallel to the base of the whole triangle.) Let the square have side of length d. Considering the ratio of altitude to base in each triangle, we have 8/21 = (8 − d)/d = 8/d − 1. Therefore the length of the side of the square is 168/29. ANSWER:B #### B QUESTION:jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all? options: A)5 B)10 C)15 D)20 E)14 SOLUTION:10+5=15. Answer is C #### C QUESTION:The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? options: A)27 B)30 C)31 D)33 E)34 SOLUTION:The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 A #### A QUESTION:For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 * 5 * 5. How many two-digit positive integers have length 6? options: A)None B)One C)Two D)Three E)Four SOLUTION:The best (quickest) way I can think of to get the answer, is start with 2^6, then move on from there. 2^6=64 2^5*3=96 Obviously 2^5*5 will be more than 2 digits, as will 2^4*3^2. So 64 and 96 are it. Answer is 2 (C). #### C QUESTION:What is the smallest positive integer x, such that 6000x is a perfect cube? options: A)4 B)6 C)36 D)12 E)18 SOLUTION:Take out the factors of 6000 that will come 2*3*10^3. for perfect cube you need every no. raise to the power 3. for 6000x to be a perfect cube, need two 2 and 2 3 that means 36 or 6^2 C is the answer. #### C QUESTION:In how many W ways can 5 people from a group of 6 people be seated around a circular table options: A)56 B)80 C)100 D)120 E)144 SOLUTION:W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner) = 6 * 4! = 6 * 24 = 144 Answer - E #### E QUESTION:A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? options: A)1/3 B)2by3 C)2/5 D)3/5 E)4/5 SOLUTION:Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol. Let x ml be the amount removed ---> total alcohol left = 4-0.4x New quantity of whiskey added = x ml out of which 0.19 is the alcohol. Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml. Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3. Hence, B is the correct answer. #### B QUESTION:The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes. options: A)$0.94 B)$0.96 C)$0.99 D)$1.00 E)$1.20 SOLUTION:Assume the manager bought 100 tomatoes. Cost Price = 80 Given: 10% are damaged --> Available tomatoes to sell = 90 90 * x - 80 = 0.12 * 80 90x - 80 = 9.6 90x = 89.6 x = 89.6/90 = 0.995 x is slightly under 0.9955 = 0.99 Answer: C #### C QUESTION:A bag contains 2 red, 3 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball? options: A)5/7 B)9/14 C)13/21 D)17/28 E)23/35 SOLUTION:P(no red balls) = 6/8*5/7*4/6 = 5/14 P(at least one red ball) = 1 - 5/14 = 9/14 The answer is B. #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere interest rate is increased by 8%, it would amount to bow mucb ? options: A)Rs 990 B)Rs 995 C)Rs 997 D)Rs 992 E)Rs 999 SOLUTION:S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _ . R = ((100 x 120)/(800*3) ) % = 5%. New rate = (5 + 3)% = 8%. New S.l. = Rs. (800*8*3)/100 = Rs. 192. :. New amount = Rs.(800+192) = Rs. 992 Answer is D. #### D QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/9) B)Rs. 2(2/9) C)Rs. 2(1/9) D)Rs. 4(2/9) E)Rs. 3(1/9) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B #### B QUESTION:The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation? options: A)1 B)5 C)7 D)8 E)11 SOLUTION:Let me define terms: in g(p) = R p is argument, R is result, g() is function, in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1:1 Even g2: 1*(Even,Odd ) =1 Even 1 Odd g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8 Ans D it is! #### D QUESTION:A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match options: A)36 B)37 C)38 D)39 E)40 SOLUTION:Explanation: Let the average after 17th match is x then the average before 17th match is x-3 so 16(x-3) + 87 = 17x => x = 87 - 48 = 39 Answer: Option D #### D QUESTION:Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 23 years. Father's age when Ayesha's brother was born = (29 + 3) years = 32 years. Required difference = (32 - 23) years = 9 years. Answer: Option E #### E QUESTION:A work can be finished in 30 days by 30 women. The same work can be finished in fifteen days by 15 men. The ratio between the capacity of a man and a woman is options: A)1:3 B)4:3 C)2:3 D)4:1 E)2:4 SOLUTION:Work done by 30 women in 1 day = 1/30 Work done by 1 woman in 1 day = 1/(30×30) Work done by 15 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×15) Ratio of the capacity of a man and woman =1/(15×15) : 1/(30×30)) = 1/225 : 1/900 = 1/1 :1/4 = 4:1 Option D #### D QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)800 B)700 C)750 D)850 E)900 SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265 253/160p=1265==> p =800 ANSWER A #### A QUESTION:Which 2 digit number has its digits reversed when you double it and take 1? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:reverse it and you get 73 which is 2*37-1. ANSWER:E #### E QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:If 2x = 3y = 10, then 9xy = ? options: A) 1,200 B) 200 C) 150 D) 40 E) 20 SOLUTION:2x = 10;x=5 3y = 10;y=10/3 Multiply: 9xy=9*5*10/3=150 Answer: C. #### C QUESTION:A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B? options: A)3999 B)7799 C)2500 D)2772 E)2912 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 200 B capital = 15000*1/6 = 2500.Answer: C #### C QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:In how many ways can you seat 8 people on a bench if one of them does not want to sit in one of the two middle seats or at either end? options: A)17,540 B)18,360 C)19,320 D)20,160 E)21,480 SOLUTION:One person can choose 4 possible chairs to sit. The remaining 7 people can sit in 7! ways. The number of arrangements is 4*7! = 20,160. The answer is D. #### D QUESTION:Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: options: A)11:5 B)3 : 2 C)1:2 D)3:5 E)7:8 SOLUTION:Answer: Option B Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. #### B QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320 C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5 Difference = (360.5 - 320) = Rs. 40.5 Answer: C #### C QUESTION:On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80? options: A)18% B)21% C)33.35 D)33.3% E)37.5% SOLUTION:let the total no of campers be 100 total amount = (25*110)+(35*80)+(40*65) = 2750+2800+2600= $8150 required percentage = (2800/8150)*100=33.35% C #### C QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: 1) 80% of the team consists of spinners. 2) The opening batsmen were spinners. options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow. D #### D QUESTION:The population of a city increases by 6% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years? options: A)9% B)9.27% C)27% D)15.76% E)None of these SOLUTION:Actual increase in population=5% Let, earlier population=100 then the population after 3 years =100(1+5/100)^3=115.7625 ∴Required percentage=15.7625% ANSWER:D #### D QUESTION:In a class of 150 students 55 speak English;85 speak Telugu and 30 speak neither English nor Telugu How many speak both English and Telugu? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Total=150 English=55 Telugu=85 none/ neither English nor Telugu=30 No. of Students who speak only one or both=150-30=120 so, 120 stud's can speak english or telugu or both. then, No. of Stud's speak only English= 120-85(telugu)=35 " " " " " Telugu= 120-55=65 Remaining 120-(65+35)=20 stud's can speak both. B) #### B QUESTION:Find the number such that when 15 is subtracted from 7 times the number,the result is 10 more than twice the number? options: A)4 B)3 C)5 D)2 E)6 SOLUTION:Let the number be x. 7x-15=2x+10 7x-2x=15+10 5x=25 x=5 answer is option C #### C QUESTION:If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events. options: A)7/25 B)3/25 C)8/25 D)2/13 E)3/17 SOLUTION:P (A n B) = P(A) . P(B) P (A n B) = 4/5 . 2/5 P (A n B) = 8/25. C #### C QUESTION:If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be options: A)2 B)5 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 5*8820 = 44, 100, which is a square of 210 B #### B QUESTION:If $500 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years? options: A)500 (1.056)(3) B)500 (3+1.056) C)500 (1+3(0.056)) D)500 (1.056)^3 E)500 (1+(0.056)^3) SOLUTION:the formula is CI=P(1+r/100)^t in this case i think D is the ans #### D QUESTION:If f(c)=c^2 and c is a positive integer, which of the following CANNOT be the value of f(f(c))? options: A)81 B)16 C)300 D)256 E)625 SOLUTION:f(c)=c^2 f(f(c)) = (c^2)^2 = c^4 Therefore f(f(c)) will be numbers that are 4th power of other numbers. Checking the options: 81 = 3^4 16 = 2^4 300. This cannot be written as the 4th power of any number 256 = 4^4 625 = 5^4 Answer: C #### C QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speed∗Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:The 40 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees? options: A)4 B)6 C)8 D)9 E)10 SOLUTION:The formula is Total = A+B+C - sum of exactly two + 2*all three + neither 21+18+19-x-2*5=40 solving for x you get 8 Answer C #### C QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall? options: A)120 B)350 C)1470 D)2,520 E)5,040 SOLUTION:Number of ways to choose 2 colors among 7 - 7c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 7c2 * 2* 7c4 = 1470 C #### C QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)34 SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER:A #### A QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)6620 B)9278 C)2782 D)5772 E)5286 SOLUTION:A = 20000(11/10)3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430 ? options: A)s. 832 B)s. 830 C)s. 822 D)s. 812 E)s. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2430 = 20 (2430/60) = Rs. 810. Answer: E #### E QUESTION:Machine T can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? options: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33 SOLUTION:Let the following be true: T makes x in time t Then the following follows: N makes x in 4t/3 O makes x in 3/2(4t/3) = 2t M:N:O = 1:4/3:2=3:4:6 So N=4/(3+4+6)=4/13=C #### C QUESTION:The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 5 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 18 seconds? options: A)18 miles per hour B)90 miles per hour C)216 miles per hour D)324 miles per hour E)5400 miles per hour SOLUTION:Since Velocity is proportional to Time Velocity =k*Timewhere k is the constant of proportionality Time= 5 seconds Velocity = 5k = 90 miles per Hour i.e. k = 18 i.e. The relation between Velocity and Time becomes Velocity =18*Time Time= 18 seconds Velocity = 18*18 = 324 miles per hour Answer: Option D #### D QUESTION:A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 980gm. for a kg.His gain is …%. options: A)2.04% B)5.36% C)4.26% D)6.26% E)7.26% SOLUTION:His percentage gain is 100*20/980 as he is gaining 20 units for his purchase of 980 units. so 2.04%..ANSWER:A #### A QUESTION:P sells an article to Q at 10 % profit. Q sells it to R at 25 % profit. If R pays Rs. 250 for it, What did P pay for it ? options: A)Rs. 181.81 B)Rs. 181.88 C)Rs. 181.82 D)Rs. 181.89 E)Rs. 181.812 SOLUTION:Explanation: Selling price of P = Cost price of Q Selling Price of Q = Cost price of R = Rs. 250 ….. Given Q sold it to R with 25 % profit. Cost price of Q = 100/125 * 250/1 = Rs. 200 = Selling price of P. P sold it to Q with 10 % profit. Cost price of P = 100 / 110 * 200 / 1 = Rs. 181.81 ANSWER: A #### A QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5 hours, then the distance covered at 40 kmph is options: A)130 km B)120km C)100km D)140km E)none of these SOLUTION:Let the partial distance covered at 40 kmph be X Let the another partial distance covered at 60 kmph be (250 - x) Thus, x/40 - (250 - x)/60 = 5 or, x/40 + (250 - x)/60 = 5 or, (3x + 500 - 2x)//120 = 5 or 500 + x = 600 x=100 ANSWER:C #### C QUESTION:In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r? options: A)-4/3 B)1/4 C)-4 D)3/4 E)4/3 SOLUTION:The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x. Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3. Answer: A. #### A QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:Let S be the set of values which can be written as the sum of 5 consecutive perfect squares. What is the smallest element of S which is divisible by 17? options: A)255 B)355 C)522 D)355 E)664 SOLUTION:Each element of S can be written in the form (x- 2)2 + (x - 1)2 + x2 + (x + 1)2 + (x + 2)2 = x2 + 2x2 + 2 + 2x2 + 8 = 5x2 + 10 = 5(x2 + 2) where x is some positive integer with x 3. By iterating over values of x, we observe that when x = 7, x2 + 2 = 51 = 3 * 17; no smaller value of x exists which satisfies the problem statement. Hence, the solution is 5(x2 + 2) = 5 *51 = 255 correct answer A #### A QUESTION:For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6? options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4. SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6 = 6*0 + 2*7.2 + 8 - 6.6 = 0 +14.4 +1.4 15.8 Answer B #### B QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)190/827 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways Total ways of getting outcome on two dice =6*6=36 Probability of getting sum as 10 in any attempt =3/36=1/12 Probability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12 Probability of losing game =(11/12)*(11/12)*(11/12)=637/827 I.e. Probability of wining game = 1-(637/827) = 190/827 Answer : Option C #### C QUESTION:Find the sum of all odd numbers upto 100. options: A)200 B)1000 C)2500 D)3140 E)3200 SOLUTION:Sol. The given numbers are 1, 3, 5, 7, ..., 99. This is an A.P. with a = 1 and d = 2. Let it contain n terms. Then, 1 + (n - 1) x 2 = 99 or n = 50. Required sum = (n/2) (first term + last term) = 50(1 + 99)/2 = 2500. ANSWER C 2500 #### C QUESTION:Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 36 have long fur, 27 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown? options: A)26 B)19 C)11 D)8 E)6 SOLUTION:No of dogs=45 Long fur=36 Brown=27 Neither long fur nor brown=8 Therefore, either long fur or brown=45-8=37 37=36+27-Both Both=26 Answer A #### A QUESTION:If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day? options: A)10 B)15 C)20 D)25 E)None of them SOLUTION:Let the required number of days be x. More men, Less days (indirect proportion) Less hours per day, More days (indirect proportion) Men 18 : 15 Hours per day 8: 9 } : :16 : x (18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15 Hence, required number of days = 15. Answer is B. #### B QUESTION:1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:1/5 , 1/2 , 1/3 1/5*2 , 1/2*2 ,1/3*2 1/5*3 , 1/2*3 ,1/3*3 1/5*4 , 1/2*4 ,1/3*4 so 1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,2 ANSWER:B #### B QUESTION:If each data point in a certain set Q is increased by a factor of 20, what happens with the set's standard deviation? options: A)Doesn't Change B)Decreases by Factor 20 C)Can't be determined D)Increases by 20 E)Increases by Factor 20 SOLUTION:Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 20, the standard deviation will increase proportionately, giving us answer choice E #### E QUESTION:Two planes take off from neighboring runways at the same time. The British Airways Jet heads directly East at 300 Km/Hr, while the American Airlines Jet takes off heading directly west at 250km/hr. At this speed, how long before the two planes are 2,000 Km away from each other? options: A)4 hours B)3.75 hours C)3.0 hours D)3.5 hours E)3.63 Hours SOLUTION:For every hour the planes travel in opposite directions, they are 550 Km away from each other. So to be 2,000 Km away, it would take (2,000 Km/550 Km/Hour= 3.63 Hours). Answer is E #### E QUESTION:Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop? options: A)128 B)64 C)32 D)16 E)8 SOLUTION:Before stop 3, there were 2 passengers on the bus. Before stop 2, there were 4 passengers on the bus. Before stop 1, there were 8 passengers on the bus. The answer is E. #### E QUESTION:A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? options: A)450. B)412. C)432. D)502. E)522. SOLUTION:Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30 Only option A satisfies the condition, and hence is the answer #### A QUESTION:A person buys an article at $500. At what price should he sell the article so as to make a profit of 20%? options: A)560 B)449 C)600 D)740 E)460 SOLUTION:C 600 Cost price = $500 profit = 20% of 500 = $100 Selling price = Cost price + Profit = 500 + 100 = 600 #### C QUESTION:Agatha has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have? options: A) 32 B) 30 C) 29 D) 28 E) 27 SOLUTION:5n + 10m = 460 n > m Pick an easy number to work with. suppose n=30. Then you have 150. You need another 310 and that means you need m=31 which is greater than n. Therefore, n > 30. The only answer choice where n> 30 is if n = 32. A is the answer. #### A QUESTION:Lisa earns a profit of $3 on each ribbon that she sells, and $5 on each bracelet. If at the end of the day Lisa has earned $120 and she has sold at least 10 pieces of each item. At least how many bracelets she has sold? options: A)2 B)5 C)9 D)12 E)15 SOLUTION:Since Lisa has sold at least 10 pieces for each item, let us say Lisa sells (10 + r) number of ribbons and (10 + b) number of bracelets, her profit for the day = 3(10 + r) + 5(10 + b) => 3(10 + r) + 5(10 + b) = 120 => 30 + 3r + 50 + 5b = 120 => 3r + 5b = 120 - 30 - 50 = 40 => 5b = 40 - 3r => b = 8 - (3/5)r To minimize b, we need to maximize r and it will be a multiple of 5. r = 5, b = 8 - (3/5)5 = 5 r = 10, b = 8 - (3/5)10 = 2 Beyond that b will become -ve. So Lisa has sold at least 10 + 2 = 12 bracelets. Answer: D #### D QUESTION:If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s? options: A)8 B)2 C)− 2 D)− 3 E)− 5 SOLUTION:Given: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x - 5)(x + 3) = (x + r)( x + s) Rewrite as: (x + -5)(x + 3) = (x + r)( x + s) So, it's possible that r = -5 and s = 3 Here, r - s = (-5) - 3 = -8 Try REVERSING the factorization: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x + 3)(x - 5) = (x + r)( x + s) Rewrite as: (x + 3)(x + -5) = (x + r)( x + s) So, it's possible that r = 3 and s = -5 Here, r - s = 3 - (-5) = 8 Answer: A #### A QUESTION:Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other? options: A)300 kms from A B)280 kms from A C)305 kms from A D)295 kms from A E)265 kms from A SOLUTION:DETAILED SOLUTION Bus A Travels 200km @ 40kmph the next 200km @ 50kmph and the final 200km @ 60kmph So, Bus A will be at a distance of 200km from city M after 5 hours, and at a distance of 400km after 9 hours, and reach N after 12 hours and 20 mins Bus B Travels at an overall average speed of 50kmph, so will take 12 hours for the entire trip. So, Bus B will travel 160 kms in the first 4 hours 200 kms in the next 4 hours and 240 in the final 4 hours So, both buses cross each other when they are in their middle legs. After 5 hours, bus A will be at a position 200kms from city M. At the same time, bus B will be at a distance 210kms from city N (4 * 40 + 50). The distance between them will be 190kms (600 - 200 - 210). Relative speed = Sum of the the two speeds = 50 + 50 = 100 kmph. Time taken = 190/100 = 1.9 hours. = 1 hour and 54 minutes. So, the two buses will meet after 6 hours and 54 minutes. Bus B will have travelled 210 + 95 = 305 kms. So, the two buses will meet at a point that is 305 kms from City N and 295 kms from city A. CORRECT ANSWER D #### D QUESTION:a goes to place x and b goes to place y. after a travelled 180 km more than b they together meet at a point between xy. they together had their lunch for half an hour. after that a took 2 hrs to reach x and b took 4.5 hrs to reach y. find distance between x and y? options: A)900km B)540km C)720km D)820km E)920km SOLUTION:let speed of A be-------Sa let speed of B be--------Sb let the distance covered by B while going to position XY be-----------x so distance covered by A in same time while going to XY is----------180 +x(it's given in the question) so total distance b/w X and Y is=x+(x+180) while going to position XY :- time taken by A = time taken by B (x+180)/Sa= x/Sb Sa/Sb=(x+180)/x---------------------1 After lunch:- A.C.T(according to question) Sa=x/2 Sb=(x+180)/4.5 dividing Sa/Sb=(x*4.5) / ((x+180)*2)--------------------2 equating equations 1 and 2 9/4 = (x+180)^2 / x^2 now taking square root on both sides we get 3/2 = (x+180) / x x=360 therefore distance between x and y =x+(x+180)=900km ANSWER:A #### A QUESTION:You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs. options: A)180 B)181 C)182 D)178 E)168 SOLUTION:add the max weights 52+50+78=180 ANSWER:A #### A QUESTION:A boy has eight trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)80 ways B)86 ways C)88 ways D)108 ways E)89 ways SOLUTION:The boy can select one trouser in eight ways. The boy can select one shirt in 10 ways. The number of ways in which he can select one trouser and one shirt is 8 * 10 = 80 ways. Answer:A #### A QUESTION:A group of people,dogs, and birds has seventy legs, thirty heads, and twenty tails. How many cats are among this group? (Assume all birds have two legs and a tail.) options: A)0 B)5 C)13 D)15 E)20 SOLUTION:Write P, C, and B for the number of people, dogs, and birds respectively, so that we have 2P + 4C + 2B = 70, P + C + B = 30,C + B = 20: Comparing the last two equations we obtain P = 10, and the first equation simplifies to 4C + 2B = 50, or 2C + B = 25. Therefore, C = (2C + B) -(C + B) = 25- 5 = 5 correct answer B #### B QUESTION:An athlete runs 200 metres race in 24 seconds. His speed is : options: A)20 km/hr B)24 km/hr C)28.5 km/hr D)30 km/hr E)None of these SOLUTION:Speed = 200/24 m/sec=25/3 m/sec=(25/3*18/5)km/hr=30 km/hr. Correct Option: D #### D QUESTION:On increasing the price of T.V. sets by 60%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? options: A)4 B)5 C)56 D)28 E)7 SOLUTION:Explanation: Let the price be = Rs.100, and number of units sold = 100 Then, sale value = Rs.(100 × 100) = Rs.10000 New sale value = Rs.(160 × 80) = Rs.12800 Increase% = 2800/10000 × 100 = 28% Answer: D #### D QUESTION:A man can row his boat with the stream at 19 km/h and against the stream in 11 km/h. The man's rate is? options: A)4 kmph B)2 kmph C)7 kmph D)8 kmph E)3 kmph SOLUTION:DS = 19 US = 11 S = ? S = (19 - 11)/2 = 4 kmph Answer:A #### A QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length. options: A)12sec B)20sec C)15sec D)18sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec Answer : E #### E QUESTION:Two numbers when divided by a divisor leave remainders of 238 and 362 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor. options: A)276 B)552 C)414 D)1104 E)2202 SOLUTION:Let x be the divisor. N1 = xa + 238 N2 = xb + 362 N1 + N2 = x(a+b) + 600 = xc + 68 x(c-a-b) = 532 but we know that x>362, thus (c-a-b) must equal 1. The answer is B. #### B QUESTION:What is the rate percent when the simple interest on Rs.1000 amount to Rs.400 in 4 Years? options: A)5% B)6% C)2% D)95% E)10% SOLUTION:Interest for 4yrs = 400 Interest for 1yr = 100 Interest rate = 100/1000 x 100 = 10% Answer : E #### E QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform? options: A)338 B)240 C)287 D)400 E)191 SOLUTION:Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m. Answer: D #### D QUESTION:A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)30 B)60 C)75 D)90 E)105 SOLUTION:Answer : A Let number of notes of each denomination be x. Then, x + 5x + 10x = 160 16x = 160 x = 10. Hence, total number of notes = 3x = 30. #### A QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by: I. 12 II. 24 III. 48 options: A)I B)I & III C)II D)II & III E)III SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24. So answer is III Answer : E #### E QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:If x is a positive integer, which of the following must be odd? options: A)x+1 B)x^2+x C)x^2+x+7 D)x^2−1 E)3x^2−3 SOLUTION:A. X+1 = can be odd or even. Since O + O =E or E + O = O B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD] C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 7 = ODD Hence C. #### C QUESTION:Pipes A and B can fill a cistern in 10 and 90 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full? options: A)13 B)12 C)16 D)18 E)19 SOLUTION:: 1/10 + 1/90 = 1/9 9 * 2 = 18.Answer:D #### D QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(4*90+x)/5=92 x=(5*92)-(4*90) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 13 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ? options: A)38 B)39 C)40 D)41 E)42 SOLUTION:Soln:- 13x=45 --> 87/77*x=45 --> x=45*77/87=677/17=~40. Answer: C. #### C QUESTION:A start walking from a place at a uniform speed of 5 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B. options: A)4.7 kmph B)5.6 kmph C)4 kmph D)7 kmph E)5.3 kmph SOLUTION:Distance covered by A in 30 min = 1 Km B covers extra 1km in 1 hour 48 minutes (9/5 hr) i.e. Relative speed of B over A = 1/(9/5) = 5/9 So the speed of B = Speed of A + 5/9 = 5 + 5/9 = 5.55 Answer B #### B QUESTION:The ratio between the present ages of P and Q is 5:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)3:4 B)B)8:9 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 5x and 7x years respectively. Then, 7x - 5x = 4 => x = 2 Required ratio = (6x + 4) : (7x + 4) 16 : 18= 8:9 ANSWER:B #### B QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get? options: A)40% B)45% C)57% D)58% E)60% SOLUTION:tot no of votes = (1136+7636+11628) = 20400 req = > (11628/20400 * 100) = > 57% ANSWER C #### C QUESTION:What should come in place of the question mark (?) in the following equation? 45789+ 34567 = 610+ ? options: A)96543 B)13678 C)23456 D)56789 E)79746 SOLUTION:45789+ 34567 = 610+ ? 45789+ 34567 – 610 = 79746 Answer E #### E QUESTION:The sale price sarees listed for Rs.390 after successive discount is 15% and 25% is? options: A)298 B)237 C)248 D)876 E)291 SOLUTION:390*(85/100)*(75/100) = 248 Answer: C #### C QUESTION:In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 39 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake? options: A)36 B)2^4*3 C)24 D)38 E)47 SOLUTION:Working backward from the day it's covered: day 39: fully covered day 38: half covered So 38 days ANSWER:D #### D QUESTION:By walking at 3/4th of his usual speed, a man reaches office 16 minutes later than usual. What is his usual time? options: A)48min B)50min C)65min D)60min E)70min SOLUTION:let T be the usual time. time spent=4T/3 therefore, 4T/3=T+16 4T=3T+48...therefor T=48min ANSWER:A #### A QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age? options: A)22 B)15 C)77 D)21 E)182 SOLUTION:Present age is 4x and 3x, => 4x + 6 = 34 => x = 7 So Deepak age is = 3(7) = 21 Answer: D #### D QUESTION:What number should replace the question mark? 105, 87, 70, 52, ? options: A)49 B)35 C)70 D)55 E)83 SOLUTION:B 35 The sequence progresses -18, -17, -18, -17. #### B QUESTION:If x and y are integers, what is the least positive number of 24x+9y? options: A)1 B)3 C)4 D)6 E)9 SOLUTION:24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1. 8(-1) + 3(3) = 1 Then 3(8x+3y) can have a minimum positive value of 3. The answer is B. #### B QUESTION:The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers? options: A)12/35 B)1/35 C)35/8 D)7/32 E)7/33 SOLUTION:Let the numbers be a and b. Then, a + b = 12 and ab = 35. (a + b)/ab = 12/35 = (1/b + 1/a) = 12/35 Sum of reciprocals of given numbers = 12/35. ANSWER:A #### A QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 70, the three numbers in order are? options: A)60, 120, and 30 B)60, 30, and 120 C)30, 60, and 120 D)30, 120, and 60 E)120, 30, and 60 SOLUTION:Let the numbers be 2x, x and 4x (2x + x + 4x)/3 = 70 7x/3 = 70 x = 30 The numbers in order are 60, 30, and 120 The answer is B. #### B QUESTION:A furniture manufacturer has two machines, but only one can be used at a time. Machine W is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine W can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? options: A)14 B)13 C)11 D)9 E)7 SOLUTION:'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days. To finish a work Machine W say you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D #### D QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D <<<Examples ends QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)35.2 B)36.1 C)36.5 D)39.1 E)None SOLUTION:Sol. Therefore correct sum = ( 36 × 50 + 48 – 23) = 1825. Therefore correct mean = 1825 / 50 = 36.5. Answer C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail? options: A)3/4 B)1/4 C)3/8 D)1/2 E)1/8 SOLUTION:Let, H --> Head , T --> Tail Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting 3 heads Then E = {HHH,HTH,THH,HHT} P(E) = n(E)/n(S) =4/8 = 1/2 Answer is D #### D QUESTION:A seven-digit phone number is divisible by 5. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code? options: A)05. B)06. C)03. D)04. E)02. SOLUTION:Given that 7 digit number is divisible by 5 we know any number will not be divisible by 5 if the sum of all digits of the number is not the multiple of5. Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 5... hence answer is A #### A QUESTION:What positive number, when squared, is equal to the cube of the positive square root of 17? options: A)64 B)32 C)8 D)4 E)2 SOLUTION:Let the positive number be x x^2 = ((17)^(1/2))^3 =>x^2 = 4^3 = 64 => x = 8 Answer C #### C QUESTION:In a school the number of girls is 30% the number of boys. Find the number of boys as a percentage of girls? options: A)112% B)12% C)333% D)150% E)16% SOLUTION:It is given that in a school the number of girls is 30% the number of boys. If boys=10 girls=3 We are asked for the number of boys as a percentage of girls b/g=10/3=10 1/3=3.333=333% Answer is C #### C QUESTION:What is the sum of odd integers from 35 to 55, inclusive? options: A)495 B)1,500 C)1,240 D)1,120 E)1,100 SOLUTION:Number of odd integers = (55-35)/2 + 1 = 20/2 + 1 = 11 Sum of odd integers = (35+55)/2 * 11 = 495 Answer A #### A QUESTION:The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 guards will be available to patrol the fairgrounds on the following Saturday night? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:For any given day, only the guards patrolling on the previous day won't be available. So, 3 guards who patrolled on Friday won't be available. We are thus left with 4 guards. To choose 3 out of 4, we will have 4C3 = 4 different groups. The answer is B. #### B QUESTION:If 4 men and 1 boy working together, can do two times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:4M + 1B =2(1M + 1B) 4M + 1B = 2M + 2B 2M = 1B The required ratio of work done by a man and a boy = 1:2 D #### D QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300 B)320 C)350 D)345 E)568 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 39 = 50/3 3(x + 300) = 1950 è x = 350 Answer: Option C #### C QUESTION:Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 3.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn? options: A)1/3 B)1/30 C)1/42 D)2 E)30 SOLUTION:Pete covered 3.5*60=210 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/210=1/42. Answer: C. #### C QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? options: A)240 B)65 C)110 D)130 E)200 SOLUTION:Adult + Children = 200 Let, Children = y then, Adult = y+20 i.e. y+(y+20) = 200 i.e. y = 900 i.e. Adult = 90+20 = 110 Adults include only Men and Women i.e. Men + Women = 110 Let women, W = x then Men, M = x+20 i.e. x+(x+20) = 2x+20 = 110 i.e. x = 45 i.e. Men, M = 45+20 = 65 Answer: Option B #### B QUESTION:In a simultaneous throw of pair of dice .find the probability of getting the total more than 7? options: A)12/5 B)5/12 C)6/4 D)2/3 E)4/7 SOLUTION:Here n(S)=(6*6)=36 let E=event of getting a total more than 7 ={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)} P(E)=n(E)/n(S)=15/36=5/12 Option B #### B QUESTION:(3 x 10^2) + (2 x 10) + 4 = options: A)302400 B)32400 C)30240 D)3240 E)324 SOLUTION:When you multiply a number by 10 you just add a zero => 3 x 10^2 => add 2 zeros => 3 x 10^2 = 300 =>2 x 10 = 20 => 4 = 4 =>3 x 10^2 + 2 x 10 + 4 = 300 + 20 + 4 = 324 => answer is E ( 324) #### E QUESTION:There are 8 people and 5 chairs. In how many different ways people can occupy the chairs? options: A)1640 B)1650 C)1660 D)1670 E)1680 SOLUTION:number of ways = 8*7*6*5 = 1680 Answer is E #### E QUESTION:A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1? options: A)A-20. B)A-12. C)A-9. D)A-10. E)A-13. SOLUTION:We could use the following logic: since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n). The condition here should now be 11K + 1 = <operation> such that it gives us an integer 11k +1 = A -20 => A = 11K + 21 Not divisible by 11 11K +1 = A -12 => A = 11K + 31 Not Divisible by 11 11K +1 = A -9 => A = 11K + 10 Not Divisible by 11 11K +1 = A -10 => A = 11K + 11Divisible by 11 11K +1 = A -13 => A = 11K + 14 Not Divisible by 11 Answer therefore is A -10 (D) #### D QUESTION:The following sets each have a mean of 8 and the standard deviations are given in variable form. Set I = {8, 8, 8, 8, 8, 8}, standard deviation = A Set II = {2, 2, 2, 14, 14, 14}, standard deviation = B Set III = {5, 6, 7, 9, 10, 11}, standard deviation = C Rank these three standard deviations from least to greatest. options: A)A, B, C B)B, C, A C)C, A, B D)C, B, A E)A, C, B SOLUTION:The answer should be E as the mean is least deviated in Set I followed by Set III and then Set II. #### E QUESTION:A rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 4 inches B)b) 6 inches C)c) 5 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 35=5*7 45=3*3*5 GCF = 5 P.S you can make squares with side of 5 Answer : C #### C QUESTION:The population of a town is 10000. It increases annually at the rate of 25% p.a. What will be its population after 2 years? options: A)14000 B)14400 C)14500 D)15625 E)14700 SOLUTION:Formula : 10000 × 125/100 × 125/100 = 15625 Answer : D #### D QUESTION:When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters? options: A)10/9 n B)4/3 n C)9/2 n D)9/4 n E)7/3n SOLUTION:C is the answer. To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra. Given - tank was already 1/3 full. - When n ltr added, it became 5/9 So 1/3 + n = 5/9 n = 5/9 - 3/9 n = 2/9 capacity of the tank is full fraction . i.e. 1 i.e. 9/9 so the question is 9/9 is how much times n = 9/9 = 1 = xn so x = 9/2 and total = 9/2n #### C QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%? options: A)20% B)28% C)29% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 86 2/3 SP1 = 86 SP1 = 129 100 --- 29 => 29% Answer:C #### C QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)16 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 324/3 = 108 sq m l b = 108 i.e., l * l/3 = 108 l2 = 324 => l = 18. Answer:C #### C QUESTION:Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)876 m B)157 m C)235 m D)156 m E)167 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: C #### C QUESTION:The G.C.D. of 1.08, 0.33 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.33 and 0.90. H.C.F. of 108, 33 and 90 is 3, H.C.F. of given numbers = 0.03. Answer A #### A QUESTION:If the speed of a man is 54 km per hour, then what is the distance traveled by him in 25 seconds ? options: A)275m B)360m C)375m D)420 m E)440 m SOLUTION:The distance traveled in 25 sec = 54*(5/18) *25 =375m ANSWER:C #### C QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green? options: A)23/35 B)23/38 C)23/18 D)53/18 E)23/22 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂ = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7 = 46/70 = 23/35 Answer:A #### A QUESTION:If 125(5^y) = 1 then y= options: A)–2 B)–1 C)0 D)1 E)-3 SOLUTION:5^x = 1/125 5^x = 1/5^3 5^x= 5^-3 x = -3 E #### E QUESTION:Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)3 hours B)6 hours C)4 hours D)8 hours E)10 hours SOLUTION:Number of pages typed by Ronald in one hour = 32/6 = 16/3 Number of pages typed by Elan in one hour = 40/5 = 8 Number of pages typed by both in one hour = ((16/3) + 8) = 40/3 Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours. ANSWER:D #### D QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 4 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank? options: A)1.6 B)1 C)0.4 D)0.16 E)0.016 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi*16*10 = pi*h*100*100 (h is distance that the oil level dropped) h = 160/10,000 = 16/1000 = 0.016 ft The answer is E. #### E QUESTION:A single letter is selected at random from the word 'SIMS'. The probability that it is a vowel is..?? options: A)1/4 B)3/11 C)4/11 D)3/7 E)1/2 SOLUTION:total vowels = 1, total number of letters = 4 so probability = 1/4 ANSWER:A #### A QUESTION:The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is? options: A)Rs. 2000 B)Rs. 3000 C)Rs. 4000 D)Rs. 4500 E)Rs. 5000 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) M + O = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv) Subtracting (ii) from (iv), we get M = 4000. M's monthly income = Rs. 4000 C #### C QUESTION:In how many different number of ways 9 men and 2 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)170 C)C)190 D)D)210 E)E)1663200 SOLUTION:11p7 = 11 x 10 x 9 x 8 x 7 × 6 × 5 = 1663200 Option 'E' #### E QUESTION:((-1.9)(0.6) – (2.6)(1.2))/2.0 = ? options: A)-0.71 B)1.0 C)1.07 D)1.71 E)-2.13 SOLUTION:Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option. -2.13 Answer E #### E QUESTION:3889 + 13.952 - ? = 3854.002 options: A)48.95 B)49.75 C)45.97 D)47.59 E)45.79 SOLUTION:Let 3889 + 13.952 - x = 3854.002. Then x = (3889 + 13.952) - 3854.002 = 3902.952 - 3854.002 = 48.95. Answer is A #### A QUESTION:It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? options: A)8:50 a.m B)5:50 a.m C)7:50 a.m D)6:50 a.m E)7:00 a.m SOLUTION:The time it takes Kannan to get to work: time to walk to car park + time to drive 10 + 110 = 120 minutes = 2 hours Kannan needs to get out of the house 2 hours before 9:00 am at 9:00 - 2:00 = 7:00 a.m correct answer E #### E QUESTION:Sonika bought a V.C.R. at the list price of 18,700. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R. options: A)20,196 B)19,780 C)19,680 D)19,380 E)None of these SOLUTION:Sol. List price of V.C.R. =18,700 Rate of sales tax = 8% ∴ Sales tax = 8% of 18,700 = 8⁄100 × 18700 = 1496 So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,700 + 1496 = 20,196. Answer A #### A QUESTION:Two pipe A and B fill a tank in 6 hours and 8 hours respectively.and C empty that tank in 12 hour.if all three pipe open together in empty tank then how much time it take to fill the tank? options: A)19/3 B)23/2 C)24/5 D)18 E)16 SOLUTION:all three pipe resultant fill tank in 1 hour=[1/6+1/8-1/12]=5/24 total time taken to fill tank=24/5 hour answer C #### C QUESTION:If 0 < n < 1, what is the median of the values n, n^-1, n^2, n^1/2 and n^3? options: A)n B)n^-1 C)n^2 D)n^1/2 E)n^3 SOLUTION:A. To make the problem less confusing, I picked a number between 0 and 1 such as n = 1/4 and calculate: n = 1/4 n^-1 = 4 n^2 = 1/16 n^(1/2) = 1/2 n^3 = 1/8. From this, rearrange the number and the median is 1/4, which is n. Answer A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 7 sec. What is the length of the train? options: A)112.21 B)27.21 C)117.66 D)277 E)116.66 SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 7 = 116.66 Answer: E #### E QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 10800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)60000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 10800 ( 18 × 600 = 10800) 100% -------> 60000 votes (100 × 600 = 60000) C #### C QUESTION:12.5 * 6.2 * 8.8 = ? options: A)352 B)435 C)224 D)682 E)742 SOLUTION:D 682 ? = 12.5 * 6.2 * 8.8 = 682 #### D QUESTION:Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are: options: A)39,30 B)41,32 C)42,33 D)43,34 E)35,36 SOLUTION:Let their marks be (x + 9) and x. then x+9 = 56/100(x+9+x) 3x=99 x=33 their marks 42 and 33 ANSWER C #### C QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3×7/36 = 7/12 Remaining work = 1 – 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5 Option A #### A QUESTION:If x=-2, which of the following is(are) true? I. x^2=-|x| II |x|=-x III x/-3 = -2/3 options: A)II only B)I only C)III only D)I,II only E)II, III only SOLUTION:I. x^2=-|x| -2^2 = - |-2| Not true II |x|=-x |-2| =-( -2 ) true III x/-3 = -2/3 Not true Answer : A #### A QUESTION:A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2? options: A)1/4 B)2/4 C)1/2 D)1/3 E)2/3 SOLUTION:Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by (number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3 correct answer D #### D QUESTION:A and B together can do a work in 6 days. If A alone can do it in 10 days. In how many days can B alone do it? options: A)10 B)15 C)77 D)55 E)21 SOLUTION:1/6 – 1/10 = 1/15 => 15 Answer: B #### B QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 *12=45,000*8 1:1 Madhu's share=1/2*60,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by : options: A)7 only B)13 only C)11 only D)1001 only E)1003 only SOLUTION:256256 = 256 x 1001; 678678 = 678 x 1001, etc. So, any number of this form is divisible by 1001 ANSWER:D #### D QUESTION:If 0.6 : x :: 5 : 8, then x is equal to: options: A)A)0.96 B)B)1.2 C)C)1.25 D)D)1.3 E)E)0.8 SOLUTION:(x * 5) = (0.6 * 8) x = 4.8/5 x = 0.96 Answer = A #### A QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? options: A)32 Yrs B)36 Yrs C)40 Yrs D)48 Yrs E)None SOLUTION:Explanation: Let the mother's present age be x years. Then, the person's present age = (2/5)*x years. ((2/5)*x)+8 = (1/2)(x+8) 2(2x + 40) = 5(x + 8) x = 40. Answer: C #### C QUESTION:If 22 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect? options: A)125 B)187 C)231 D)375 E)460 SOLUTION:If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line. The number of ways to select 2 lines from 22 lines is 22C2 = 231 The answer is C. #### C QUESTION:A high school has 400 students 1/2 attend the arithmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 3/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs. options: A)35 B)45 C)55 D)60 E)50 SOLUTION:A-Club has 200 members (1/2 of 400) B-Club has 250 members (5/8 of 400) C-Club has 300 members (3/4 of 400) We can create an equation to solve this: 200+250+150 = n + x + 2y where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs. The question provides y for us (150). 750 = 400 + x + 300 x = 50 E #### E QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence? options: A)−164 B)0 C)16 D)32 E)64 SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term) sum of 64 terms = 32 ANSWER:D #### D QUESTION:If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p? options: A)p B)2p C)5p D)7p E)p^2 SOLUTION:Y=30p other number is 5p then GCF(30p,5P)=5P; C is the correct answer #### C QUESTION:If Hema walks at 12 km/hr instead of 8 km/hr, she would have walked 20 km more. The actual distance travelled by Hema is ? options: A)40 kms B)30 kms C)46 kms D)32 kms E)36 kms SOLUTION:Explanation: Let the actual distance travelled be x km. Then x/8=(x+20)/12 => 12x = 8x + 160 => 4x = 160 => x = 40 km. ANSWER IS A #### A QUESTION:How many factors of 60 are odd numbers greater than 1? options: A)3 B)4 C)5 D)3 E)7 SOLUTION:prime factors of 60 are 2^2,3^1,5^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,) = (1+1)(1+1)=4 since we need odd divisors other than 1 =>4-1 = 3 odd divisors D is the answer #### D QUESTION:we have 7 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg one of 15 kg one of 20 kg by using only five weight how many weight u can weight options: A)19 B)18 C)24 D)21 E)32 SOLUTION:select 5 weight out of 7, 7C5=21 ANSWER:D #### D QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)56 B)28 C)45 D)24 E)45 SOLUTION:D 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### D QUESTION:50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be: options: A)20 cm B)25 cm C)35 cm D)50 cm E)None of these SOLUTION:Explanation: Total volume of water displaced =(4 x 50) m3 = 200 m3 Rise in water level = 200/40×20= 0.25m = 25cm Answer: B #### B QUESTION:If r is a positive integer and r^2 is divisible by 12, then the largest positive integer that must divide r ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since r is an integer so r cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making r^2 as a multiple of 12)) r^2 is divisible by 12 (12 = 2*2*3), So, r should have at least one 2 and one 3 so that r^2 has a 2^2 and two 3 So, r will have a 2 and a 3. Or r will be a multiple of 6 So, largest possible integer than should divide r^3 is 6^3 So, Answer will be D #### D QUESTION:A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred. options: A)Rs. 5750 B)Rs. 6000 C)Rs. 5500 D)Rs. 5000 E)Rs. 7000 SOLUTION:The price varies as the square of the weight, P = K x W2 12250 = K x 352 K = 10 Thus, P = 10W2 When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively. Their values should be : 10g piece: 10 x 102 = Rs. 1000; 25g piece: 10 x 252 = Rs. 6250. Total value of stone now, = 1000 + 6250 = Rs. 7250 Loss incurred = 12250 - 7250 = Rs. 5000 ANSWER:D #### D QUESTION:In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? options: A)1/48 B)11/16 C)11/12 D)5/16 E)23/48 SOLUTION:First lets get the overview Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2) Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6) Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4) So now as above we have three events A,BC. 1st method(This is lengthy method) Possible cases in which it's a win( the highlighted green event is a win and red is loose. 1.ABC= 1/2*5/6*3/4 OR 2.ABC= 1/2*1/6*3/4 OR 3.ABC= 1/2*5/6*1/4 OR 4.ABC= 1/2*1/6*3/4 OR 5.ABC= 1/2*5/6*1/4 OR 6.ABC= 1/2*5/6*1/4 OR 7.ABC= 1/2*1/6*1/4 As we now OR means add Adding up all of them we'll get the probability of winning ie 11/16 Answer : B #### B QUESTION:A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation? options: A)20 B)30 C)37 D)40 E)39 SOLUTION:There are three ladies and five gentlemen and a committee of 5 members to be formed. Number of ways such that two ladies are always included in the committee = ⁶C₃ = (6 * 5 * 4)/6 = 20. Answer:A #### A QUESTION:Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)1 years B)7 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 36 years. Father's age when Ayesha's brother was born = (38 + 4) = 42 years. Required difference = (42 - 36) = 6 years. Answer: C #### C QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 * 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left? options: A)8/15 B)7/15 C)6/15 D)5/15 E)4/15 SOLUTION:Amount of work P can do in 1 day = 1/15 Amount of work Q can do in 1 day = 1/20 Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15 Fraction of work left = 1 – 7/15= 8/15 Answer is A. #### A QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12*100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? options: A)A)452000 B)B)200000 C)C)800000 D)D)500000 E)E)652000 SOLUTION:3 children got = 3*15% = 45% wife got = 30% orphan house = 5% total = 45+30+5 = 80% remaining = 100-80 = 20% 20% = 40000 100% = 40000*100/20 = $200000 Answer is B #### B QUESTION:On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every six minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period? options: A)25% B)50% C)75% D)100% E)150% SOLUTION:Dolphin once in 3 min; Beluga once in 6 min; So, dolphin comes up 2 times frequently than beluga, which is 150% (6-3)/2*100. Answer: E. #### E QUESTION:A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? options: A)3.6 sec B)18 sec C)36 sec D)72 sec E)None of these SOLUTION:Speed of train relative to jogger = (45 – 9) km/h = 36 km/h = (36 × 5⁄18) m/sec = 10 m/sec Distance to be covered = (240 + 120) m = 360 m. ∴ Time taken = (360⁄10) sec = 36 sec. Answer C #### C QUESTION:What is the value of √36% ? options: A)10% B)20% C)30% D)60% E)40% SOLUTION:Explanation: br>√16% =√36/√100 =6/10 =60/100=60% correct answer is D)60% #### D QUESTION:If a = 105 and a^3= 21 * 35 * 45 * b, what is the value of b? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so, (105)^3 = 3 * 7 * 7 * 5 * 3 *3 *5 *b Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 *b Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2 b = 5*7 = 35 Correct answer A. #### A QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest? options: A)57% B)60% C)58% D)50% E)20% SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years => C.I - S.I => 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100 => 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5 => 16r/100 + 8r2/(100)2 = 20r/100 => 4r/10 = 8r2/(100)2 => 8[r/100]2 - 4r/100 = 0 => r/100 {8r/100 -4} = 0 => r = 0% of 50% Since r!= 0%, r =50% Answer:D #### D QUESTION:What is the greatest positive integer x such that 5^x is a factor of 125^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:125^10 = (5^3)^10 = 5^30 ANSWER:E #### E QUESTION:What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years? options: A)228777 B)26788 C)26088 D)28800 E)67881 SOLUTION:Simple interest = (18000 * 4 * 15)/100 = Rs. 10800 Amount = P + I = 18000 + 10800 = Rs. 28800 Answer: D #### D QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.988] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ? options: A)0 B)1 C)27 D)54 E)Cannot be determined SOLUTION:It cannot be determined.As we do not know the actual value of K. however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer K=[lCM of 80 and 45] * (any integer) for value of k(60) * any integer unit value will be always zero . A #### A QUESTION:Josh spends a total of $5.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following? options: A)99 B)100 C)101 D)109 E)140 SOLUTION:Let x be the number of single bubblegums and y be the number of bubblegum pack. then 5x+50y=550 or x+10y=110 or x=110-10y Now, let y=0, then x= 110 and N=x+y or N=0+110 =110. let y=1, then x=100 and N=100+1= 101 (given in the options) let y=2, then x= 90 and N=92 the value will further decrease and hence we do not need to calculate anymore values. ANSWER:- C #### C QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l * l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:If the number 653ab is divisible by 90, then (a + b) = ? options: A)2 B)3 C)4 D)6 E)8 SOLUTION:90 = 10 x 9 Clearly, 653ab is divisible by 10, so b = 0 Now, 653a0 is divisible by 9. So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4. Hence, (a + b) = (4 + 0) = 4. ANSWER:C #### C QUESTION:For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is options: A)Rs. 8000 B)Rs. 9000 C)Rs. 9900 D)Rs. 98900 E)Rs. 10000 SOLUTION:Sol. Income in first year = * x 42000 = Rs. 24000 Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000) = 66000 - S6000 = Rs. 10000 E #### E QUESTION:hree 6 faced dice are thrown together. The probability that all the three show the same number on them is ? options: A)1/39 B)1/36 C)1/32 D)1/287 E)1/29 SOLUTION:It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways. Hence the probability is 6/216 = 1/36 Answer: B #### B QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph. SOLUTION:DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A #### A QUESTION:Two goods trains each 375 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)40 B)45 C)48 D)51 E)36 SOLUTION:Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 375 + 375 = 750 m. Required time = 750 * 6/125 = 36 sec. Answer: Option E #### E QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:Conversation between two mathematicians: First: I have three children. The product of their ages is 36. If you sum their ages, it is exactly same as my neighbor's door number on my left. The second mathematician verifies the door number and says that it is not sufficient. Then the first says "Ok one more clue is that my youngest is really the youngest". Immediately the second mathematician answers. Can you answer the question asked by the first mathematician? What are the children ages? options: A)6,6, 1 B)6,6, 2 C)6,5, 1 D)6,5, 2 E)6,6, 3 SOLUTION:Possible options for same sum of ages ( 13 here)with product of ages as 36 are 2,2,9 and 6,6,1 but in case of 2,2,9 youngest is not really youngest as two children of age 2 years are twins. whereas in case of 6,6,1 youngest is really youngest. so 6,6, 1 is correct. ANSWER:A #### A QUESTION:Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 41 films, and broke even on none of them, how many of their films were profitable? options: A)18 B)19 C)20 D)21 E)40 SOLUTION:After fiddling some more, this is how I got to answer choice E...but did I get here using voodoo math or is it sound? (.60*.75) + (.40*.25) = .44 + .10 = .55 55/100 = 11/20 Then subtract from 41: 41 - 11/20 = 40 (answer E) #### E QUESTION:A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing? options: A)191 B)400 C)737 D)840 E)1,560 SOLUTION:Let weight of side of beef before processing = x (60/100)*x = 240 => x = (240 * 100)/60 = 400 Answer B #### B QUESTION:if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no. options: A)24 B)25 C)26 D)27 E)28 SOLUTION:25 m^3 = (3+1)(3+1) = 16 then m^4 = (4+1)(4+1)=25 ANSWER:B #### B QUESTION:Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? options: A)5 B)3 C)4 D)6 E)1 SOLUTION:Rate of one machine = 1 job / (20*4) days let X = number of machines needed to complete the job in 10 days 1/(4*20) * 10 * X = 1 job X = 8 8-4= 4 ANSWER: C #### C QUESTION:A grocer has a sale of Rs. 3435, Rs. 3920, Rs. 3855, Rs. 4230 and Rs. 3560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500? options: A)500 B)1000 C)6000 D)7000 E)2000 SOLUTION:Total sale for 5 months = Rs. (3435 + 3920 + 3855 + 4230 + 3560) = Rs. 19000. Required sale = Rs. [ (3500 x 6) - 19000 ] = Rs. (21000 - 19000) = Rs. 2000 Answer: Option E #### E QUESTION:What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x options: A)1 B)2 C)34 D)12 E)13 SOLUTION:46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A #### A QUESTION:Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10? options: A)2140 B)2520 C)2980 D)3260 E)3680 SOLUTION:The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5. The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520 The answer is B. #### B QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)10 B)20 C)21 D)22 E)23 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days ANSWER : OPTION B #### B QUESTION:A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A? options: A)Rs.240 B)Rs.340 C)Rs.260 D)Rs.280 E)Rs.440 SOLUTION:LCM = 180 Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c = (180/15)/(180/15 +180/20 + 180/45) = (12/25) * 500 = Rs.240 ANSWER:A #### A QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent? options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these SOLUTION:Let CP of an book = 100 MP of an book = 120 Discount 30 % on 120 = 36 SP of the book = 120 - 36 = 84 loss = 16% Answer : C #### C QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is options: A)Rs 9600 B)Rs 8500 C)Rs 8450 D)Rs 8400 E)None of these SOLUTION:Explanation: Ratio of their shares = 22500 : 35000 =9 : 14 Deepak's share = Rs.(13800×14/23) = Rs. 8400 Option D #### D QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio E of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture. Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water. Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1. Shortcut. We are essentially replacing water in the mixture with pure milk. Let W_o be the amount of water in the mixture originally = 8 litres. Let W_r be the amount of water in the mixture after the replacements have taken place. Then,{W_r}/{W_o}= (1-R/M)^n where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated. Hence, {W_r}/{W_o} =(1/2)^2  =1/4 Therefore E,W_r ={W_o}/4= 8/4 = 2 litres.B #### B QUESTION:John throws a coin until a series of four consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fifth throw? options: A)1/16 B)2/16 C)3/16 D)7/16 E)9/16 SOLUTION:Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are H-T-T-T-T ----> P = (1/2)^5 = 1/32 T-H-H-H-H ----> P = (1/2)^5 = 1/32 Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability. 1/32 + 1/32 = 2/32 = 1/16 Answer(A). #### A QUESTION:Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg. How much amount did he pay to the shopkeeper? options: A)A)1040 B)B)1045 C)C)1055 D)D)1190 E)E)1075 SOLUTION:Cost of 8 kg apples= 70 × 8 = 560. Cost of 9 kg of mangoes = 70 × 9 = 630. Total cost he has to pay = 560 + 630 = 1190. D) #### D QUESTION:On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is? options: A)22 B)99 C)27 D)11 E)37 SOLUTION:Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30. S.I for one year = Rs. 330. S.I. on Rs. 330 for 1 year = Rs. 36.30 Rate = (100 * 36.30)/(330 * 1) = 11%.Answer: D #### D QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.157. Find the unknown rate of two blankets? options: A)420 B)550 C)490 D)450 E)520 SOLUTION:10 * 157 = 1570 3 * 100 + 5 * 150 = 1050 1570 – 1050 = 520 Answer:E #### E QUESTION:A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck? options: A)2:1 B)3:4 C)4:3 D)1:4 E)5:6 SOLUTION:Given; 4 duck = 3 hen; Or, duck/hen = 3/4; Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter. Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''Answer: 2:1; #### A QUESTION:A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)120 m B)225 m C)300 m D)360 m E)280 m SOLUTION:Speed = 54 x 5/18 m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/35 = 15 x + 300 = 525 x = 225 m.Answer: Option B #### B QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:6 B)7:3 C)7:4 D)7:2 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer: B #### B QUESTION:Find compound interest on Rs. 7500 at 4% per year for 2 years, compounded annually. options: A)812 B)712 C)412 D)512 E)612 SOLUTION:Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112. therefore, Compound Interest = Rs. (8112 - 7500) = Rs. 612. Answer is E. #### E QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(4*90+x)/5=92 x=(5*92)-(4*90) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? options: A)5/5 B)5/9 C)3/4 D)5/7 E)5/2 SOLUTION:In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27 The probability = 27/36 = 3/4. Answer: C #### C QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)13.9 sec B)12.1 sec C)17.9 sec D)61.9 sec E)47.98 sec SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec. Answer:B #### B QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in? options: A)15 hours B)12 hours C)76 hours D)16 hours E)81 hours SOLUTION:The part of the tank filled by three pipes in one hour = 1/8 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12. The tank can be filled in 12 hours. Answer: B #### B QUESTION:If n is a positive integer, what is the remainder when (6^(4n+3))(6^n) is divided by 10? options: A)7 B)2 C)4 D)6 E)8 SOLUTION:This one took me bout 3 1/2 min. Just testin numbers and what not. First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p. 1-7 stands for ^1 thru 6 1: 7*1=7 2: 7*7=9 3: 7*9=3 4: 7*3=1 5: 7*1=7 6: 7*7=9 7: 7*9=3 Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems. so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8 Now from here if id double check just to make sure. 7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit). Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern) so again 3*6=18/10 ---> R =7. A or J in this problem. #### A QUESTION:In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way? options: A)3 sec B)4 sec C)8 sec D)6 sec E)7 sec SOLUTION:T = 52/24 * 18/5 = 8 sec ANSWER:C #### C QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced? options: A)70% B)15% C)20% D)25% E)30% SOLUTION:price of a coat in a certain store = $500 the price of the coat is to be reduced by $350 % change = (Final Value - Initial Value)*100 / Initial Value % Reduction= (Reduction in Price)*100 / Initial Value i.e. % Reduction= (350)*100 / 500 = 70% Answer: Option A #### A QUESTION:35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days? options: A)87 B)18 C)42 D)16 E)10 SOLUTION:Binders Books Days 35 1400 21 x 1600 20 x/35 = (1600/1400) * (21/20) => x = 42 Answer:C #### C QUESTION:Two numbers are in the ratio of 7:6. If 18 be subtracted from each, they are in the ratio of 6:5. Find the numbers? options: A)5,9 B)7,9 C)4,7 D)7,6 E)6,9 SOLUTION:(7x-18):(6x-18) = 6:5 x = 1 => 7,6 Answer: D #### D QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2 SOLUTION:42/360 * 22/7 * 12 * 12 = 52.8 m2 Answer: C #### C QUESTION:One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in: options: A)180 min B)160 min C)280 min D)18 min E)190 min SOLUTION:Let the slower pipe alone can fill the tank in x minutes Then the faster pipe can fill the tank in x/4 minutes Part filled by the slower pipe in 1 minute = 1/x Part filled by the faster pipe in 1 minute = 4/x Part filled by both the pipes in 1 minute = (1/x)+(4/x) Answer is A It is given that both the pipes together can fill the tank in 36 minutes ⇒ Part filled by both the pipes in 1 minute = 1/36 (1/x)+(4/x)=1/36 5/x=1/36 x=5×36=180 i.e.,the slower pipe alone fill the tank in 180 minutes #### A QUESTION:A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? options: A)299m B)287m C)279m D)100m E)277m SOLUTION:A can give B (5 min - 4 1/2 min) = 30 sec start. The distance covered by B in 5 min = 1000 m. Distance covered in 30 sec = (1000 * 30)/300 = 100 m. A can give B 100m start. Answer:D #### D QUESTION:A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? options: A)7/11 B)6/7 C)1/5 D)2/7 E)None of these SOLUTION:Explanation : Let, the vessel initially contains 8 litres of liquid. Let x litres of this liquid be replaced with water then quantity of water in new mixture =>3−(3x/8)+x litres. Quantity of syrup in new mixture =5−5x/8 litres. Therefore, =>3−(3x/8)+x=5−5x/8. =>5x+24=40−5x. =>x=8/5. So part of the mixture replaced, =>(8/5)×(1/8)=1/5. Answer : C #### C QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:In honor of the year 2013, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive? options: A)18 B)36 C)42 D)52 E)56 SOLUTION:All options other than 'D' are factors of 2013. Hence, 'D' is the answer #### D QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 14 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)13 B)13.5 C)14 D)14.5 E)15 SOLUTION:Ans is E Given d_ab = 2*d_bc let d_ab = d and d_bc = x so d=2x for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time) #### E QUESTION:which of the following could be the greatest common factor of positive integers 10 and 15 ? I) 5 II) 4 III) 2 options: A)II only B)I only C)III only D)I,II only E)I,III only SOLUTION:10=2*5 15=3*5 GCF =5 Answer : B #### B QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2 = 134 m2. answer :E #### E <<<Examples ends QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 10P pots? options: A)M/10 B)6/M C)600M D)M/6 E)10M SOLUTION:The time it takes to wash 10P pots is 10M minutes which is 10M / 60 = M/6 hours. The answer is D. #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there? options: A)24 B)30 C)36 D)42 E)48 SOLUTION:Let the number of pens be 5x and the number of pencils be 6x. 6x - 5x = 5 x = 5 The number of pencils is 30. The answer is B. #### B QUESTION:A train 330 m long passed a pole in 11 sec. How long will it take to pass a platform 760 m long? options: A)76 sec B)89 sec C)87 sec D)35 sec E)36 sec SOLUTION:Speed = 330/11 = 30 m/sec. Required time = (330 + 760)/30 = 36 sec. Answer:E #### E QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? options: A)180m B)180m C)287m D)216m E)865m SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer:B #### B QUESTION:How many numbers from 10 to 1000 are exactly divisible by 9? options: A)100 B)10 C)11 D)12 E)14 SOLUTION:10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100 Answer : A #### A QUESTION:By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)20 kmph B)30 kmph C)87 kmph D)99 kmph E)77 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph. Answer:A #### A QUESTION:Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 70 white marbles. How many red marbles could be in bag A? options: A)1 B)3 C)4 D)6 E)14 SOLUTION:6 is the answer. Bag A- R:W:B = 2:6:9 Let W in bag A be 6K Bab B - R:W = 1:4 Let W in bag B be 4k W = 70 = 6K+4k =>k=7 Total Red's in bag A will be 2K = 14 E #### E QUESTION:90, 180, 12, 50, 100, 80, ?, 3, 20, 4, 25, 2, 6, 30, 3 options: A)100 B)150 C)180 D)90 E)60 SOLUTION:30*3=90 6*30=180 6*2=12 25*2=50 4*25=100 20*4=80 3*20=60 ans is 60 ANSWER:E #### E QUESTION:If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n? options: A)10 B)12 C)15 D)18 E)20 SOLUTION:There are 10 numbers divisible by 2 There are 5 numbers divisible by 4 There are 2 numbers divisible by 8 There is 1 number divisible by 16. Hence the total number of 2’s in 20! are 10+5+2+1=18 ANSWER:D #### D QUESTION:In the number 10,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A? options: A)0 B)5 C)10 D)15 E)25 SOLUTION:You should notice that 55*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*5=15 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25). Answer: E. ! Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/ Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the mainMath forum. D #### D QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)? options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5 SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57) 4.5/(4.5 - 2) = 9/5 (1.8) 3.5/(3.5 - 2) = 7/3 (~2.33) 2.5/(2.5-2) = 5 1.5/(1.5 - 2) = -3 Thus, the answer is D. #### D QUESTION:10 people can write 55 book in 12 days working 8 hour a day.then in how many day 198 can be written by 48 people? options: A)9 B)13 C)21 D)24 E)23 SOLUTION:work per day epr hour per person= 55/(12*8*10) // eq-1 people=48; let suppose day=p; per day work for 8 hours acc. to condition work per day epr hour per person= 198/(p*8*48) // eq-2 eq-1==eq-2; p= 9 ANSWER:A #### A QUESTION:A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ? options: A)1000 B)1100 C)1200 D)1300 E)1400 SOLUTION:let profit rate of b = x acc to question profit rate of a becomes 5/3 x and that of c= 1/3 x which is given as 10% 1/3 x= 10 therefore x=30 now b=30% , a=50% now we will find out c's price- 11/10 * price = 2145 price = 1950 in similar way we will find out b's price as we know that profit is 30% therefore 130/100 * price = 1950 so b 's price =1500 similarly for a ('profit is 50%) 150/100 * price = 1500 on solving it we get a's price = 1000 ANSWER:A #### A QUESTION:A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 6%. What was its profit on the items sold in February? options: A)27.5% B)30% C)35% D)37.5% E)41% SOLUTION:Assume the total price = 100x Price after 20% markup = 120x Price after 25%further markup = 1.25*120x = 150x Price after the discount = 0.94*150x = 141x Hence total profit = 41% Option E #### E QUESTION:In the graph below, no axes or origin is shown. If point B's coordinates are (10,4), which of the following coordinates would most likely be A's? options: A)(17, -2) B)(10, 6) C)(6, 8) D)(-10, 3) E)(-2, -17) SOLUTION:wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10. B rules.. #### B QUESTION:There are different 15 circles. What is the number of the greatest possible points with which the circles intersect? options: A)390 B)100 C)110 D)180 E)210 SOLUTION:Maximum points of intersection between n different circles = n*(n - 1) = 15*14 = 210 Answer: E #### E QUESTION:A,B,C invested the capitals in a business. If A invested Rs. 20,000 more than B and C invested Rs.10,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000 options: A)5500, 2500, 6000 B)5200, 2800, 6000 C)4250, 2250, 7500 D)5250, 1750, 7000 E)5300, 2700, 6000 SOLUTION:A==30,000 B==10,000 C==40,000 so, ration are3:1:4 profit 14000 so,, 14000/8==1750 so,, A==5250, B==1750,, C==7000 ANSWER:D #### D QUESTION:The average of the marks of 30 students in a class is 45. If the marks of each student are doubled, find the new average? options: A)85 B)77 C)33 D)90 E)75 SOLUTION:Sum of the marks for the 30 students = 30 * 45 = 1350. The marks of each student are doubled, the sum also will be doubled. The new sum = 1350 * 2 = 2700. So, the new average = 2700/30 = 90. Answer:D #### D QUESTION:A batsman scored 210 runs which included 3 boundaries and 8 sixes. What % of his total score did he make by running between the wickets options: A)40% B)50% C)65% D)71.4% E)75% SOLUTION:Number of runs made by running = 210 - (3 x 4 + 8 x 6) = 210 - (60) = 150 Now, we need to calculate 60 is what percent of 120. => 150/210 * 100 = 71.4 % D #### D QUESTION:A store reduced the price of all items in the store by 9% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? options: A)80.0 B)80.9 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 9% price becomes = 0.91 *100 = $ 91 after the final reduction of 10% price becomes = 0.9* 91 = $ 81.9 price of all items on second day is 81.9% of price on first day correct answer option E #### E QUESTION:A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 45 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C? options: A)40 B)45 C)50 D)55 E)60 SOLUTION:A- B = 120 Miles B - C = 60 Miles Avg Speed = 45 Miles Time taken for A-B 3t and B-C be t avg speed = (120+60) / Total time 45 = 180/4t t = 60 B-C = 60 mph Answer E #### E QUESTION:Find 60/42*4 options: A)14.7653 B)0.5897 C)3.6974 D)0.3571 E)1.2587 SOLUTION:Answer=60/42*4 =60/168=0.3571 Option D is correct #### D QUESTION:What is the smallest positive integer x such that 108x is the cube of a positive integer? options: A)2 B)4 C)8 D)10 E)7 SOLUTION:Given 108x is a perfect cube so we will take 216 = 6*6*6 108x = 216 x = 216/108 = 2 correct option is A #### A QUESTION:There are two concentric circles with radii 5 and 4. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase? options: A)56 B)156 C)256 D)356 E)456 SOLUTION:The area of a circle is piR^2, where R is the radius. The area of the big circle is 25pi. The area of the small circle is 16pi. The area A1 between the circles is 9pi. When the big circle's radius increases, the new area is 36pi. When the small circle's radius decreases, the new area is 4pi. The area A2 between the circles is 32pi. The ratio of A2/A1 is 32/9 = 3.56 which is an increase of 256%. The answer is C. #### C QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? options: A)Rs:567 B)Rs:518 C)Rs:519 D)Rs:500 E)Rs:520 SOLUTION:P - 340 = (P*4*8)/100 P = 500 Answer:D #### D QUESTION:In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is : options: A)12 B)11 C)10 D)27 E)22 SOLUTION:Explanation: Total employees = \inline \frac{(25-10)\times 20}{10}=30 Hence number of educated employees = 30-20 = 10 Answer: C) 10 #### C QUESTION:How much water must be added to 60 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)10 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 60 litres of milk = (1⁄4 × 60) litres = 15 litres. Answer C #### C QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 48 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)99 SOLUTION:Let the son's present age be x years .Then, (48 - x) = x x= 24. Son's age 5 years back = (24 - 5) = 19 years Answer: D #### D QUESTION:The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area? options: A)197 B)240 C)279 D)268 E)269 SOLUTION:4a = 68 => a = 17 172 – 82 = 152 1/2 * 16 * 30 = 240 Answer:B #### B QUESTION:A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? options: A)1/7 B)2/9 C)1/12 D)4/17 E)2/3 SOLUTION:Total number of balls = 7+2 = 9 n(S) = 9C3 = 9*8*7 / 3*2 = 84 n(E) = 2C2* 7C1 = 7 Probability = 7/84 = 1/12 Answer is C #### C QUESTION:The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle? options: A)300 square meters B)400 square meters C)500 square meters D)600 square meters E)700 square meters SOLUTION:If L and W be the original length and width of the rectangle and its area is given by L ? W After increase the length becomes 2 L and the width becomes 3 W. The area is then given by (2 L) ? (3 W) and is known. Hence (2 L) ? (3 W) = 1800 Solve the above equation to find L ? W 6 L ? W = 1800 L ? W = 1800 / 6 = 300 square meters , area of original rectangle correct answer A #### A QUESTION:Sum of Rs.4000 is given out in 2 pieces, one at 8% S.I. and the other at 10% S.I. If the annual interest is Rs 352, the sum is given at 8% is options: A)2000 B)2200 C)2300 D)2400 E)None of these SOLUTION:Explanation : i) Given the total sum = Rs. 4000 If the sum given at 8% be Rs.a ie) P = a , n=1, R = 8% (aX18/100) = (8a/100) If the addition given at 10% be Rs. 4000 – a P = 4000-a , n=1, R = 10% (4000 – aX1X10)/(100) = (40000-10a)/100 Given Annual interest is Rs. 352 (8a/100) + (40000-10a)/100 = 352 8a – 10a = 35200 – 40000 -2a = -4800 X = (4800/2)= Rs.2400/- Answer : D #### D QUESTION:HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 10% options: A)36 B)40 C)32 D)42 E)45 SOLUTION:Let the weight of tea(25 per kg) to be used - X The total cost of the blend - total cost of 25 RS tea + total cost of 30 RS tea - 25X + 900 ( as the total weight of 30 RS tea is already given i.e 30) total weight of the blend = X + 30 ( which should be sold per 30 RS and result in 10% profit) The equation follows like this 25X + 900 + (10 % of (25X + 900)) = 30( X + 30) 25X + 900 +2.5 X + 90 = 30 X + 900 27.5 X + 990 = 30 X + 900 2.5 X = 90 X= 90/2.5 = 36 ANSWER:A #### A QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ? options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:Just putting values, the LHS becomes n=0 --> 11 n=-1 --> 11/10 n=-2 --> 11/100 n=-3 --> 11/1000 Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3. Answer is B. #### B QUESTION:what is the smallest integer that is multiple of 3,7 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 3,7 and 20 which is 420 #### E QUESTION:Find 283/1983×100 options: A)14.29 B)14.21 C)14.22 D)14.27 E)14.23 SOLUTION:Never start finding common factors. Adjust the denominator to 2000. So we are introducing an error of 17 which is 171983=1117171983=1117 th of the denominator. 283002000=14.15283002000=14.15 But this answer is slightly less than actual answer. Now 14.1511714.15117 = 0.12 approximately. Adding 0.12 to 14.25 gives 14.27. Option B is correct. #### B QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? options: A)50 B)75 C)69 D)79 E)82 SOLUTION:number of pens = 100 number of pencils = 50 Required number of students = H.C.F. of 100 and 50 = 50 Answer is A #### A QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:Walking 7/6 of his usual rate, a boy reaches his school 7 min early. Find his usual time to reach the school? options: A)22 B)28 C)99 D)49 E)66 SOLUTION:Speed Ratio = 1:7/6 = 6:7 Time Ratio = 7:6 1 -------- 7 7--------- ? 49 m Answer:D #### D QUESTION:A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days? options: A)3.75 days B)3.99 days C)2.67 days D)2.98 days E)2.44 days SOLUTION:1/4 + 1/8 = 3/8 8/3 = 2.67 days Answer: C #### C QUESTION:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar? options: A) 9 B) 12 C) 15 D) 18 E) 21 SOLUTION:(Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins) í.ẹ. Red*White = Blue*Total Coins Let, Red = 3a White = 3b Blue = 3c Total Coins = 3(a+b+c) í.ẹ. 3a * 3b = 3c*3(a+b+c) í.ẹ. a*b = c*(a+b+c) For smallest values of a, b and c 2*3 = 1*(1+2+3) í.ẹ. Minimum Total Coins = 3*(1+2+3) = 15 Answer: Option C #### C QUESTION:Tough and Tricky questions: Distance/Rate. On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 200 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey? options: A)20 B)40 C)50 D)80 E)100 SOLUTION:Say, if speed is 40, 200/40 = 5 hrs and 200/50 = 4 hrs (a reduction of 1 hr -> Correct answer) Answer (B) #### B QUESTION:If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true? I. b-a = 2 II. abc is an even integer. III. (a + b + c)/3 is an integer. options: A) I only B) II only C) I and II only D) II and III only E) I, II, and III SOLUTION:Since a, b, and c are consecutive positive integers and a < b < c, thenb= a + 1, from which it follows that b - a = 1. So, I is false. Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true. Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well. Answer: D. #### D QUESTION:Average between two sets of numbers is closer to the set withmore numbers? options: A)70 B)80 C)90 D)95 E)98 SOLUTION:If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86. Here, 90 has a weight of 3 => it occurs 3 times. Whereas 80 has a weight of 2 => it occurs 2 times. So the average is closer to 90 than to 80 as we have just calculated. B #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 5 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)153602 D)60000 E)153604 SOLUTION:Perimeter = Distance covered in 5 min. =(12000/60) x 5m = 1000 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1000 or x = 100. Length = 300 m and Breadth = 200 m. Area = (300 x 200) m2 = 60000 m2. Answer: D #### D QUESTION:The total age of A and B is 18 years more than the total age of B and C. C is how many years younger than A ? options: A)12 B)27 C)21 D)18 E)11 SOLUTION:(A+B) - (B+C) = 18 A - C = 18. C is younger than A by 18 years. Answer: D #### D QUESTION:A sum of Rs.1420 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls options: A)8B, 5G B)5B, 8G C)4B, 9G D)9B, 4G E)6B, 7G SOLUTION:120B+100G=1420-----i B+G=13-------ii from i 100B+20B+100G=1420 100(B+G)+20B=1420 100(13)+20B=1420 By simplifing we get B=6;G=7 ANSWER:E #### E QUESTION:Subtracting 10% from X is the same as multiplying X by what number? options: A)80% B)90% C)10% D)50% E)60% SOLUTION:Explanation: X - (10/100) X = X * ? ? = 90% ANSWER IS B #### B QUESTION:A person X working alone can complete a work in 5 days. A person Y completes the same amount of work in 10 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:The fraction of work completed in two days is 2/5 + 2/10 + 2/30 = 20/30 The fraction of work remaining is 1 - 20/30 = 10/30 The number of days required for Z is 10 days. The answer is E. #### E QUESTION:Find the missing in the series: 70, 54, 45, 41,___ options: A)22 B)287 C)2679 D)2767 E)2771 SOLUTION:Answer:B #### B QUESTION:All the faces of cubes are painted with red colour.It is then cut into 64 equal small cubes.Find How many small cubes are there whose three faces are coloured ? options: A)4 B)8 C)16 D)24 E)2 SOLUTION:There are 64 small cubes,Hence one side side of the big cube is 3√64=4 cm Number of small cubes having three faces coloured = No. of corners = 8 Answer: B #### B QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)15,2 B)15, 4 C)15, 8 D)15, 5 E)15,7 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer:D #### D QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 40%? options: A)700 B)882 C)772 D)652 E)271 SOLUTION:Cost price = Rs.500 profit = 40% of 500 = Rs.200 Selling price = Cost price + Profit = 500 + 200 = 700 Answer:A #### A QUESTION:Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 48 seconds. Find the length of the faster train? options: A)270 B)288 C)266 D)299 E)480 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 48 * 10 = 480 m. The length of the faster train = 480 m. Answer: E #### E QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time S will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank S= 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is? options: A)38 B)27 C)75 D)28 E)21 SOLUTION:Explanation: The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75. Answer: C #### C QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days? options: A)4 B)16 C)8 D)1 E)2 SOLUTION:Explanation: Let the required number of mats be x More mat-weavers, more mats (direct proportion) More days, more mats (direct proportion) Hence we can write as (mat-weavers) 4:8 (days) 4:8}::4:x ⇒4×4×x=8×8×4 ⇒x=2×2×4=16 Answer: Option B #### B QUESTION:At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 7 liters of forest green to change it to Verdant green? options: A)5/3 B)2/7 C)7/3 D)1/7 E)1/4 SOLUTION:7 liter of Forset green have 4 liter of blue and 3 liter of yellow Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is Blue/yellow =4/(3+x) = ¾ 9+3x=16 => x =7/3 Answer : C #### C QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race? options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m SOLUTION:C 111.12 m X runs 1000 m while Y runs 900 m and Z runs 800 m. The number of meters that Z runs when Y runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. Y can give Z = 1000 - 888.88 = 111.12 m. #### C QUESTION:Complete the series: 16, 06 , 68 , 88 , ? , 98 options: A)L8 B)B6 C)S5 D)E8 E)M5 SOLUTION:A L8 To know why, just read the number series upside down and you will find that the numbers are 91, 90, 89, 88, __, 86 So L8 when read upside down reads as 87. #### A QUESTION:What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:the number of 7s in 21!= 21/7=3.. ans B #### B QUESTION:If the two hands in a clock are 15 minutes divisions apart,then the angle between them is options: A)3° B)18° C)24° D)90° E)None of these SOLUTION:In a clock, each minute makes 6° ∴ 15 minutes will make 6 × 15 = 90° Answer D #### D QUESTION:A rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 4 inches B)b) 6 inches C)c) 5 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 35=5*7 45=3*3*5 GCF = 5 P.S you can make squares with side of 5 Answer : C #### C QUESTION:The area of the largest circle that can be drawn inside a square of side 98 Cm in length is: options: A)8600 B)3646 C)7546 D)7636 E)1606 SOLUTION:Radius of required circle = 49 Cm its area = 22/7 × 49 × 49 154 × 49 = 7546 Cm(power)2 Answer is C. #### C QUESTION:By the how much is two-fifth of 300 greater than three -fifths of 125? options: A)15 B)3 C)5 D)45 E)None of these SOLUTION:Reqd no. = 2⁄5 × 300 - 3⁄5 × 125 = 120 - 75 = 45 Answer D #### D QUESTION:Series Problem like 4 12 x 44 46 132 134 begin of the Skype highlighting 44 46 132 134 end of the Skype highlighting. Find x? options: A)13 B)14 C)15 D)16 E)17 SOLUTION:134-132=2 46-44=2 x-12=2 x=14 ANSWER:B #### B QUESTION:At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.50. What is the price of 2 doughnuts? options: A)$ 0.55 B)$ 1.00 C)$ 1.10 D)$ 1.30 E)$ 1.50 SOLUTION:3D + C = 2.25......(1) 2D + C = 1.5........(2) (1) - (2) --> D = 0.75 --> 2D = 1.5 Answer: E #### E QUESTION:In an exam, Dibi scored 25 percent, Balan scored 38 percent and Cristen 23 percent. The maximum score awarded in the exam is 1200. Find the average mark scored by all the three boys? options: A)322 B)342 C)344 D)328 E)320 SOLUTION:Average mark scored by all the three boys = [25/100 (1200) +38 /100 (1200) + 23/100 (1200)] / 3 300+456+276= 344 Answer: C #### C QUESTION:Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%? options: A)30000 B)40000 C)50000 D)60000 E)70000 SOLUTION:let first parrt is x and second part is y then x+y=50000----------eq1 total profit=profit on x +profit on y 7000=(x*10*1)/100 + (y*20*1)/100 70000=x+2y-----------------------------------eq2 70000=50000+y so y=20000 then x =50000-20000=30000 first part =30000 ANSWER:A #### A QUESTION:The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally? options: A)11 B)77 C)12 D)99 E)887 SOLUTION:x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 3*4 = 12 Answer: C #### C QUESTION:If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars? options: A)3⁄20 B)11⁄60 C)9⁄40 D)1⁄5 E)2⁄15 SOLUTION:Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car. Half of them are men, and the other half are women, more precisely 60. It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total. Answer E #### E QUESTION:Which of the following is NOT the sum of the squares of two integers? options: A)36 B)37 C)65 D)146 E)147 SOLUTION:List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. (A) 36 - 9+25. NO. (B) 37 - 1+36. NO. (C) 65 - 1+64. NO. (D) 146 - 25+121. NO. (E) - must be the answer. ANSWER:E #### E QUESTION:Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics? options: A)7/12 B)4/9 C)5/9 D)1/4 E)2/3 SOLUTION:Lets pick smart numbers. Total number of students: 12 Biology (1/2): 6 Chemistry (1/3): 4 Physics (1/6): 2 After leaving school Biology: 4 Chemistry: 4 Physics: 1 New Total number of students: 9 Biology and Physics: 5 Answer 5/9 or C #### C QUESTION:The least number, which when divided by 12, 31, 20 and 54 leaves in each case a remainder of 8 is: options: A)448 B)488 C)16748 D)548 E)560 SOLUTION:Required number = (L.C.M. of 12, 31, 20, 54) + 8 = 16740+ 8 = 16748. answer :C #### C QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:The triplicate ratio of 1:3 is? options: A)1:0 B)1:8 C)1:27 D)1:2 E)1:1 SOLUTION:13: 33 = 1:27 Answer: C #### C QUESTION:Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $18.00, how many discounted tickets did he buy? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:Let x be the number of tickets he bought at $2 per ticket. then 2 x + (10-x)1.6 = 18 0.4x = 2 => x = 5 discounted tickets = 10 -x = 5 Ans : C #### C QUESTION:What approximate value should come in place of question mark (?) in the following equation 287.532 + 1894.029 – 657.48 = 743.095 + ? options: A)870 B)790 C)780 D)770 E)890 SOLUTION:? = 285 + 1895 – 655 – 745 or, ? = 780 Answer C #### C QUESTION:The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? options: A)18 2/18% B)18 2/11% C)18 2/91% D)18 9/11% E)12 2/11% SOLUTION:13 CP = 11 SP 11 --- 2 CP 100 --- ? =>18 2/11% Answer: B #### B QUESTION:The tax on a commodity is diminished by 10% and its consumption increased by 15%. The effect on revenue is? options: A)2% decrease B)3.5% increase C)9% decrease D)3% decrease E)2% increase SOLUTION:100 * 100 = 10000 90 * 115 = 10350 ----------- 10000-----------350 100-----------? => 3.5% decrease Answer: B #### B QUESTION:5800 * 99 options: A)574580 B)574200 C)584250 D)576460 E)None of these SOLUTION:Explanation: 5800 * (100 - 1) = 580000 - 5800 = 574200 Option B #### B QUESTION:Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age? options: A)1 B)2 C)4 D)5 E)6 SOLUTION:Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years. (4x + 8) = 5 (x + 8) 2 8x + 16 = 5x + 40 3x = 24 x = 8. Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2. B #### B QUESTION:A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows? options: A)24 B)72 C)720 D)336 E)420 SOLUTION:The left window will have permutations of the 5 fiction books, so the number of possibilities for that window is permutations = 5! = (5)(4)(3)(2)(1) = 120 The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is permutations = 3! = (3)(2)(1) = 6 Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 120*6 = 720 Answer: C. #### C QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: options: A)14 B)67 C)56 D)89 E)34 SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer:A #### A QUESTION:A contest will contain n questions each of which is to be answered either true or false. Anyone who answers all n questions correctly will be a winner what is the least value of n for which the probability is less then 1/1000 then a person who randomly guesses the answer to each q's will be a winner? options: A)5 B)10 C)50 D)100 E)1000 SOLUTION:The probability that a person will randomly guess all nn questions correctly is 1/2n1, so we want the value of nmin for which 1/2n<1<11000 --> 2n>1000 as nn is an integer nmin==10 (2^10=1024>1000). Answer: B. #### B QUESTION:P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings? options: A)1:5 B)1:8 C)1:2 D)1:1 E)1:6 SOLUTION:Ratio of investments of P and Q is 2 : 5 Total salary claimed by P = 12 * 5000 = Rs. 60000 Total profit = Rs. 2 lakhs. Profit is to be shared = Rs. 140000 Share of P = (2/7) * 140000 = Rs. 400000 Share of Q = Rs. 100000 Total earnings of P = (60000 + 40000) = Rs. 100000 Ratio of their earnings = 1:1 Answer: D #### D QUESTION:A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass? options: A)6 B)8 C)10 D)12 E)16 SOLUTION:1)If the two sides are co-prime, SUM of sides -1.. 2)and if not co-prime , Sum of sides - HCF of sides.. the difference is related to the diagonal passing through a vertex of squares at some place.. here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12 ANSWER:D #### D QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points? options: A)25 B)29 C)48 D)26 E)54 SOLUTION:A 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. #### A QUESTION:A student can select one of 6 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science. options: A)22 B)72 C)99 D)37 E)01 SOLUTION:6C1×3C1×4C16C1×3C1×4C1 = 6x3x4=72 ways Answer:B #### B QUESTION:The inverse ratio of 4: 2: 1 is? options: A)2:4:8 B)2:3:9 C)2:3:2 D)2:3:6 E)2:3:1 SOLUTION:1/4: 1/2: 1/1 = 2:4:8 Answer:A #### A QUESTION:There are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)141 D)154. E)166. SOLUTION:Let the foam generators capacity be - A = 12 lit/hr B = 12 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate 42 + 21 => 63 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 12 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 60 litres {2 (12+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 12 => 18 litres So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C) #### C QUESTION:On January 1, 2010, Dolly invests 30% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 40% in Antarctic smallcaps. In 2010, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 20% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dolly has the same total amount of retirement savings as he did two years before, then x is between options: A)10 and 20 B)20 and 30 C)30 and 40 D)40 and 50 E)50 and 60 SOLUTION:Pick a smart number for the total retirement savings Dolly starts with—say, $10,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.) Here are the starting values: L = $3000 M = $3000 S = $4000 Apply the first year’s changes, so that you have these numbers on 1/1/2012: Newer L = $3000 + 10% = $3300 Newer M = $3000 + 20% = $3600 Newer S = $4000 + 15% = $4600 Now apply the second year’s changes to L and M: Newest L = $3300– 20% = $3300– $660 = $2640 Newest M = $3600– 10% = $3600– $360 = $3240 Add these to get $5880. So the newest S must be $10,000 (the target final total of Dolly’s retirement savings) minus $5880, $4120 The dollar change in S from 1/1/12 to 1/1/13 is $4600 – $480 = $4120. So the question is this: what percent change does $480 represent, from a starting point of $4600? Since $4600 is a nasty divisor, switch to benchmarks: 10% of $4600 = $460. So 20% is just double that, or $920. And so on. From this $480 lies between $460 and $920 The correct answer is A. #### A QUESTION:If q and r are even integers, which of the following is an odd integer? options: A)qr + 2 B)q(r − 1) C)q(q + 5) D)3q + 4r E)(q + 3)(r − 1) SOLUTION:If q and r are even integers, then: A. qr + 2: even + even = even B. q(r − 1): even(odd) = even C. q(q + 5): even(odd) = even D. 3q + 4r: even + even = even E. (q + 3)(r − 1): (odd)(odd) = odd. Answer is E. #### E QUESTION:If a number is exactly divisible by 11 and 13, which of the following types the number must be? options: A)Divisible by (11 + 13) B)Divisible by (13 - 11) C)Divisible by (11 x 13) D)Divisible by (13 ÷ 11) E)None SOLUTION:Answer LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13). Correct Option: C #### C QUESTION:In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made? options: A)1:4 B)1:3 C)2:3 D)3:4 E)None of these SOLUTION:Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B #### B QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean m. 72 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.6 years and the standard deviation is 2.6 years, what percent of the distribution has more than 10.2 years as a shelf’s average life? options: A)17% B)16% C)15% D)14% E)13% SOLUTION:Average = 7.6 SD = 2.6 7.6 - 2.6 < 72% of distribution < 7.6 + 2.6 5.0 < 72% of distribution < 10.2 28% is outside this range. Given: Distribution is symmetric. So 14% of distribution is less than 5.0 and the other 14% of distribution is greater than 10.2. Answer: D #### D QUESTION:In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively? options: A)10,16 B)8,14 C)16,22 D)14,20 E)12, 18 SOLUTION:Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10. Given (x + 4) + (x + 10) = 30 => 2x + 14 = 30 => x = 8 The third number = x + 4 = 8 + 4 = 12. The sixth number = x + 10 = 8 + 10 = 18. Answer: E #### E QUESTION:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds? options: A)$5500 B)$11000 C)$22000 D)$2750 E)$44000 SOLUTION:Explanatory Answer Shawn received an extra amount of ($605 - $550) $55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year. The extra interest earned on the compound interest bond = $ 55 The interest for the first year = $550/2 = $ 275 Therefore, the rate of interest = (55/275)*100 = 20% p.a. 20% interest means that Shawn received 20% of the amount he invested in the bonds as interest If 20% of his investment in one of the bonds = $275, then his total investment in each of the bonds = (275/20)*100 = $ 1375 As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = $ 2750. correct choice is (D) #### D QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? options: A)27 B)50 C)98 D)77 E)51 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.Answer: B #### B QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)81 km/hr B)88 km/hr C)62 km/hr D)46 km/hr E)56 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y - 4.5)(10/36) ---(1) x/8.5 = (y - 5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y - 4.5)/ (y - 5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5 × 5.4 0.1y = 8.5 × 5.4 - 8.4 × 4.5 => .1y = 45.9 - 37.8 = 8.1 => y = 81 km/hr ANSWER:A #### A QUESTION:If A:B is 3:4 and B:C is 4:5 then A:C is equal to options: A)1:3 B)3:5 C)3:4 D)3:7 E)1:5 SOLUTION:The two ratios given are having the same number 4 for B in both the ratios. Hence- A:B = 3:4 B:C = 4:5 => A:C = 3:5 Answer B #### B QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? options: A)5/20 B)9/25 C)8/20 D)9/20 E)6/20 SOLUTION:Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20} answer 9/20 Answer D #### D QUESTION:In what ratio should a variety of rice costing $6 per kg be mixed with another variety of rice costing $8.75 per kg to obtain a mixture costing $7.50 per kg? options: A)4/7 B)5/6 C)5/9 D)4/8 E)3/8 SOLUTION:B 5/6 Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6 #### B QUESTION:A garrison of 150 men has provisions for 31 days. At the end of 16 days, a reinforcement arrives, and it is now found that the provisions will last only for 5 days more. What is the reinforcement? options: A)150 B)450 C)400 D)600 E)300 SOLUTION:150 ---- 31 150 ---- 15 x -----5 x*5 = 150*15 x = 450 150 ------- 300 Answer: E #### E QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)21% C)21.33% D)22.109% E)23% SOLUTION:Lets say the indicated weight is x for $10 but the trader actually get 1.1x for $10 now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1 so profit % = (12.1-10)/ 10 = 0.21 = 21% ANSWER:B #### B QUESTION:Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number? options: A)7 B)9 C)11 D)13 E)15 SOLUTION:Let the three numbers be x, x+2, and x+4. 3x = 2(x+4) + 3 x = 11 and then the third number is x+4 = 15. The answer is E. #### E QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 2 rows or 7 rows or 9 rows, then no tree will be left. Find the least number of trees required options: A)22 B)60 C)126 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(2, 7, 9) = 126 Answer: C #### C QUESTION:Two brothers took the GMAT exam, the higher score is M and the lower one is N. If the difference between the two scores is equal to their average, what is the value of N/M ? options: A)3 B)2 C)1/2 D)1/3 E)There isn't enough data to answer the question. SOLUTION:M - N = (M + N)/2 Solving for N/M = 1/3 D #### D QUESTION:A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain? options: A)12.5% B)16.7% C)22.5% D)27.5% E)33.3% SOLUTION:Let x be the original number of each color so there are a total of 5x candies. Kaz eats all of the green candies and half of the orange ones. There are 0 green candies and 0.5x orange candies remaining. He eats half of the remaining pieces of each color. There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies. He eats red and yellow candies in equal proportions. orange+blue+red+yellow = 0.75x + red + yellow = 1.2x red + yellow = 0.45x red = 0.225x, since red = yellow. The answer is C. #### C QUESTION:A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? options: A)63 B)336 C)567 D)3024 E)5040 SOLUTION:All the cordinates are integer hence, possible AT values are {-1,0}, {-1,1} ....{-1,7}: 8 ways .... {7,-1}, {7,0} ......{7,6}: 8 ways 9*8 ways = 72 for AC values can be {1,2}, {1,3} .... {1,7} : 6ways ...... {7,1}, {7,2} ..... {7,6} : 6 ways 7*6 = 42 Total = 72 * 42 = 3024 hence D #### D QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble? options: A)134 B)167 C)125 D)113 E)111 SOLUTION:C lb : reverse the calculations: So 48.75 ÷ 0.75 = 65, 65 ÷ 0.8 = 81.25 and 81.25 ÷ 0.65 = 125. #### C QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is? options: A)39yr B)42yr C)45yr D)32yr E)50yr SOLUTION:Let B's present age = x years Then A's present age = x+9 years x+9+10 = 2(x-10) x + 19 = 2x - 20 x = 39years Answer is A #### A QUESTION:Pipes A and B can fill a tank in 10 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in options: A)1 13/17 hours B)2 8/11 hours C)3 9/17 hours D)5 5/11 hours E)None SOLUTION:Solution Net part filled in 1 hour = (1/10 + 1/6 -1/12) = 11/60. Therefore, the tank will be full in 60/11 hrs. ‹=› 5 5/11 hrs. Answer D #### D QUESTION:The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article? options: A)1:3 B)2:5 C)3:2 D)9:4 E)4:2 SOLUTION:Explanation: Let C.P. = Rs. 5x and S.P. = Rs. 7x. Then, Gain = Rs. 2x Required ratio = 2x : 5x = 2:5 Answer: Option B #### B QUESTION:Excluding stoppages,the speed of the bus is 54kmph and including stoppages,it is 27kmph. For how many minutes does the bus stop per hr options: A)12 min B)11 min C)13 min D)20 min E)30 min SOLUTION:Due to stoppages,it covers 27km less. time taken to cover 27 km is [27/54 *60] min = 30min Answer is E. #### E QUESTION:A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color? options: A)49/153 B)18/153 C)49/153 D)40/153 E)24/72 SOLUTION:Explanation: Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random. Therefore, n(S) = 18C2 = 153 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 49/153 ANSWER:A #### A QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions? options: A)707 B)704 C)709 D)705 E)701 SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m Answer:B #### B QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:Find the smallest number which should be multiplied with 520 to make it a perfect square options: A)337 B)297 C)266 D)116 E)130 SOLUTION:Explanation: 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 Required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square. Answer: E #### E QUESTION:The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? options: A)27 B)30 C)31 D)33 E)34 SOLUTION:The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 A #### A QUESTION:There are between 500 and 510 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection? options: A) 501 B) 503 C) 506 D) 507 E) 510 SOLUTION:Let number of cards = x If the cards are counted 3 at a time , there are 2 left over- x= 3p+2 x can take values 503 , 506 , 510 If the cards are counted 4 at a time , there is 1 left over x= 4q+1 x can take values 501 , 506 Therefore , x = 506 Answer C #### C QUESTION:A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning? options: A)12 B)17 C)15 D)19 E)26 SOLUTION:Let the average after the 16th inning be P. So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P = 19 Answer:D #### D <<<Examples ends QUESTION:If f(x)= 5x^3- 2x+8 and h(y)= 4y-4, then h(f(x)) = options: A)11x^2+4x+4 B)11x^2-12x+44 C)8x^3-8x+32 D)30x^3+4x+4 E)20x^3-8x+28 SOLUTION:h(f(x)) = 4(f(x)) -4 = 4(5x^3- 2x+8) - 4 = 20x^3-8x+28 =>E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If (1 – 1.5)N = 1, then N = options: A) −400 B) −140 C) −2 D) 4 E) 400 SOLUTION:(1 – 1.5)N = 1 Simplify to get: -0.5N = 1 Rewrite as (-1/2)N = 1 Multiply both sides by -2 to get: N = -2 Answer: C #### C QUESTION:Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next? options: A)7 B)10 C)14 D)15 E)16 SOLUTION:Explanation: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on. Answer: Option D #### D QUESTION:Find the odd man out 4, 10, 22, 40, 84, 94 options: A)22 B)40 C)94 D)84 E)10 SOLUTION:Differnce is multiple of 6 4 and 10 diff is 6 10 and 22 diff is 12 22 and 40 diff is 18 40+24 = 64 but in series it is mentioned as 84 64+30 = 94 ANSWER:D #### D QUESTION:Which of the following is equal to 3.14 x 10^6) ? options: A)3.14 B)3140000 C)31400 D)314 E)314000 SOLUTION:= 3.14 x 10^6 = 3.14 x 1000000 = 3140000. Answer is B. #### B QUESTION:m:n = 5: 8 , n: p = 6 : 7 , m:n:p = ? options: A)30 : 48 : 54 B)30 : 48 : 56 C)30 : 48 : 50 D)30 : 48 : 52 E)30 : 48 : 58 SOLUTION:m:n = 5: 8 n: p = 6 : 7 m:n:p =30 : 48 : 56 Answer : B #### B QUESTION:If k is a non-negative integer and 15^k is a divisor of 823,435 then 5^k - k^5 = options: A)0 B)1 C)35 D)120 E)245 SOLUTION:8+2+3+4+3+5 = 25, so this number is not divisible by 3 and thus not divisible by 15. Therefore, k=0 5^k - k^5 =1-0=1 The answer is B. #### B QUESTION:How many positive integers less than 100 are neither multiples of 2 or 3? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:1) multiples of 2 till 100 = 100/2 = 50 2) multiples of 3 till 100 = 100/3 = 33.33= 33 add the two 50+33=83 ; subtract common terms that are multiple of both 2 and 3.. LCM of 2 and 3 = 6 Multiples of 6 till 100 = 100/6 = 16.66 = 16 so total multiples of 2 and 3 = 83-16 = 67 100-67 = 33 Answer : D #### D QUESTION:Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)16.80 × 4.50 + 4.4 B)1600 ÷ 40 + 16 × 2 C)5.5 × 8.4 + 34.6 D)1620 ÷ 20 – 1 E)1856.95 – 1680.65 – 96.3 SOLUTION:Others equal 80 whereas (c) equals 80.8. Answer C #### C QUESTION:If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true? I. c is even II. ab is even III. ab > 0 options: A)I only B)II only C)I and II D)I and III E)I, II, and III SOLUTION:Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above. II only.letter B #### B QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)47/5 B)13 C)17 D)21 E)23 SOLUTION:Let A contains A, B contains B liters so, (A-4)/(B+4)= 1/3.......(1) again, (B-5)/(A+5)= 1/2..........(2) from (1)(2) we find A= 47/5 ans: (A) #### A QUESTION:If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod? options: A)22.8 kg B)26.6 kg C)28 kg D)26.5 kg E)None of these SOLUTION:Explanation : Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion) => 11.25 : 7 :: 42.75 : x => 11.25 x x = 7 x 42.75 => x = (7 x 42.75) / 11.25 => x = 26.6 Answer : B #### B QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent? options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these SOLUTION:Let CP of an book = 100 MP of an book = 120 Discount 30 % on 120 = 36 SP of the book = 120 - 36 = 84 loss = 16% Answer : C #### C QUESTION:The speed of a car is 50 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)55 kmph D)23 kmph E)14 kmph SOLUTION:S = (55 + 60)/2 = 55 kmph Answer:C #### C QUESTION:Jill works as a waitress at the local diner where she earns an hourly wage of $7.00 per hour and a standard tip rate of 5% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week? options: A)280 B)300 C)320 D)432 E)400 SOLUTION:Jill earns 7 dollars/hour and the hourly tip is (1/20)*40. Jill thus earns 7*12+12*2 per day(or 7(12)+2(12)=9(12)=108). Jill has worked for 4 days -> 108*4=432. This matches answer choice D. #### D QUESTION:If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? options: A)$28000 B)$15000 C)$12000 D)$10000 E)$9000 SOLUTION:Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($7,000*2)*2=$28,000 (after 9 years investment will become $7,000*2=$14,000 and in another 9 years it'll become $14,000*2=$28,000). Answer: A. #### A QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.27 C)Rs.51.79 D)Rs.51.8 E)Rs.51.93 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs.51.25. Answer: A #### A QUESTION:How many multiples of 5 are there between 5 to 95? options: A)9 B)18 C)17 D)16 E)15 SOLUTION:As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the unit’s place). So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. Answer C #### C QUESTION:The G.C.D. of 1.08, 0.33 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.33 and 0.90. H.C.F. of 108, 33 and 90 is 3, H.C.F. of given numbers = 0.03. Answer A #### A QUESTION:The probability that a man will be alive for 10more yrs is 1/3 & the probability that his wife will alive for 10 more yrs is 5/8. The probability that none of them will be alive for 10 more yrs, is options: A)1/8 B)1/4 C)2/3 D)3/4 E)2 SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/4 Ans.(B) #### B QUESTION:A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i options: A)8 km / hr B)9 km / hr C)10 km / hr D)12.5 km / hr E)None SOLUTION:Sol. Man's rate in still in water = (12- 2) km / hr = 10km / hr. Man's rate against the current = (10 - 2) km / hr = 8 km / hr. Answer A #### A QUESTION:A train 100m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train? options: A)45kmph B)55kmph C)32kmph D)61kmph E)70kmph SOLUTION:Let the speed of the train be x kmph Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec 100/[(x+5)*5/18] = 6 30(x+5) = 1800 x = 55kmph Answer is B #### B QUESTION:What is the probability of flipping a fair coin five times and the coin landing on heads on at least two flips? options: A)5/8 B)7/8 C)11/16 D)13/16 E)27/32 SOLUTION:The number of possible outcomes is 2^5=32. 0 heads: There is 1 way to have all tails. 1 head: There are 5 ways to have one head. P(0 or 1 head)=6/32=3/16 P(at least 2 heads)=1 - 3/16 = 13/16 The answer is D. #### D QUESTION:A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)75 ways B)87 ways C)66 ways D)108 ways E)21 ways SOLUTION:Explanation: The boy can select one trouser in five ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 5 * 15 = 75 ways. Answer: A #### A QUESTION:John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him? options: A)10 B)67 C)32 D)44 E)55 SOLUTION:75-20=55. Answer is E #### E QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? options: A)4.5 B)5 C)5.6 D)5.7 E)6.5 SOLUTION:if $x$ is the number, x/6 * 12 = 9 => 2x = 9 => x = 4.5 A #### A QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)30 C)42 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 45, 100%= 45*100/60= 75.. ans 40% of 75 =30 B #### B QUESTION:If Z = 52 and ACT = 48, then BAT will be equal to options: A)33 B)88 C)77 D)46 E)99 SOLUTION:Explanation: In the given code, A = 2, B = 4, C = 6,.... , Z = 52. So, ACT = 2 + 6 + 40 = 48 and BAT = 4 + 2 + 40 = 46 Answer: D) 46 #### D QUESTION:If y > 0, (8y)/20 + (3y)/10 is what percent of y? options: A)40% B)50% C)60% D)70% E)80% SOLUTION:can be reduced to 4y/10+3y/10 =7y/10=70% Answer D #### D QUESTION:Median H of price of the car is 52,000. which could be the median of the other two. 35000, 44000, x, y, 57000. options: A)38000 B)47000 C)48000 D)51,000 E)56,000 SOLUTION:Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits H is 56,000.E #### E QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 13 km/hr downstream and 10 km/hr upstream. options: A)3 kmph B)9 kmph C)4 kmph D)8 kmph E)6 kmph SOLUTION:Speed in still water = (13 + 5)1/2 kmph = 9 kmph. answer :B #### B QUESTION:15 men take 20 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? options: A)27.57 B)28.57 C)29.57 D)30.57 E)32 SOLUTION:3W = 2M 15M ------ 20 * 8 hours 21 W ------ x * 6 hours 14 M ------ x * 6 15 * 20 * 8 = 14 * x * 6 x = 28.57 ANSWER:B #### B QUESTION:If n + 14 is a positive odd integer, which of the following must be true about the sum of the next four integers? options: A)It is a multiple of 3 B)It is a multiple of 4 C)It is a multiple of 2 D)It is a multiple of 5 E)It is a prime number SOLUTION:n+14 is a positive odd integer. This means n will be an odd integer The next 4 integers would be: n + 14, n + 15, n + 16, n + 17 Sum = 4n + 62 This sum will always be even. Option C #### C QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159 SOLUTION:46 + 28 + 10 = 84% 100 – 84 = 16% 850 * 16/100 = 136 Answer:A #### A QUESTION:At Pete’s Pet Shop, 35 cups of bird seed are used every 5 days to feed 14 parakeets. How many cups of bird seed would be required to feed 9 parakeets for 7 days? options: A)27 B)9 C)31.5 D)16 E)54 SOLUTION:Let's go step-by-step. 35 cups are used over a 5 day period, which means 7 cups a day. This feeds 14 parakeets, which means each parakeet needs 1/2 of a cup every day. For 9 parakeets, we need 9*1/2cups = 4.5 cups a day. Over 7 days, we need 31.5 cups. Choice c. #### C QUESTION:Two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)28 B)266 C)990 D)20 E)22 SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 160 + 280 = 440 m. The time required = d/s = 440/20 = 22 sec. Answer: E #### E QUESTION:The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Ans: E - 4 pairs (xˆ2)(yˆ2) = 900 [square root both sides] xy = 30 20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15 Cancel the repeats This leaves us with exactly 4 options. Hence, E #### E QUESTION:If 3<x<6<y<7, then what is the greatest possible positive integer difference of x and y? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:3 < x < 6 < y < 7; 3 < x y < 7 3 + y < x + 7 y - x < 4. Positive integer difference is 3(for example y = 6.5 and x = 3.5) Answer:A. #### A QUESTION:2 + 2 + 2 + 2 × 2^2 + 2 × 2^3 + 2 × 2^4 + 2 × 2^5 + 2 × 2^6 + 2 × 2^7 = options: A)2^7 B)2^14 C)2^10 D)2^15 E)2^16 SOLUTION:We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*2^7 we would have: sum=9*(2*2^7)=18*2^7=~2^11, so the actual sum is less than 2^11 and more than 2^7 (option A) as the last term is already more than that. So the answer is clearly C. Answer: C #### C QUESTION:Sonika bought a V.C.R. at the list price of 18,700. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R. options: A)20,196 B)19,780 C)19,680 D)19,380 E)None of these SOLUTION:Sol. List price of V.C.R. =18,700 Rate of sales tax = 8% ∴ Sales tax = 8% of 18,700 = 8⁄100 × 18700 = 1496 So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,700 + 1496 = 20,196. Answer A #### A QUESTION:If a : b = 5 : 9 and b : c = 4: 7, find a : b : c options: A)63:36:20 B)36:20:63 C)20:63:36 D)20:36:63 E)None of them SOLUTION:a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4 a:b:c = 5:9:63/4 =20:36:63. Answer is D. #### D QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:There are 40 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)6 B)12 C)20 D)24 E)27 SOLUTION:40*2/3 *3/4= 20 Answer: C #### C QUESTION:Car Dealership X, the total profit from sales increased by 30 percent over the previous years, while the number of cars sold decreased by 30 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year. options: A)18% B)30% C)52% D)63% E)85.71% SOLUTION:Let Profit be x and cars sold be y Originally Profit/Car = x/y Now it is 1.3x / 0.7 y = 13/7 (x/y) Increase in profit per car = ((6/7) (x/y)) / (x/y) * 100 = 85.71% Answer = E #### E QUESTION:If f(a)=4a+6b+8, what is the value of (f(3a)-f(2b)) ? options: A)6a+8b+6 B)8a-6b C)5a+3b-8 D)6a+7b+3 E)8a-2b+9 SOLUTION:f(a)=4a+6b+8 f(3a) = 12a+6b+8 f(2b) = 4a+12b+8 (f(3a)-f(2b)) = 12a+6b+8-4a-12b-8 = 8a-6b Answer is B #### B QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1). options: A)320 B)350 C)340 D)360 E)400 SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there? 99+(912-9-90*2)/3=340 Answer : C #### C QUESTION:Weights of two friends Ram and Shyam are in the ratio 2:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased? options: A)17% B)10% C)21% D)16% E)None SOLUTION:Solution: given ratio of Ram and Shayam's weight = 2:5 Hence, (x-15)/(15-10) = 2/5 Or, x = 17%. Answer: Option A #### A QUESTION:A sporting goods store sold 60 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $200, what is the fewest number of $4 Frisbees that could have been sold? options: A)24 B)12 C)20 D)4 E)2 SOLUTION:The wording of the question is slightly misleading. When a question asks what is thefewestthatcouldhave been sold, it is suggesting that there could be many different quantities sold. In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold. To solve, we have 2 equations and 2 unknowns Let x = number of $3 Frisbees sold Let y = number of $4 Frisbees sold x + y = 60 3x + 4y = 200 x = 60 - y 3(60-y) + 4y = 200 180 - 3y + 4y = 200 y = 20 Answer: C #### C QUESTION:Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet? options: A)U B)Y C)O D)Y E)R SOLUTION:10th letter from your left is J 7th letter from your right is T The mid letter between J and T is O. Answer: Option 'C' #### C QUESTION:From a number of mangoes, a man sells half the number of existing mangoes plus 1 to the first customer, then sells 1/3rd of the remaining number of mangoes plus 1 to the second customer, then 1/4th of the remaining number of mangoes plus 1 to the third customer and 1/5th of the remaining number of mangoes plus 1 to the fourth customer. He then finds that he does not have any mangoes left. How many mangoes did he have originally? options: A)12 B)14 C)15 D)13 E)16 SOLUTION:Let the No. of mangoes that the man had originally = X No. of mangoes sold balance 1st customer = (X/2) + 1 (X - 2)/2 2nd customer = (X - 2)/6 + 1 (X - 5)/3 3rd customer = (X - 5)/12 + 1 (X - 9)/4 4th customer = (X - 9)/20 + 1 0 (X - 9)/20 + 1= (X - 9)/4 => X = 14 ANSWER:B #### B QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line? options: A)30sec B)45sec C)36sec D)29sec E)52sec SOLUTION:Speed of the train = 50*5/18 = 250/18 m/sec Distance moved in passing the standing man = 500m Required time taken = 500/(250/18) = 500*18/250 = 36sec Answer is C #### C QUESTION:On a map, 1 centimeter represents 17 kilometers. Two cities 663 kilometers apart would be separated on the map by how many centimeters? options: A)15 B)27 C)39 D)270 E)480 SOLUTION:X=663/17= 39 Answer: C #### C QUESTION:If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be options: A)2 B)4 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 4*11025 = 44, 100, which is a square of 210 B #### B QUESTION:A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? options: A)5/8 B)6/13 C)5/16 D)5/13 E)5/11 SOLUTION:Two balls can be picked from thirteen balls in 13Câ‚‚ ways. We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵ ways. The required probability = (9 * 4) = 36/78 = 6/13 Answer: B #### B QUESTION:A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 B)67 C)108 D)26 E)27 SOLUTION:Length = Speed * time Speed = L/T S = 600/20 S = 30 M/Sec Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 108 Kmph Answer:C #### C QUESTION:A grocery shop has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? options: A)4857 B)4184 C)4012 D)4991 E)5291 SOLUTION:Let the sale in the sixth month =x Then (6435+6927+6855+7230+6562+x)/6 =6500 =>6435+6927+6855+7230+6562+x =6×6500 => 34009+x=39000 => x=39000−34009 =4991 ANSWER:D #### D QUESTION:A milk man has 30 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is: options: A)20% B)25% C)33.33% D)35% E)None of these SOLUTION:Explanation: when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 30 liters of milk. Therefore, profit percentage = 35 %. Answer: D #### D QUESTION:Claire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have? options: A)39 B)50 C)66 D)57 E)60 SOLUTION:G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300 G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66 C #### C QUESTION:Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(a + y) / t B)2(a + t) / ay C)2ayt / (a + y) D)2(a + y + t) / ay E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for a 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost? options: A)24 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 60 : x 250 * x = (100 * 60) x = (100 * 60) / 250 x = 24 ANSWER: A #### A QUESTION:A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get: options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these SOLUTION:Explanation: Ratio of working days of A : B = 10 : 15 Therefore, their wages ratio = reverse ratio = 15 : 10 Therefore, A will get 15 units of ratio Total ratio = 25 1 unit of ratio =3100/25 = 124 So, A’s amount = 124 × 15 = Rs.1860. Answer: Option C #### C QUESTION:In the quadrilateral PQRS d=10 cm, h1=4.6 cm and h2=2.3 cm. Find the area options: A)21 B)22 C)23 D)34.5 E)25 SOLUTION:area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona) so 1/2*10*(4.6+2.3)=34.5 ANSWER:D #### D QUESTION:Which of the following CANNOT be the median of the 3 positive integers a, b, and c? options: A)a B)c C)a+c D)(a+c)/2 E)(a+c)/3 SOLUTION:The median of a set with odd number of terms is justa middle term, so it's a, b or c. Eliminate A and B right away. Now, the median can also be (a+c)/2 and (a+c)/3 (for example: {1, 2, 3} and {1, 2, 5}). But since a, b, and c are positive integers then it no way can be a+c . Why? Because a middle term (the median) cannot possibly be greater than two terms (a and c) in a set with 3 terms. Answer: C. #### C QUESTION:The value of (4.7×13.26 + 4.7×9.43+4.7×77.31) is options: A)0.47 B)47 C)470 D)4700 E)None SOLUTION:Solution Given expression = 4.7×(13.26+9.43+77.31) = 4.7 ×100 = 470. Answer C #### C QUESTION:A group of five people are weighed with the results as follows (in pounds): 135, 140, 165, 178, 199. If the weight of the heaviest person is increased by 9 pounds, which of the following statements best describes the change in the mean and the median of the weights? options: A) The mean and the median will remain unchanged. B) The mean will remain unchanged but the median will increase. C) The mean will increase but the median will remain unchanged. D) The mean and the median will increase by the same amount. E) The mean and the median will increase by different amounts. SOLUTION:Old set = {135, 140, 165, 178, 199}. New set = {135, 140, 165, 178, 208} --> the median (middle term) will remain the same and the mean will increase. Answer: C. #### C QUESTION:Company X provides bottled water to its employees in 5 liter bottles, $2 each. At least how many 5L bottles must Company X buy monthly, so that new contract with $100 fixed monthly rate and $1 for 10L bottle each paid off? (Assume that no other costs apply) options: A) 121 B) 125 C) 132 D) 134 E) 138 SOLUTION:let the no. of 5 liter bottles be x, so the no. of 10l bottles will be x/2 (to equate the vol.) since the total cost will be equal , 2x= 100+x/2 so x= 133.33 or 134. Answer is (D). #### D QUESTION:A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate? options: A)480 B)580 C)680 D)280 E)380 SOLUTION:Let the total no of mangoes in the crate be x Then the no of bruised mango = 1/30 x Let the no of unsalable mangoes =3/4 (1/30 x) 1/40 x =12 x=480 Answer is A. #### A QUESTION:the banker's discount on a bill due 4 months hence at 15% is Rs.420. what is the true discount? options: A)41 B)400 C)390 D)380 E)480 SOLUTION:TD= (BD * 100)/(100+TR)= (420 * 100)/100+((4/12)*15)= (420 * 100)/100+((1/3)*15) =(420 * 100)/100+5= (84 * 100)/21 = 4*100=400 correct answer: (B) #### B QUESTION:If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true? I. x = y II. y = 1 III. x and y are prime integers. options: A)None B)I only C)II only D)III only E)I and II SOLUTION:given 2x/y is prime and greater than 2. => 2x/y could be any of the following 3,5,7.... => 2x/y is odd and prime (as 2 is the only even prime number and its not in this set) 1. x = y , can't be true if x=y , 2x/y = 2 which is not odd and prime. 2. y=1. can't be true. if y=1,2x/y = 2x = even which is not odd & prime. 3. x and y are prime integers, need not be true. lets say 2x/y = 3 and say y=2 prime =>x = 6/2 = 3 prime satisfies the given condition here. but when 2x/y = 3 and y=5 prime => x = 15/2 not prime My Answer is A #### A QUESTION:A boat moves upstream at the rate of 1 km in 25 minutes and down stream 1 km in 12 minutes. Then the speed of the current is : options: A)1 kmph B)2 kmph C)3 kmph D)1.3 kmph E)3.5 kmph SOLUTION:Rate upstream = (1/25 *60) = 2.4 kmph Rate dowm stream = 1/12 * 60 = 5 kmph Rate of the current = ½ (5-2.4) = 1.3 kmph ANSWER:D #### D QUESTION:#88 A necklace is made by stringing C individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then C could equal options: A)16 B)32 C)41 D)54 E)58 SOLUTION:You can just write out the pattern and count: RGWBYRGWBYRGWBY... But to save time a good test taker will just look for a pattern. Min # is 3, because W is the third one. Then every 5 beads another white comes, so it must be 3+5+5+5.. and so on... 3+5 = 8 3+5+5 = 13 3+5+5+5=18 3+5+5+5+5=23 So you see it ends in either 8 or 3. 58 IS THE NO. E #### E QUESTION:What is the sum of all the multiples of 10 between 0 and 75? options: A)500 B)620 C)450 D)340 E)280 SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280. Final Answer: E #### E QUESTION:The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Perimeter = 2(W+L) = 5W 3W = 2L W = 2L/3 WL = 54 2L^2/3 = 54 L^2 = 81 L = 9 cm The answer is D. #### D QUESTION:The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %? options: A)18% B)20.5% C)30% D)45% E)12% SOLUTION:1800 ---- 370 100 ---- ? => 20.5% Answer:B #### B QUESTION:Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. After 10 minutes, the water level decreases 9 meters. What is value of the radius in meters? options: A)1/2 B)1/3 C)1.5 D)3 E)6 SOLUTION:10*0.31 = 3.1 = pi*R^2*h R^2 = 3.1 / (pi*9) which is about 1/9 R = 1/3 The answer is B. #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 1 : 4. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)102400 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 1x metres and breadth = 4x metres. Then, 2(1x + 4x) = 1600 or x =160. Length = 160 m and Breadth = 640 m. Area = (160 x 640) m2 = 102400 m E #### E QUESTION:The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160.The time after which it is due is : options: A)6 months B)8 months C)9 months D)10 months E)None SOLUTION:Solution P.W = Rs.(1760 - 160)= Rs.1600. ∴ S.I. on Rs.1600 at 12% is Rs.160. ∴ Time =(100x160/1600x12 ) = 5/6years = ( 5/6x12) months = 10 months Answer D #### D QUESTION:Narendra started a business, investing 45000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)A)Rs.7000 B)B)Rs.8000 C)C)Rs.8571 D)D)Rs.8600 E)E)Rs.8700 SOLUTION:The ratio of their investments = 45000 × 12 : 15000 × 6 = 6 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 6/7 = Rs.8571. C) #### C QUESTION:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 20 terms of the sequence? options: A)201/100 B)99/100 C)100/101 D)1/10000 E)20/21 SOLUTION:Easy task and accomplish X1=1-1/2 x2=1/2-1/3 x3=1/3-1/4 ..... x20=1/20-1/21 sum=X1+X2+X3+....X20=1-1/2+1/2-1/3+.......1/20-1/21=1-1/21=20/21 E is the answer #### E QUESTION:Insert the missing number 3, 7, 6, 5, 9, 3, 12, 1, 15, ... options: A)18 B)33 C)-1 D)3 E)-3 SOLUTION:3, 7, 6, 5, 9, 3, 12, 1, 15, ... has two different series 1) 3, 6, 9, 12, 15..... 2) 7, 5, 3, 1, ..... -1 is the next number ANSWER:C #### C QUESTION:Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)NOne SOLUTION:Sol. Average = 66 + 65 + 77 + 62 + 75 / 5) = (345 / 5) = 69. Answer B #### B QUESTION:A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B? options: A)128228 B)12800 C)12819 D)12818 E)12812 SOLUTION:16*8: x*4 = 5:2 x = 12.8 => Rs.12800 Answer: B #### B QUESTION:An article is bought for Rs.600 and sold for Rs.900, find the gain percent? options: A)50% B)63 1/3% C)33 1/3% D)93 1/3% E)33 1/3% SOLUTION:Explanation: 600 ---- 300 100 ---- ? => 50% Answer:A #### A QUESTION:A group of 11 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase? options: A) E/(12 - n) B) (12 - n)/E C) E/[12(12-n)] D) nE / [11(11-n)] E) (12-n)E/(12n) SOLUTION:total cost =E no of people willing to participate initially =11 initial cost for each =E/11 when n people decided not to participate Cost for each =E/11-n D #### D QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? options: A)25 B)30 C)99 D)88 E)61 SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr. = 72 * 5/18 = 20 m/sec. Time taken to pass the man = 500 * 1/20 = 25 sec. Answer: A #### A QUESTION:For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y? options: A)14 B)12 C)10 D)16 E)18 SOLUTION:we know that : x > 1, y > 1, and x + 3y < 1000, and it is given that length means no of factors. for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal. hence, lets start with smallest no 2. 2^1 =2 2^2 =4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256 2^9=512 2^10 =1024 (it exceeds 920, so, x can't be 2^10) so, max value that X can take is 2^9 , for which has length of integer is 9. now, since x =512 ,x+3y<920 so, 3y<408 ==> y<136 so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7 for 2^7 has length of integer is 7. SO, combined together : 9+7 = 16. D #### D QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)4.1 B)3.6 C)2.6 D)5.0 E)5.5 SOLUTION:B 3.6 In this simple subtraction series, each number decreases by 0.4. #### B QUESTION:Three (rather lazy) men A, B and C working together can do a work in 5 days. They start the work together and A works for 1 day and takes rest on the second day, B works for 2 days and takes rest on the next two days and C works for 2 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate) options: A)7 days B)8 days C)9 days D)10 days E)11 days SOLUTION:Total work is 3*5 = 15 units. A does 1 day of work every 2 days. B does 2 days of work every 4 days. C does 2 days of work every 5 days. Test the options. In 7 days: A will do 1*3 + 1 = 4 units (3 complete cycles and 1 day of work). B will do 2*1+ 2= 4 units (1 complete cycle, 2 days of work, and 1 day of rest). C will do 2*1 + 2 =4 units (1 complete cycle and 2 days of work). Total = 4 + 4 + 4 = 12 units. In 8 days: A will do 1*4 = 4 units (4 complete cycles). B will do 2*2= 4 units (2 complete cycles). C will do 2*1 + 2 =4 units (1 complete cycle, 2 days of work, and 1 day of rest). Total = 4 + 4 + 4 = 12 units. In 9 days: A will do 1*4 + 1 = 5 units (4 complete cycles and 1 day of work). B will do 2*2+ 1 = 4 units (2 complete cycles and 1 day of work). C will do 2*1 + 2 = 4 units (1 complete cycle, 2 days of work, and two days of rest). Total = 5 + 5 + 4 = 14 units. In 10 days: A will do 1*5 = 5 units (5 complete cycles). B will do 2*2+ 2= 6 units (2 complete cycle and 2 days of work). C will do 2*2 =4 units (2 complete cycles). Total = 5 + 6 + 4 = 15 units. Therefore, the answer is D. #### D QUESTION:The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 13%? options: A)31.5% B)35.9% C)37.5% D)39.5% E)30.5% SOLUTION:Let marked price = $100. Then, C.P. = $64, S.P. = $87 Gain % = 23/64 * 100 = 35.9%. B #### B QUESTION:David covered a distance of 50 miles on his first trip. On a later trip he traveled 75 miles while going six times as fast. His new time compared with the old time was: options: A)twice as much B)three times as much C)the same D)half as much E)a fourth as much SOLUTION:Let t be the time of the first trip. On the later trip, David can travel 300 miles in time t. The trip of 75 miles takes t/4. The answer is E. #### E QUESTION:A rectangular tiled patio is composed of 48 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 48 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout? options: A)5 B)6 C)10 D)13 E)28 SOLUTION:Suppose there are c columns and there are r rows Original Situation So, Number of tiles = c*r = 48 Also. Reach column has r tiles and each row has c tiles New Situation Number of tiles in each column is r-2 and number of tiles in each row is c+4 So, number of rows = r-2 and number of columns is c+4 So, Number of tiles = (r-2)*(c+4) = 48 Comparing both of them we get c*r = (r-2)*(c+4) => 4r -2c = 8 c = 2r - 4 Putting it in c*r=48 (2r-4)*r = 48 2r^2 - 4r - 48=0 r cannot be negative so r = 6 and c = 8 So, Answer will be B #### B QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? options: A)289 B)132 C)279 D)277 E)278 SOLUTION:2 * 22/7 * 14 = 88 88 * 1 1/2 = Rs.132 Answer: B #### B QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required ? options: A)34 B)40 C)68 D)88 E)None of these SOLUTION:Solution We have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. ∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D #### D QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n? options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years SOLUTION:Explanatory Answer Let us say Braun invested $100. Then, at the end of 'n' years he would have got back $700. Therefore, the Simple Interest earned = 700 - 100 = $600. We know that Simple Interest = (Principal * number of years * rate of interest) / 100 Substituting the values in the above equation we get 600 = (100 * n * 8) / 100 Or 8n = 600 Or n = 75 years. correct choice is (E) #### E QUESTION:In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is : options: A)12 B)11 C)10 D)27 E)22 SOLUTION:Explanation: Total employees = \inline \frac{(25-10)\times 20}{10}=30 Hence number of educated employees = 30-20 = 10 Answer: C) 10 #### C QUESTION:Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they? options: A)350 B)400 C)500 D)550 E)590 SOLUTION:N * 50 = (325000 - 300000) = 25000 N = 25000 / 50 = 500 C #### C QUESTION:If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. ab < 1 III. a/b < 2 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:MANHATTAN GMATOFFICIAL SOLUTION: You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term: 1 > 1 - ab > 0 0 > -a b > -1 Subtract 1 from all three terms. 0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs. Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true. Therefore, the correct answer is (D). #### D QUESTION:In the graph below, no axes or origin is shown. If point B's coordinates are (10,4), which of the following coordinates would most likely be A's? options: A)(17, -2) B)(10, 6) C)(6, 8) D)(-10, 3) E)(-2, -17) SOLUTION:wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10. B rules.. #### B QUESTION:In a garden, there are 10 rows and 16 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is options: A)32 m B)22 m C)24 m D)26 m E)28 m SOLUTION:Explanation: Each row contains 16 plants. There are 15 gapes between the two corner trees (15 x 2) metres and 1 metre on each side is left. Therefore Length = (30 + 2) m = 32 m. Answer: A #### A QUESTION:A wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face? options: A)52.9% B)55.4% C)58.3% D)61.7% E)64.5% SOLUTION:There are a total of 9*9*9 = 729 cubes. All the exterior cubes will have at least one face painted red. The interior is formed by 7*7*7 = 343 cubes. The number of cubes with at least one side painted red is 729 - 343 = 386 cubes The probability that a cube has at least one side painted red is 386/729 which is about 52.9% The answer is A. #### A QUESTION:A research team that must consists of 3 members is to be formed from a pool of 6 scientists. How many different teams are possible? options: A)17 B)10 C)40 D)26 E)20 SOLUTION:Note that the team must consist of 3 members, not at least 3 members. Hence, all you have to do is 6C3 = 20 Answer (E) #### E QUESTION:If a square mirror has a 20-inch diagonal, what is the approximate perimeter E of the mirror, in inches? options: A) 40 B) 60 C) 80 D) 100 E) 120 SOLUTION:if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other. And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter E must be less than 80, so we can eliminate answer choice C, D and E. so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A. Now we are left with is B #### B QUESTION:Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ? options: A)0.5% B)1% C)5% D)50% E)500% SOLUTION:x percent can be written as x/100 So, we get: (30/100)(40/100)(50) = (60/100)(x/100)(200) Simplify all fractions to get: (3/10)(2/5)(50) = (3/5)(x/100)(200) Expand: 300/50 = 600x/500 Simplify: 6 = 6x/5 Multiply both sides by 5 to get: 30 = 6x Solve: x = 5 Answer: C #### C QUESTION:A person buys an article at $500. At what price should he sell the article so as to make a profit of 20%? options: A)560 B)449 C)600 D)740 E)460 SOLUTION:C 600 Cost price = $500 profit = 20% of 500 = $100 Selling price = Cost price + Profit = 500 + 100 = 600 #### C QUESTION:In how many years will a sum of money doubles itself at 30% per annum on simple interest? options: A)7% B)3% C)5% D)8% E)2% SOLUTION:P = (P*30*R)/100 R = 3% Answer:B #### B QUESTION:The average age of students in section A of 122 students is 28 years and the average age of students in section B of 180 students is 35 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)25years E)32years SOLUTION:The required average = (122*28+180*35)/122+180 = 32 years Answer is E #### E QUESTION:A book is bought for $60 and sold for $75. What is the profit in percentage? options: A)12 B)15 C)20 D)25 E)30 SOLUTION:75/60 = 1.25 The answer is D. #### D QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/7) B)Rs. 2(1/9) C)Rs. 3(2/11) D)Rs. 2(2/13) E)Rs. 2(2/7) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B #### B QUESTION:Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.7 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect? options: A)1/6 B)1/2 C)5/8 D)5/4 E)15/16 SOLUTION:X - fraction of products Jane inspected (1 - X) - fraction of products John inspected 0.7(X) + 0.5(1-X) = 0.75 0.2X = 0.75 - 0.5 X = 0.25/0.2 X = 5/4 Therefore the answer is D: 5/4. #### D QUESTION:121,112,...?..,97,91,86 options: A)99 B)104 C)102 D)108 E)100 SOLUTION:121. 112. 104. 97. 91. 86 the decreasing difference is reducing by 1 at each step so,missing no. will be 104 answer B #### B QUESTION:Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck. options: A)150 B)160 C)170 D)180 E)190 SOLUTION:Let the 1st paycheck be x (integer). Dawson got a weekly raise of $ 160. So after completing the 1st week she will get $ (x+160). Similarly after completing the 2nd week she will get $ (x + 160) + $ 160. = $ (x + 160 + 160) = $ (x + 320) So in this way end of every week her salary will increase by (B)$ 160. #### B QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time? options: A)70 min B)94 min C)110 min D)112 min E)120 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) And now we have 4 robots So Total = (1) + (2) = 70 minutes Answer - A #### A QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)288 B)266 C)120 D)287 E)212 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P? options: A)20% B)40% C)50% D)60% E)80% SOLUTION:65% is 15%-points below 80% and 10%-points above 55%. So the ratio of solution P to solution Q is 2:3. Mixture P is 2/5 = 40% of the volume of mixture PQ. The answer is B. #### B QUESTION:The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number? options: A)12 B)20 C)45 D)60 E)52 SOLUTION:Given ratios 5 : 3 4 : 9 20:12:27 The second number = 177/(20+12+27) * 15 = 45 Answer is C #### C QUESTION:100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads? options: A)33/100 B)41/101 C)51/101 D)87/101 E)98/101 SOLUTION:Let aa be the number of coins showing heads Then, P(A=50)=P(A=51)P(A=50)=P(A=51) ⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101 C #### C QUESTION:If the LCM and HCF of 8 and another number is 24 and 4 respectively. Find the other number ? options: A)11 B)12 C)14 D)15 E)16 SOLUTION:HCF x LCM = Product of Numbers 4 x 24 = 8 x the other number other number = (4 x 24) / 8 other number = 12 ANSWER : B #### B QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2 SOLUTION:Solution Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 Answer A #### A QUESTION:What is the average of xx,2x2x,and 66? options: A)x+2 B)x+2x C)x+2x+2 D)2x+2 E)x+2x-2 SOLUTION:By the definition of an average, we get: x+2x+63=3x+63x+2x+63=3x+63 =3(x+2)3=x+2.=3(x+2)3=x+2. Hence, the answer is x+2x+2 or Option C #### C QUESTION:8 men, working 8 hours a day can complete a work in 18 days. How many hours a day must 12 men work to complete the same work in 12 days? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:The number of hours required to complete the work is 8*8*18 = 1152 12 × 12 × (x) = 1152 x = 8 The answer is C. #### C QUESTION:Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1055 B)1065 C)1070 D)1075 E)1080 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 A #### A QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: options: A)No profit, no loss B)5% C)8% D)10% E)11% SOLUTION:Explanation: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =80/100X100%=5% ANSWER IS B #### B QUESTION:For a certain exam,a score of 86 was 5 standard deviations above mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam? options: A)50 B)55 C)48 D)42 E)49 SOLUTION:Mean+5SD=86 Mean+2.5SD=67 By solving above equations we get, SD (absolute value)=7.6 Mean=48 ANS. C #### C QUESTION:Find the value of (28 + 48/69) × 69 options: A)1980 B)1982 C)1930 D)1988 E)1680 SOLUTION:=(28 + 48/69) × 69 =(1932+ 48)/69× 69 =1980/69× 69 =1980 Answer is A. #### A QUESTION:A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 27,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary? options: A)Rs. 2000 B)Rs. 4000 C)Rs. 6000 D)Rs. 3000 E)None of these SOLUTION:Explanation: A's capital : B 's capital 20000 : 40000 = 1 : 2 Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2 Profit of A = (1/3) * 27,000 = Rs. 9,000 Salary of A = Rs. (15000 – 9000) = Rs. 6000 ANSWER: C #### C QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 > b^2 > c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=1, b=2, and c=3. None of the options must be true. Answer: A. #### A QUESTION:The ratio of spinsters to cats is 2 to 9. If there are 63 more cats than spinsters, how many spinsters are there? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:Let 2x be the number of spinsters. Then 9x is the number of cats. 9x-2x=63 x=9 and the number of spinsters is 2(9)=18. The answer is E. #### E QUESTION:The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 8, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median? I. 3 II. 7 III. 12 options: A)I only B)II only C)III only D)I and III only E)I, II, and III SOLUTION:C for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8 #### C <<<Examples ends QUESTION:If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD? options: A) 62 B) 55 C) 48 D) 31 E) 25 SOLUTION:I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square. 25 is a perfect square. Ans:E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar? options: A)2288 B)2677 C)6000 D)2700 E)2881 SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x 10 * 20 * 90 = 15 * 2 * x => x = 6000 Answer: C #### C QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit? options: A)Rs.10528 B)Rs.10521 C)Rs.10511 D)Rs.10411 E)Rs.10500 SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 24500 * 3/7 = Rs.10500 Answer: E #### E QUESTION:Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is: options: A)13/109 B)13/162 C)13/111 D)13/102 E)13/112 SOLUTION:Let S be the sample space. Then, n(S) = \inline {\color{Black}52C_{2} }=(52 x 51)/(2 x 1) = 1326. Let E = event of getting 1 spade and 1 heart. n(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = \inline {\color{Black}13C_{1}\times 13C_{1} } = 169. P(E) = n(E)/n(S) = 169/1326 = 13/102. Answer: D) 13/102 #### D QUESTION:Two cars start at the same time from opposite ends of a highway that is 333 miles long. One car is riding at 54 mph and the second car is riding at 57 mph. How long after they begin will they meet? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:As cars are moving in opposite directions their speeds will be added. So their relative speeds: 57+54 = 111 mph Total distance to be covered = 333 miles. Time taken would be: 333 miles/111 mph = 3 hours C is the answer. #### C QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E QUESTION:There are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)141 D)154. E)166. SOLUTION:Let the foam generators capacity be - A = 12 lit/hr B = 12 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate 42 + 21 => 63 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 12 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 60 litres {2 (12+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 12 => 18 litres So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C) #### C QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(6900*6)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? options: A)A B)B C)C D)all alike E)None of these SOLUTION:Let B = 100 A = 50 C * (150/100) = 50 3C = 100 C = 33.3 then 'C' Cheapest ANSWER:C #### C QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water? options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3 SOLUTION:G = 10W C = 5W Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy 1gm gold + x gm copper = x+1 gm of alloy 10W+5Wx = x+1 * 6W 10+5x = 6(x+1) x = 4 Ratio of gold with copper = 1:4 = 1:4 Answer is B #### B QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)sec B)sec C)sec D)sec E)sec SOLUTION:The distance to be covered = Sum of their lengths = 200 + 300 = 500 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 500/10 = 50 sec. Answer: A #### A QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture? options: A)1 : 9 B)1 by 5 C)1 : 7 D)1 : 3 E)1 : 1 SOLUTION:Selling price of the mixture = 70 and profit = 20% Cost price of the mixture = 70×100120=70×5670×100120=70×56 By applying alligation rule: So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5 Answer:B #### B QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)22277 B)29977 C)267676 D)14000 E)18811 SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 Answer: D #### D QUESTION:In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color? options: A)a) 8 B)b) 23 C)c) 29 D)d) 32 E)e) 53 SOLUTION:Thats 29 in C. #### C QUESTION:There are 6 red shoes, 2 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)5/9 D)3/4 E)2/3 SOLUTION:total 8 from take one. 8c1=8 red 6 from one 6c1=6 6/8=3/4 ANSWER:D #### D QUESTION:If Renee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased? options: A)1/4 B)1/5 C)1/10 D)2/25 E)1/20 SOLUTION:5% is 5/100 = 1/20 10% is 10/100 = 1/10 The increase must be greater than 1/20 and less than 1/10. 1/4, 1/5, and 1/10 are not less than 1/10. 1/20 is not greater than 1/20. The only option left is 2/25, which is in the specified range. ANSWER:D #### D QUESTION:The ratio of 2 numbers is 2:7 and their H.C.F. is 18. Their L.C.M. is ? options: A)252 B)243 C)521 D)361 E)600 SOLUTION:Let the numbers be 2x and 7x Their H.C.F. = 18 so the numbers are 2*18 , 7*18 = 36,126 L.C.M. = 252 Answer is A #### A QUESTION:A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)11 sec C)88 sec D)33.33 sec E)10 sec SOLUTION:Speed = 54 * 5/18 = 15 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 1/15 = 33.33 sec Answer: D #### D QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? options: A)4.5 B)5 C)5.6 D)5.7 E)6.5 SOLUTION:if $x$ is the number, x/6 * 12 = 9 => 2x = 9 => x = 4.5 A #### A QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760 SOLUTION:After one year: 1.2 * $2500 After two years: (1.2)^2 * $2500 After three years: (1.2)^3 * $2500 = $4320 The answer is D. #### D QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)190 C)109 D)278 E)211 SOLUTION:Explanation: 624/6 = 104 kmph Answer:C #### C QUESTION:A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails? options: A)1/8 B)1/4 C)3/8 D)1/2 E)9/16 SOLUTION:We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin. Using the binary formula and defining a head as a success, P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2 t= 6/16 = 3/8 The answer is therefore (C) #### C QUESTION:How many integers are between 3 and 86/7, inclusive? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:86/7 = 12.xx We are not concerned about the exact value of 86/7 as we just need the integers. Since the values are small, we can write down the integers. The different integers between 3 and 86/7 would be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Total number of integers = 10 Option C If we need to find the number of integers between two numbers n and m, where m > n The number of integers = m - n + 1 In the given question, the number of integers = 12 - 3 + 1 = 10 ANSWER:C #### C QUESTION:A triangle has sides 10, 17, and 21. A square is inscribed in the triangle. One side of the square lies on the longest side of the triangle. The other two vertices of the square touch the two shorter sides of the triangle. What is the length of the side of the square? options: A)148/29 B)168/29 C)168/26 D)158/29 E)198/29 SOLUTION:By Heron's Formula, the area, A, of a triangle with sides a, b, c is given by A = square root[s(s − a)(s − b)(s − c)], where s = ½(a + b + c) is the semi-perimeter of the triangle. Then s = ½(10 + 17 + 21) = 24, and A = 84. A square inscribed in a 10 by 17 by 21 triangle, with perpendicular dropped onto the side of length 21. Now drop a perpendicular of length h onto the side of length 21. We also have A = ½ × base × perpendicular height. Hence A = 21h/2 = 84, from which h = 8. Notice that the triangle above the square is similar to the whole triangle. (This follows because its base, the top of the square, is parallel to the base of the whole triangle.) Let the square have side of length d. Considering the ratio of altitude to base in each triangle, we have 8/21 = (8 − d)/d = 8/d − 1. Therefore the length of the side of the square is 168/29. ANSWER:B #### B QUESTION:If you are given $5, and the amount doubles every day, how much money will you have after 4 days? options: A)$256 B)$512 C)$1024 D)$625 E)$720 SOLUTION:5^4=625 The answer is D #### D QUESTION:If A:B is 3:4 and B:C is 4:5 then A:C is equal to options: A)1:3 B)3:5 C)3:4 D)3:7 E)1:5 SOLUTION:The two ratios given are having the same number 4 for B in both the ratios. Hence- A:B = 3:4 B:C = 4:5 => A:C = 3:5 Answer B #### B QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000*(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500? options: A)s. 1991 B)s. 2991 C)s. 3991 D)s. 4991 E)s. 5991 SOLUTION:Explanation: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009. Required sale = Rs. [ (4500 x 6) – 24009 ] = Rs. (27000 – 24009) = Rs. 2991. Answer B #### B QUESTION:When 242 is divided by a certain divisor the remainder obtained is 15. When 698 is divided by the same divisor the remainder obtained is 27. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor? options: A)11 B)17 C)13 D)23 E)37 SOLUTION:let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27. now 242-15=227 =kx (k is an integer and 234 is divisble by x) similarly 698-27=671 = lx (l is an integer and 689 is divisible by x) adding both 698 and 242 = (227+671)+15+27 =x(k+l) + 42 when we divide this number by x then remainder will be equal to remainder of (42 divided by x) = 5 hence x = 42-5 = 37 hence E #### E QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)152 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:If 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days? options: A)127 B)237 C)360 D)450 E)281 SOLUTION:Explanation: Let the required no of hectares be x. Then Men --- Hectares---Days 10---------80---------24 36---------x---------30 More men, More hectares (Direct proportion) More days, More hectares (Direct proportion) x=36/10*30/24*80 x= 360 Answer: C #### C QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 60 percent, then the value of T decreases by what percent? options: A)25% B)33 ¹/₃% C)50% D)66 ²/₃% E)75% SOLUTION:We can assign numbers: lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T) Now increasing S by 50% gives S=4, K remains constant, so T = 2 (6/2=3) decrease in T= 1, percent decrease in T = (1/4)*100 = 25% Answer A #### A QUESTION:Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number? options: A)6 B)9 C)11 D)12 E)15 SOLUTION:Explanation: 3x/5 – x/5 = 6 => x =15 1 + 5 = 6 A) #### A QUESTION:If the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers? options: A)4:9 B)4:3 C)3:7 D)2:5 E)1:6 SOLUTION:The ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9. The ratio of apples to bananas to cucumbers is 4 to 3 to 9. The answer is A. #### A QUESTION:At what rate percent on simple interest will a sum of money double itself in 20 years? options: A)2% B)6% C)3% D)4% E)5% SOLUTION:P = (P*20*R)/100 R = 5% ANSWER:E #### E QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 18%. How much will an air-conditioning unit cost in November? options: A)$466 B)$470 C)$472 D)$484 E)$491 SOLUTION:if its prevoius november (before discount) then price is $470. but if its November of next year then 16% discount on $470=470(1-16/100)=$394.8 again a corrected raised price of 18% over $394.8=394.8(1+18/100)=465.86~$466 Ans A #### A QUESTION:A man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water? options: A)11 B)77 C)30 D)88 E)35 SOLUTION:US = 25 DS = 45 M = (45 + 25)/2 = 35 Answer:E #### E QUESTION:The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees. options: A)$2291.7 B)$1546.8 C)$2546.5 D)$1879.3 E)$3125.3 SOLUTION:mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7 Answer is A #### A QUESTION:Pipe A can fill the tank in 30 minutes and pipe B in 20min and pipe C can empty the tank in 90 minutes. How long it will take to fill the tank if three of the pipes are operating together? options: A)10.55 B)12.0 C)13.1 D)13.85 E)15.2 SOLUTION:Pipe A fills 1/30th of the tank in a minute and pipe B, 1/20th. Pipe C empties in 90min (1/30)+(1/20)-(1/90)=(1/x) 13/180=1/x => x=180/13 => x=13.85 minutes Answer: D #### D QUESTION:The average of first 20 natural numbers is? options: A)5.6 B)10.5 C)10.1 D)5.8 E)5.2 SOLUTION:Sum of 20 natural no. = 420/2 = 210 Average = 210/20 = 10.5 Answer:B #### B QUESTION:Three walls have wallpaper covering a combined area of 280 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 36 square meters. What is the area that is covered with three layers of wallpaper? options: A)5 Square Meters B)32 Square Meters C)42 Square Meters D)83.3 Square Meters E)120 Square Meters SOLUTION:280 - 180 = 100 sq m of the wallpaper overlaps (in either two layers or three layers) If 36 sq m has two layers, 100 - 36 = 64 sq m of the wallpaper overlaps in three layers. 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m. Answer (B). #### B QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A QUESTION:The mean of 20 observations was 36. It was found later that an observation 25 was wrongly taken as 40. The corrected new mean is options: A)30 B)25.4 C)40 D)35.25 E)26.55 SOLUTION:Explanation: Correct Sum = (36 * 20 + 25 - 40) = 705 Correct mean = = 705/20 = 35.25 Answer: D #### D QUESTION:A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)30 B)60 C)75 D)90 E)105 SOLUTION:Answer : A Let number of notes of each denomination be x. Then, x + 5x + 10x = 160 16x = 160 x = 10. Hence, total number of notes = 3x = 30. #### A QUESTION:Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.? options: A)28 B)60 C)32 D)36 E)44 SOLUTION:the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13. using the elimination method look for a number that is both divisible by 7 and 13, of all the options only 60 is divisible by 4 and 20. [ 60/4=15 and 60/20=3] answer :B #### B QUESTION:A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 3 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.) options: A)1/5 B)1/2 C)2/3 D)4/5 E)6/5 SOLUTION:Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B FOR THE FIRST BUCKET ... Red color - 2 Blue color - 2 FOR THE SECOND BUCKET Red color - 3 Blue color -2 In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios : Scenario I - He picks Red color from List A and Blue color from List B Scenario II - He picks Blue color from List A and Red color from List B Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5 Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ... Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ... We get 1/5 + 3/10 = 2/3 (C) #### C QUESTION:A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these SOLUTION:Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: C #### C QUESTION:Of the science books in a certain supply room, 50 are on botany, 60 are on zoology, 90 are on physics. 40 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? options: A)81 B)159 C)309 D)285 E)324 SOLUTION:First, you can take all 50 Botany books, all 60 zoology books and all 40 geology books because you're sure to never pick 80 of them. There are still 90 on physics and 110 on chemistry The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry. Minimum number of books picked to reach 80 in the same science should be : 50 + 60 + 40 + 79 +79 + 1 = 309 C #### C QUESTION:A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job? options: A)6 B)8 C)3 D)4 E)0 SOLUTION:Explanation: Use formula For a work Members × days = constant 8 × 3 = 4 × a a = 6 so answer is 6 days Answer: A #### A QUESTION:In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 28 more than twice the number of heads => 2(d + 2c) = 28 + 2(c + d) => d + 2c = 14 + c + d => 2c = 14 + c => c = 14 i.e., total number of cows = 14 Answer is B. #### B QUESTION:Find the least number must be subtracted from 11070 so that remaining number is divisible by 22. options: A)2 B)3 C)4 D)7 E)8 SOLUTION:On dividing 11070 by 22 we get the remainder 4, so 4 should be subtracted. Answer is A. #### A QUESTION:If the sum of the interior angles of a regular polygon measures up to 1440 degrees, then how many sides does the polygon have? options: A)10 B)16 C)12 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1440 180n - 360 = 1440 180n = 1800 n = 1800/180 = 10 ANSWER:A #### A QUESTION:What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive? options: A)90 B)80 C)100 D)105 E)110 SOLUTION:10 and 190 inclusive would mean there are 17 terms. No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170 The middle term is the average which is the tenth term = 80 B is the answer. #### B QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)2% C)1% D)6% E)7% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\ Rate = (100 * 3000) / (12500 * 4) = 6% Answer: D #### D QUESTION:Gary had an average score of 70 on his first four quizzes. He had an average score of 75 on his first five quizzes. What score did he receive on his fifth quiz? options: A)90 B)95 C)65 D)42 E)43 SOLUTION:The sum of Gary's first 4 scores is 4 · 70 and the sum of his first 5 scores is 5 · 75, so he received 5 · 75 − 4 · 70 on his 5th quiz. You can do the arithmetic or note that the answer ends in a 5 and eliminate answer C because it is lower than the average. The correct answer is B. #### B QUESTION:In what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way? options: A)3 B)5.4 C)4.3 D)6.5 E)7 SOLUTION:T = 75/50 * 18/5 = 5.4 sec Answer:B #### B QUESTION:In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters? options: A)125.5 meters B)126.5 meters C)127.5 meters D)128.5 meters E)None of these SOLUTION:Explanation: When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters. Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters. So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C. So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters. Answer: C #### C QUESTION:The area of a triangle is with base 4m and height 5m? options: A)20 m2 B)10 m2 C)82 m2 D)54 m2 E)28 m2 SOLUTION:1/2 * 4 * 5 = 10 m2 Answer:B #### B QUESTION:After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is? options: A)Rs.2989 B)Rs.5029 C)Rs.5000 D)Rs.5197 E)Rs.5029 SOLUTION:Given SP = Rs. 6800 Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000 If SP = Rs. 8000, profit 60% CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs.5000 Answer: C #### C QUESTION:In a group of 25 factory workers, 13 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes. options: A)10 B)9 C)8 D)7 E)5 SOLUTION:Total number of worker (M+W): 25 No. of men (M): 11 (Inferred fromHow many of the 11 men) No. of women (W): 14 Total no. of workers who have brown eyes (B): 13 No. of women who do not have brown eyes: 6 Therefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8 Remaining 5 are men. (B - 8= 13 - 8= 5) So 5 out of 11 men have brown eyes. E #### E QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)30 SOLUTION:In order x! to be divisible by 1,0, it should have at least 1 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 1. 5! = 120 has 1 trailing zeros. Answer: A #### A QUESTION:A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in? options: A)12 B)13 C)13 5/7 D)13 ¾ E)None of these SOLUTION:Explanation: (A+B)’s 2 day work = 1/16 + 1/12 = 7/18 work done in 6 pairs of days=7/48 x 6 = 7/8 remaining work = 1/8 work done by A on 13th day =1/16 remaining work = 1/16 on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day total time taken =13 ¾ days Answer: Option D #### D QUESTION:3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day? options: A)33 B)77 C)26 D)12 E)99 SOLUTION:Let the required number of working hours per day be x. More pumps, Less working hours per day (Indirect Proportion) Less days, More working hours per day (Indirect Proportion) Pumps 4 : 3 :: 8 : x Days 1 : 2 4 x 1 x x = 3 x 2 x 8 x = (3 x 2 x 8) (4) x = 12. Answer:D #### D QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:8, the price of the cheapest item is? options: A)2379 B)2889 C)5625 D)9000 E)28311 SOLUTION:Let their prices be 3x, 5x and 7x. Then, 2x + 6x + 8x = (15000 * 3) or x = 2812.5. Cost of cheapest item = 2x = Rs. 5625. Answer: C #### C QUESTION:A set of 11 positive integers has an average of 20. Which of the following is the greatest possible value for the median of this set? options: A)25 B)30 C)35 D)45 E)46 SOLUTION:for the median to bé max , we should take all the values below meadian to be the lowest and the remaining values to be the same.. here 1 is the lowest value(positive int) số thẻ lowest 5 int will equal 5.. remaining 6= 20*11-5=215.. therefore each valueof these 6 int =215/6=35 ans C #### C QUESTION:Two cars cover the same distance at the speed of 50 and 61 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)273 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 61x X = 4.55 60 * 4.55 = 273 km ANSWER:B #### B QUESTION:A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. options: A)40 B)50 C)62 D)45 E)56 SOLUTION:Let the average after 11th inning = x Then, average after 10th inning = x-5 10(x-5)+100 = 11x x = 100-50 = 50 Answer is B #### B QUESTION:If x and y are even integers, which of the following is an odd integer? options: A)x+y B)xy C)xy+2 D)x^2+y^2 E)None of these SOLUTION:even+even = even even * even = even even+even =even Answer : E #### E QUESTION:he L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is: options: A)30 B)40 C)38 D)36 E)39 SOLUTION:Let the numbers be 2x and 3x. Then, their L.C.M. = 6x. So, 6x = 48 or x = 8 The numbers are 16 and 24. Hence, required sum = (16 + 24) = 40. Answer: Option B #### B QUESTION:The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ? options: A)6 B)8 C)9 D)10 E)12 SOLUTION:Let the number be xy. Given xy – yx = 36. This means the number is greater is than the number got on reversing the digits. This shows that the ten’s digit x > unit digit y. Also given ratio between digits is 1 : 2 => x = 2y (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4. Hence, (x + y) – (x – y) = 3y – y = 2y = 8 B #### B QUESTION:SCORE INTERVAL----------------NUMBER OF SCORES 50-59-------------------------- 2 60-69--------------------------10 70-79--------------------------16 80-89--------------------------5 90-99--------------------------2 The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 35 scores? options: A)16th B)20th C)22th D)24th E)18th(70-79) SOLUTION:Total scores= 2+10+16+5+2 = 35, which is odd, therefore the median is the Floor(35/2)+1 = 18th score. And the 18th score is in the 70-79 range, because 50-69 only reference 12 scores. E #### E QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)None of these SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111.. Answer : Option C #### C QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:If the integer N = 139,k50 where k is the hundreds digit, N can NEVER be divisible by which of the following? options: A)2 B)3 C)4 D)6 E)9 SOLUTION:It is divisible by 2 irrespective of k value as unit digit's value is even(0). It can be divisible by 3 for k values 2,5,8 as sum will be divisible by 3 It can be divisible by 6 if divisible by 2 and 3. It can be divisible by 9 for k value 2 as sum will be divisible by 9. Therefore answer is 4 as number is divisible if last two digits are divisible.In this case 50(No) Hence answer C #### C QUESTION:What approximate value should come in place of the question mark (?) in the following equation? 1.542 × 2408.69 + 5134.632 = ? options: A)4600 B)4800 C)5200 D)6400 E)8800 SOLUTION:Explanation 3700 + 5100 = 8800 Answer E #### E QUESTION:The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 25 feet on a side. What will be the volume of the new building in cubic feet? options: A)3,937,500 cubic feet B)15,750 cubic feet C)11550√3 cubic feet D)7,160,947 cubic feet E)3,937,500√3 cubic feet SOLUTION:Volume of the Hexagon with side 200 and height 70 = Area * height = 6*(sqrt(3)/4)(200^2)(70) Volume of the center bull's eye that is similar in shape of a hexagon but side 25 = 6 * (sqrt(3)/4)(25^2)*70 Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(25^2)*70=7,160,947 Answer is D #### D QUESTION:The sector of a circle has radius of 24 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)104.6 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 24) + 2(24) = 56.6 + 48 = 104.6 cm Answer:C #### C QUESTION:If x is negative and y is positive, which of the following cannot be positive? options: A)x/y B)-x*y C)-x/y D)x^2+y E)x^6+y SOLUTION:- /+ = - x/y is negative. Answer : A #### A QUESTION:The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is options: A)62 kg B)60 kg C)64 kg D)72 kg E)None of these SOLUTION:Explanation : Let the weight of student be x kg. Given, Difference in average weight = 8 kg => (96-x)/4 = 8 => x = 64 Answer : C #### C QUESTION:If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? options: A)100 B)10 C)0.01 D)0.0001 E)0.0001 SOLUTION:Given that 100 microns = 1 decimeter =10,000 angstroms So, 1 micron = 10,000/100 =100 Answer : A #### A QUESTION:The ratio of the two natural numbers is 6 : 5. If a certain number is subtracted to both the numbers, the ratio becomes 5 : 4. If the larger number exceeds the smaller number by 5, find the number subtracted? options: A)8 B)5 C)15 D)22 E)6 SOLUTION:Let the two numbers be 6x and 5x. Let the numbers subtracted to both so that their ratio becomes 5 : 4 be k. (6x - k) / (5x - k) = 5/4 => 24x - 4k = 25x - 5k => k = x. 6x - 5x = 5 => x = 5 k = x = 5. Answer:B #### B QUESTION:If x > 3 and y < -3, then which of the following must be true ? options: A)x/y > 1 B)x/y < -1 C)x/y < 0 D)x + y > 0 E)xy > 0 SOLUTION:Pick x=3, y = -3 A) x/y > 1 - Incorrect as x/y = -1 B) x/y < -1 - Incorrect as x/y = -1 C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0 D) x + y > 0 - Incorrect. x + y = 0 E) xy > 0 - Incorrect. XY = -9 which is less than zero. D should be the answer. #### D QUESTION:Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length? options: A)6 B)8 C)10 D)14 E)16 SOLUTION:In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT. So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10. Answer: C. #### C QUESTION:When the positive integer c is divided by 11, the quotient is d and the remainder 3. When c is divided by 19, the remainder is also 3. What is the remainder when d is divided by 19? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r where k = LCM (d1,d2) In this case the divisors are 1119 and remainder is 3. so LCM (11,19) = 209 So N= 209+3 = 212 Also c=d1q+3 ; which means d1q=209d1=11 therefore q=19 And ( d divided by 19)19/19 leaves remainder 0. Answer is E #### E QUESTION:A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than five people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month? options: A)x/4 B)x/5 C)x/9 D)x/20 E)4x/9 SOLUTION:If 5 people share the rent, each person would pay x/5. If 4 people share the rent, each person will pay x/4. The extra amount each person pays is x/4 - x/5 = 5x/20 - 4x/20 = x/20 The answer is D. #### D QUESTION:The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is: options: A)45 B)50 C)51.4 approx. D)54.6 approx. E)54 SOLUTION:Let the required means score be x. Then, 20 * 80 + 25 * 31 + 55 * x = 52 * 100 = 1600 + 775 + 55x = 5200 = 55x = 2825 = x = 565/11 = 51.4. ANSWER:C #### C QUESTION:All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes? options: A)26(26^3 + 26^4) B)26(26^3 + 26^5) C)27(26^3 + 26^5) D)27(26^3) + 26^5 E)26^3 + 27(26^5) SOLUTION:3-letter codes = 26^3; 4-letter codes = 26^4; 5-letter codes = 26^5; Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5. Answer: D. #### D QUESTION:Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for r dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month? options: A)x/(y - r) B)x/(r - y) C)x D)x/r E)x/y SOLUTION:Two ways... 1) let t be the total number, so cost = t*y+x and selling price=t*r.. No profit no loss....t*y+x=t*r.....T=x/(r-y)... B #### B QUESTION:A man can row his boat with the stream at 25 km/h and against the stream in 13 km/h. The man's rate is? options: A)1 kmph B)2 kmph C)6 kmph D)8 kmph E)3 kmph SOLUTION:DS = 25 US = 13 S = ? S = (25 - 13)/2 = 6 kmph Answer:C #### C QUESTION:The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is options: A)51:53 B)52:53 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (102% of x) / (106% of x) =102/106 =51/53 = 51:53. Answer: A #### A QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left? options: A)400 B)991 C)881 D)771 E)551 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A #### A QUESTION:Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point? options: A)20sec B)15sec C)30sec D)24sec E)1min SOLUTION:They meet every 360/7+8 = 24sec Answer is D #### D QUESTION:Joe has a total of $200 in his two pockets. He takes one fourth of the money in his left pocket and puts it in his right pocket. He then takes $20 from his left pocket and puts it in his right pocket. If he now has an equal amount of money in each pocket, then how much money did he originally have in his left pocket? options: A)$120 B)$130 C)$140 D)$150 E)$160 SOLUTION:Joe had $100 in his left and $100 in his right pocket at the end. So, he had $120 in his left pocket (and $80 in his right pocket) before moving $20 from his left to his right pocket. Thus, he had $160 in his left pocket originally (solve x − x/4 = 120). correct answer E #### E QUESTION:A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set? I. 1 II. -4 III. 5 options: A)I only B)II only C)I and III only D)II and III only E)I, II, and III SOLUTION:The question is which of the following must be in the set, not could be in the set. If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set. Answer: C. #### C QUESTION:The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet? options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am SOLUTION:meet x hrs after 8 a.m. (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330 ==>60x+75(x-1) = 330 x=3. So,they meet at (8+3). i.e 11a.m. ANSWER A #### A QUESTION:The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class? options: A)1:2 B)3:4 C)3:5 D)2:3 E)None of these SOLUTION:let x = number of girls y = number of boys sum of girls ages / x = 15.4 sum of boys ages / y = 16.4 The sum of the girls' ages is 15.4x, and boys' sum is 16.4y (sum of girls ages + sum of boys ages) / (x+y)= 15.8 (15.4x + 16.4y) / (x+y) = 15.8 15.4x + 16.4y = 15.8(x+y) 15.4x + 16.4y = 15.8x + 15.8y 0.6y = 0.4x 0.6y/x = 0.4 y/x = 0.4/0.6 y/x = 2/3 which is the ratio of boys to girls ANSWER:D #### D QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these SOLUTION:Explanation: Let their ages be x and (x + 24) years. 5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11. Their present ages are 35 years and 11 years Option D #### D QUESTION:The first half of a 600-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal to the average speed, in miles per hour, for the entire trip? options: A)300/(x + y) B)600/(x + y) C)150/x + 150/y D)300/x + 300/y E)600/x + 600/y SOLUTION:Time taken to cover first half i.e 300 miles of a 600 mile trip = x time taken to cover the second half i.e 300 miles of a 600 mile trip = y Total time taken = x+y Average speed for the entire trip =total distance /total time =600/(x+y) Answer B #### B QUESTION:P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}? options: A){6, 12} B){6, 15} C){21,28} D){9, 15} E){15, 24} SOLUTION:p/q= d=p/q+7 d= .75 q d= .6(q+7) we get d = 21 and q = 28. Answer = C. #### C QUESTION:A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 117 pounds? options: A)8 B)7 C)12 D)9 E)none of the above SOLUTION:Ans is C: 39 pounds --> 6 days 117 pounds --> x days x = 117*6/39 = 18 the animal has already consumed food in 6 days so the the number of days for it's total consumption be 117 pounds is 18-6 = 12 #### C QUESTION:A large research project was scheduled over the course of a 25-month period, and a budget of $100,000 was allotted for the course of the entire project. After 9 months, the project had spent $35,800. Was the project at this point over budget or under budget, and by how much? options: A)under, $200 B)under, $1200 C)under, $7000 D)over $1800 E)over $5800 SOLUTION:cost per month = 100,000/25 = 4,000. Now, multiply by nine months: 9*($4000) = $36,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is less than this, so it is under budget. $36,000 – #35,800 = $200 Answer = (A) #### A QUESTION:What is the value of m and n ? if log3m/log3n=log 52 options: A)1,5 B)2,5 C)3,5 D)4,5 E)2,3 SOLUTION:log (base a) b=log(base n)b/log(base n)a here base are same in reverse way of formula so log(base n)m=log(base 5) 2 hence n=5,m=2 ANSWER:B #### B QUESTION:The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : options: A)144 m2 B)140 m2 C)108 m2 D)158 m2 E)None of these SOLUTION:Area of the outer rectangle = 23 × 16 = 368 m2 Area of the inner rectangle = 19 × 12 = 228 m2 Required area = (368 – 228) = 140 m2 Answer B #### B QUESTION:x =3 4 5 y= 27 36 9 then what is the relation between x and y options: A)1*X)^2 B)1*X)^3 C)1*X)^4 D)1*X)^5 E)1*X)^6 SOLUTION:Y=(1*X)^2 9=(1*3)^2 9=9 ANSWER:A #### A QUESTION:A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 7. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used. The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost? options: A)7000 B)1000 C)1011 D)1101 E)1110 SOLUTION:The number of codes possible if leading zero is allowed = 10*10*10*10=10^4 The number of codes possible if leading zero is NOT allowed = 7*10*10*10=9*10^3 The difference = 10^4 - 7*10^3 = 10^3(10-7) = 7*10^3. Answer: A. Similar questions to practice: Hope it helps. #### A QUESTION:A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together? options: A)16 days B)12 days C)3 days D)5 days E)9 days SOLUTION:Sol. (A + B)'s 1 day's work = (1/18) (B + C)'s 1 day's work = (1/24) and (A + C)'s 1 day's work = (1/36) Adding, we get: 2 (A + B + C)'s 1 day's work =¬(1/18 + 1/24 + 1/36) =9/72 =1/8 (A +B + C)'s 1 day's work =1/16 Thus, A, Band C together can finish the work in 16 days. Ans: A #### A QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)1 B)2 C)8 D)7 E)0 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer: C #### C QUESTION:A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is options: A)2 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(28-10) kmph = 4 kmph. Answer B #### B QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea? options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None SOLUTION:Solution: 1st Method: Let the original price of tea be Rs. x/kg. After reduction the price becomes = x -10% of x = 9x/10 per kg. Now, (22500/(9x/10))-22500/x = 25 Or, 22500[10/9x- 1/x] = 25 Or, 25*9x = 22500; Or, x = (22500/2589) = Rs. 100. Hence, new price = 90 per kg. Thought process Method: Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg. After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg. So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea. Answer: Option C #### C QUESTION:The inverse ratio of 4: 2: 1 is? options: A)2:4:8 B)2:3:9 C)2:3:2 D)2:3:6 E)2:3:1 SOLUTION:1/4: 1/2: 1/1 = 2:4:8 Answer:A #### A QUESTION:The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary? options: A)2888 B)1266 C)1000 D)2779 E)2661 SOLUTION:X * (110/100) * (95/100) = 1045 X * (11/10) * (1/100) = 11 X = 1000 Answer: C #### C QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work? options: A)11 days B)16 days C)13 days D)15 days E)19 days SOLUTION:B 16 days P = 3Q P + Q = 3Q + Q = 4Q These 4Q people can do the work in 12 days, which means Q can do the work in 48 days. Hence, P can do the work in 16 days. #### B QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 82. How many points altogether did the team score? options: A)662 B)672 C)652 D)646 E)721 SOLUTION:8 * 82 = 656 – 10 = 646 ANSWER:D #### D QUESTION:Find the value of (X) in the given equation ? 35% of 1500 + X = 45% of 4200 – 320 options: A)910 B)980 C)1012 D)1045 E)None of these SOLUTION:Explanation: 35% of 1500 + X = 45% of 4200 – 320 (35/100 * 1500) + X = (45/100 * 4200) – 320 525 + X = 1890 – 320 X = 1890 – 320 – 525 X = 1890 – 845 X = 1045 ANSWER: D #### D QUESTION:If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $81, how much does one shirt cost? options: A)$10 B)$12 C)$13.20 D)$21 E)$16.80 SOLUTION:3J + 2S = 69 2J + 3S = 81 ---------------- 5J + 5S = 150 ----(divide by 5)---> J + S = 30 3J + 2S = J + 2(J + S) = J + 60 = 69 ---> J = 9 3*9 + 2S = 69 27 + 2S = 69 2S = 42 S = 21 Answer: D #### D QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)30% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 45 are employed males, hence 19% are employed females. (employed females)/(total employed people)=19/64=30% Answer: C. #### C QUESTION:The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 32 ? options: A)440 B)512 C)550 D)620 E)750 SOLUTION:Large numbers are made in two ways: Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place. 31*2 = 62 (large prime number) 2^6 = 64 (many small prime numbers) To get a sum as large as 32 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers. You are left with 620 which is 31*2*2*5 (sum greater than 32) Answer D #### D <<<Examples ends QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is: options: A)45:56 B)45:51 C)47:56 D)47:51 E)None SOLUTION:Solution: Let the CP be 100. Hence, SP = 100 + 12% of 100 = 112. If the marked price be X, then 90% of X = 112 => X = (112*100)/90 = Rs. 1120/9 Hence, Required ratio = 100:1120/9 = 900:1120 = 45:56. Answer: Option A #### A QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is? options: A)767 km B)975 km C)678 km D)900 km E)546 km SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km. x/40 = (x + 100)/50 50x = 40x + 4000 => x = 400 So, distance between P and Q = (x + x + 100)km =900 km. Answer: D #### D QUESTION:what is the integer among the following that represents a sum of 3 consecutive even integers? options: A)200 B)303 C)400 D)554 E)588 SOLUTION:Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers) Divisibility of 3: Sum of the digits of the number must be divisible by 3 Divisibility of 2: Unit digit of the number must be divisible by 2 A. 200NOT A MULTIPLE OF 3 SO RULED OUT B. 303NOT A MULTIPLE OF 2 SO RULED OUT C. 400NOT A MULTIPLE OF 3 SO RULED OUT D. 554NOT A MULTIPLE OF 3 SO RULED OUT E. 588A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!! #### E QUESTION:The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers? options: A)7 and 12 B)8 and 12 C)9 and 12 D)10 and 12 E)None of these SOLUTION:Let x and y be the two numbers such that x is larger than y. The statement "the larger number is four less than twice the smaller number" may be formulated by x = 2y - 4 We use the sum of the two numbers to write a second equation. x + y = 20 Substitute x by 2y - 4 in x + y = 20 to obtain 2y - 4 + y = 20 Solve for y to find y = 8 and x = 2y - 4 = 12 Answer B #### B QUESTION:The length of a train and that of a platform are equal. If with a speed of 108 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)752 B)799 C)719 D)750 E)900 SOLUTION:Speed = [108 * 5/18] m/sec = 30 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 30 è x = 30 * 60 / 2 = 900 Answer: E #### E QUESTION:A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute? options: A)1,200 meters / minute B)1,300 meters / minute C)1,450 meters / minute D)1,550 meters / minute E)1,650 meters / minute SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 72 kilometers per hour = 72 km/hr = (72 * 1000 meters) / (60 minutes) = 1,200 meters / minute correct answer A #### A QUESTION:A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 18 = 6 + 12 - {Both} + 0; {Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: A. #### A QUESTION:If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be . options: A)90 seconds B)150 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B #### B QUESTION:Three unbased coins are tossed. the probability of getting at least two head is ? options: A)1/4 B)1/2 C)3/4 D)2/3 E)2/5 SOLUTION:S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH} E be the event of getting at least two head is {THH,HTH,HHT,HHH} P(E)=n(E)/n(S)=4/8=1/2 Answer(B) #### B QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 4*5*6*7*8=6720. ANS:A #### A QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)876 m B)157 m C)235 m D)156 m E)167 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: C #### C QUESTION:In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is: options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Solution: Let there were x teams participating in the games, then total number of matches, nC2 = 153. On solving we get, => n =−17 and n =18. It cannot be negative so, n = 18 is the answer. Answer: Option C #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)123 B)166 C)240 D)157 E)198 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: C #### C QUESTION:A sum was put at simple interest at a certain rate for 6 years Had it been put at 4% higher rate, it would have fetched 144 more. Find the sum. options: A)500 B)600 C)700 D)800 E)900 SOLUTION:Difference in S.I. = P×T/100(R1−R2) ⇒ 144 = P×6x4/100(∵ R1 - R2 = 2) ⇒ P = 144×100/6×4=600 Answer B #### B QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? options: A)8 B)12 C)15 D)21 E)27 SOLUTION:As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain: A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15 B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12 A+B=15+12=27 Answer: E. #### E QUESTION:3, 5, 7, 11, 13, 17, 19, ____ options: A)25 B)36 C)23 D)49 E)27 SOLUTION:The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23.... Answer : C. #### C QUESTION:Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n. What is the value of 30~ ? options: A)1 B)0 C)2 D)8 E)31 SOLUTION:n~ = (n-1)! so 30~ = (30-1)! = 29! when 29!/30 we have 16*2 inside 29! hence 30 gets cancelled and we get remainder as 0 B #### B QUESTION:A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in. options: A)17 days B)97 days C)19 days D)60 days E)15 days SOLUTION:A = 140 days B = 105 days 1/140 + 1/105 = 7/420 = 1/60 =>60 days Answer: D #### D QUESTION:Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number? options: A)7 B)9 C)11 D)13 E)15 SOLUTION:Let the three numbers be x, x+2, and x+4. 3x = 2(x+4) + 3 x = 11 and then the third number is x+4 = 15. The answer is E. #### E QUESTION:From a number of mangoes, a man sells half the number of existing mangoes plus 1 to the first customer, then sells 1/3rd of the remaining number of mangoes plus 1 to the second customer, then 1/4th of the remaining number of mangoes plus 1 to the third customer and 1/5th of the remaining number of mangoes plus 1 to the fourth customer. He then finds that he does not have any mangoes left. How many mangoes did he have originally? options: A)12 B)14 C)15 D)13 E)16 SOLUTION:Let the No. of mangoes that the man had originally = X No. of mangoes sold balance 1st customer = (X/2) + 1 (X - 2)/2 2nd customer = (X - 2)/6 + 1 (X - 5)/3 3rd customer = (X - 5)/12 + 1 (X - 9)/4 4th customer = (X - 9)/20 + 1 0 (X - 9)/20 + 1= (X - 9)/4 => X = 14 ANSWER:B #### B QUESTION:In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary options: A)42,000 B)43,000 C)44,000 D)45,000 E)46,000 SOLUTION:as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned) Rest amounts are in the form of greater than or lesser than , Hence C $45000 answer is D #### D QUESTION:If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream options: A)1.5kmph B)0.5kmph C)0.4kmph D)1.6kmph E)2.5kmph SOLUTION:Speed upstream = 32/4 = 8 kmph Speed down stream = 72/8 = 9 kmph Speed of stream = ½ (9-8) = 0.5kmph ANSWER:B #### B QUESTION:Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144? options: A) 0 B) 25 C) 49 D) 81 E) 100 SOLUTION:144 =12 *12 (1!)^3=1 2!=2, therefore (2!)^3=2*2*2=8 3!=6, therefore (3!)^3=6*6*6=216 4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144 thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0 now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144 now remainder when 225 is divided by 144 is 81. hence answer should be D #### D QUESTION:A soccer coach is preparing his starting lineup of 11 players chosen from 15 players. He considers 8 of his players good at defense and 7 of his players good at offense. If he wants to pick 6 players best at defense and 5 players best at offense, how many different ways can he do this? options: A)264 B)328 C)460 D)588 E)642 SOLUTION:(8c6)*(7c5) [8!/(6!*2!)]*[7!/(5!*2!)] 28*21 588 D #### D QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)2 C)3 D)4 E)6 SOLUTION:The distance between the nest and the ditch is 200 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 200 = 6000. D = ST 6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km) D) #### D QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr options: A)25 Seconds B)28 Seconds C)30 Seconds D)35 Seconds E)40 Seconds SOLUTION:Explanation: Relative Speed = 63-3 = 60 Km/hr = 60 *(5/18) = 50/3 m/sec Time taken to pass the man will be 500∗3/50=30seconds ANSWER IS C #### C QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased? options: A) 100% B) 500% C) 300% D) 600% E) 800% SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%. Answer: B. #### B QUESTION:The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.90 per metre. options: A)2399 B)3888 C)2999 D)5808 E)6468 SOLUTION:Explanation: Area = (13.86 x 10000) sq.m = 138600 sq.m Circumference = Cost of fencing = Rs. (1320 x 4.90) = Rs. 6468. Answer: E) 6468 #### E QUESTION:A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? options: A)1/3 B)2by3 C)2/5 D)3/5 E)4/5 SOLUTION:Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol. Let x ml be the amount removed ---> total alcohol left = 4-0.4x New quantity of whiskey added = x ml out of which 0.19 is the alcohol. Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml. Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3. Hence, B is the correct answer. #### B QUESTION:A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ? options: A)7.5km/hr B)3.5km/hr C)9km/hr D)4km/hr E)5km/hr SOLUTION:given upstream(u) =5km/hr down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C) #### C QUESTION:When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8? options: A)3 B)4 C)5 D)6 E)2 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 24) 3n = 3(6) =18, which leaves a remainder of 2 when divided by 8. Answer E #### E QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)1.3 sec C)7.6 sec D)10 sec E)3.6 sec SOLUTION:Answer: Option A Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. #### A QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)12, 9 B)10, 5 C)12, 7 D)11, 6 E)12, 6 SOLUTION:x – y = 5 4x – 6y = 6 x = 12 y = 7 ANSWER:C #### C QUESTION:Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution? options: A)62.0 B)65.25 C)68.75 D)70.15 E)72.35 SOLUTION:SOL: Lets assume that 46L of sol1 was mixed with 10L of sol2. Alcohol in Sol1: 46*3/4 = 34.5L Alcohol in Sol2: 10*2/5 = 4L Total Alcohol in the mixed solution of 56L = 34.5 + 4 = 38.5L Alcohol concentration in the new sol: (38.5/56)*100 = 68.75% ANSWER:C #### C QUESTION:If the speed of X meters per second is equivalent to the speed of Y kilometers per minute, what is Y in terms of X? (1 kilometer=1000 meters) options: A)0.06x B)6x/5 C)18x/5 D)60x E)3600000x SOLUTION:x=1000y/60 y = 0.06x Answer : A #### A QUESTION:Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings? options: A)1/2 B)1/4 C)1/6 D)1/8 E)1/16 SOLUTION:Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible). Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8. Answer: D. #### D QUESTION:a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles? options: A)0.76 B)0.86 C)0.96 D)1.16 E)1.26 SOLUTION:let the radius of circle is 'r' area of the circle which is at corner = (22/7*r^2)/4 hence the area of all four circles are = 22/7*r^2 areaof circle which is made on center of suare is = 22/7*r^2 total area of all circles are = 2*22/7*r^2...........................(1) if we construct the diagram we get the relation 4r = 2sqrt2 r = 1/sqrt2 put the value of r in eqn 1 and we get 2*22/7*1/2 = 22/7 = 3.14 area of suare = 2^2 = 4 area of remaining part = 4-3.14 = 0.86 ANSWER:B #### B QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 16 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)128% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,16 = 16/100 x= 80*16/100 x= 12.8 12.8/10 = 1,28 = 128%, Answer E #### E QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 11 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)64 B)72 C)80 D)90 E)99 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 11 and the total number of coins is 9k = 99. The answer is E. #### E QUESTION:what is the least number by which 15,625 must be divided to get a number perfect square options: A)21 B)25 C)24 D)40 E)45 SOLUTION:15,625/25=625 625=(25)^2 Ans-25 ANSWER:B #### B QUESTION:On dividing 22 by a number, the quotient is 7 and the remainder is 1. Find the divisor. options: A)1 B)2 C)3 D)6 E)7 SOLUTION:d = (D-R)/Q = (22 - 1)/7 = 21/7 = 3 C #### C QUESTION:Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water? options: A)2 : 3 B)3 : 2 C)1 : 3 D)2 : 1 E)None of these SOLUTION:? Required ratio = 6?4 = 3 : 2 Answer B #### B QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? options: A) 4 B) 2 C) 2 D) 10 E) 12 SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. Answer A #### A QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:20000*2+8*x=15665*10 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums? options: A)30 B)36 C)70 D)80 E)150 SOLUTION:Method I: the rates solution “Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Rane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time: T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36 BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Rane and Zane need 36 weeks to make 15 drums. Answer = B. #### B QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 5400 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)30000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 5400 ( 18 × 300 = 5400) 100% -------> 30000 votes (100 × 300 = 30000) C #### C QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00 SOLUTION:Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer: Option D #### D QUESTION:There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? options: A)941,1009 B)991,1001 C)991,1009 D)791,1009 E)931,1009 SOLUTION:999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a2-b2=(a+b)(a-b) =(1000+9)*(1000-9) = (1009)*(991) Given that number of cats is less than number if mice. So number of cats is 991 and number of mice were 1009 Answer C #### C QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 46 years, was replaced by a new person. Find the age of the new person? options: A)18 B)56 C)16 D)17 E)14 SOLUTION:Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 46 + Q => Q = 16 Answer:C #### C QUESTION:Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? options: A)8 B)6 C)4 D)10 E)12 SOLUTION:Together they make 5/4 w widgets in 3 days. So they make w widgets in 3*4/5 = 12/5 days. 1/(t+2) + 1/t = 5/12 Now, calculating this is really cumbersome so try to plug in options to get to the answer. If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4. 1/6 + 1/4 = 5/12 It works so t = 4. Answer : A #### A QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:The mean of (54,825)^2 and (54,827)^2 = options: A)(54,821)^2 B)(54,821.5)^2 C)(54,820.5)^2 D)(54,826)^2 + 1 E)(54,821)^2 – 1 SOLUTION:54825^2 = (54826-1)^2 = 54826^2 + 1^2 - 2*54826*1 54827^2 = (54826+1)^2 = 54826^2 +1^2 + 2*54826*1 Taking the average of above 2 , we get (54826)^2 +1 hence the answer is D #### D QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 616 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 616 ⇒ y[12/10 + 1] = 616 ⇒ 22y/10 = 616 ⇒ 22y = 6160 ⇒ y = 6160/22 = 560/2 = Rs.280 B #### B QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 30¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)66 E)49.5 SOLUTION:Total price of six cans = 6*36.5 = 219 Total price of 4 cans = 4*30 = 120 Total rice of two cans = 219 - 120 = 99 Average price of two cans = 99/2 = 49.5 c Another way to do it is this: Assume that the four leftover cans were of 30c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 2*36.5 + 4*6.5 = 99 Avg cost of the two cans = 99/2 = 49.5c Answer (E) #### E QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall? options: A)120 B)350 C)1470 D)2,520 E)5,040 SOLUTION:Number of ways to choose 2 colors among 7 - 7c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 7c2 * 2* 7c4 = 1470 C #### C QUESTION:150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice? options: A)90days B)60days C)67days D)70days E)66days SOLUTION:Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day Let us say 70 men take x days to consume 150 kg. Quantity consumed by each item in x days = 7x/30 kg. Quantity consumed by 70 men in x days = (7x/30)(70)kg (7x/30)(70) = 980 x = (980 * 30)/490 => x = 60 days Answer & Answer: B #### B QUESTION:When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country? options: A)166 2/7 B)166 2/1 C)166 2/2 D)166 2/3 E)166 2/8 SOLUTION:5% - 2% = 3% 3% ---- 5 100% ---- ? => 166 2/3 Answer:D #### D QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:A and B are two partially filled buckets of water. If 6 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 6 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)66/5 B)13 C)17 D)21 E)23 SOLUTION:Let Bucket A be A and Bucket B be B Scenario 1 A-6 = 1/3 (B+6) ----> 3A-18 =B+6 Scenario 2 B-6 = 1/2 (A+6) -----> 2B-12 = A+6 From Scenario 1, B = 3A-24 Substitute B with this information in Stmt 2 2 (3A-24) -12 = A+6 ------> 6A -48-12 = A+6 ------> 6A- A = 60+6 ---> 5A= 66 A= 66/5, Answer choice A #### A QUESTION:Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are options: A)4, 8, 12 B)5, 10,15 C)10, 20, 30 D)12, 24, 36 E)None SOLUTION:Solution Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So x = 12. The numbers are 12, 24, 36. Answer D #### D QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4 Total factors = (4+1)*(4+1) = 6*4 = 24 Answer C. #### C QUESTION:Eight children — A, B, C, D, E, F, G and H — are going to sit in eight chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children? options: A)600 B)720 C)10080 D)14320 E)14800 SOLUTION:for such questions , we can treat both as one then total person=7.. these 7 can be arranged in 7! ways.. but within these 7 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080 ans C #### C QUESTION:The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 60 with him, what was the average amount with the group before his joining the group? options: A)s. 25.6 B)s. 25 C)s. 16.6 D)s. 26 E)s. 25.6 SOLUTION:Total members in the group = 7 Average amount = Rs. 30 Total amount with them = 7 * 30 = Rs. 210 One number has Rs. 60. So, the amount with remaining 6 people = 210 - 60 = Rs. 150 The average amount with them = 150/6 = Rs. 25 ANSWER:B #### B QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes at 13 km/hr downstream and 4 km/hr upstream. options: A)4.5 kmph B)9.5 kmph C)7.5 kmph D)8.5 kmph E)5.5 kmph SOLUTION:Speed in still water = (13 + 4)1/2 kmph = 8.5 kmph. answer :D #### D QUESTION:If a is an odd integer and b is an even integer which of the following must be an integer : options: A)a/b B)ab C)2a+b D)2(a+b) E)option B C and D SOLUTION:a= odd = e.g 3 b=even = e.g 6 A. odd/even for example 3/6 = 0.5 no even no odd B. odd * even = 3 * 6 = 18 even C. 2*odd + even = even + even even D. 2(even + odd) = 2(odd) even Hence E it is. #### E QUESTION:If x=kc and y=kt,then 2y+x =? options: A)k(t-c) B)k(c-t) C)c(k-t) D)k(2t+c) E)k(1-t) SOLUTION:Just put in the given values of y and x 2y +x =2 kt +kc Now take k common 2y + x = k(2t +c) You get (D) as your answer. #### D QUESTION:By selling 8 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 10%? options: A)6.54 B)9.45 C)7.34 D)6.67 E)5.09 SOLUTION:90% --- 8 110% --- ? 90/110 * 8 = 6.54 Answer: A #### A QUESTION:In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 30 ducks and in the larger pond there are 50 ducks. If 20% of the ducks in the smaller pond are green and 12% of the ducks in the larger pond are green, then what percentage of ducks are green? options: A)13% B)14% C)15% D)16% E)17% SOLUTION:Number of ducks in small pond = 30 green ducks in small pond = 20 % of 30 = 6 ducks Number of ducks in large pond = 50 green ducks in large pond = 12 % of 50 = 6 ducks Total number of ducks = 30 + 50 = 80 total number of green ducks = 6 + 6 = 12 ducks percentage of green ducks = 12/80 * 100 = 15% Answer: C #### C QUESTION:Find out the wrong number in the given sequence of numbers. 1, 2, 6, 15, 31, 55 options: A)55 B)6 C)15 D)31 E)91 SOLUTION:1(result) + (1*1) = 2. 2(result) + (2*2) = 6. 6(result) + (3*3) = 15. 15(result) + (4*4) = 31. 31(result) + (5*5) = 56. Now we are getting 56 not 55.. So 55 is the wrong number of the given. answer : A #### A QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ? options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5 SOLUTION:Explanation: Let the capacity of 1 bucket = x. Then, capacity of tank = 25x. New capacity of bucket = 2/5 x. Required no of buckets = 25x / (2x /5) = 62.5 ANSWER IS B #### B QUESTION:A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)29 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 180, so from 2003 to 2005 it increased by (180-140)/140=40/140=2/7=~29%. Answer: E. #### E QUESTION:40% of x is greater than 1/3rd of x by 110.what is x? options: A)1100 B)2100 C)1300 D)1650 E)1400 SOLUTION:4x/10-x/3=110 1x/15=110 x=1650 ANSWER:D #### D QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 9 and 10. The larger of the two numbers is: options: A)276 B)299 C)230 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 9) and (23 x 10). Larger number = (23 x 10) = 230. Answer: Option C #### C QUESTION:If the number 24*32 is completely divided by 6. what is the smallest whole number in the place of * ? options: A)4 B)3 C)1 D)2 E)5 SOLUTION:Solution The number is divisible by 6 means it must be divisible by 2 and 3. Since the number has 2 as its end digit it is divisible by 2. Now, 2+4+x+3+2=11+x which must be divisible by 3. Thus x=1 Answer C #### C QUESTION:At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day? options: A) 100 B) 1,800 C) 1,090 D) 200 E) 1,000 SOLUTION:Let the total number of sunlasses produced be x % of high quality sunglasses = 70% % of low quality sunglasses = 25% % of sunglasses defective = 100% - 95% = 5% But this number is given as 50 so 5% of x = 50 and x = (50)(100/5)) x = 180 Therefore there a total of 1,000 sunglasses made per day. Correct answer - E #### E QUESTION:Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:A man invested Rs. 26000 in 5% stock at 104. He sold the stock when the price rose to Rs. 120 and invested the sale proceeds in 6% stock. By doing this his income increased by Rs. 2500. At what price did he purchase the second stock? options: A)125 B)40 C)48 D)35 E)50 SOLUTION:Assuming that face value of the first stock = Rs.100 as it is not given in the question Since it is a 5% stock, we can take the dividend per stock = Rs.5 Market Value of the first stock = Rs.104 Investment on the first stock = Rs.26000 Number of stocks purchases = 26000/104 = 250 His total income from all these stocks = Rs.250 × 5 = Rs.1250 He sells each of this stock at Rs.120 ie, amount he earns = Rs.120 × 250 = Rs.30000 He invest this Rs.30000 in 6% stock (here also face value is not given and hence take it as Rs.100) His new income = Rs.(1250 + 2500) = Rs.3750 ie, By Rs.30000 of investment , he earns an income of Rs.3750 To get an income of Rs.6, investment needed = 30000×6/3750=Rs.48 This is the market value of the second stock Answer is C. #### C QUESTION:A student traveled 10 percent of the distance of the trip alone, continued another 30 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip? options: A)75 B)100 C)125 D)150 E)175 SOLUTION:Let x be the total length of the trip. 0.1x + 30 miles + 0.5x = x 30 miles = 0.4x x = 75 miles The answer is A. #### A QUESTION:There are two concentric circles with radii 5 and 4. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase? options: A)56 B)156 C)256 D)356 E)456 SOLUTION:The area of a circle is piR^2, where R is the radius. The area of the big circle is 25pi. The area of the small circle is 16pi. The area A1 between the circles is 9pi. When the big circle's radius increases, the new area is 36pi. When the small circle's radius decreases, the new area is 4pi. The area A2 between the circles is 32pi. The ratio of A2/A1 is 32/9 = 3.56 which is an increase of 256%. The answer is C. #### C QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea? options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None SOLUTION:Solution: 1st Method: Let the original price of tea be Rs. x/kg. After reduction the price becomes = x -10% of x = 9x/10 per kg. Now, (22500/(9x/10))-22500/x = 25 Or, 22500[10/9x- 1/x] = 25 Or, 25*9x = 22500; Or, x = (22500/2589) = Rs. 100. Hence, new price = 90 per kg. Thought process Method: Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg. After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg. So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea. Answer: Option C #### C QUESTION:A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? options: A)40.4 sec B)40.5 sec C)50.4 sec D)50.5 sec E)60.4 SOLUTION:Speed = 55 Km/hr (to convert km/hr in to M/s) = 55 x 5/18 M/s Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, ) = 770 m Time = Distance / Speed = 770 x 18 / (5 x 55) = 50.4 sec correct Answer: option a #### A QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age? options: A)22 B)15 C)77 D)21 E)182 SOLUTION:Present age is 4x and 3x, => 4x + 6 = 34 => x = 7 So Deepak age is = 3(7) = 21 Answer: D #### D QUESTION:An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 1/2M + 15, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold? options: A)a. A - 10 B)b. B - 15 C)c. C – 22.5 D)d. D – 30 E)e. E – 67.5 SOLUTION:A --- 10/2 + 15 = 20 --- CORRECT B --- 15/2 + 15 = not an integer --- wrong C --- 22.5(1/2) + 15 = not an integer --- wrong D --- 30/2+15 =30 --- wrong This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method. A #### A QUESTION:What is the next number of the following sequence 2, 12, 4, 24, 8, 48, (...) options: A)10 B)12 C)16 D)20 E)22 SOLUTION:The series is 2*6=12 12/3=4 4*6=24 24/3=8 8*6=48 48/3=16 ANSWER: C #### C QUESTION:If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 4, which of the following could NOT be a possible value of M+N? options: A)76 B)52 C)36 D)28 E)10 SOLUTION:M=4p+1 N=4q+3 We need M+N=4p+1+4q+3=4(p+q)+4 Pick numbers for pq Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers), we just need to choose values so that we get integer multiples of 6 so p+q=0 ; M+n = 4 p+q=1 ; M+N = 8 P+q=2 ; M+N = 12 and so on, so basically you get something like - 4,8,12,16,20,24,28,..... all the other options were turning up. Then I directly tried p+q=2because it was closer to 10, i got 12, So Answer E. #### E QUESTION:Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)80% C)100% D)180% E)200% SOLUTION:We can use fractional equivalents here to solve the problem 80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears 10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours Now we come to productivity Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour Hence the productivity is double with the assistant i.e. the increase in productivity is 180% D #### D QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? options: A)52% B)64% C)72% D)76% E)80% SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A QUESTION:A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested? options: A)25 B)37 C)36 D)29 E)21 SOLUTION:Explanation: From the information provided we know that, Principal + 8% p.a. interest on principal for n years = 180 …….. (1) Principal + 4% p.a. interest on principal for n years = 120 ……… (2) Subtracting equation (2) from equation (1), we get 4% p.a. interest on principal for n years = Rs.60. Now, we can substitute this value in equation (2), i.e Principal + 60 = 120 = Principal = Rs.60. We know that SI = , where p is the principal, n the number of years and r the rate percent of interest. In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60. Therefore, 60 =(60*n*4)/100 => n = 100/4 = 25 years. Answer: A) 25years #### A QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in: options: A)180 min B)160 min C)280 min D)18 min E)190 min SOLUTION:Let the slower pipe alone can fill the tank in x minutes Then the faster pipe can fill the tank in x/4 minutes Part filled by the slower pipe in 1 minute = 1/x Part filled by the faster pipe in 1 minute = 4/x Part filled by both the pipes in 1 minute = (1/x)+(4/x) Answer is A It is given that both the pipes together can fill the tank in 36 minutes ⇒ Part filled by both the pipes in 1 minute = 1/36 (1/x)+(4/x)=1/36 5/x=1/36 x=5×36=180 i.e.,the slower pipe alone fill the tank in 180 minutes #### A QUESTION:9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90.5% B)87.5% C)80.5% D)77.5% E)70.5% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.212; 10+0.3} = {9.788; 10.212}. From the 8 listed numbers, 7 are within this range so 6/8=87.5%. Answer: B. #### B QUESTION:The area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:L * W = 750 : area , L is the length and W is the width. 2 L + 2 W = 110 : perimeter L = 55 - w : solve for L (55 - W) * W = 750 : substitute in the area equation W = 25 and L = 30 correct answer E #### E QUESTION:A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain? options: A)12.5% B)16.7% C)22.5% D)27.5% E)33.3% SOLUTION:Let x be the original number of each color so there are a total of 5x candies. Kaz eats all of the green candies and half of the orange ones. There are 0 green candies and 0.5x orange candies remaining. He eats half of the remaining pieces of each color. There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies. He eats red and yellow candies in equal proportions. orange+blue+red+yellow = 0.75x + red + yellow = 1.2x red + yellow = 0.45x red = 0.225x, since red = yellow. The answer is C. #### C QUESTION:Find the unit's digit in the product 2467 153 * 34172? options: A)1 B)3 C)2 D)5 E)7 SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172 Now 7 4 gives unit digit 1 7 152 gives unit digit 1 7 153 gives 1*7=7.Also 172 gives 1 Hence unit's digit in the product =7*1=7. Option A #### A QUESTION:If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? options: A)$28000 B)$15000 C)$12000 D)$10000 E)$9000 SOLUTION:Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($7,000*2)*2=$28,000 (after 9 years investment will become $7,000*2=$14,000 and in another 9 years it'll become $14,000*2=$28,000). Answer: A. #### A QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ? options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters SOLUTION:Let x ltr water to be added 2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x))) 2=5%*(13+x)-------->x=27 Ans B #### B QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3. What is the ratio of their heights? options: A)A)3:4 B)B)2:7 C)C)2:2 D)D)2:1 E)E)2:9 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(3)2h2 => h1/h2 = 3/4 i.e. h1 : h2 = 3: 4 Answer: A #### A QUESTION:Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 36/49, what is the probability that the next one she draws will be pink? options: A)1/7 B)4/7 C)3/7 D)16/49 E)40/49 SOLUTION:The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 36/49 = (6/7) * (6/7) Therefore probability that the next one she draws is pink = 1/7 Option (A) #### A QUESTION:A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long? options: A)20 sec B)21 C)22 D)23 E)24 SOLUTION:Speed = 120/6 = 20 m/sec. Required time = (120 + 360)/20 = 24 sec. Answer:E #### E QUESTION:If two-third of a bucket is filled in one minute then the time taken to fill the bucket completely will be . options: A)90 seconds B)70 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 1 mint 1/3 filled in 1/2 mint thn 2/3+1/3=1 in mint 60 sec+30 sec=90 sec ANSWER:A #### A QUESTION:A batsman scored 210 runs which included 3 boundaries and 8 sixes. What % of his total score did he make by running between the wickets options: A)40% B)50% C)65% D)71.4% E)75% SOLUTION:Number of runs made by running = 210 - (3 x 4 + 8 x 6) = 210 - (60) = 150 Now, we need to calculate 60 is what percent of 120. => 150/210 * 100 = 71.4 % D #### D QUESTION:Concentrated pineapple juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated pineapple juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 60 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne? options: A)1 hour B)1 hour 20 minutes C)2 hours 30 minutes D)1 hour 40 minutes E)2 hours 10 minutes SOLUTION:v1 and V2 are speeds. v1.t /60 = v2 v2.t/40 = v1 v1/v2 = 3/2 which train A would 60. 2/3 mins to cover the same distance 40 + 40 = 80 mins (ANS B) #### B QUESTION:If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is: options: A)3:4:5 B)12:15:20 C)20:15:12 D)6:8:10 E)8:4:12 SOLUTION:Explanation: 6A = 8B = 10 C A:B:C = 1/6:1/8:1/10 = 20:15:12 ANSWER IS C #### C QUESTION:Calculate the percentage increase in the area of a square if each of its sides is increased by 15%? options: A)32.25% B)39.25% C)36.25% D)35.25% E)31.25% SOLUTION:Assume original length = 100m by 50m original area = 100*50= 5000 15% increase on each side l = 100 + 15 = 115 w = 50 + 7.5 = 57.5 new area = 115*57.5= 6612.5 increase in area = 6612.5 - 5000 = 1612.5 %increase =21% Answer A #### A QUESTION:In a apartment, 70% of the people speak English, 10% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi? options: A)1/3 B)2/3 C)2/5 D)1/2 E)2/9 SOLUTION:P (E) = 70 / 100 = 3 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E ∩ H) = 30 / 100 = 3 / 10 P (E or H) = P (E U H) = P (E) + P (H) - P (E ∩ H) = (7 / 10) + (1 / 10) - (3 / 10) = 3 / 10 = 1/2 D #### D QUESTION:A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday SOLUTION:This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B #### B QUESTION:A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is? options: A)6 km B)3 km C)9 km D)5 km E)1 km SOLUTION:Let the total distance be 3x km. Then, x/3 + x/4 + x/5 = 47/60 47x/60 = 47/60 => x = 1. Total distance = 3 * 1 = 3 km. Answer: B #### B QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 54 km/hr? options: A)2.5 B)2.9 C)6.67 D)2.8 E)2.1 SOLUTION:Speed = 54 * 5/18 = 15 m/sec Time taken = 100/15 = 6.67 sec. Answer:C #### C QUESTION:Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other? options: A)1:2 B)2:1 C)1:3 D)3:1 E)1:4 SOLUTION:root (b):root(a) 2:1 ANSWER:B #### B QUESTION:How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3? options: A)14 B)13 C)12 D)11 E)10 SOLUTION:The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers. The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form. So, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number. We get a total of 19−5=1419−5=14 numbers. Answer A #### A QUESTION:In case N is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)O and P E)T and U SOLUTION:O and P should serve on A ANSWER:D #### D QUESTION:The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)24years E)20years SOLUTION:The required average = (125*23+162*25)/125+162 = 24 years Answer is D #### D QUESTION:A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle? options: A)Rs.1148 B)Rs.1160 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 82% of Rs.1400 = Rs.(82/100×1400) Rs.1148. Answer A #### A QUESTION:Which of the following equations represents a line that is perpendicular to y=1/2*x+3? options: A)y−2x=8 B)2x+4y=10 C)3y+6x=12 D)4y−8x=16 E)5x−10y=20 SOLUTION:For two lines to be perpendicular, the product of slopes should be equal to -1. Slope of line 1 = 1/2 Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2 Answer: E #### E QUESTION:The length of the room is 3m and width is 3m. Find the cost of paving the floor by slabs at the rate of Rs.300 per sq meter? options: A)1800 B)1500 C)1700 D)1600 E)1540 SOLUTION:l=3m w=3m area of the floor = 3 x 3 = 9 sq m cost of paving = 200 x 9 = Rs. 1800 Answer: A #### A QUESTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, is options: A)131 B)176 C)274 D)405 E)495 SOLUTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}. 6 times 40 something is approx north of 240 Hence the answer is (C) 274 #### C QUESTION:Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics? options: A) 20% B) 42% C) 44% D) 66% E) 84% SOLUTION:You are correct. People who cover local politics are a subset of people who cover politics. 25% of reporters who cover politics do not cover local politics so 75% DO cover local politics. Reporters covering local politics= 75% of reporters covering politics= 25% of all reporters Reporters covering politics/All Reporters = 25/75 = 1/3 Reporters not covering politics/All Reporters = 2/3 = 66%=D #### D QUESTION:What is the area of a square field whose diagonal of length 20 m? options: A)228 B)271 C)200 D)277 E)181 SOLUTION:d2/2 = (20 * 20)/2 = 200 Answer:C #### C QUESTION:The smallest value of n, for which n+2 is not a prime number, is options: A)1,2 B)4,6 C)2,4 D)8,12 E)9,6 SOLUTION:(1 + 2) = 3. (2 + 2) = 4. (3 + 2) = 5. (4 + 2) = 6. which is not prime , n=2,4. ANSWER:C #### C QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/9) B)Rs. 2(2/9) C)Rs. 2(1/9) D)Rs. 4(2/9) E)Rs. 3(1/9) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B #### B QUESTION:The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is options: A)22 B)30 C)99 D)28 E)17 SOLUTION:Explanation: Total age increased = (8 * 2) years = 16 years. Sum of ages of two new men = (21 + 23 + 16) years = 60 years Average age of two new men = (60/2) years = 30 years Answer: B #### B QUESTION:You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg. And each emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What should you collect to get the maximum wealth? options: A)20 rubies and 15 emeralds B)40 rubies C)28 rubies and 9 emeralds D)None of these E)Cannot be determined SOLUTION:Explanation : The limits our wealth is the capacity of bag which is 12 Kg. So we should make each unit of weight to worth the max. Rubee: 0.3 Kg worth 4 Crore, so 1 Kg of Rubee is worth 4/(0.3) = 40/3 = 13.33 Crore. Emerald: 0.4 Kg worth 5 crore so 1 Kg of Emerald is worth 5/(0.4) = 50/4 = 12.5 Crore. As value per kilogram is more for Rubee we should pick max rubees for max wealth. Here we can accomadate the whole 12Kg with 40 rubees which is worth 160 Crore. Answer : B #### B <<<Examples ends QUESTION:A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left? options: A)400 B)197 C)278 D)270 E)279 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? options: A)5760 lr B)6000 lr C)6500 lr D)4000 lr E)4500 lr SOLUTION:1/x - 1/6 = -1/8 x = 24 hrs 24 * 60 * 4 = 5760 ANSWER A #### A QUESTION:Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work? options: A)13 B)14 C)18 D)11 E)10 SOLUTION:(5 + x)/20 + 5/25 = 1 => x = 11 days Answer:D #### D QUESTION:if (p/q)-(q/p)=21/10 then what ia the value of(4p/q)+(4q/p) options: A)58/5 B)59/5 C)121/105 D)101/105 E)1/2 SOLUTION:p/q =a then q/p = 1/a a+1/a=21/10 by solving this we get a=5/2 then 4*5/2+4*2/5 = 58/5 ANSWER:A #### A QUESTION:After a mathematics exam, 20 percent of the students reported that they didn't study, while 20 percent of the students who didn't study refused to admit they hadn't studied. What percent of the students didn't study? options: A)15% B)50% C)35% D)20% E)25% SOLUTION:Statement: 20% of Students (S) Reported they Didn't Study (RDS). Of the students who didn't study (DS) 20% refused to admit they didn't study (notRDT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RDS/S = 20% notRDS/DS = 20% => 100% - 20% => RDS/DS = 80% DS/S = (20)/(80)% = 25% Answer: E #### E QUESTION:Which expression is the greatest? options: A)3252/3257 B)3456/3461 C)3591/3596 D)3346/3351 E)3453/3458 SOLUTION:Let 3252/3257 be the original fraction. Notice that it is a positive Proper fraction. Hence adding the same constant to both the numerator and the denominator will increase the fraction as the fraction will move closer to one. Hence we just have to pick the number that adds the greatest value to both the numerator and the denominator. Options can be re-written as (x-5)x => 1-(5/x) A) 1- (5/3257) B) 1- (5/3461) C) 1- (5/3596) D) 1- (5/3351) E) 1- (5/3458) ANSWER:C #### C QUESTION:How many possible integer values are there for x if |4x - 3| < 6 ? options: A)One B)Two C)Three D)Four E)Five SOLUTION:Solution: |4x-3| < 6 let 4x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left (the less than sign represents that the a must be within boundaries ) (3-6)----------3----------(3+6) now, we have -3<a<9 but a =4x ==> -3<4x<9 dividing all values by +4 we have -0.75 <x < 2.24 Now question says Integer values (not rational ) therefore we have 0,1,2 ANSWER:C #### C QUESTION:A man spends Rs. 1900 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income? options: A)2075 B)2175 C)2275 D)2375 E)2475 SOLUTION:Explanation: Total expenditure for the first 3 months = 3 × 1900 = 5700 Total expenditure for 4 months = 4 × 1550 = 6200 Total expenditure for 5 months = 5 × 1800 = 9000 Total expenditure and saving (which is income for one year) = 5700 + 6200 + 9000 + 5200 = Rs. 25200 So, Average monthly income = 26100/12 = Rs. 2175 Answer B #### B QUESTION:If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x? options: A)-1 B)2 C)1 D)-2 E)0 SOLUTION:If we solve the question, we get x=-2. Option: D #### D QUESTION:The probability that a man will be alive for 10more yrs is 1/3 & the probability that his wife will alive for 10 more yrs is 5/8. The probability that none of them will be alive for 10 more yrs, is options: A)1/8 B)1/4 C)2/3 D)3/4 E)2 SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/4 Ans.(B) #### B QUESTION:In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 240 vote’s majority. What is the total number of votes polled? options: A)600 B)700 C)800 D)850 E)None of these SOLUTION:Explanation: Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %) 40 % = 70 % - 30 % 40% -----> 280 (40*6 = 240) 100% -----> 600 (100*6 = 600) Answer: Option A #### A QUESTION:A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? options: A)65 sec B)89 sec C)100 sec D)150 sec E)160 sec SOLUTION:Explanation: Speed =240/24 m/sec = 10 m/sec Required time =(240+650 /10)sec=89sec ANSWER IS B #### B QUESTION:A line of 24 children walk single file down the 54-meter hallway of their school at a speed of 20 meter/min. If each child takes up 1/4 meter of space in line, how long does it take for all of them to traverse the full length of the hallway? options: A)1 min B)2 min C)3 min D)4 min E)5 min SOLUTION:C 3 min d = 24 * 1/4 m + 54 m = 60 m T = 60 meters / 20 meters/min = 3 min #### C QUESTION:The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? options: A)91.5 B)91.4 C)91.7 D)91.3 E)91.1 SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 49.5 + 42 = 91.5 cm Answer:A #### A QUESTION:A man can row with a speed of 10 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is? options: A)10 kmph B)5 kmph C)40 kmph D)22 kmph E)25 kmph SOLUTION:M = 10 S = 30 DS = 10 + 30 = 40 ANSWER:C #### C QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$11,000 B)$50,000 C)$16,500 D)$ 6,600 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 2200 less between 3 people(x-(2200*3))/3 Set both eq. equal to each other. 16,500 Answer C) #### C QUESTION:A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/5 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ? options: A)x + 2000 = 1/3*(x - 3000) B)1/3*(x - 3000) = x C)x + 3000 = 1/3*x D)x - 7000 = 1/3*x E)x - 3000 = 1/5*x SOLUTION:Plane's original altitude = x Plane's new altitude after ascending 2000 ft = x+2000 Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000 So, after two changes plane is at 1/5 its original altitude => x-3000 = x/5 Answer (E) #### E QUESTION:A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? options: A)32 B)55 C)6 D)78 E)81 SOLUTION:S = (100 + 300)/45 = 400/45 * 18/5 = 32 Answer: A #### A QUESTION:Mr. Sane invested a total amount of 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was 3,620, what was the amount invested in scheme B? options: A)8,000 B)8,600 C)8,150 D)Data inadequate E)None of these SOLUTION:% interest on total amount per annum = 3620×100/16500×2=362/33% Now, use Alligation method. Hence, ratio of amount invested in schemes A and B = (12 - 362⁄33) : (362⁄33 - 10) = 17 : 16 Hence, amount invested in B = 16×16500/(17+16)=8000 Answer A #### A QUESTION:597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred’s and ten’s places are respectively: options: A)3 and 6 B)7 and 9 C)2 and 6 D)4 and 7 E)None SOLUTION:Solution : Let the given number be 597xy6. Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3 And, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0 => y=x+3 27+x+y) =>(27+x+x+3) =>(30+2x) => x = 3 and y = 6. Answer A #### A QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 4:3 and B:C = 4:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)20.23 B)20.13 C)30.93 D)20.93 E)10.93 SOLUTION:A:B = 4:3 B:C = 4:5 A:B:C = 16:12:15 12/43 * 75 = 20.93 ANSWER:D #### D QUESTION:A company pays 12.5% dividend to its investors. If an investor buys Rs.40 shares and gets 25% on investment, at what price did the investor buy the shares? options: A)20 B)66 C)18 D)19 E)01 SOLUTION:Explanation: Dividend on 1 share = (12.5 * 40)/100 = Rs.5 Rs.25 is income on an investment of Rs.100 Rs.5 is income on an investment of Rs. (5 * 100)/25 = Rs.20 ANSWER: A #### A QUESTION:In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class? options: A)12 Years B)12.6 Years C)13.6 Years D)14 Years E)14.5 Years SOLUTION:Total age of 50 students (30X 13+20 X 12) = 630 Average = 630/50 = 12.6 Years \ B #### B QUESTION:A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days? options: A)3.75 days B)3.99 days C)2.67 days D)2.98 days E)2.44 days SOLUTION:1/4 + 1/8 = 3/8 8/3 = 2.67 days Answer: C #### C QUESTION:In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 150 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ? options: A)40 ml B)100/3 ml C)30 ml D)20/3 ml E)10 ml SOLUTION:There are 0.3*100=30 ml of element X in the initial solution. We need X to be 1/3rd of 150 ml in the resulting solution, so 50 ml. Thus out of 50 ml of solution added, 20 must be X (in order it to become 50 ml) ans the remaining 30 must be Y. Answer: C #### C QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)15% B)25% C)115% D)75% E)55% SOLUTION:Explanation: SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer: B #### B QUESTION:(a/2)/(b/c) In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression? options: A)8/2 B)2/4 C)1/8 D)2/4 E)4/6 SOLUTION:(a/2)/(b/c) = (a*c)/2b The expression will have the largest value when numerator (a*c) is the largest. = (2*4)/2*1 =8/2 Answer A #### A QUESTION:The present ratio of students to teachers at a certain school is 35 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:We are given that the ratio of students to teacher is 35 to 1. We can rewrite this using variable multipliers. students : teachers = 35x : x We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation: Students/Teachers  25/1 = (35x + 50)/(x + 5) If we cross multiply we have: 25(x + 5) = 35x + 50 25x + 125 = 35x + 50 7.5 = x x~8 Since x is the present number of teachers, currently there are 8 teachers. Answer B. #### B QUESTION:What is the 9th term in this sequence? 2,4,6,13,22,35,60 options: A)138 B)148 C)158 D)168 E)178 SOLUTION:2+4 =6 +0 =6 6+4 =10+3 =13 13+6 =19+3 =22 22+13=35+0 =35 35+22=57+3 =60 60+35=95+3 =98 98+60=158+0=158 so 9th term is 158 ANSWER:C #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts and we should calculate how many sandwiches holds 1 part: 120 / 20 = 6 sandwiches in one part For bologna we have 7 parts so: 5* 6 = 30 Answer is B #### B QUESTION:By selling a watch for Rs.560/-, a man loses 20% what is that watch cost price options: A)s. 700/- B)s. 800/- C)s. 880/- D)s. 900/- E)s. 990/- SOLUTION:80 % ------> 560 (80 * 7 = 560) 100 % ------>700 (100 * 7 = 700) Cost price = Rs. 700/- A #### A QUESTION:A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 4 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)4/9. C)6/11. D)3/5. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 4buckles = 5buckles + 4buckles = 9buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 9 = x*15 x = 9/15=3/5 Answer: D #### D QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 740 will be: options: A)Rs. 300 B)Rs. 200 C)Rs. 240 D)Rs. 350 E)None of these SOLUTION:Z share = Z, Y = 1.2Z X = 1.25×1.2Z, X+Y+Z =740 (1.25× 1.2+1.2+1)Z=74 3.7Z=740, Z=200 Answer: . B. #### B QUESTION:An enterprising businessman earns an income of Re 5 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 10th day of business, he earns an income of: options: A)21 B)22 C)20 D)45 E)30 SOLUTION:2nd day he earns = 3(2 – 5) 3rd day he earns = 3(3 – 5) On 20th day he earns 3(20 -5) = 45 rupees ANSWER:D #### D QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5. O=12.5*6 = 75=E #### E QUESTION:If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true? I. c is even II. ab is even III. ab > 0 options: A)I only B)II only C)I and II D)I and III E)I, II, and III SOLUTION:Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above. II only.letter B #### B QUESTION:Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 45 days. On which day of the week in February was the task completed? options: A)Tuesday B)Wednesday C)Saturday D)Sunday E)Monday SOLUTION:This type of story problem is essentially just about a repeating pattern and a 'remainder.' We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 45 DAYS. We're asked on what day of the week the task was actually completed on. Since the task was supposed to be completed on a Wednesday.... A 1 day postponement would be Thursday A 2 day postponement would be Friday A 3 day postponement would be Saturday A 4 day postponement would be Sunday A 5 day postponement would be Monday A 6 day postponement would be Tuesday A 7 day postponement would be Wednesday A 8 day postponement would be Thursday Etc. So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 45 days. 45/7 = 6 remainder 3 This means that there are 6 full weeks AND 3 extra days after a Wednesday....Thus, the task was completed on a Saturday. C #### C QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is options: A)83.33 ml B)83.03 ml C)93.33 ml D)63.03 ml E)82.33 ml SOLUTION:Explanation: Profit (%) = 9.09 % = \inline \frac{1}{11} Since the ratio of water and milk is 1 : 11, Therefore the ratio of water is to mixture = 1:12 Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml] Answer: A) 83.33 ml #### A QUESTION:On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1? options: A) 8 B) 12 C) 24 D) 32 E) 36 SOLUTION:Jan 1 = C Feb 1 = C - 3 March 1 = C - 6 April 1 = C - 9 May 1 = C - 12 June 1 = C - 15 July 1 = C - 18 Aug 1 = C - 21 Sept 1 = C - 24 Difference between stock on September 1 than were in stock on January 1 will be - C - ( C - 24 )= 24 Hence answer will be (C) #### C QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5 SOLUTION:36 * 5/18 = 12.5 20:25 => 4:5 Answer: E #### E QUESTION:If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:Which is greater than 16 options: A)1.6 B)66 C)6 D)-6 E)6.1 SOLUTION:66 greater than 16. Answer: B #### B QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)12.6 B)12.0 C)12.1 D)12.3 E)12.2 SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec.Answer: B #### B QUESTION:The radius of a semicircular plot is 25. What is the approximate perimeter of the plot? options: A)114 B)150 C)129 D)25 E)57 SOLUTION:perimeter of a circle =2pi*r perimeter of a semicircle = pi*r + 2r aprox perimiter = 3.14*25 + 2*25 = 128.50 approximately 129 answer C #### C QUESTION:A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? options: A)5/6 km/hr B)25 km/hr C)79.2 km/hr D)15 km/hr E)38 km/hr SOLUTION:Explanation: Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr Answer:C #### C QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 145% D) 150% E) 180% SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80 So the approximate answer is E #### E QUESTION:A regular octagon is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ? options: A)48 degrees B)54 degrees C)67.5 degrees D)84 degrees E)108 degrees SOLUTION:its a regular pentagon so divide the globe by 8. = 360/8 = 45 45 would be the angle at O. Angles at A and B are equivalent, so 45 + 2x = 180 2x = 135 x = 67.5 Angles OAB and OBA will be 67.5 degrees each. C #### C QUESTION:A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 6 Gallons of water and 12 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x? options: A)37.5 B)75 C)100 D)150 E)90 SOLUTION:Nope, 150. I can only get it by following PR's backsolving explanation. I hate that. Original mixture has 20% salt and 80% water. Total = x Out of which Salt = 0.2x and water = 0.8x Now, 1/4 water evaporates and all salt remains. So what remains is 0.2x salt and 0.6x water. Now 12 gallons salt is added and 6 gallons of water is added. So salt now becomes -> (0.2x + 12) and water --> (0.6x+6) Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water. So (0.2x+12) = (0.6x+6)/2 => 0.4x+24=0.6x+6 ->0.2x=18 Solving, x = 90 Answer : E #### E QUESTION:The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches? options: A)31.23 B)25.12 C)36.25 D)23.17 E)27.66 SOLUTION:Total score of the batsman in 22 matches = 616. Total score of the batsman in the next 13 matches = 195. Total score of the batsman in the 35 matches = 811. Average score of the batsman = 811/35 = 23.17. Answer: D #### D QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3 SOLUTION:600 dollars in 2 years means 300 dollars in 1 year. To get 2400 dollars' it will take 8 years. To get 2400 in 3 years, we need 8/3 times money. Answer is E. #### E QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold? options: A) 11 B) 13 C) 15 D) 17 E) 19 SOLUTION:(x+5)*150 +x*85=2160 =>x=6 total lens=6+(6+5)= 17 Answer D #### D QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:A man can row upstream at 10kmph and downstream at 18 kmph. The speed of the stream is options: A)2.5 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(18 -10) kmph = 4 kmph. Answer B #### B QUESTION:The diameter of a garden roller is 1.4 m and it is 3 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22⁄7) options: A)60 m2 B)64 m2 C)68 m2 D)66 m2 E)None of these SOLUTION:Required area covered in 5 revolutions = 5 × 2Ï€rh = 5 × 2 × 22⁄7 × 0.7 × 3 = 66 m2 Answer D #### D QUESTION:Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture? options: A)294 B)235 C)350 D)288 E)580 SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)11*10! B)9*8! C)8*7! D)7*6! E)6*5! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=11*10! Ans:A #### A QUESTION:If n is an integer greater than 8, which of the following must be divisible by 3? options: A)1. n (n+1) (n-4) B)2. n (n+2) (n-1) C)3. n (n+3) (n-5) D)4. n (n+4) (n-2) E)5. n (n+5) (n-6) SOLUTION:We need to find out the number which is divisible by three, In every 3 consecutive integers, there must contain 1 multiple of 3. So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three 1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1) 2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1) 3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n) 4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1) 5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2) from the above onlyoption Ais product of consecutive three numbers. C #### C QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS: options: A)15 B)16 C)18 D)25 E)NONE OF THESE SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4 SUPPOSE TANYA TAKES X DAYS TO DO THE WORK; 5:4::20:X, X=(4x20/5), X=16 DAYS. CORRECT OPTION: B #### B QUESTION:A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is options: A)240 B)250 C)260 D)230 E)220 SOLUTION:Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 36 => 300+L = 15×36 = 540 => L = 540-300 = 240 meter Answer is A. #### A QUESTION:Here 10 programmers, type 10 lines within 10 minutes then 60 lines can type within 60 minutes. How many programmers are needed? options: A)16 B)10 C)6 D)60 E)50 SOLUTION:10 10 programmer 10 line 10 mins. 10 programmer 20 line 20 mins. . . . .10 programmer 60 line 60 mins. ANSWER:D #### D QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit? options: A)s.2323 B)s.2380 C)s.2329 D)s.2660 E)s.2312 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 7790 * 14/41 = Rs.2660. Answer: D #### D QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:1) Draw a simple cube 2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes. 3) Remember that the OUTSIDE of the cube is the part that's painted.... The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. J=4 + 4 + 4 = 12. Answer A #### A QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as a(f+l)/2----------------1) a= total no. of terms =80 f= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? options: A)17% increase B)44% decrease C)60% increase D)66% increase E)66% decrease SOLUTION:if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater. ANSWER:A #### A QUESTION:At what rate percent per annum will a sum of money double in 16years? options: A)10.6% B)3.65% C)6.25% D)8.32% E)11% SOLUTION:Let principle = P S.I. = P T = 16yrs Rate = 100*P/P*16 = 25/4% = 6.25% Answer is C #### C QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)800 B)700 C)750 D)850 E)900 SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265 253/160p=1265==> p =800 ANSWER A #### A QUESTION:The population of a village is 6000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)5000 B)4860 C)5400 D)4800 E)5120 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 6000 × 90/100 × 90/100 = 4860 B #### B QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:20000*2+8*x=15665*10 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? options: A)615 m B)240 m C)168 m D)197 m E)691 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m Answer: B #### B QUESTION:In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 30 ducks and in the larger pond there are 50 ducks. If 20% of the ducks in the smaller pond are green and 12% of the ducks in the larger pond are green, then what percentage of ducks are green? options: A)13% B)14% C)15% D)16% E)17% SOLUTION:Number of ducks in small pond = 30 green ducks in small pond = 20 % of 30 = 6 ducks Number of ducks in large pond = 50 green ducks in large pond = 12 % of 50 = 6 ducks Total number of ducks = 30 + 50 = 80 total number of green ducks = 6 + 6 = 12 ducks percentage of green ducks = 12/80 * 100 = 15% Answer: C #### C QUESTION:The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 32 ? options: A)440 B)512 C)550 D)620 E)750 SOLUTION:Large numbers are made in two ways: Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place. 31*2 = 62 (large prime number) 2^6 = 64 (many small prime numbers) To get a sum as large as 32 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers. You are left with 620 which is 31*2*2*5 (sum greater than 32) Answer D #### D QUESTION:If a certain number X is divided by 82, the reminder is 5. what is the reminder when X+13 is divided by 41? options: A)3 B)18 C)6 D)16 E)5 SOLUTION:X can be written as 82K + 5 or X = 5,87,169,etc. X + 13 = 82K + 5+13= 82K +18 or X + 13 = 18,100, 182 etc. When divided by 41, we will get the remainder 18. B #### B QUESTION:Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds? options: A)22 B)24 C)99 D)27 E)17 SOLUTION:Explanation: Less Cogs more turns and less time less turns Number of turns required=80 × × = 24 times Answer: B) 24 #### B QUESTION:Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day A on which the buses leave at the same time. options: A)A=Tuesday B)Wednesday C)Thursday D)Sunday E)A=The busses will never leave at the same time SOLUTION:The answer is E. I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide. Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E #### E QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/55000 * 100 = 21.6% ANSWER:D #### D QUESTION:If the sum of 5 consecutive integers is x, which of the following must be true? I. x is an even number II. x is an odd number III. x is a multiple of 5 options: A)I only B)II only C)III only D)I and III E)II and III SOLUTION:I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true. II. Same as above. This need not be always true. III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4) = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases. Therefore C is the answer. #### C QUESTION:It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 120 pages? options: A)12 B)18 C)20 D)24 E)36 SOLUTION:If it takes 4 more minutes for A to print 40 pages than it takes B, it takes 5 more minutes for A to print 50 pages than it takes B. Thus if b is the number of minutes than B takes to print 50 pages, we can write: 1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job) 6(2b+5)=b(b+5) b^2-7b-30=0 (b-10)(b+3)=0 b=10 Thus it takes A 15 minutes to print 50 pages and 15*120/50=36 minutes to print 120 pages (ANSWER E) #### E QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:The product of the prime numbers between 0 and 20 is closest to... options: A)10^5 B)10^6 C)10^7 D)10^8 E)10^9 SOLUTION:Write out the primes 1 - 20 2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 Round the numbers off in multiples of 5. Try to alternate rounding up and down 5 x 5 x 5 x 5 x 10 x 10 x 20 x 20 25 x 25 x 10 x 10 x 20 x 20 pull out 10 from each number 10^6 (2.5 x 2.5 x 2 x 2) 10^6 (5 x 4) 10^7 (2) round off the 2. answer is C #### C QUESTION:Find the sum of all odd numbers upto 100. options: A)200 B)1000 C)2500 D)3140 E)3200 SOLUTION:Sol. The given numbers are 1, 3, 5, 7, ..., 99. This is an A.P. with a = 1 and d = 2. Let it contain n terms. Then, 1 + (n - 1) x 2 = 99 or n = 50. Required sum = (n/2) (first term + last term) = 50(1 + 99)/2 = 2500. ANSWER C 2500 #### C QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4 Total factors = (4+1)*(4+1) = 6*4 = 24 Answer C. #### C QUESTION:If cost of sugar increases by 12%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? options: A)7.5 B)9.2 C)10.7 D)15.3 E)18.6 SOLUTION:100 112 ----- 112 ----- 12 100 ------ ? => 10.7% Answer:C #### C QUESTION:Find the invalid no.from the following series 15 46 63 71 75 77 78 options: A)32 B)35 C)46 D)49 E)67 SOLUTION:In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46 C #### C QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? options: A)37 B)38 C)30 D)77 E)27 SOLUTION:US = 25 DS = 35 M = (35 + 25)/2 = 30 Answer:C #### C QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51 kmph, find the speed of the stream? options: A)12 kmph B)13 kmph C)14 kmph D)15 kmph E)17 kmph SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 51/3 = 17 kmph ANSWER:E #### E QUESTION:A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is? options: A)25/42 B)25/46 C)25/41 D)25/49 E)25/23 SOLUTION:Total fruits = 9 Since there must be at least two apples, (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42. Answer:A #### A QUESTION:A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to options: A)the same as one 45 percent discount B)the same as one 38 percent discount C)the same as one 36 percent discount D)the same as one 30 percent discount E)the same as one 28 percent discount SOLUTION:0.9*0.8*x=0.72x from initial value, meaning 0.28 or 36% discount E #### E QUESTION:Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent? options: A)11 1/8 B)11 1/7 C)11 1/9 D)11 1/1 E)11 1/2 SOLUTION:900 --- 100 100 --- ? => 11 1/9%.Answer: C #### C QUESTION:The first republic day of the India was celebrated on 26th January,1950. It was options: A)221 B)28 C)276 D)20 E)22 SOLUTION:1-1-1 AD fall on Monday. We calculate the number of odd days till 24th december, 1995. Number of odd days till 1600 years = 0 1601 to 1700 = 5 1701 to 1800 = 5 1801 to 1900 = 5 49 years contains = 37 normal + 12 leap years =12 × 2 + 37 = 61 odd days = 61/7 = 5 odd days 25th January 1950 = 25/7 = 4 odd days Total odd days =15 + 5 + 4 = 24/7 = 3 odd days So 26th January,1950 is Thursday Answer:B #### B QUESTION:There are two sections C and D of a class, consisting of 18 and 22 students respectively. If the average weight of sections C is 20 kg and that of sections D is 18 kg. Find the average weight of the whole class options: A)18.7 B)18.8 C)18.9 D)19.9 E)None SOLUTION:Solution Total weight of(18+22)Students = (18x20+22x18)Kg = 756 kg. Average weight of the whole class = (756 /40 ) = 18.90. Answer C #### C QUESTION:A 25% stock yielding 20% is quoted at: options: A)s. 83.33 B)s. 110 C)s. 112 D)s. 125 E)s. 140 SOLUTION:Income of Rs 20 on investment of Rs 100 Income of Rs 25 on investment of ? = (25*100)/20=125 ANSWER:D #### D QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? options: A)21 B)36 C)39 D)60 E)65 SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96. Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room. Therefore there are 3/8*96=36 people in the room under the age of 21. Answer: B. #### B QUESTION:Two men are going along a track rail in the opposite direction. One goods train crossed the first person in 20 sec. After 10 min the train crossed the other person who is coming in opposite direction in 18 sec .After the train has passed, when the two persons will meet? options: A)95 minutes B)90 minutes C)88 minutes D)95 minutes E)None of these SOLUTION:Explanation : Let us consider that speed of train , first man and second man are respectively t, f and s. According to first given condition goods train crossed the first person moving in same direction in 20 sec. So length of the will be 20(t-f) Similarly train crossed the second man in 18 sec. So length of the train will be 18(t+s) on comparing these two equations, we get 20(t-f) = 18(t+s) => 2t = 20f + 18s => t = 10f + 9s Now it is given that After 10 min the train crossed the other person who is coming in opposite direction. So,If we consider this way of train as L then the next equation will be L = 600t (here 600 is used for 10 minutes) Finally as asked in the question the time required to meet the two man after the train has passed will be given by Time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes} => = (600t-600f) / (f+s) => = [600(10f+9s)-600f] / (f+s) => = 600(10f+9s-f) / (f+s) = 600 * 9(f+s) / (f+s) => =600*9 seconds => = 600*9/60min => = 90 minutes Hence (B) is the correct answer. Answer : B #### B QUESTION:Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt? options: A)25/33 B)31/44 C)41/55 D)53/66 E)65/77 SOLUTION:Total possible ways to choose 4 students out of 12 = 12C4 = 495 The number of ways to choose 4 students with no green shirts = 9C4 = 126 P(no green shirts) = 126/495 = 14/55 P(at least 1 green shirt) = 1 - 14/55 = 41/55 The answer is C. #### C QUESTION:A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? options: A)4 : 3 B)9:2 C)18:20 D)1:4 E)18:4 SOLUTION:A: B =24000 : 18000 = 8 : 6 = 4 : 3 ANSWER:A #### A QUESTION:Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number? options: A)150 B)125 C)140 D)180 E)200 SOLUTION:3x+4x = 420 x=60== 3x=180 ANSWER D #### D QUESTION:Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank? options: A)14 min 80 sec B)14 min 48 sec C)14 min 42 sec D)14 min 40 sec E)14 min 43 sec SOLUTION:Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15 Remaining part = 1 - 7/15 = 8/15 Part filled by B in 1 minute = 1/20 1/20 : 8/15 :: 1 ; x x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec. The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec. Answer:D #### D QUESTION:The average weight of 16 children in a class is 50.25 kg and that of the remaining 8 children is 45.15 kg. Find the average weights of all the children in the class. options: A)A)48.55 B)B)49 C)C)51 D)D)61 E)E)62 SOLUTION:Required average = (50.25 x 16 + 45.15 x 8)/(16 + 8) = (804 + 361.20)/24 = 1165.20/24 = 48.55kg Answer is A #### A QUESTION:Two numbers are in the ratio 5:8 and thier H.C.F is 4. Find the numbers. options: A)25 and 40 B)20 and 32 C)30 and 48 D)15 and 24 E)16 and 25 SOLUTION:Explanation: Let two numbers 5x, 8x their H.C.F = 4 Therefore H.C.F is 4 i.e, x in this case. Therefore The numbers are 5 x 4 = 20 8 x 4 = 32 Answer: Option B #### B QUESTION:A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week? options: A)605 B)505 C)105 D)100 E)200 SOLUTION:earning 35 surveys using her cell phone = 13*35 = 455 balance 15 surveys = 10 x 15 = 150 Total = 455+150 = 605 Answer : A #### A QUESTION:Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ? options: A)500 B)600 C)450 D)550 E)None of these SOLUTION:Explanation: Let the lent at 5% be 'A' (A x 5 x 1)/100 + [(1500 - A)x 6 x 1]/100 = 85 5A/100 + 90 – 6A/100 = 85 A/100 = 5 => A = 500 ANSWER IS A #### A QUESTION:If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years? options: A)(1+k/100)^n B)(1+k)^n C)(1+kn/100) D)(1+k/100)^4n E)(1+kn) SOLUTION:Amount after 7n years will be = x ( 1 + k/100)^4n Amount after 3n years will be = x ( 1 + k/100)^3n So, required ratio will be - { x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n Hence answer will be a. (1+k/100)^4n D #### D QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 8? options: A)2/13 B)3/45 C)5/36 D)6/73 E)4/15 SOLUTION:n(S) = 6*6 = 36 E = {(2,6),(3,5),(4,4),(5,3),(6,2)} Probability = 5/36 Answer is C #### C QUESTION:10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)90 B)98 C)35 D)99 E)80 SOLUTION:Though 2*(10C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used. The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches. Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches. This continues like this and the total matches are 18+16+14...+2 18+16+...+2 = 2(9+8+...+1) = 2((9*10)/2) = 9*10 = 90. ANSWER:A #### A QUESTION:What should come in place of the question mark (?) in the following equation? 5978 + 6134 + 7014 = ? options: A)19226 B)16226 C)19216 D)19126 E)None of these SOLUTION:? = 5978 + 6134 + 7014 = 19126 Answer D #### D QUESTION:Albert invested an amount of $8000 in a fixed deposit scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit? options: A)$8100 B)$8820 C)$8800 D)$8810 E)$8825 SOLUTION:Amount = 8000 x (1 + 5/100)^2) = 8000 x 21/20 x 21/20 =8820. Answer B)$8820 #### B QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? options: A)15% B)25% C)35% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(300) / 1000 = 15% The answer is A. #### A QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase? options: A)$32 B)$50 C)$320 D)$400 E)$500 SOLUTION:Property tax as a percentage of its assessed value = 8% Increase in assessed value of the property = 24000 - 20000 = 4,000 $ Increase in property tax = (8/100)* 4000 = 320 $ Answer C #### C QUESTION:The sum of three integers A, B and C is 60. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C? options: A)40 B)45 C)35 D)50 E)55 SOLUTION:A is one third of the sum of B and C.. or A=1/3(B+C)... But A+B+C=60 so 1/3(B+C)+B+C=60 4(B+C)/3= 60 B+C =60*3/4 = 45 A=60-45=15 2)B is one fifth of the sum of A and C or B=1/5(A+C)... But A+B+C=60 so 1/5(A+C)+A+C=60 A+C=60*5/6=50 but A=15, so C=50-15=35 Answer :C #### C QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone? options: A)6 B)12 C)14 D)15 E)17 SOLUTION:Renu’s one day’s work = 1/6 Suma’s one day’s work = 1/3 - 1/6 = 1/6 Suma can do it alone in 6 days. ANSWER:A #### A QUESTION:Three friends X, Y, Z rented a auto for Rs.520. A used it for 6 hours, B used it for 9 hours and C used it for 11 hours. What is the hire charges paid by Y: options: A)Rs 140 B)Rs 160 C)Rs 180 D)Rs 200 E)None SOLUTION:X : Y : Z = 7 : 8 : 11. Hire charges paid by Y = Rs(520×9/26) = Rs.180. Answer C #### C QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9 Probability to become a secretary = (9/10 * 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:Find the option to replace the question mark in the series below 5 ? 15 75 525 4725 options: A)2 B)6 C)7 D)5 E)8 SOLUTION:ol: 5 x 1 = 5 5 x 3 = 15 15 x 5 = 75 75 x 7 = 525 525 x 9 = 4725 So ? = 5 Answer:D #### D QUESTION:Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? options: A)5 B)3 C)4 D)6 E)1 SOLUTION:Rate of one machine = 1 job / (20*4) days let X = number of machines needed to complete the job in 10 days 1/(4*20) * 10 * X = 1 job X = 8 8-4= 4 ANSWER: C #### C QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ? options: A)6 B)4 C)2 D)5 E)1 SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B #### B QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:In what ratio should a variety of oil costing Rs. 9 per ltr be mixed with another variety of oil costing Rs. 17.25 per ltr to obtain a mixture costing Rs. 11.75 per ltr? options: A)4 : 1 B)1 : 3 C)3 : 1 D)1 : 2 E)2 : 1 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (17.25 - 11.75) / (11.75 - 9) = 22/11=2/1 ANSWER:E #### E QUESTION:Three numbers are in the ratio 5 : 4 : 6 and their average is 750. The largest number is : options: A)30 B)98 C)900 D)21 E)22 SOLUTION:Explanation: Let the numbers be 5x, 4x and 6x, Then, (5x + 4x + 6x ) / 3 = 750 => 15x = 750*3 => x = 150 Largest number 6x = 6*150 = 900 Answer: C #### C QUESTION:A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper? options: A)140 B)388 C)238 D)119 E)112 SOLUTION:when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 14*10 = 140 sq cmV Answer: A #### A QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? options: A)1/48 B)1/42 C)1/40 D)1/41 E)1/43 SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42 Answer: B #### B QUESTION:The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)18 years B)88 years C)77 years D)10 years E)17 years SOLUTION:Let their ages be x and (x + 20) years. 5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10. Their present ages are 30 years and 10 years Answer:D #### D <<<Examples ends QUESTION:The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number? options: A)3 B)6 C)9 D)12 E)15 SOLUTION:Sol. Let the numbers be x, x + 2 and x + 4. Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7. ∴ Middle number = x + 2 = 9. Answer C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer: A #### A QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘POWER’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word ‘POWER’ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 5*4*3*2*1 = 120 ANSWER:E #### E QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? options: A)1000 B)817 C)278 D)268 E)280 SOLUTION:2 * 22/7 * 1.75 * x = 11000 x = 1000 Answer: A #### A QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house? options: A)$96,000 B)$94,000 C)$88,000 D)$75,000 E)$40,000 SOLUTION:Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer. #### B QUESTION:In how many W ways can 5 people from a group of 6 people be seated around a circular table options: A)56 B)80 C)100 D)120 E)144 SOLUTION:W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner) = 6 * 4! = 6 * 24 = 144 Answer - E #### E QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre. options: A)$8250 B)$8350 C)$8650 D)$8450 E)$8500 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $400 Hence, total cost =5.5×3.75×400= $8250 A #### A QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3600 C)Rs. 3900 D)Rs. 4000 E)Rs. 4100 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C #### C QUESTION:Q. How many 9-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6, 6, 7? options: A)180 B)140 C)210 D)270 E)300 SOLUTION:the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2 i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _ case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6 when the units digit is 2 i.e 1 _ _ _ _ _ 2 number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60 when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30 case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6) number of ways this can be done would be 5! / (2!) for 2 =60 and 5! / 2! for 6 ... = 60 adding all of these ... gives the answer 140 ... the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat B #### B QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 15 years? options: A)2:6 B)3:5 C)1:4 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×9/100) /(P×R×15/100)]=9PR/15PR=9/15=3:5 Answer B #### B QUESTION:On Monday Joshua sold 90 phones, Rob sold 30% more phones than Joshua, Prerna sold 11 more phones than Rob, and Declan sold 3/4 of what Prerna sold. How many phones did Declan sell? options: A)111 B)75 C)29 D)128 E)96 SOLUTION:E 96 Joshua sold 90 phones. Rob sold 30 % more phones than Joshua Rob = 90 + 90 × 30% = 90 + 90 × 0.30 = 90 + 27 = 117 Prerna sold 11 more phones than Rob Prerna = 117 + 11 = 128 Declan sold 3/4 of what Prerna sold. Declan= 128 x 3/4 =96 Declan sold 96 phones. The correct answer is E. #### E QUESTION:What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive? options: A)90 B)80 C)100 D)105 E)110 SOLUTION:10 and 190 inclusive would mean there are 17 terms. No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170 The middle term is the average which is the tenth term = 80 B is the answer. #### B QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)None of these SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111.. Answer : Option C #### C QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5? options: A) 94 B) 99 C) 26 D) 73 E) None of the Above SOLUTION:Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 5 = 10x +y = x^2 y^2 -10 Thus 2xy +5 = x^2 + y^2 - 10 x^2 + y^2 -2xy = 15 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 15 or 94 Thus the answer is A #### A QUESTION:If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ? options: A)11. B)13. C)17. D)10. E)7. SOLUTION:If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd) If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option which implies y is odd, Now M(odd)+Y(odd)=Even 10 is the only option that is even=D #### D QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.79 B)5.71 C)5.76 D)5.79 E)5.73 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 Answer: C #### C QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse? options: A)27 B)98 C)27 D)80 E)71 SOLUTION:CP = SP + 1CP = SP - g 620 + x = 860 - 2x 3x = 240 => x = 80 Answer:D #### D QUESTION:The ratio of two quantities is 2 to 5. If each of the quantities is increased by 5, what is the ratio of these two new quantities? options: A)2/5 B)5/8 C)7/13 D)22/25 E)It cannot be determined from the information given. SOLUTION:Correct Answer: E Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5. For example, if x = 2 and y = 5, then (x+5)/(y+5) = (2+5)/(5+5) = 7/10. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+5)/(y+5) = (4+5)/(10+5) = 9/15. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E). #### E QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:In what time will a train 100 meters long cross an electric pole, if its speed is 126 km/hr options: A)8.5 seconds B)2.86 seconds C)3.5 seconds D)2.5 seconds E)2.6 seconds SOLUTION:First convert speed into m/sec Speed = 126*(5/18) = 35 m/sec Time = Distance/speed = 100/35 = 2.86 seconds Answer: B #### B QUESTION:The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).? options: A)180.27 cm B)180.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 182 cm. Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm = 182 cm - 1.71 cm = 180.29 cm. Answer: B #### B QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5. options: A)140 B)142 C)146 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M? options: A)278 B)2890 C)270 D)2702 E)1050 SOLUTION:504/M = 384/800 (504 * 800) / 384 = M M = 1050 Answer:E #### E QUESTION:Find the area of a cuboid of length 10cm , breadth 8 cm . and height 6cm. options: A)400 cm cube B)410 cm cube C)420 cm cube D)430 cm cube E)480 cm cube SOLUTION:Area of a cuboid = lxbxh =10cm x 8cm x 6cm = 480 cm cube answer :E #### E QUESTION:What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? options: A)s.2.04 B)s.2.08 C)s.3.67 D)s.2.83 E)s.2.42 SOLUTION:C.I. when interest is compounded yearly = [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100] = 9000 * 26/25 * 51/50 = Rs. 9547.2 C.I. when interest is compounded half-yearly = [9000 * (1 + 2/100)2] = (9000 * 51/50 * 51/50 * 51/50) = Rs. 9550.87 Difference = (9550.87 - 9547.2) = Rs.3.67. Answer: C #### C QUESTION:40, 45, 50, 55, 60, 75, 75, 90, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 21.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 55, 60, 75, 75, 90, 100, 100} is 69. 1 standard deviation below the mean is 69 - 21.2 = 47.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 10P pots? options: A)M/10 B)6/M C)600M D)M/6 E)10M SOLUTION:The time it takes to wash 10P pots is 10M minutes which is 10M / 60 = M/6 hours. The answer is D. #### D QUESTION:In how many ways a committee of 10 men and 8 women can be made out of total of 15 men and 12 women? options: A)336/987 B)1001/165 C)1245/789 D)3256/789 E)256/85 SOLUTION:Required number of ways = 15C10 * 12C8 = 15C5 * 12C4 = 3003/495 = 1001/165 Answer is B #### B QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)190 C)109 D)278 E)211 SOLUTION:Explanation: 624/6 = 104 kmph Answer:C #### C QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)$37.5 B)$40 C)$50 D)$48 E)$52 SOLUTION:Dividend on 1 share = $(10/100*50) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(100*2/25*5)=40 Thus, cost of 1 share =$40 option B #### B QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have? options: A)10 B)16 C)8 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1080 180n - 360 = 1080 180n = 1440 n = 1440/180 = 8 ANSWER:C #### C QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P? options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36 SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house. J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs Answer:B #### B QUESTION:Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute). options: A)2 hours 2 minutes B)3 hours 5 minutes C)4 hours 6minutes D)5 hours 7 minutes E)7 hours 9 minutes SOLUTION:In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill 1/5 + 1/8 = 13 / 40 of a tank Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving (13/40) t = 1 t = 40 / 13 = 39/13 + 1/13 hours = 3 hours and (1/13)*60 minutes = 3 hours 5 minutes (rounded to the nearest minute) correct answer B #### B QUESTION:Ajay, Bhavan and Chetan started a business together. Thrice the investment of Ajay, twice the investment of Bhavan and the investment of Chetan are equal. Find the ratio of their respective profits at the end of the year? options: A)1:2:1 B)2:3:6 C)3:2:1 D)1:2:3 E)1:4:3 SOLUTION:Let the investments of Ajay, Bhavan and Chetan be Rs,a, Rs.b and Rs.c respectively. 3b = 2b = c. a = c/3. b = c/2. Ratio of profits of Ajay, Bhavan and Chetan at the end of one year = Ratio of their respective investments = 2:3:6. ANSWER:B #### B QUESTION:Find the total number of divisors of 1728(including 1 and 1728) options: A)28 B)29 C)30 D)31 E)32 SOLUTION:1728=2^6*3^3 no. of divisors = (6+1)*(3+1)=28 ANSWER:A #### A QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 5 years ago? options: A)152460 B)214560 C)138214 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^5 Answer is C #### C QUESTION:38 69 22 43 31 47 13 82 Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above? options: A)56 B)69 C)70 D)71 E)73 SOLUTION:Arrange the numbers in ascending order: 13, 22, 31, 38, 43, 47, 69, 82 (Just cross check the count to ensure that you didn't miss anything) How many numbers do we see? 8, alright. What's (1/4)8? 2. What's (3/4)8? 6. We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two. 13, 22, 31, 38, 43, 47, 69, 82 13, 22, 31, 38, 43, 47: Find a number greater than any of these numbers. 69, 82: Find a number smaller than any of these numbers. Only 56 fits the description. Ans:A #### A QUESTION:The average of four consecutive odd numbers is 24. Find the largest number. options: A)25 B)27 C)29 D)31 E)32 SOLUTION:Explanation: Let the numbers are x, x+2, x+4, x+6, then =>x+(x+2)+(x+4)+(x+6)4=24 =>4x+12)4=24 =>x+3=24=>x=21 So largest number is 21 + 6 = 27 Answer: Option B #### B QUESTION:A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? options: A)22 days B)4 days C)13 days D)6 days E)9 days SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12). B's 1 day's work =((1/4)-(1/12))=(1/6) Hence, B alone can complete the work in 6 days. Answer is D. #### D QUESTION:Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price? options: A)$1 B)$1.84 C)$1.92 D)$2.13 E)$2.15 SOLUTION:Ordering the data from least to greatest, we get: $1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11 The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.) B #### B QUESTION:Myra drove at an average speed of 30 miles per hour for the first 30 miles of a trip & then at an average speed of 60 miles/hr for the remaining 30 miles of the trip. If she made no stops during the trip what was her average speed in miles/hr for the entire trip? options: A)The average speed is 35 miles per hour. B)The average speed is 40 miles per hour. C)The average speed is 55 miles per hour. D)The average speed is 66 miles per hour. E)The average speed is 45 miles per hour. SOLUTION:Here, distance for which Myra traveled at the two speeds is same. Average Speed = 2ab/(a+b) = 2*30*60/(30 + 60) = 40 mph Answer (B) #### B QUESTION:If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates? options: A) 4 B) 8 C) 12 D) 15 E) 20 SOLUTION:I understand this might not be required but I used the equation of a circle. Since the origin is at 0, x^2+y^2=5^2. X,Y could be +/- (0,5 or 5,0) - 4 possibilities. X,Y could be +/- (3,4 or 4,3) - 8 possibilities. Ans: J=C #### C QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D QUESTION:A die is thrown twice and the sum of the numbers appearing is observed to be 6. find the conditional probability that the number 4 has appeared at least once? options: A)2/5 B)3/5 C)3/11 D)3/13 E)3/17 SOLUTION:Let E be the event that ‘number 4 appears at least once’ and F be the event that ‘the sum of the numbers appearing is 6’. Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4)} and F = {(1,5), (2,4), (3,3), (4,2), (5,1)} We have P(E) = 11/36 and P (F) = 5/36 Also EnF = {(2,4), (4,2)} Therefore P(EnF) = 2/36 the required probability P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5. A) #### A QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B QUESTION:A computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed to the final retail price. options: A)$1,000 B)$960 C)$240 D)$200 E)$150 SOLUTION:Cost price=1000 Profit=20% =20% of 1000=200 selling price=CP+ Profit SP=1200 a Discount of 20% to employees means 20% off on 1200 so 20% of 1200= 240 so a employee thinks he saved 240.. Answer: C #### C QUESTION:A goods train runs at the speed of 72 kmph and crosses a 250m long platform in 26seconds. what is the length of the goods train? options: A)230 m B)240 m C)260 m D)270 m E)250 m SOLUTION:Speed =(72 *5/18)m/sec= 20 m/sec. then (x+250)/26=20 x+250 =520 x=520-250 then x=270 Answer: D #### D QUESTION:The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle? options: A)8m. B)6m. C)4m. D)2m. E)5m. SOLUTION:Explanation: Let the sides of the rectangle be l and b respectively. From the given data, (√l2 + b2) = (1 + 108 1/3 %)lb => l2 + b2 = (1 + 325/3 * 1/100)lb = (1 + 13/12)lb = 25/12 lb => (l2 + b2)/lb = 25/12 12(l2 + b2) = 25lb Adding 24lb on both sides 12l2 + 12b2 + 24lb = 49lb 12(l2 + b2 + 2lb) = 49lb but 2(l + b) = 28 => l + b = 14 12(l + b)2 = 49lb => 12(14)2 = 49lb => lb = 48 Since l + b = 14, l = 8 and b = 6 l - b = 8 - 6 = 2m. Answer: Option D #### D QUESTION:Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day? options: A)Rs. 120 B)Rs. 150 C)Rs. 250 D)Rs. 400 E)None of these SOLUTION:Solution: Ratio of number of men, women and children, = (18/6): (10/5):(12/3) = 3:2:4 Total (Men +Women +Children) = 18 3X +2X +4X = 18 9X = 18 X = 2 Hence, number of women = 2X = 2*2 = 4 Share of all women = (10*4000)/40 = Rs. 1000 [18+10+12 =40] Thus, share of each woman = 1000/4 = Rs. 250. Answer: Option C #### C QUESTION:Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%. options: A)429.3 B)270 C)177 D)166 E)111 SOLUTION:Explanation: Cost of each share = (20 + 2.5% of 20) = Rs.20.5 Therefore, number of shares = 8800/20.5 = 429.3 ANSWER:A #### A QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)20 SOLUTION:In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3. 5! = 120 has 1 trailing zeros. 10! will have 2 trailing zeros. 15! will have 3 trailing zeros. 20! will have 5 trailing zeros. Answer: E. #### E QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)800 B)700 C)750 D)850 E)900 SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265 253/160p=1265==> p =800 ANSWER A #### A QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate? options: A)2 B)4 C)6 D)8 E)12 SOLUTION:To fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible so we will take the base as 12 feet by 8 feet Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less. Therefore the radius of the cylinder will become Diameter 2===>8/2=4 Diameter ANSWER:D #### D QUESTION:Two trains 200m and 250m long run at the speed of 72kmph and 18kmph in opposite directions in parallel tracks. The time which they take to cross each other is? options: A)5.6sec B)8.9sec C)10.8sec D)12.6sec E)18 sec SOLUTION:Relative speed = 72+18 = 90 kmph * 5/18 = 25 m/s Distance covered in crossing each other = 200+250 = 450m Required time = 450*1/25 = 18 sec Answer is E #### E QUESTION:In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 35 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class ? options: A)22 B)27 C)75 D)29 E)271 SOLUTION:Explanation: Let the number of students in the class be 100 and let this required average be x. Then, (10 * 95) + (20 * 90) + (70 * x) = (100 * 80) => 70x = 8000 - (950 + 1800) = 5250 => x = 75. Answer: C) 75 #### C QUESTION:Car Dealership X, the total profit from sales increased by 30 percent over the previous years, while the number of cars sold decreased by 30 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year. options: A)18% B)30% C)52% D)63% E)85.71% SOLUTION:Let Profit be x and cars sold be y Originally Profit/Car = x/y Now it is 1.3x / 0.7 y = 13/7 (x/y) Increase in profit per car = ((6/7) (x/y)) / (x/y) * 100 = 85.71% Answer = E #### E QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show? options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30 SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour. The two clocks show 2:00 at 2 0'clock At 3:00 - Clock B is at 3:00 Clock A is at 3:20 (1 hour + gains 20 minutes) AT 4:00 - Clock B is at 4:00 Clock A is at 4:40 (2 hours + gains 40 minutes) In 4 hours the clock A gains 4*20=80 minutes or 1 hour 20 minutes If clock A is at 7:20 the clock B is at 6:00 Answer is B #### B QUESTION:In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 5%.what is population of after 2 year. options: A)140 B)141 C)142 D)143 E)146 SOLUTION:next year total population=[150^2+90^2]^.5=174.92=175 man decreased by 5% so total man =150*.95=142.5 women will be= 175-142.5=32.5 so population after two years= [135^2+32.5^2]^.5=146.15=146 so population after two year= 146 ANSWER:E #### E QUESTION:The factorial expression 10!/2! is not divisible by which of the following integers? options: A)3 B)5 C)6 D)7 E)None of these SOLUTION:10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3 (A) 3 Can divide 12 or 9 (B) 5 Can divide 10 (C) 6 Can divide 12 (D) 7 can divide 7,21,28 Hence answer will be (E) #### E QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:5800 * 99 options: A)574580 B)574200 C)584250 D)576460 E)None of these SOLUTION:Explanation: 5800 * (100 - 1) = 580000 - 5800 = 574200 Option B #### B QUESTION:A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,750 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week? options: A)25% B)30% C)35% D)40% E)45% SOLUTION:E for me. Let managers comminsion rate be M. m*5000+ 2*0.05*5000=2750 5000*m=2250 m=45/100=45% #### E QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)235 m B)245 m C)247 m D)249 m E)252 m SOLUTION:length of the bridge = x meter Total distance covered = 130+x meter total time taken = 30s speed = Total distance covered /total time taken = (130+x)/30 m/s = 45 × (10/36) = (130+x)/30 = 45 × 10 × 30 /36 = 130+x = 45 × 10 × 10 / 12 = 130+x = 15 × 10 × 10 / 4 = 130+x = 15 × 25 = 130+x = 375 = x = 375-130 =245 #### B QUESTION:A family has two children. find the probability that both the children are girls given that at least one of them is a girl? options: A)1/3 B)1/5 C)1/7 D)1/9 E)2/3 SOLUTION:Let b stand for boy and g for girl. The sample space of the experiment is S = {(g, g), (g, b), (b, g), (b, b)} Let E and F denote the following events : E : ‘both the children are girls’ F : ‘at least one of the child is a girl’ Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)} Now E n F = {(g,g)} Thus P(F) = 3/4 and P (E n F )= 1/4 Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3 A) #### A QUESTION:The positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true? I. c > a II. c = a III. c < a options: A)I only B)II only C)III only D)I and II only E)II and III only SOLUTION:Let q = 10% then l = 100/11 % let b = 100 then a = 110 after increasing a by l and decreasing b yq we get c= 108 therefore c<a C it is answer #### C QUESTION:Of the 25 cupcakes in the bakery, 20 percent are chocolate. How many vanilla cupcakes must be sold in order to bring the number of chocolate cupcakes up to 50 percent of the cupcakes in the bakery? options: A)1 B)5 C)10 D)15 E)20 SOLUTION:Now, there are 5 chocolate cupcakes (20% of 25) and 25-5=20 vanilla cupcakes at the bakery. We need there to be 5 chocolate and 5 vanilla cupcakes, in this case there will be 50% chocolate and 50% vanilla. Therefore 20-5=15 vanilla cupcakes must be sold. Answer: D. #### D QUESTION:Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year? options: A)142% B)150% C)165% D)176% E)188% SOLUTION:Let last year's salary be x. Last year, Sandy save 0.1x This year, Sandy saved 0.15*1.1x = 0.165x 0.165x / 0.1x = 1.65 = 165% The answer is C. #### C QUESTION:A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent? options: A)Rs.400 B)Rs.450 C)Rs.550 D)Rs.500 E)Rs.650 SOLUTION:Explanation: P - 340 = (P*4*8)/100 P = 500 ANSWER IS D #### D QUESTION:In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am SOLUTION:In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours. Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am. Answer: D #### D QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:What is the median from the below series 92, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)82 C)92.25 D)98 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88,92, 93, 95, 96, 98 The median quiz score was 92.25 (Four quiz scores were higher than 92.25 and four were lower.) C #### C QUESTION:Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share twice, no apples were left.How many apples were there? options: A)62 B)63 C)64 D)65 E)66 SOLUTION:Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 6 times. So answer is (2^6)-1=63. ANSWER:B #### B QUESTION:what is the least number. which should be added to 221 to make it a perfect square? options: A)5 B)8 C)4 D)6 E)7 SOLUTION:221+4=225 15^2 ANSWER:C #### C QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision? options: A)2008 B)2004 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008. Answer: A. #### A QUESTION:A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1996 has to be the ring finger Answer is (D) #### D QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 * 12 = 9 => 2x = 9 => x = 4.5 A #### A QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 9 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? options: A)72% B)80% C)100% D)120% E)125% SOLUTION:For A, r=8/2pi. Its capacity = (4pi)^2 * 9= 144pi For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi A/B = 144pi/200pi = 0.72 A #### A QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:A present value of a machine is $400. Its value depletiation rate is 25% per annum then find the machine value after 2 years? options: A)$125 B)$100 C)$200 D)$215 E)$225 SOLUTION:P= $400 R = 25% T = 2 years Machine value after 2 years = P[(1-R/100)^T] =400*3/4 * 3/4 =$225 approximately Answer is E #### E QUESTION:A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)? options: A)1250 B)1280 C)1320 D)1340 E)1450 SOLUTION:Explanation: Speed = 5 km/hr Time = 15 minutes = 1/4 hour Length of the bridge = Distance Travelled by the man = Speed × Time = 5×1/4 km = 5 × 1/4 × 1000 metre=1250 metre Answer: Option A #### A QUESTION:A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars? options: A)500 000 B)1 000 000 C)2 000 000 D)5 000 000 E)250 000 SOLUTION:The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is. 5+3+2 = 10 10/2 = X/100 000 5*100 000 = X 500 000 = X Answer: A) #### A QUESTION:In a group of 160 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20? options: A)0.44 B)0.55 C)0.65 D)0.75 E)0.85 SOLUTION:Number of people whose age is less than 20 is given by 160 - 90 = 70 Probability P that a person selected at random from the group is less than 20 is gieven by 70 / 160 = 0.4375 ~ 0.44 correct answer A #### A QUESTION:A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist? options: A)9km/hr B)7km/hr C)12km/hr D)15km/hr E)18km/hr SOLUTION:Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr Ans:E #### E QUESTION:What is the are of an equilateral triangle of side 8 cm? options: A)64√5 B)64√9 C)16√3 D)64√3 E)64√2 SOLUTION:Area of an equilateral triangle = √3/4 S2 If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2; Answer: C #### C QUESTION:Thompson had the following scores in an exam (out of 100): Social Studies: 60 Science: 89 Art: 62 Music: 69 Spanish:84 Biology: 89 What are his average marks ? options: A)61.5 B)72.5 C)71.5 D)85.5 E)75.5 SOLUTION:Explanation: Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75. Answer: E) 75.5 #### E QUESTION:If a is an odd integer and b is an even integer which of the following must be an integer : options: A)a/b B)ab C)2a+b D)2(a+b) E)option B C and D SOLUTION:a= odd = e.g 3 b=even = e.g 6 A. odd/even for example 3/6 = 0.5 no even no odd B. odd * even = 3 * 6 = 18 even C. 2*odd + even = even + even even D. 2(even + odd) = 2(odd) even Hence E it is. #### E QUESTION:Calculate the percentage increase in the area of a square if each of its sides is increased by 15%? options: A)32.25% B)39.25% C)36.25% D)35.25% E)31.25% SOLUTION:Assume original length = 100m by 50m original area = 100*50= 5000 15% increase on each side l = 100 + 15 = 115 w = 50 + 7.5 = 57.5 new area = 115*57.5= 6612.5 increase in area = 6612.5 - 5000 = 1612.5 %increase =21% Answer A #### A QUESTION:If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 280, 511, 1023 and x? options: A)395 B)375.8 C)355 D)415 E)365 SOLUTION:The mean of numbers 28, x, 42, 78 and 104 is 62: 28+x+42+78+104=62*5 --> x=58; So, the mean of 128, 255, 511, 1023 and x is (128+255+280+511+1023+58)/6=375.8. Answer: B. #### B QUESTION:A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1? options: A)A-20. B)A-12. C)A-9. D)A-10. E)A-13. SOLUTION:We could use the following logic: since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n). The condition here should now be 11K + 1 = <operation> such that it gives us an integer 11k +1 = A -20 => A = 11K + 21 Not divisible by 11 11K +1 = A -12 => A = 11K + 31 Not Divisible by 11 11K +1 = A -9 => A = 11K + 10 Not Divisible by 11 11K +1 = A -10 => A = 11K + 11Divisible by 11 11K +1 = A -13 => A = 11K + 14 Not Divisible by 11 Answer therefore is A -10 (D) #### D QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 38.7%. What would have been the percentage of profit earned if no discount had been offered? options: A)28.5 B)46 C)30 D)Data inadequate E)None of these SOLUTION:Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100. Then printed price = 100×(100+38.7)/(100−5) =146 Hence, required % Profit = 146 – 100 = 46% Answer B #### B QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)95 SOLUTION:number of handshakes = 10C2= 10*9/2 = 45 ANSWER:B #### B QUESTION:A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.? options: A)30 min B)35 min C)45 min D)50 min E)55 min SOLUTION:there are 9 hours in between 9 a.m. to 6 p.m. 9*5=45 minutes. ANSWER:C #### C QUESTION:Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A) $ 165 B) $ 145 C) $ 175 D) $ 180 E) $ 170 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 145. So after completing the 1st week she will get $ (x+145). Similarly after completing the 2nd week she will get $ (x + 145) + $ 145. = $ (x + 145 + 145) = $ (x + 290) So in this way end of every week her salary will increase by (B)$ 145. #### B QUESTION:If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new numbers is : options: A)22 B)40 C)88 D)27 E)11 SOLUTION:Explanation: Let the numbers are By Hypothesis , ......(i) Mean of new numbers = By (i) Answer: B) 40 #### B QUESTION:A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? options: A)3.6 sec B)18 sec C)36 sec D)72 sec E)None of these SOLUTION:Speed of train relative to jogger = (45 – 9) km/h = 36 km/h = (36 × 5⁄18) m/sec = 10 m/sec Distance to be covered = (240 + 120) m = 360 m. ∴ Time taken = (360⁄10) sec = 36 sec. Answer C #### C QUESTION:In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 10,290,000, how many red beads were removed? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:10,290,000 = 2^4 * 5^4 * 1029 = 2^4 * 3 * 5^4 * 343 = 2^4 * 3 * 5^4 * 7^3 The answer is B. #### B QUESTION:How many multiples of 5 are there between 5 to 95? options: A)9 B)18 C)17 D)16 E)15 SOLUTION:As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the unit’s place). So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. Answer C #### C QUESTION:From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 27 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning options: A)20 B)10 C)30 D)50 E)40 SOLUTION:Assume the number of boys at present = x Then, the number of girls at present = 5x Before the boys left, the number of boys were (x+27) and number of girls were 5x Hence, 2(5x) = x + 27 => 10x = x + 27 => x = 3 Number of girls in the beginning = (5x + 15) = (5×3 + 15) = 30 Answer is C. #### C QUESTION:x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20. Answer: C. #### C QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work ? options: A)5 days B)6 days C)7 days D)8 days E)9 days SOLUTION:Explanation: Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them, So, A's 1 day work = 1/10 B's 1 day work = 1/15 (A+B)'s 1 day work = (1/10+1/15)=(3+2/30)=1/6 So together they can complete work in 6 days. Option B #### B QUESTION:Today is Monday. After 61 days, it will be: options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)sunday SOLUTION:EXPLANATION Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer B #### B QUESTION:There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men? options: A)1932 B)1933 C)1934 D)1935 E)1936 SOLUTION:(5c3*11c3)+(5c4*11c2)+(5c5*11c1) 1936 ANSWER:E #### E QUESTION:A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)29 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 180, so from 2003 to 2005 it increased by (180-140)/140=40/140=2/7=~29%. Answer: E. #### E QUESTION:If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element? options: A)27 grams B)28 grams C)29 grams D)42 grams E)32 grams SOLUTION:Let original mass be 100 The final mass of that element will be 7 So whatever option we have it will be divisible by 7 Check for the options the one that doesn't produce non terminating decimal is our answer A. 27 grams 27/7 = 3.857... B. 25 grams 25/7 = 3.571... C. 29 grams 29/7 = 4.142....... D. 42 grams 42/7 = 6 E. 32 grams 32/7 = 4.571.... Hence our answer will be (D) #### D QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)315 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 7C2 Number of ways of selecting 2 non fiction books = 6C2 7C2 * 6C2 = 21 * 15 = 315 Answer: C #### C QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased? options: A)8% B)7% C)10% D)6% E)9% SOLUTION:Explanation: Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol, such that Benson buys 1 litre of petrol After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125 Since Benson spends additional 15% on petrol, amount spent by Benson = 100× (100+15)/100 = Rs.115 Hence Quantity of petrol that he can purchase = 115/125 Litre Quantity of petrol reduced = (1−115/125) Litre Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8% Answer: Option A #### A QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33*100 = 180% of 3.33. Answer: E. #### E QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:If a trader sold two cars each at Rs. 404415 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is ? options: A)1.44 % B)2.02 % C)1.04 % D)2.25 % E)3.40 % SOLUTION:Explanation: SP of each car is Rs. 404415, he gains 15% on first car and losses 15% on second car. In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (15)(15)/100 % = 2.25% ANSWER IS D #### D QUESTION:Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE? options: A)1/15 B)1/14 C)1/12 D)1/13 E)1/17 SOLUTION:Explanation : Let two digit number that Shiwani thought be 'xy', where x and y are single digit number. Therefore, 10x+y=p(x+y)+3, where p is a natural number p=10x+y−3x+y. Also, y+x>3. Possible values of x and y for which p is a natural number are :- (x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9), (x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null), (x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4) There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits. Probability that Devesh thought of the same number as Shiwani = 1/14 Answer : B #### B QUESTION:If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips? options: A)1/4 B)1/8 C)1/2 D)1/16 E)1/32 SOLUTION:(1/2) * (1/2) * (1/2) * (1/2) = 1/16 Answer: D #### D QUESTION:Bob finishes the first half of an exam in one-thirds the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam? options: A)20 B)24 C)27 D)30 E)40 SOLUTION:Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/3's the time of the second half (3/3's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 1:5 and the second half is 3:5). With each fifth of an hour being 15 minutes (60/4), the first half of the exam would have taken 30 minutes. Correct answer is D. #### D QUESTION:Denise is trying to open a safe whose combination she does not know. IF the safe has 3000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one correct combination. options: A)1 B)159/160 C)157/160 D)0.875 E)0.975 SOLUTION:If Denise does not pick the correct combination in first 75 try, then the correct combination is one of remaining 2925. So Probability = 2925/3000 = 0.975. answer is E #### E QUESTION:If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a eight-percent vinegar solution, what was the concentration of the original solution? options: A)9.3% B)17.3% C)26.67% D)35.5% E)41.3% SOLUTION:Let X be the quantity of non-vinegar in the strong vinegar solution Thus vinegar quantity will be 12 - X When 50 ounces of water were added the percentage of vinegar becomes 8%, thus (12 - X)/62 = 8/100 From this equation X = 7.04 Answer (12-7.04)/12 = 41.3% ANSWER:E #### E QUESTION:Given two fair dice, what is the probability E that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. E=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:If a certain sample of data has a mean of 22.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean? options: A)12.0 B)13.5 C)14.5 D)23.5 E)26.5 SOLUTION:The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is C. #### C QUESTION:Two pipes A and B can fill a cistern in 20 and 40 minutes respectively, and a third pipe C can empty it in 80 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)19 1/7 min B)15 1/7 min C)17 1/7 min D)7 1/7 min E)16 min SOLUTION:1/20 + 1/40 - 1/80 = 5/80 80/5 = 16 ANSWER:E #### E QUESTION:A certain street contains 100 buildings.They are numbered from 1 to 100. How many 9s are used in numbering these buildings? options: A)21 B)20 C)19 D)18 E)9 SOLUTION:9,19,29,39,49,59,69,79,89,90,91,92,93,94,95,96,97,98,99 so number of 9's=20 ANSWER:B #### B QUESTION:35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days? options: A)87 B)18 C)42 D)16 E)10 SOLUTION:Binders Books Days 35 1400 21 x 1600 20 x/35 = (1600/1400) * (21/20) => x = 42 Answer:C #### C <<<Examples ends QUESTION:Which of the following numbers is divisible by 4? options: A)27767 B)10224 C)26778 D)26679 E)26711 SOLUTION:10224. This is the only option with last two digits divisible by 4 Answer:B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=u ii. u is not equal to v iii. s > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true. Answer: D. #### D QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 7 is 7!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!5!. # of arrangements when 3 boys do not sit together would be: 7!-3!5!. Answer: D). #### D QUESTION:Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week? options: A)$0.00 B)$133.00 C)$250.05 D)$66.74 E)$10000.00 SOLUTION:Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be n/4, n/8, n/16, n/32 So, answer will be D #### D QUESTION:A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:60% is 20%-points above 40% and 20%-points below 80%. Thus the ratio of "the first 30 games" to "remaining games" is 1:1. So the team played a total of 30+30 = 60 games. The answer is B. #### B QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 40*9/40 = 9 seconds. Answer: C #### C QUESTION:What is the median from the below series 92, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)82 C)92.25 D)98 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88,92, 93, 95, 96, 98 The median quiz score was 92.25 (Four quiz scores were higher than 92.25 and four were lower.) C #### C QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/9 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)11/30 B)29/60 C)17/30 D)13/18 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/2*1/3=x/6 Platinum card unspent limit is= x-1/9x=8/9x So if gold card balance is transferred then the rest unspent will be 8/9x-x/6=13/18x So the ans is D #### D QUESTION:If y = ||x – 3| – 2|, for how many values of x is y = 5? options: A)2 B)1 C)3 D)4 E)5 SOLUTION:y = ||x – 3| – 2| can be 4 only and only when X-3= +/-7. so there are 2 values of X Answer : A #### A QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. options: A)125/128 B)115/122 C)125/126 D)125/122 E)125/112 SOLUTION:Required probability = 1 - 1/126 = 125/126 Answer:C #### C QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members 51* 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres? options: A)20 B)200 C)300 D)400 E)100 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 9540 [4L - 40] = 9540 / 26.50 = 360 4L = 400 L = 400/4= 100 meters. Answer: E #### E QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)15 C)20 D)22 E)23 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15 Answer: Option B #### B QUESTION:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required? options: A)18 B)20 C)24 D)36 E)42 SOLUTION:Use weighted average: 2% and 12% solutions mix to give 5% solution. w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3 You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution. If total 5% solution is actually 60 litres, you need 7*6 = 42 litres of 2% solution and 3*6 = 18 litres of 12% solution. Answer (E) #### E QUESTION:In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done? options: A)6^6 ways B)8^9 ways C)7^8 ways D)8^7 ways E)8^6 ways SOLUTION:6 people can be prized with distinct prizes in 6^6 ways ANSWER:A #### A QUESTION:One pipe can fill a pool four times faster than a second pipe. When both pipes are opened, they fill the pool in eight hours. How long would it take to fill the pool if only the faster pipe is used? options: A)5 hr B)8 hr C)10 hr D)16 hr E)20 hr SOLUTION:fast pipe + slow pipe = together One pipe fills the pool four times faster than the other pipe so, hourly fill rates: 1/x + 1/4x = 1/8 Let x = number of hours it would take the fast pipe to fill the pool thus, x=10 hours Answer: C #### C QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock? options: A)30000 B)20000 C)23000 D)21020 E)28211 SOLUTION:Explanation: Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 400 => x = 20000 Answer: B #### B QUESTION:For prime numbers x and y, x^3*y^5=z^4. How many positive factors does positive integer z have? options: A)One B)Two C)Three D)Four E)Five SOLUTION:Solution: given x^3*y^5=z^4; here if x and y are two different prime numbers then z = x^3/4 * y^5/4 in this case z can not be and integer. now to make z = (x^3*y^5)^1/4 an integer it is required to have x=y then equation will become z=x^2 or z=y^2 hence total positive factors will be 3. ANSWER:C #### C QUESTION:Find the odd man out 4, 10, 22, 40, 84, 94 options: A)22 B)40 C)94 D)84 E)10 SOLUTION:Differnce is multiple of 6 4 and 10 diff is 6 10 and 22 diff is 12 22 and 40 diff is 18 40+24 = 64 but in series it is mentioned as 84 64+30 = 94 ANSWER:D #### D QUESTION:Excluding stoppages,the speed of the bus is 54kmph and including stoppages,it is 27kmph. For how many minutes does the bus stop per hr options: A)12 min B)11 min C)13 min D)20 min E)30 min SOLUTION:Due to stoppages,it covers 27km less. time taken to cover 27 km is [27/54 *60] min = 30min Answer is E. #### E QUESTION:When positive integer F is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when F is divided by B? options: A) 13 B) 14 C) 15 D) 16 E) 17 SOLUTION:the remainder will be obtained from the decimal part when F is divided by B i.e. 0.35 0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this PS: for B-14 F=174 and B=40 #### B QUESTION:The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is? options: A)625 B)298 C)269 D)200 E)267 SOLUTION:Let the sum be Rs. x. Then, [x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x S.I. = (x * 4 * 2)/100 = 2x/25 51x/625 - 2x/25 = 1 or x = 625.Answer: A #### A QUESTION:The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit? options: A)337 B)960 C)278 D)211 E)191 SOLUTION:Explanation: Let C.P. = Rs. x. Then, 832 - x = x - 448 2x = 1280 => x = 640 Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960. Answer: B #### B QUESTION:Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take? options: A)40 B)50 C)70 D)80 E)90 SOLUTION:L+M=M+N-40 / N=2L+10 40=M+N-L-M 40=N-L 40=2L+10-L 30=L 2(30)+10=70 C #### C QUESTION:what is the radius of a circle that has a circumference of 3.14 meters? options: A)0.5 mtr B)1.5 mtr C)2.3 mtr D)0.2 mtr E)1.2 mtr SOLUTION:circumference of a cirlce = 2nr, given circumference= 3.14 mtr. 2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (A) #### A QUESTION:The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum. options: A)33498 B)17000 C)2665 D)28876 E)313 SOLUTION:The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a. So P = (100 * 10200)/ (30 * 2) = Rs.17000 Answer:B #### B QUESTION:How many times the keys of a writer have to be pressed in order to write first 400 counting no.'s? options: A)998 B)1000 C)1092 times D)1100 E)1200 SOLUTION:1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 400 = 301 * 3 = 903 ----------- 1092 C #### C QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:A sum amounts to Rs.8820 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? options: A)s.4000 B)s.5000 C)s.4500 D)s.4800 E)s.8000 SOLUTION:CI=8820,R=5,N=2 CI=P[1+R/100]^2 =P[1+5/100]^2 8820=P[21/20]^2 8820[20/21]^2 8000 ANSWER:E #### E QUESTION:One out of every 4000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch? options: A)450 B)900 C)90,000 D)1800,000 E)900,000 SOLUTION:(D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 4000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/4000 = 450/y. Solve for y and you will get the total number of chips in the batch: 1800,000. The answer is (D). #### D QUESTION:The captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team? options: A)20 years B)21 years C)22 years D)23 years E)24 years SOLUTION:Explanation: Let the average age of the whole team by x years. 11x – (24 + 27) = 9(x -1) 11x – 9x = 42 2x = 42 x = 21. So, average age of the team is 21 years. Answer B #### B QUESTION:Simplify: 244 x 301 options: A)73144 B)73143 C)73200 D)72956 E)73444 SOLUTION:244 x 301 = 244 x (300 + 1) = 73200 + 244 =73444 Answer is E #### E QUESTION:What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5? options: A) 94 B) 99 C) 26 D) 73 E) None of the Above SOLUTION:Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 5 = 10x +y = x^2 y^2 -10 Thus 2xy +5 = x^2 + y^2 - 10 x^2 + y^2 -2xy = 15 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 15 or 94 Thus the answer is A #### A QUESTION:A train 320 m long passed a pole in 28 sec. How long will it take to pass a platform 700 m long? options: A)12 sec B)59 sec C)93 sec D)89 sec E)46 sec SOLUTION:Speed = 320/28 = 11 m/sec. Required time = (320 + 700)/11 = 92.7 sec. Answer: C #### C QUESTION:If 9^y = 3^14, what is y? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:9^y = 3^2y = 3^14 2y=14 y = 7 The answer is E. #### E QUESTION:In 1 hour, a boat goes 5 km along the stream and 9 km against the stream. The speed of the boat in still water (in km/hr) is : options: A)3 km/hr. B)2 km/hr. C)7 km/hr. D)8 km/hr. E)5 km/hr. SOLUTION:Speed in still water = 1/2(9 + 5) km/hr = 7 km/hr. ANSWER :C #### C QUESTION:A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 63 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents? options: A)14 B)45 C)54 D)65 E)81 SOLUTION:Just check the answers and reverse the numbers until you get 63. 81 - 18 = 63 Answer E #### E QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E QUESTION:Sharmila works 10 hours per day on Monday, Wednesday and Friday, and 8 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $460 per week. How much does she earn in dollars per hour? options: A)8 B)9 C)9.5 D)10 E)11 SOLUTION:So, she works 30 hours in 3 days So, she works 16 hours in 2 days So in a week she works 46 hours ( 30 + 16 ) and earns $460 So, Hourly wage is 460/46 => 10 Hence answer will be (D) 10 #### D QUESTION:At a certain organisation, the number of male members went up by 15% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000? options: A)1:2 B)1:3 C)2:3 D)3:2 E)2:1 SOLUTION:men increase by 15% ==> 1.15M = males in 2001 women decrease by 6% ==> 0.94F = women in 2001 total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001 Obviously (males in 2001) + (females in 2001) = total number of employees in 2001 1.15M + 0.94F = 1.012*(M + F) 1.15M + 0.94F = 1.012M + 1.012F 1.15M - 1.012M = 1.012F - 0.94F 0.138M = 0.072F M/F = (0.072)/(0.138) = 72/138 = 1/2 Answer =(A) #### A QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)255 B)267 C)225 D)277 E)211 SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m. Answer:C #### C QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:If Z = 52 and ACT = 48, then BAT will be equal to options: A)33 B)88 C)77 D)46 E)99 SOLUTION:Explanation: In the given code, A = 2, B = 4, C = 6,.... , Z = 52. So, ACT = 2 + 6 + 40 = 48 and BAT = 4 + 2 + 40 = 46 Answer: D) 46 #### D QUESTION:Two employees X and Y are paid a total of Rs. 616 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.250 B)s.280 C)s.290 D)s.299 E)s.300 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 616 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 616 ⇒ y[12/10 + 1] = 616 ⇒ 22y/10 = 616 ⇒ 22y = 6160 ⇒ y = 6160/22 = 560/2 = Rs.280 B #### B QUESTION:How many cubes of 5cm edge can be cut out of a cube of 20cm edge options: A)36 B)64 C)216 D)484 E)None of these SOLUTION:Explanation: number of cubes=(20 x 20 x 20) / (5 x 5 x 5) = 64 Answer: B #### B QUESTION:In how many ways can you seat 8 people on a bench if one of them does not want to sit in one of the two middle seats or at either end? options: A)17,540 B)18,360 C)19,320 D)20,160 E)21,480 SOLUTION:One person can choose 4 possible chairs to sit. The remaining 7 people can sit in 7! ways. The number of arrangements is 4*7! = 20,160. The answer is D. #### D QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3. What is the ratio of their heights? options: A)A)3:4 B)B)2:7 C)C)2:2 D)D)2:1 E)E)2:9 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(3)2h2 => h1/h2 = 3/4 i.e. h1 : h2 = 3: 4 Answer: A #### A QUESTION:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? options: A)88 B)90 C)96 D)98 E)102 SOLUTION:2 multiples-choice questions can be answered in = 4 x 4 = 16 ways 3 true-false questions can be answered in = 2x2x2 = 8 ways But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways Total ways to answer the quiz = 16 x 6 = 96 Answer C #### C QUESTION:Set R has a mean of 15 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){11,26} B){18,19} C){16,18} D){16,16} E){14,16} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 15,the values (14,16) are closer than others. Hence Answer : E #### E QUESTION:A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose? options: A)120 B)335 C)784 D)217 E)210 SOLUTION:Let x be the number he chose, then 2*x*138=102 2x=240 x=120 correct answer A #### A QUESTION:On a test consisting of 30 questions. No. of wrong answers is 50% less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers? options: A)1 : 3 B)2 : 3 C)2 : 1 D)3 : 1 E)4 : 5 SOLUTION:Sol. Let the number of wrong answer - x and number of right answer = 30-x x = 50/100 of (30-x) x = 10 Required ratio = 20 : 10 = 2 : 1 C #### C QUESTION:A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work ? options: A)30 days B)15 days C)45 days D)24 days E)None of these SOLUTION:Let C completes the work in x days. Work done by (A + B) in 1 day = 1⁄10 Work done by (B + C) in 1 day = 1⁄18 A’s 5 days’ work + B’s 10 days’ work + C’s 15 days’work = 1 or (A + B)’s 5 days’ work + (B + C)’s 5 days’ work + C’s 10 days’ work = 1 or 5⁄10 + 5⁄18 + 10⁄x = 1 or x = 45 days Answer C #### C QUESTION:The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 10 points after 5 games, what is the least number of the remaining matches it has to win to reach the 45-point mark by the end of the tournament? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:To get 45 points as end of season we need another 35 points or more from remaining 15 matches: Option A= 6*3+9*1=27 Option B=7*3 + 8*1=29 Option C=8*3+7*1=31 Option D=9*3+6*1=33 Option E=10*3+5*1=35 hence option E-10 #### E QUESTION:The moon revolves around the earth at a speed of approximately 0.9 kilometers per second. This approximate speed is how many kilometers per hour? options: A)60 B)61.2 C)3240 D)3,600 E)3,672 SOLUTION:moon revolves around the earth at a speed of 1.02kilometers per second. one hour equal to 60 minutes. one minute equals to 60 seconds. so one hour equals to 3600seconds. so one hour, speed= 0.9*3600=3240kilometers per hour. Option C is correct #### C QUESTION:The age of teacher is the same as the digit in the student's age, but in reverse order. In five years teacher will be twice as old as student will be then. what is the difference in their current age ? options: A)18 B)12 C)25 D)13 E)7 SOLUTION:Teacher's age= 10x+y so student's age= 10y+x.. after 5 years , 10x+y+5=2*(10y+x+5).... so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is A..18 #### A QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D QUESTION:The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is options: A)25 years B)30 years C)35 years D)40 years E)None SOLUTION:Sol. Let their ages of x years and (x + 10) years respectively. Then, (x + 10) - 15 = 2(x - 15) ⇔ x - 5 = 2x - 30 ⇔ x = 25. ∴ Present age of the elder person = (x + 10) = 35 years. Answer C #### C QUESTION:Three houses of the same type were advertised to be let in a locality. four men made separate applications for a house. What is the probability that each of them applied for the same house. options: A)1/4 B)1/6 C)1/8 D)1/9 E)3/256 SOLUTION:Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 3 houses 1/3 Let us consider case where all 4 men choose House no 1 So for First men it will be 1/4,second men 1/4 , third men also 1/4 and fourth man 1/4 So probability of selecting house no 1 is 1/4*1/4*1/4*1/4= 1/256 And since there are 3 such house so probability that each men select the same house is 3*1/256 Ans is E #### E QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle? options: A)16 B)25 C)33 D)46 E)58 SOLUTION:The perimeter of a circle is 2*pi*r. The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r The perimeter is pi*9 + 2*9 which is about 46. The answer is D. #### D QUESTION:If x = 3 and y = 2, what is the value of 5(x-y)^2 - xy ? options: A)-8 B)-7 C)-1 D)-2 E)-5 SOLUTION:x = 3 and y = 2 x-y = 3 - 2 = 1 x*y = 3 * 2 = 6 Now we apply it in the equation 5(x-y)^2 - xy =5 (1)^2-6 ==>5*1 -6 = 5-6 =-1 Answer : C #### C QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2490 ? options: A)Rs. 832 B)Rs. 830 C)Rs. 822 D)Rs. 812 E)Rs. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830. Answer: B #### B QUESTION:When n is divided by 24, the remainder is 3. Find thee difference between previous remainder and the remainder when 9n is divided by 7 ? options: A)2 B)7 C)5 D)3 E)6 SOLUTION:Let n=3 (leaves a remainder of 3 when divided by 24) 9n = 9(3) =27, which leaves a remainder of 6 when divided by 7. difference = 6 - 3 = 3. Answer D #### D QUESTION:There are 10 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have? options: A)7/17 B)5/12 C)4/11 D)3/10 E)2/9 SOLUTION:P(first stamp is different) = 5/10 P(second stamp is different) = 4/9 P(both stamps are different) = 5/10*4/9 = 2/9 The answer is E. #### E QUESTION:I came across this problem in the GMATprep software and got it totally wrong! A company consists of 6 senior and 4 junior staff officers. If a committee is created with 4 senior and 1 junior staff officers, how many possible committees are there? options: A)12 B)44 C)56 D)60 E)200 SOLUTION:6C4*4C1 =60=D #### D QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true? options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9 SOLUTION:x^2−x=k => x^2−x - k = 0 For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative. b^2-4ac ≥0 => 1- 4*1*(-k) ≥0 =>1 + 4k ≥0 => k ≥ -14 Answer A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)267 B)240 C)166 D)111 E)121 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book? options: A)229 B)270 C)877 D)266 E)281 SOLUTION:Let xx be the total number of pages in the book, then she finished 23⋅x23⋅x pages. Then she has x−23⋅x=13⋅xx−23⋅x=13⋅x pages left. 23⋅x−13⋅x=9023⋅x−13⋅x=90 13⋅x=9013⋅x=90 x=270x=270 So the book is 270 pages long. Answer:B #### B QUESTION:The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Solution Let the toatl number of workers be x. Then 8000x=(12000 x 7) + 6000 (x -7) 2000x =42000 x= 21. Answer B #### B QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:A train 250 m long is running at a speed of 58 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)18 sec E)15 sec SOLUTION:Answer : D. Speed of the train relative to man = (58 - 8) kmph = (50* 5/18) m/sec = (125/9)m/sec Time taken by the train to cross the man = Time taken by It to cover 250 m at 125/9 m / sec = 250 *9/ 125 sec = 18sec #### D QUESTION:A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 12 multiples of 14, how many multiples of 7 are there in Q? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Halfway between the multiples of 14, there will be another multiple of 7. The total number of multiples of 7 is 12+11 = 23. The answer is D. #### D QUESTION:If the quotient a/b positive, which of the following must be true? options: A)a > 0 B)b > 0 C)ab > 0 D)a-b > 0 E)a+b > 0 SOLUTION:a/b>0 means aa and bb have the same sign, either both are negative or both are positive. Thus, their product will also be positive: ab>0. Answer: C. #### C QUESTION:A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A? options: A)2: 7 B)2: 0 C)2: 4 D)2: 3 E)2: 1 SOLUTION:80* 7: x* 3 = 1:1 1/2 560: 3x = 2: 3 x = 280.Answer:D #### D QUESTION:If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above? A. B. C. D. E. options: A)(−8,8) B)(4,−4) C)(5,−5) D)(2,−2) E)(−4,4) SOLUTION:Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A) Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B) Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C) Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D) Answer: Option C #### C QUESTION:The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is : options: A)120 B)123 C)125 D)128 E)130 SOLUTION:Time from 11 May to 10 September, 1987 =21+30+31+31+10 = 123 days Time : 123 days = 123/365 year S.I =(7300x123x5)/(365x100)=Rs.123 answer :B #### B QUESTION:Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window? options: A)a 100 B)b 112 C)c 90 D)d 120 E)e 30 SOLUTION:D David's position is fixed. Now we need to arrange all others around David. There are 5x4x3x2x1= 120 ways to arrange five people. #### D QUESTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:If n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 8p have. p = 3 --> 8p = 24--> 24 has 6 even divisors: 2, 4, 6, 8, 12, 24. Answer: D. #### D QUESTION:From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys? options: A)120 B)140 C)185 D)190 E)210 SOLUTION:The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are: (i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a '''' (iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185 C #### C QUESTION:A father is four times as old as his son. In twenty years, he'll be twice as old. How old are they now? options: A)5,40 B)10,40 C)20,40 D)10,30 E)15,30 SOLUTION:If F is age of father and s is age of son f=4s f+20 = 2*(s+20) 4s+20 = 2s+40 2s=20 s=10 F=40 ANSWER:B #### B QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour. options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these SOLUTION:Explanation: We know Time = Distance/speed So total time taken = (120/60+160/80)=4hours Time taken for 280 Km = 280/4=70.km/hr Option A #### A QUESTION:How many integers between 323,700 and 458,600 have tens digit 1 and units digit 3? options: A)10,300 B)10,030 C)1,353 D)1,352 E)1,349 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ... The difference between 323,700 and 458,600 is 458,600-323,700=134,900 - one number per each hundred gives 134,900/100=1,349 numbers. Answer: E. #### E QUESTION:A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get: options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these SOLUTION:Explanation: Ratio of working days of A : B = 10 : 15 Therefore, their wages ratio = reverse ratio = 15 : 10 Therefore, A will get 15 units of ratio Total ratio = 25 1 unit of ratio =3100/25 = 124 So, A’s amount = 124 × 15 = Rs.1860. Answer: Option C #### C QUESTION:Sakshi can do a piece of work in 10 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work : options: A)8 B)16 C)18 D)25 E)10 SOLUTION:Solution Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 . Suppose Tanya taken x days to do the work. 5 : 4 : : 10 : x ⇒ x = (10x4/5) ⇒ x = 8 days. Hence,Tanya takes 8 days is complete the work. Answer A #### A QUESTION:The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Ans: E - 4 pairs (xˆ2)(yˆ2) = 900 [square root both sides] xy = 30 20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15 Cancel the repeats This leaves us with exactly 4 options. Hence, E #### E QUESTION:If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be options: A)2 B)5 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 5*8820 = 44, 100, which is a square of 210 B #### B QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ? options: A)24 B)17 C)18 D)9 E)11 SOLUTION:Explanation: Less Men, means more Days {Indirect Proportion} Let the number of days be x then, 72 : 36 :: 18 : x x = 9 Answer: D) 9 days #### D QUESTION:If (x + 1)^2 = 144, which of the following could be the value of 2x? options: A)–26 B)–13 C)–10 D)12 E)-21 SOLUTION:You can also get to the answer by backsolving using answer choices Starting with choice B = -13 (x + 1)^2 = 144 (-13 + 1)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -13 will result in 144 in the equation so x must be -11, Then 2x = 2 * -13 = -26 Answer: A #### A QUESTION:33 1/3% OF 330? options: A)80 B)90 C)110 D)120 E)130 SOLUTION:33 1/3 % = 1/3 1/3 × 330 = 110 C) #### C QUESTION:It takes Jim three hours to wash the gym and it takes Julia two hours to wash the gym. Working together, how many minutes will it take them to wash the gym? options: A)70 B)72 C)74 D)76 E)78 SOLUTION:Jim can wash (1/3) of the gym per hour. Julia can wash (1/2) gym per hour. Together they can wash 1/3+1/2=5/6 of the gym per hour. 1 gym / (5/6) of the gym per hour = 6/5 hours = 72 minutes. The answer is B. #### B QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760 SOLUTION:After one year: 1.2 * $2500 After two years: (1.2)^2 * $2500 After three years: (1.2)^3 * $2500 = $4320 The answer is D. #### D QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? options: A)8:50 a.m B)5:50 a.m C)7:50 a.m D)6:50 a.m E)7:00 a.m SOLUTION:The time it takes Kannan to get to work: time to walk to car park + time to drive 10 + 110 = 120 minutes = 2 hours Kannan needs to get out of the house 2 hours before 9:00 am at 9:00 - 2:00 = 7:00 a.m correct answer E #### E QUESTION:If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%? options: A)41 B)48 C)49 D)44 E)43 SOLUTION:96% ---- 72 144% ---- ? 96/144 * 72 = 48 Answer: B #### B QUESTION:An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? options: A)$480 B)$489.60 C)$634.64 D)$800.32 E)$240 SOLUTION:1.04*1.04*6000 = $6489.60 The answer is B. #### B QUESTION:I. m-14, m, m, m, m+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A QUESTION:The average salary of all the workers in a workshop is $1000. The average salary of 5 technicians is $5000 and the average salary of the rest is $500. The total number of workers in the shop is? options: A)25 B)20 C)15 D)30 E)18 SOLUTION:Let the total number of workers be x 1000x = 5000*5 + 500(x-5) x = 25 Answer is A #### A QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 11, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)26/165 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 11 = (5,6)(6,5)= 2 ways Total ways of getting outcome on two dice =6*6=36 Probability of getting sum as 11 in any attempt =2/36=1/18 Probability of NOT getting sum as 11 in any attempt = 1-(1/18)= 17/18 Probability of losing game =(17/18)*(17/18)*(17/18)=139/165 I.e. Probability of wining game = 1-(139/165) =26/165 Answer : Option C #### C QUESTION:The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 16000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is options: A)Rs. 7000 B)Rs. 8000 C)Rs. 8500 D)Rs. 9000 E)None SOLUTION:Answer Average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = Rs. 9000 Correct Option: D #### D QUESTION:What number is 60 more than two-fourth of itself? options: A)180 B)225 C)288 D)324 E)336 SOLUTION:2/4x+60= x That means 60=2/4x x= 60*3= 180 A is the answer #### A QUESTION:Each student at a certain university is given a four-character identification code, the rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules? options: A)135,200 B)67,600 C)64,000 D)60,840 E)58,500 SOLUTION:First two parts for the code, are digits between 0-9, therefore, 10 options for the first part of the code, and as characters may be repeated, 10 options for the second part as well Therefore, we have 10 X 10 possibilities for the first and second part of the code Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code, and as characters may be repeated, 26 options for the fourth part as well Therefore, we have 26 X 26 possibilities for the third and fourth part of the code so, in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600 Answer B #### B QUESTION:Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 1800 options: A)30 B)70 C)210 D)300 E)180 SOLUTION:27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3. 100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10. Then we want to know what is the largest possible GCF of x and 2100. Well 1800 = 3 * 6 * 10 * 10 We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible. We know x has one factor of 3, but not two factors --- that takes the 3. We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking. 3*6*10 = 180 If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 1800. E #### E QUESTION:The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of? options: A)6:8 B)6:1 C)6:5 D)6:2 E)6:3 SOLUTION:4:5 3:2 ------- 12:15:10 12:10 6:5 Answer: C #### C QUESTION:Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A? options: A)10.21 B)10.27 C)10.25 D)10.23 E)60.25 SOLUTION:Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs. Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs = 2 5/6 = 2 hrs 50 min Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min. So, Anna reached city A at 10.25 a.m. Answer: E #### E QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)70 E)58 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70. Thus D is the correct answer choice #### D QUESTION:A farmer spent $33 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined? options: A)$36.30 B)$38.50 C)$39.20 D)$39.50 E)$40.60 SOLUTION:A farmer spent 40% money on chicken feed, so he spent 0.4*$33=$13.2 on chicken feed, thus he spent the remaining 33-13.2=$19.8 on goat feed. Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$13.2 --> x=$16.5. Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 16.5+19.8=$36.3. Answer: A #### A QUESTION:A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ? options: A)220 metre B)230 metre C)250 metre D)260 metre E)270 metre SOLUTION:Distance covered in 26 seconds = 26×72×5/18=520 meter Length of the train = 520-250=270 meter ANSWER: E #### E QUESTION:At what rate percent per annum will a sum of money double in 16years? options: A)10.6% B)3.65% C)6.25% D)8.32% E)11% SOLUTION:Let principle = P S.I. = P T = 16yrs Rate = 100*P/P*16 = 25/4% = 6.25% Answer is C #### C QUESTION:Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible? options: A)48 B)66 C)72 D)78 E)90 SOLUTION:Total number of 5 digit numbers that can be formed = 5! = 120. Total number of 5 digit numbers in which 3 and 4 are adjacent = 48. This can be calculated by taking 3 and 4 as a pair and considering positions where they can appear. Number of 5 digit numbers in which 3 and 4 are not adjacent = Total number of 5 digit numbers - Total number of 5 digit numbers in which 3 and 4 are adjacent. Ans = 120 - 48 = 72 C #### C QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? options: A)600 B)2877 C)208 D)1882 E)191 SOLUTION:Explanation: Cost price = Rs.500 profit = 20% of 500 = Rs.100 Selling price = Cost price + Profit = 500 + 100 = 600 Answer:A #### A QUESTION:Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%? options: A)30000 B)40000 C)50000 D)60000 E)70000 SOLUTION:let first parrt is x and second part is y then x+y=50000----------eq1 total profit=profit on x +profit on y 7000=(x*10*1)/100 + (y*20*1)/100 70000=x+2y-----------------------------------eq2 70000=50000+y so y=20000 then x =50000-20000=30000 first part =30000 ANSWER:A #### A QUESTION:Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer? options: A)2388 B)2799 C)2877 D)4266 E)2881 SOLUTION:CI = 14800{ [ 1 + 13.5/100]2 - 1 } = 14800 { [1 + 27/200]2 - 1 = 14800 { 2 + 27/200}{27/200} = (74)[2 + 27/200](27) = 1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266.Answer:D #### D QUESTION:If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: options: A)0 B)1 C)2 D)3 E)None of these SOLUTION:(5+1+7+A+3+2+4)=(22+A)MUST BE DIVISIBLE BY 3. HENCE THE SMALLEST WHOLE No. must be 2 ANSWER:B #### B QUESTION:If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be . options: A)90 seconds B)150 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B #### B QUESTION:A man swims downstream 40 km and upstream 56 km taking 8 hours each time, what is the speed of the man in still water? options: A)6 B)24 C)8 D)12 E)44 SOLUTION:40 --- 8 DS = 5 ? ---- 1 56 ---- 8 US = 7 ? ---- 1 M = ? M = (5 + 7)/2 = 6 Answer: A #### A QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 37 kmph. Of how many minutes does the train stop per hour? options: A)73 B)83 C)12 D)83 E)11 SOLUTION:Explanation: T = 8/45 * 60 = 11 Answer: Option E #### E QUESTION:Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops? options: A)white − wheat − wheat B)wheat − wheat − rye C)rye − white− wheat D)rye − rye − rye E)rye − rye − white SOLUTION:In a single round Lucy drops 6 morsels. Remainder (2000/6) = 2 Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated Answer: A #### A QUESTION:A group of men decided to do a work in 20 days, but 8 of them became absent. If the rest of the group did the work in 28 days, Find the original number of men? options: A)60 B)28 C)40 D)50 E)25 SOLUTION:Original number of men = 8*28 / (28-20) = 28 Answer is B #### B QUESTION:If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture? options: A)3⁄7 B)4⁄7 C)3⁄4 D)4⁄3 E)7⁄4 SOLUTION:Should be a sub-600 level Q.. volume= {3/7}/{4/7}=3/4 ANSWER:C #### C QUESTION:If n = 20! + 15, then n is divisible by which of the following? I. 15 II. 17 III. 19 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:15 divides 20! so 15 also divides 20! + 15. 17 and 19 divide 20! so they do not divide 20! + 15. The answer is A. #### A QUESTION:The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.90 per metre. options: A)2399 B)3888 C)2999 D)5808 E)6468 SOLUTION:Explanation: Area = (13.86 x 10000) sq.m = 138600 sq.m Circumference = Cost of fencing = Rs. (1320 x 4.90) = Rs. 6468. Answer: E) 6468 #### E QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A QUESTION:The average marks of a class of 30 students is 50 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)56.25 B)52.9 C)52.1 D)52.3 E)42.5 SOLUTION:Sum of the marks for the class of 30 students = 30 * 50 = 1500 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 80 students = 1500 + 3000 = 4500 Average marks of all the students = 4500/80 = 56.25 Answer:A #### A QUESTION:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $400 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds? options: A)3000 B)5000 C)2000 D)4000 E)6000 SOLUTION:So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $200, thus 0.2x = $200 --> x = $1,000. Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,000 = $2,000. Answer:C #### C QUESTION:The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@[email protected],whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$430 per month. The salary of the new supervisor is: options: A)870 B)600 C)287 D)771 E)191 SOLUTION:Explanation: Total salary of 8 workers and supervisor together = 9 × 430 = 3870 Now total salary of 8 workers = 3870 − 870 = 3000 Total salary of 9 workers including the new supervisor = 9 × 430 = 3870 Salary of the new supervisor = 3870 − 3000 = 870 Answer: A #### A QUESTION:A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours. What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75). options: A)1 hour B)2 hour C)3 hour D)4 hour E)5 hour SOLUTION:In one hour, Soln 1: the large inlet tube fills 1 / 3 of the tank; the small inlet tube fills 1 / 6 of the tank; the outlet tube empties 1 / 9 of the tank; and therefore all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. Soln 2: Let V be the total volume of the tank. From equation (1), Flow Rate (large inlet tube) = V / 3 Flow Rate (small inlet tube) = V / 6 Flow Rate (outlet tube) = V / 9. Substituting in equation (2), Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9). Using the above result in equation (1), Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ]. Note that V cancels out on simplifying the above expression. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. #### A QUESTION:In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.64.50 per Kg? options: A)3 : 1 B)3 : 2 C)4 : 3 D)5 : 3 E)None SOLUTION:Required ratio = 750 : 250 = 3 : 1 Answer A #### A <<<Examples ends QUESTION:In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what q percent of all the people in Smithtown are left-handed women? options: A) 50% B) 40% C) 25% D) 20% E) 10% SOLUTION:looking at the ratio we can take total number of people q=20.. ans 5/20 or 25% C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If x = 1- 3t and y = 2t - 3, then for what value of t does x = y? options: A) 5/2 B) 3/2 C) 2/3 D) 4/5 E) 0 SOLUTION:We are given x = 1 – 3t and y = 2t – 3, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 3t for x and 2t – 3 for y in the equation x = y. This gives us: 1 – 3t = 2t – 3 4 = 5t 4/5 = t The answer is D. #### D QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes options: A)18kms B)16kms C)50kms D)30kms E)40kms SOLUTION:total eastward distance= 25kmph*1/4hr=6.25 km total westward distance= 40kmph*1/4hr=10 km total distn betn them= 6.25+10=16.25km ans 16km ANSWER:B #### B QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)16 SOLUTION:1. We need to find out the time taken by 7 workers after day 1. 2. total no.of wokers * total time taken = time taken by 1 worker 3. Time taken by 1 worker = 16*8 = 128 days 4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job. 5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7* total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days. 6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days. The answer is choice E #### E QUESTION:The average age of a husband and his wife was 23 years at the time of their marriage.After 5 years they have a one year old child.The average of the family is now? options: A)18 years B)23 years C)29 years D)26 years E)19 years SOLUTION:sum of the present age of husband, wife and child =(23*2+5*2)+1 = 57 years required average = 57/3 = 19 years. Answer :E #### E QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is options: A)100 B)250 C)260 D)416 E)None of these SOLUTION:Explanation: Let the number of boys and girls be 8x and 5x. Total number of students = 13x = 13 × 32 = 416. Answer: D #### D QUESTION:A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? options: A)A)452000 B)B)200000 C)C)800000 D)D)500000 E)E)652000 SOLUTION:3 children got = 3*15% = 45% wife got = 30% orphan house = 5% total = 45+30+5 = 80% remaining = 100-80 = 20% 20% = 40000 100% = 40000*100/20 = $200000 Answer is B #### B QUESTION:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold? options: A) 11 B) 13 C) 15 D) 17 E) 19 SOLUTION:(x+5)*150 +x*85=2160 =>x=6 total lens=6+(6+5)= 17 Answer D #### D QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+99)=? options: A)7000 B)7250 C)7500 D)7750 E)6750 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 99=1+(n-1)2 => n=50 Use value of n in (1) then, Sn = (50/2)(1+99) = 2500 Ans:- 3(Sn) = 7500 Answer : C #### C QUESTION:In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number? options: A)26 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=3x Therefore x + 3x = 8 ‹=›4x = 8 ‹=›x= 2. So, ten's digit = 2, unit's digit = 6. Hence, the required number is 26. Answer A #### A QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:What is 35% of 4/13 of 585? options: A)52 B)63 C)74 D)85 E)96 SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate. The number 585 is between 540 and 630, so (1/9)*585 will be about 65. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently. The closest answer is 63, so this is the answer to choose. The answer is B. #### B QUESTION:What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected? options: A)76 ways B)66 ways C)30 ways D)56 ways E)43 ways SOLUTION:The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5 = 30 ways. Answer: C #### C QUESTION:By selling 66 bags, a shopkeeper gains the price of 33 bags. His gain per cent is options: A)91% B)100% C)95% D)98% E)93% SOLUTION:Suppose S.P of 66 bags = Rs 66 Therefore, Gain = Rs 33 => C.P = Rs 33 Gain % = 33/33 x 100 = 100% Gain = 100% ANSWER:B #### B QUESTION:In how many different number of ways 5 boys and 4 girls can sit on a bench? options: A)700 B)710 C)720 D)362880 E)740 SOLUTION:npn = n! 9p9 = 9 X 8 X 7 X 6 × 5 × 4 × 3 × 2 × 1 = 362880 D #### D QUESTION:If 13 = 13w/(1-w) ,then (4w)2 = options: A)1/4 B)1/2 C)1 D)2 E)4 SOLUTION:13-13w=13w 26w=13 w=1/2 4w=2 4w*2=2*2=4 ANSWER:E #### E QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:The side of a cube is 8 m, Find the voiume? options: A)515 B)509 C)502 D)508 E)512 SOLUTION:Cube Volume = a(power)3 a(power)3 = 8(power)3 = 512 m(power)3. Answer is E. #### E QUESTION:Which of the following number is divisible by 24 ? options: A)22 B)24 C)26 D)27 E)28 SOLUTION:24 = 3 x8, where 3 and 8 co-prime. Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8. Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8. Consider option (D), Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3. Also, 736 is divisible by 8. 3125736 is divisible by (3 x 8), i.e., 24. B #### B QUESTION:The average of first four prime numbers greater than 50 is? options: A)50 B)57 C)89 D)56 E)60 SOLUTION:53 + 59 + 61 + 67 = 240/4 = 60 Answer: E #### E QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 9 and 10. The larger of the two numbers is: options: A)276 B)299 C)230 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 9) and (23 x 10). Larger number = (23 x 10) = 230. Answer: Option C #### C QUESTION:At Pete’s Pet Shop, 35 cups of bird seed are used every 5 days to feed 14 parakeets. How many cups of bird seed would be required to feed 9 parakeets for 7 days? options: A)27 B)9 C)31.5 D)16 E)54 SOLUTION:Let's go step-by-step. 35 cups are used over a 5 day period, which means 7 cups a day. This feeds 14 parakeets, which means each parakeet needs 1/2 of a cup every day. For 9 parakeets, we need 9*1/2cups = 4.5 cups a day. Over 7 days, we need 31.5 cups. Choice c. #### C QUESTION:A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube? options: A)8p B)pq C)pq + 27 D)-p E)(p - q)^6 SOLUTION:A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject. B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject. C. Hold. D. since p is a perfect cube, -p will also be a perfect cube. reject. E. (p-q)^6, is a perfect cube, so reject. By elimination C is the answer. Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube. ANSWER:C #### C QUESTION:There are 14 songs in that 5 Rock songs, 6 western songs & 3 Hindi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song & 1 western song? options: A)15624 B)16478 C)17953 D)19655 E)28958 SOLUTION:15624 A #### A QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. #### C QUESTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ? options: A) None B) Two C) Four D) Five E) Seven SOLUTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain? R=2,4,6,8,10,12... S=4,16,36,64... Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets. Solution: Five Answer: D #### D QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 110/100 × 110/100 = 12100 C #### C QUESTION:In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters? options: A)125.5 meters B)126.5 meters C)127.5 meters D)128.5 meters E)None of these SOLUTION:Explanation: When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters. Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters. So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C. So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters. Answer: C #### C QUESTION:If x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z? options: A)Y2 = xz B)Y2 = xy C)Y2 = Yz D)Y3 = xz E)Y5 = xY SOLUTION:X = (Y*NR)/100 Y = (Z*NR)/100 X/Y = NR/100 Y/Z = NR/100 X/Y = Y/Z Y2 = XZ.Answer:A #### A QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:Machine A can put caps on a set of bottles in 8 hours at a constant rate. If Machine A does the job for 6 hours and Machine B does the rest of the job, which works at 1/4 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job? options: A)4hrs B)6hrs C)8hrs D)10hrs E)16hrs SOLUTION:machine A will do 6/8 in 6 hrs, so A does 3/4 of the work .. Therefore, B will do the remaining 1/4 th work alone.. As the speed of B is 1/4 rate of A, B will do the 1/4th work in same time that A takes to complete full job... ans 8 C #### C QUESTION:f a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:A marketing firm determined that, of 200 households surveyed, 80 used neither Brand W nor Brand B soap, 60 used only Brand W soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? options: A) 15 B) 20 C) 30 D) 40 E) 45 SOLUTION:SOLUTION FOR SOAP W AND SOAP B (D) 40 #### D QUESTION:A man purchased 3 blankets @ Rs.100 each, 4 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)600 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 A #### A QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28 SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 70 students = 800 + 3000 = 3800 Average marks of all the students = 3800/70 = 54.28 ANSWER:B #### B QUESTION:30 carrots on a scale weigh 5.94 kg. When 3 carrots are removed from the scale, the average weight of the 27 carrots is 200 grams. What is the average weight (in grams) of the 3 carrots which were removed? options: A)165 B)170 C)175 D)180 E)185 SOLUTION:27*200=5400. The other 3 carrots weigh a total of 540 grams. The average weight is 540/3 = 180 grams. The answer is D. #### D QUESTION:In store A there are 10 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores B earned to the total amount store A earned? options: A)3:1 B)2:3. C)1:3. D)3:4. E)2:5. SOLUTION:1st statement : ratio of pants Store A : Store B 10x : 40x X:4X Price : 4y:3y Total revenue 4xy : 12xy 3:1 Answer : A #### A QUESTION:Pandiyan buys an old scooter for Rs. 6000 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is : options: A)20% B)12% C)9.09% D)5% E)None of these SOLUTION:Explanation : Solution: C.P. =Rs. (6000+600) =Rs. 6600; S.P. = Rs. 7200. Gain% = 7200-6600/6600*100 = 9.09% Answer : C #### C QUESTION:The area of an isosceles trapezoid with sides of length 5 and bases of length 10 and 16 is? options: A)48 B)40 C)52 D)54 E)58 SOLUTION:Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 16 will be divided into 3 parts= 10, 3 and 3 (Making one square and two right triangles) For the right triangle, height will be= (5^2-3^2)^1/2= 4 And the area of trapezoid = 1/2 (B1+B2)H= 1/2*26*4= 52 C is the answer #### C QUESTION:Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ? options: A)500 B)600 C)450 D)550 E)None of these SOLUTION:Explanation: Let the lent at 5% be 'A' (A x 5 x 1)/100 + [(1500 - A)x 6 x 1]/100 = 85 5A/100 + 90 – 6A/100 = 85 A/100 = 5 => A = 500 ANSWER IS A #### A QUESTION:The population of a village is 6000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)5000 B)4860 C)5400 D)4800 E)5120 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 6000 × 90/100 × 90/100 = 4860 B #### B QUESTION:If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. ab < 1 III. a/b < 2 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:MANHATTAN GMATOFFICIAL SOLUTION: You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term: 1 > 1 - ab > 0 0 > -a b > -1 Subtract 1 from all three terms. 0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs. Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true. Therefore, the correct answer is (D). #### D QUESTION:The area of a triangle is with base 4m and height 5m? options: A)15 B)19 C)56 D)10 E)36 SOLUTION:Explanation: Area=1/2*b*h 1/2 * 4 * 5 = 10 m^2 Answer : D #### D QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is : options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None SOLUTION:Explanation: Ratio of rents =(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3) =72:50:140:63 Let total rent = Rs.x Then, A's share = Rs.(x×72/325)= Rs.(72x/325) 72x/325=360 or x = 325×360/72=1625 Correct Option: C #### C QUESTION:The profit earned by selling on article for 900 is double the loss incurred when the same article is sold for 450. At what price should the article be sold to make 25% profit? options: A)750 B)800 C)850 D)860 E)890 SOLUTION:Let ‘x’ be the CP of the article; Then 900 – x = 2(x – 450); :. x= 600. 25% of 600 = 150 :. New SP = 600 + 150 = 750 Option 'A' #### A QUESTION:Coconuts were purchased at 150 per hundred and sold at 2 per coconut. If 2000 coconuts were sold, what was the total profit made? options: A)500 B)1000 C)1500 D)2000 E)None of these SOLUTION:C.P. for one coconut = 150⁄100 = 3⁄2 S.P. for one coconut = 2 Profit on one coconut = 2 - 3⁄2 = 1⁄2 ∴ Profit on 2000 coconut = 1⁄2 × 2000 = 1000 Answer B #### B QUESTION:Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many litres of tomato puree will be obtained from 20 litres of tomato juice? options: A)2 litres B)2.4 litres C)2.5 litres D)6 litres E)4 litres SOLUTION:Tomato Juice has 90% water and 10% tomato Tomato puree has 20% water and 80% tomato So 20 liter of tomato juice has 20*90/100=18 liters of water and 2 liters of tomato. As tomato puree has 80% content of tomato, so 2 liters of tomato from 20 liter juice corresponds to 80% so tomato purees that can be obtained=100*2/80=2.5 ANSWER:C #### C QUESTION:Six lights begin to flash together at 12:00 noon and flash respectively at intervals of 3, 4, 5, 6, 7, and 8 seconds. Not including the flash at 12:00 noon, how many more times will all six lights flash together before 1:00 pm (i.e. one hour later)? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:The least common multiple is 2*2*2*3*5*7=840. 3600 seconds / 840 = 4 + remainder. The answer is A. #### A QUESTION:Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg. options: A)2:7 B)2:3 C)2:0 D)2:1 E)2:2 SOLUTION:Explanation: By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind {\color{Blue} \therefore } Required ratio = 60 : 90 = 2 : 3 Answer: B) 2:3 #### B QUESTION:A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass? options: A)6 B)8 C)10 D)12 E)16 SOLUTION:1)If the two sides are co-prime, SUM of sides -1.. 2)and if not co-prime , Sum of sides - HCF of sides.. the difference is related to the diagonal passing through a vertex of squares at some place.. here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12 ANSWER:D #### D QUESTION:Each child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:2*8=16.Answer is A. #### A QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 160 km/hr? options: A)2.5 sec B)2.9 sec C)2.7 sec D)8.7 sec E)8.5 sec SOLUTION:Speed = 160 * 5/18 = 44 m/sec Time taken = 120/44 = 2.7 sec. Answer: C #### C QUESTION:Goldenrod and No Hope are in a horse race with 6 contestants. How many different L arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race? options: A) 720 B) 360 C) 120 D) 24 E) 21 SOLUTION:no hope finishing before goldenrod= 1/2 of the times therefore the different L arrangements are 1/2* 6! = 360 = B #### B QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)277 C)299 D)266 E)29912 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 => 675 675 * 2 = Rs.1350 Answer:A #### A QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 300 m long platform in 26 sec. What is the length of the goods train? options: A)382 B)782 C)278 D)270 E)220 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 300)/26 = 20 x = 220 m. Answer: E #### E QUESTION:If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight? options: A)80 B)86 C)92 D)98 E)104 SOLUTION:L+K = 160 and so K = 160-L L+10 = 1.5K = 1.5(160-L) 2.5L = 230 L = 92 The answer is C. #### C QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3? options: A)897 B)164,850 C)164,749 D)149,700 E)156,720 SOLUTION:Explanatory Answer Step 1: Identify the series The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101. The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107. The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998. It is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2). So, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3. Step 2: Compute the sum Sum of an Arithmetic Progression (AP) = [first term + last term/2]n We know the first term: 101 We know the last term: 998. The only unknown is the number of terms, n. In an A.P., the nth term an = a1 + (n - 1)*d In this case, therefore, 998 = 101 + (n - 1)* 3 Or 897 = (n - 1) * 3 (n - 1) = 299 or n = 300. Sum of the AP will therefore, be [101+998/2]∗300 = 164,850 Choice B is the correct answer. #### B QUESTION:At an election 2 candidates are participated a candidate got 45% of votes and defeated by 9000 votes. 83 votes are invalid. Find the total polled votes? options: A)100000 B)85236 C)89562 D)90083 E)95842 SOLUTION:winners votes = 100-45 = 55% invalid votes = 83 polled votes = [(100*9000)/(2*55-100)]+83 = 90083 Answer is D #### D QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)4 days B)6 days C)7 days D)9 days E)1 days SOLUTION:1 women's 1 day work = 1/28 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/28 + 10/140) = 1/4 5 women and 10 children will complete the work in 4 days. Answer: A #### A QUESTION:Which number should replace both the asterisks in (* /18) x (*/162) = 1 ? options: A)27 B)36 C)54 D)72 E)90 SOLUTION:Let (y/18) x (y/162) = 1 y^2 = 18 x 162 = 18 x 18 x 9 y = (18 x 3) = 54 The answer is C. #### C QUESTION:If n is an integer, which of the following must be an even integer? options: A)n^2-n-1 B)n^2-4n+6 C)n^2-5n+5 D)n^2+3n+8 E)n^2+2n+10 SOLUTION:Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 ) A: n^2-n-1 = -1 { If n = 1 } B: n^2-4n+6 = 3 { If n = 1 } C: n^2-5n+5 = 1 { If n = 1 } D: n^2+3n+8 = 12 { If n = 1 }n^2+3n+8 = 18 { If n = 2 } E: n^2+2n+10 = 13 { If n = 1 } Thus the only possible answer is (D) #### D QUESTION:Find the base K of the number system, if (524)8 = (664)K ? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:5*8^2 + 2*8^1 + 4*8^0 = 6*K^2 + 6*K^1 + 4*K^0 320 + 16 + 4 = 6(K^2) + 6K + 4 340 = 6(K^2) + 6K + 4 6(K^2) + 6K + 4 - 340 = 0 6(K^2) + 6K - 336 = 0 dividing by 6; (K^2) + K - 56 = 0 solving this quadratic equation we get, K=7 and K=-8 thus K=7 ANSWER:D #### D QUESTION:A garrison of 150 men has provisions for 31 days. At the end of 16 days, a reinforcement arrives, and it is now found that the provisions will last only for 5 days more. What is the reinforcement? options: A)150 B)450 C)400 D)600 E)300 SOLUTION:150 ---- 31 150 ---- 15 x -----5 x*5 = 150*15 x = 450 150 ------- 300 Answer: E #### E QUESTION:If a square mirror has a 20-inch diagonal, what is the approximate perimeter E of the mirror, in inches? options: A) 40 B) 60 C) 80 D) 100 E) 120 SOLUTION:if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other. And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter E must be less than 80, so we can eliminate answer choice C, D and E. so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A. Now we are left with is B #### B QUESTION:After decreasing 56% in the price of an article costs Rs.4400. Find the actual cost of an article? options: A)12000 B)15000 C)1200 D)1000 E)10000 SOLUTION:CP* (44/100) =4400 CP= 100 * 100 => CP = 10000 Answer:E #### E QUESTION:There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to? options: A)7!*1! B)7!*2! C)6!*2! D)8!*2! E)6!*2! SOLUTION:Total number of ways = 7!*2!. B #### B QUESTION:A small company reduced its faculty by approximately 15 percent to 195 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)229 E)E)302 SOLUTION:If x is the original number of employees, then after 15% reduction in employees number is .85x but we are given .85x = 195 x = 229 So the original number of employees is 229 Correct Answer - D #### D QUESTION:A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)22 B)71 C)54 D)77 E)99 SOLUTION:S = 240/16 * 18/5 = 54 kmph Answer: C #### C QUESTION:What is the minimum value of z for which z^2 + z - 3/14 > 0 is not true? options: A) -5/7 B) -3/7 C) -1/7 D) 1/7 E) 4/7 SOLUTION:I think B -3/7 is the best ans... #### B QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)196 E)200 SOLUTION:185 Answer is B #### B QUESTION:Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere? options: A) 6/π B) 9/π C) 6 D) 9 E) 12 SOLUTION:Given Area of the base of a hemisphere is 3 = PI * R^2 Thus R = Sqrt ( 3 / PI ) . Surface area of whole sphere = 4*PI*R^2 . = 4 * PI * 3 / PI = 12 . Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . But the total surface area = 6 + Area of the base of a hemisphere . = 6 + 3 = 9. Answer is D !! #### D QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:A computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed to the final retail price. options: A)$1,000 B)$960 C)$240 D)$200 E)$150 SOLUTION:Cost price=1000 Profit=20% =20% of 1000=200 selling price=CP+ Profit SP=1200 a Discount of 20% to employees means 20% off on 1200 so 20% of 1200= 240 so a employee thinks he saved 240.. Answer: C #### C QUESTION:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 8 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)11 D)14 E)6 SOLUTION:Given: mean=21 and SD=8 The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=13 and 2 SD below the mean ismean-2*SD=5, so the number of hours that Pat watched television was between 5 and 13 hours. Answer: C #### C QUESTION:Shaun is starting a new diet plan that offers him the choice of fruit or yogurt for breakfast, 6 different entrees for lunch, and 9 different entrees for dinner. If Shaun chooses an Italian entree for lunch, he always chooses an Italian entree for dinner. If Shaun chooses a Chinese entree for lunch, he never chooses a Chinese entree for dinner. If there are 2 Italian entrees and 2 Chinese entrees among the lunch choices, and 3 Italian entrees and 3 Chinese entrees among the dinner choices, from how many different daily menus can Shaun choose? options: A)24 B)36 C)72 D)90 E)108 SOLUTION:Let the Breakfast set be {F , Y} Lunch be {I ,I , C,C , L1,L2} Dinner be {I,I,I , C,C,C, D1,D2,D3} There are only 2 restrictions, Italian Lunch has to go with Italian Dinner and Chinese Lunch cannot go with Chinese dinner. So the set of Breakfast, Lunch and Dinner will {Any BF, Italian Lunch, Italian Dinner } = 2 * 2 * 2 {Any BF, Chinese Lunch, Not Chinese Dinner} = 2 * 2 * 6 {Any BF, Not Italian or Chinese Lunch, Any Dinner} = 2 * 2 * 9 Adding all these gives 72. Answer is C #### C QUESTION:How many integers between 10 and 100 are there such that their unit digit is odd? options: A)45 B)50 C)30 D)60 E)55 SOLUTION:90 numbers between - 10 and 100 Out of which half would be even, half odd. Number of odd unit digit number = 45. correct option is A #### A QUESTION:Two wheels are connected via a conveyor belt. The larger wheel has a 48cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r? options: A)90r B)75r C)48r D)24r E)(64π)/3 SOLUTION:Interesting to note that the larger wheel has a diameter of 48 (8*6) while the smaller one has a diameter of 32 (8*4)... If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 48pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.5 = 15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.5 = 900 revolutions per hour. If r = 10, then the answer choice must be b. A. 90r #### A QUESTION:Convert 0.30 in to a vulgar fraction ? options: A)18/50 B)16/50 C)3/10 D)19/50 E)None SOLUTION:Answer 0.30 = 30/100 = 3/10 Correct Option: C #### C QUESTION:The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 3 years? options: A)5100 B)4096 C)5200 D)5400 E)5500 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 8000 × 80/100 × 80/100 x 80/100= 4096 Answer : B #### B QUESTION:A five digit number is to be formed using each of the digits 1, 2, 3, 4 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ? options: A)12 B) 36 C) 72 D) 60 E) 120 SOLUTION:Reqd ways = (Total No. of ways - cases when both 1 and 2 are together) 4 numbers can be arranged in 4 places in 4! ways. Now tie 1 and 2 together so effectively there are 4 nos. they can be arranged in 3! ways. 1 and 2 can be arranged within themselves in 2!ways. Reqd. Answer = 4! - 3!2! = 24 - (6*2) = 12 Answer: A #### A QUESTION:There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems options: A)36 minutes B)60 minutes C)72 minutes D)100 minutes E)None of these SOLUTION:Explanation : Let x = minutes spent on a non-math problem then 2x = minutes spent on a math problem x(200-50) + 2x(50) = 180 x(150) + 2x(50) = 180 150x + 100x = 180 250x = 180 x = 0.72 minutes Time to spend on math problems: 2x(50)=100x = 100(0.72) = 72 minutes Answer : C #### C QUESTION:Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 1600 then loss of Pyarelal? options: A)600 B)700 C)840 D)940 E)1440 SOLUTION:Let the capital of Pyarelal be x, then capital of Ashok=x/9 So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x Hence out of the total loss of 1600, loss of Pyarelal= 1600*9x/10x=1440 ANSWER:E #### E QUESTION:The difference between simple interest and C.I. at the same rate for Rs.5000 for 2 years in Rs.72. The rate of interest is? options: A)11 B)12 C)77 D)85 E)65 SOLUTION:5000 = 72(100/R)2 5 R2 = 720 => R = 12.Answer:B #### B QUESTION:If x and y are integers and x + y = 7, which of the following must be true? options: A)x and y are consecutive integers. B)Both x and y are less than 5. C)If x > 0, then y < 0. D)Both x and y are even. E)If x < 0, then y > 0. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option E is right could you explain #### E QUESTION:For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? options: A)(-3)^2 B)2 C)3 D)4 E)5 SOLUTION:Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4 Step 2, For each number: subtract the Mean and square the result = (1-4)^2=(-3)^2 (2-4)^2=(-2)^2 (3-4)^2 =(-1)^2 (4-4)^2=(.0)^2 (5-4)^2=(1)^2 Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options. Hence A #### A QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+79)=? options: A)4500 B)4250 C)4350 D)4800 E)4150 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 79=1+(n-1)2 => n=40 Use value of n in (1) then, Sn = (40/2)(1+79) = 1600 Ans:- 3(Sn) = 4800 Answer : D #### D QUESTION:In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three? options: A)5 B)7 C)9 D)11 E)13 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 40 = 20 + 30 + 10 - (10) - 2x x = 5 So, answer will be A #### A QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 5*4*1=20. P(dispensing one of each color)=20/120=1/6. The answer is D. #### D QUESTION:The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability T that the next couple the maitre 'd seats will not order dessert? options: A) 20% B) 25% C) 40% D) 60% E) 75% SOLUTION:could you use a venn diagram and just go with the number 100. 60 people order dessert and coffee... which is the union of D and C. T=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither. B 25% #### B QUESTION:A basket has 6 apples and 6 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)1/3 C)1/4 D)2/5 E)3/10 SOLUTION:The total possible choices are 12C3 = 220 The ways to choose 3 apples: 6C3 = 20 The ways to choose 2 apples: 6C2 * 6C1 = 90 P(at least 2 apples) = 110/220 = 1/2 The answer is A. #### A QUESTION:For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 3, -3, 2, 5, -4, -6 ? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Given sequence: {1, -3, 2, 5, -4, -6} The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative. 1*(-3)=-3=negative; -3*2=-6=negative; 2*5=10=positive; 5*(-4)=-20=negative; (-4)*(-6)=24=positive. So there are 3 pairs of consecutive terms of the sequence for which the product is negative. Answer: A. #### A QUESTION:The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria options: A)10 B)12 C)14 D)16 E)18 SOLUTION:The question basically asks how many minutes it takes for a population to increase by factor 50(50,000 / 1,000 = 50). Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes: 2^x >= 50, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^6 = 64, i.e. the population has to double 6 times. Since it takes the population 2 minutes to double once it takes 6*2 minutes = 12 minutes to double nine times. Thus, solution B = 12 is correct. #### B QUESTION:A and B can do a piece of work in 11 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? options: A)15.5 days B)19.5 days C)17.5 days D)9.2 days E)18.5 days SOLUTION:C = 1/5 – 1/11 = 6/55 => 9.2 days ANSWER:D #### D QUESTION:The tax on a commodity is diminished by 30% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it? options: A)20% B)18% C)15% D)12% E)14% SOLUTION:100 * 100 = 10000 70 * 115 = 8050 10000------- 1950 100 ------- ? = 20% ANSWER:A #### A QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:18 C)18:22 D)18:39 E)18:39 SOLUTION:Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer:A #### A QUESTION:Car Dealership X, the total profit from sales increased by 30 percent over the previous years, while the number of cars sold decreased by 30 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year. options: A)18% B)30% C)52% D)63% E)85.71% SOLUTION:Let Profit be x and cars sold be y Originally Profit/Car = x/y Now it is 1.3x / 0.7 y = 13/7 (x/y) Increase in profit per car = ((6/7) (x/y)) / (x/y) * 100 = 85.71% Answer = E #### E QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame? options: A)10 B)20 C)30 D)40 E)54 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/3) of that of the painting so Area of frame = (1/3) * a^2 Area of Frame + Painting = a^2 + (1/3)*a^2 = (4/3)*a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2 so, b * sqrt2 = 12 so, b = 6 * sqrt2 b^2 = 72 we know that b^2 = (4/3)*a^2 so, a^2 = (3/4)*b^2 = (3/4)*72 = 54 And area of painting = a^2 = 54 So, answer will be E. #### E QUESTION:14,24,54,34,44,56,53, ? options: A)44 B)55 C)66 D)77 E)88 SOLUTION:14-24...dif -10 54-34..dif -20 44-56..dif-12 53-77...dif-24 ANSWER:D #### D QUESTION:Sandy had $231 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? options: A)$270 B)$290 C)$310 D)$330 E)$350 SOLUTION:Let the money Sandy took for shopping be x. 0.7x = 231 x = 330 The answer is D. #### D QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (5*27) - (4*25) = 135-100 = 35 Answer: Option A #### A QUESTION:Find the best average of the first 10 multiples of 7.... options: A)30.5 B)38.5 C)40 D)43.5 E)55.5 SOLUTION:the exp is - 7(1+2+3+4+5+6+7+8+9+10)/10 => 7(10(10+1)/10*2 => 7(110)/10*2 = 38.5 ANSWER B #### B QUESTION:Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings? options: A)1/2 B)1/4 C)1/6 D)1/8 E)1/16 SOLUTION:Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible). Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8. Answer: D. #### D QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? options: A)4 B)8 C)16 D)17 E)None of these SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) = 2x = 8. Answer:B #### B QUESTION:Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ? options: A)0.5% B)1% C)5% D)50% E)500% SOLUTION:x percent can be written as x/100 So, we get: (30/100)(40/100)(50) = (60/100)(x/100)(200) Simplify all fractions to get: (3/10)(2/5)(50) = (3/5)(x/100)(200) Expand: 300/50 = 600x/500 Simplify: 6 = 6x/5 Multiply both sides by 5 to get: 30 = 6x Solve: x = 5 Answer: C #### C QUESTION:The length Q of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length Q of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is options: A)70 B)71 C)72 D)73 E)74 SOLUTION:Explanation: Let the second number is x, then first is 2x, and third is 1/3(2x) =>2x+x+2x/3=264 <=>11x/3=264 =>x=72 Answer: Option C #### C QUESTION:A football field is 9600 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards? options: A)450 B)600 C)700 D)2400 E)3200 SOLUTION:Answer C) 9600 yards need 1200 lbs 1 Yard will need 1200/9600 = 1/8 lbs 3600 Yards will need 1/8* 5600 Yards = 700lbs #### C QUESTION:How many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number? options: A)4 B)10 C)11 D)12 E)15 SOLUTION:The Question basically asks how many positive odd integers less than 100 are odd multiples of 5 So we have 5,15,25,35,45,55,65,75,85,95 =10 Ans B #### B QUESTION:The difference between simple and compound interest on Rs. 1600 for one year at 10% per annum reckoned half-yearly is? options: A)8 B)3 C)9 D)4 E)2 SOLUTION:S.I. = (1600 * 10 * 1)/100 = Rs. 160 C.I. = [1600 * (1 + 5/100)2 - 1600] = Rs. 164 Difference = (164 - 160) = Rs.4. Answer:D #### D QUESTION:A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours. What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75). options: A)1 hour B)2 hour C)3 hour D)4 hour E)5 hour SOLUTION:In one hour, Soln 1: the large inlet tube fills 1 / 3 of the tank; the small inlet tube fills 1 / 6 of the tank; the outlet tube empties 1 / 9 of the tank; and therefore all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. Soln 2: Let V be the total volume of the tank. From equation (1), Flow Rate (large inlet tube) = V / 3 Flow Rate (small inlet tube) = V / 6 Flow Rate (outlet tube) = V / 9. Substituting in equation (2), Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9). Using the above result in equation (1), Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ]. Note that V cancels out on simplifying the above expression. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. #### A QUESTION:Find the value of 3 + 2 • (8 – 3) options: A)(a) 25 B)(b) 13 C)(c) 17 D)(d) 24 E)(e) 15 SOLUTION:3 + 2 • (8 – 3) = 3 + 2 (5) = 3 + 2 × 5 = 3 + 10 = 13 Answer: (D) #### D QUESTION:Which of the following lines has x-intercept and y-intercept that are integers T? options: A)y=3x+1 B)y=√x+1 C)y=-2/x D)y=x^2-1 E)xy=1 SOLUTION:Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers T and the correct answer is D. #### D QUESTION:If a number is exactly divisible by 11 and 13, which of the following types the number must be? options: A)Divisible by (11 + 13) B)Divisible by (13 - 11) C)Divisible by (11 x 13) D)Divisible by (13 ÷ 11) E)None SOLUTION:Answer LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13). Correct Option: C #### C QUESTION:If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? options: A)100 B)10 C)0.01 D)0.0001 E)0.0001 SOLUTION:Given that 100 microns = 1 decimeter =10,000 angstroms So, 1 micron = 10,000/100 =100 Answer : A #### A QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4% ANSWER:B #### B QUESTION:In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together? options: A)None of these B)48 C)32 D)64 E)57 SOLUTION:Explanation : The word 'JUDGE' has 5 letters. It has 2 vowels (UE) in it and these 2 vowels should always come together. Hence these 2 vowels can be grouped and considered as a single letter. That is, JDG(UE). Hence we can assume total letters as 4 and all these letters are different. Number of ways to arrange these letters = 4!= 4 x 3 x 2 x 1 = 24 In the 2 vowels (UE), all the vowels are different. Number of ways to arrange these vowels among themselves = 2! = 2 x 1 = 2 Total number of ways = 24 x 2 = 48. Answer : Option B #### B QUESTION:In the equation 2x – cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 6 ? options: A)0 B)-4 C)-3 D)4 E)9/2 SOLUTION:2x - cy = 18 x=6, y=2; 12-2c=18 c=-3 2x-cy=18 when y=6, c=-3, x= x=0 ANSWER:A #### A QUESTION:The cube root of what integer power of 2 is closest to 50? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Integer powers of 2 = 2 , 2^2, 2^3, 2^4, 2^5, 2^6, 2^7 etc. Let, Cube root of x is closest to 50 i.e. x is closest to cube of 50 = 50*50*50 = 125000 But x must be equivalent to an Integer power of 2 2^10 = 1024 2^7 = 128 i.e. 2^17 = 128*1024 = 128000 (approx.) i.e. 2^18 = 256*1024 = 256000 (approx.) i.e. 2^16 = 64*1024 = 64000 (approx.) i.e. 2^17 which is closest to 125000 i.e. Integer power of 2 must be 7 Answer: option B #### B QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 13260, how much money did he borrow? options: A)13000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 13260 18x + 45x + 39x = (13260* 100) 102x = 1326000 => x = 13000. Answer:A #### A QUESTION:If A : B = 4 : 9 and B : C = 5 : 9 then A : B : C is : options: A)20 : 35 : 63 B)35 : 36 : 63 C)30 : 35 : 65 D)20 :45: 81 E)None of these SOLUTION:Expl : A : B = 4 : 9 B : C = 5 :9 = 5*9/5 : 9 *9/5 = 9 : 81/5 A : B : C = 4 : 9 : 81/5 = 20 : 45 : 81 Answer: D #### D QUESTION:If x > y and y > z, which of the following represents the greatest number W? options: A) x − z B) x − y C) y − x D) z − y E) z − x SOLUTION:Because x>y>z thus W=x- z wil lbe greatest Ans: A #### A QUESTION:Walking at 4/5 of her normal speed, a worker is 10 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is options: A)30 B)35 C)40 D)45 E)50 SOLUTION:Let V be her normal speed and let T be her normal time. D = (4/5)V * (T+10) Since the distance is the same we can equate this to a regular day which is D = V*T V*T = (4/5)V * (T+10) T/5 = 8 T=40 The answer is C. #### C QUESTION:The length of a rectangle is twice its breadth. If its length is decreased by 4 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle. options: A)10/3cm B)20/3cm C)20cm D)16cm E)14cm SOLUTION:Explanation: Let breadth = x. Then, length = 2x. Then, (2x - 4) (x + 5) - 2x * x = 75 => 6x - 25 = 75 => x =20/3. Length of the rectangle = 20/3 cm. Answer: Option B #### B QUESTION:Find the median of the data 25, 37, 47, 18, 19, 26, 36. options: A)22 B)23 C)24 D)25 E)26 SOLUTION:Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47 Here, the number of observations is odd, i.e., 7. Therefore, median = (n + 1/2)th observation. = (7 + 1/2)th observation. = (8/2)th observation = 4th observation. 4th observation is 26. Therefore, median of the data is 26. ANSWER :E #### E QUESTION:What is the number which when multiplied by 13 is increased by 180? options: A)13 B)15 C)23 D)35 E)45 SOLUTION:13 × 15 = 195 Answer: B #### B QUESTION:9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90.5% B)87.5% C)80.5% D)77.5% E)70.5% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.212; 10+0.3} = {9.788; 10.212}. From the 8 listed numbers, 7 are within this range so 6/8=87.5%. Answer: B. #### B <<<Examples ends QUESTION:A part-time employee whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? options: A)9 B)13 C)17 D)20 E)33.33 SOLUTION:Let original hourly wage be x and let the no of hours worked be y Total wage will be =x*y After the increment the wage will be=1.5 x Now we need to find number of hours worked so that x*y=1.5x*z i.e z=1/1.5 y = 2/3y %decrease = (y-2/3y)/y *100=100/3=33.33%. Thus my answer is E. #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The diagonal of a rhombus are 25 m and 50 m. Its area is: options: A)900 B)800 C)700 D)625 E)650 SOLUTION:Area of the rhombus = 1/2 d1d2 = ( 1/2 × 25 × 50 ) Cm(power)2 = 25 × 25 = 625 Cm(power)2 Answer is D. #### D QUESTION:The ratio of spinsters to cats is 2 to 7. If there are 40 more cats than spinsters, how many spinsters are there? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Let 2x be the number of spinsters. Then 7x is the number of cats. 7x-2x=40 x=8 and the number of spinsters is 2(8)=16. The answer is B. #### B QUESTION:If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ? options: A)3653 B)3657 C)2977 D)3957 E)2711 SOLUTION:Explanation: Given : Letter : T I E R B A N Code : 7 1 9 3 2 4 5 Thus, the code for RENT is 3957. ANSWER:D #### D QUESTION:Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs? options: A)11 B)12 C)22 D)24 E)44 SOLUTION:22 times in a day. 12,1 hours 60/11 minutes , 2 hours 120/11 minutes , ...so on till 12( 11 hours 660/11 minutes) ANSWER:C #### C QUESTION:After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B? options: A)N/15 B)7N/8 C)14N/15 D)N/5 E)4N/5 SOLUTION:1/4 of tested had infection A, thus N/4 had infection A; Of those with infection A, 1/2 also had infection B, thus 1/2*N/4 = N/8 had both infections A and B. Therefore, N - N/8 = 7N/8 did not have both infection A and B. Answer: B. #### B QUESTION:Simplfy b - [b -(a+b) - {b - (b - a+b)} + a] options: A)a B)2a C)4a D)0 E)1 SOLUTION:Explanation: b-[b-(a+b)-{b-(b-a+b)}+a] =b-[b-a-b-{b-(2b-a)}+a] =b-[-a-{b-2b+a}+a] =b-[-a-{-b+a}+a] =b-[-a+b-a+a] =b-[-2a+b+a] =b-b+a =a Option A #### A QUESTION:According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 120 12-ounce smoothies? options: A) 120 B) 150 C) 180 D) 240 E) 600 SOLUTION:This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base? D #### D QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)12 B)18 C)22 D)24 E)none of these SOLUTION:Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x 27 * x = 36 * 18 x = (36 * 18)/27 x = 24. Answer is D. #### D QUESTION:The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article? options: A)1:3 B)2:5 C)3:2 D)9:4 E)4:2 SOLUTION:Explanation: Let C.P. = Rs. 5x and S.P. = Rs. 7x. Then, Gain = Rs. 2x Required ratio = 2x : 5x = 2:5 Answer: Option B #### B QUESTION:How many minutes does the minute hand gain in every one hour? options: A)55 B)60 C)65 D)No gain E)None of these SOLUTION:55 ANSWER:A #### A QUESTION:A certain collage has total of 410 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects? options: A)60 B)90 C)70 D)80 E)40 SOLUTION:Answer is B. Six majors are as follows: a + b + c + d + e + f Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20 4 of the majors have 300 seniors: a + b + c +d = 300 There are a total of 410 seniors. So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f =90. B #### B QUESTION:A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 2 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. options: A)1/7 B)1/12 C)1/14 D)1/18 E)1/21 SOLUTION:The total number of ways to sell 6 bottles from 10 is 10C6 = 210. The number of ways to sell 2 bottles of apple juice is 6C2*4C4 = 15*1 = 15 P(selling 2 bottles of apple juice) = 15/210 = 5/70 = 1/14 The answer is C. #### C QUESTION:Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 27 seconds. What is the length of each train (in meters)? options: A)50.5 B)88.5 C)37.5 D)55.5 E)23.5 SOLUTION:The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s In 27 seconds, the relative difference in distance traveled is 27 * 25/9 = 75 meters This distance is twice the length of each train. The length of each train is 75/2 = 37.5 meters The answer is C. #### C QUESTION:The sum of first nine prime numbers is? options: A)12 B)100 C)24 D)28 E)30 SOLUTION:Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23) = 100. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. B #### B QUESTION:If a·b·c·d=270, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a? options: A)7 B)10 C)11 D)13 E)15 SOLUTION:prime factorize : 270 = 2*3*5*9 Hence a = 2 and d = 9 . Hence answer is 9 - 2 = 7 Answer A #### A QUESTION:What is the lowest possible common multiple M of 2 distinct integers, each greater than 329? options: A)330·331 B)330^2 C)33·331 D)660 E)330 SOLUTION:Lowest possible common multiple M of 2 distinct integers will have to be multiple of the number greater than 329...which 330.. so one number will be 330...another one will be 660.. Ans is D. #### D QUESTION:Which is the following is divisible by 11 options: A)A)4305 B)B)4825 C)C)1635 D)D)4805 E)E)4906 SOLUTION:Explanation: Sum of first 'n' natural numbers = n(n + 1)/2 Sum of first 9 natural numbers = 5(5 + 1)//2 = 5 x 3 = 15 Sum of first 99 natural numbers = 55(55 + 1)//2 = 55 x 30 = 1650 1650 - 15 = 1635 Answer: Option C #### C QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:By selling 66 bags, a shopkeeper gains the price of 33 bags. His gain per cent is options: A)91% B)100% C)95% D)98% E)93% SOLUTION:Suppose S.P of 66 bags = Rs 66 Therefore, Gain = Rs 33 => C.P = Rs 33 Gain % = 33/33 x 100 = 100% Gain = 100% ANSWER:B #### B QUESTION:Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 6 and the product of the given number and the sum of its digits is equal to 136. options: A)82 B)93 C)39 D)28 E)17 SOLUTION:Using the elimination method the option that fits this description is 17 7-1 = 3 (unit's digit that exceeds its ten's digit by 3) 17*8 = 136 (the product of the given number and the sum of its digits is equal to 175) answer :E #### E QUESTION:The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)230 B)244 C)245 D)238 E)235 SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X = 235 m. Answer: Option E #### E QUESTION:At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.50. What is the price of 2 doughnuts? options: A)$ 0.55 B)$ 1.00 C)$ 1.10 D)$ 1.30 E)$ 1.50 SOLUTION:3D + C = 2.25......(1) 2D + C = 1.5........(2) (1) - (2) --> D = 0.75 --> 2D = 1.5 Answer: E #### E QUESTION:In the xy-coordinate system, what is the slope of the line that goes through point (2, 4) and is equidistant from the two points P = (9, 3) and Q = (5, 9)? options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:First, get the middle coordinate between (9,3) and (5,9). x = 9 + (5-9)/2 = 7 y = 3 + (9-3)/2 = 6 Second, get the slope of (7,6) and (2,4). m = 6-4 / 7-2 = 2/5 = 0.4 Answer: D #### D QUESTION:A car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+336*6=448c =>c=336*6/112=18 Answer B. #### B QUESTION:A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? options: A)10% B)12% C)14% D)16% E)18% SOLUTION:Let x be the amount of money paid for the first purchase. The second time, the customer paid 0.8(1.1x)=0.88x. The difference is 12%. The answer is B. #### B QUESTION:Lisa earns a profit of $3 on each ribbon that she sells, and $5 on each bracelet. If at the end of the day Lisa has earned $120 and she has sold at least 10 pieces of each item. At least how many bracelets she has sold? options: A)2 B)5 C)9 D)12 E)15 SOLUTION:Since Lisa has sold at least 10 pieces for each item, let us say Lisa sells (10 + r) number of ribbons and (10 + b) number of bracelets, her profit for the day = 3(10 + r) + 5(10 + b) => 3(10 + r) + 5(10 + b) = 120 => 30 + 3r + 50 + 5b = 120 => 3r + 5b = 120 - 30 - 50 = 40 => 5b = 40 - 3r => b = 8 - (3/5)r To minimize b, we need to maximize r and it will be a multiple of 5. r = 5, b = 8 - (3/5)5 = 5 r = 10, b = 8 - (3/5)10 = 2 Beyond that b will become -ve. So Lisa has sold at least 10 + 2 = 12 bracelets. Answer: D #### D QUESTION:A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 30%. Their gross income from sales for one month increases by what percent? options: A)9% B)11% C)13% D)15% E)17% SOLUTION:Let P be the original price and let x be the number of items sold originally. The original income is P*x. After the changes, the income is 0.9P*1.3x = 1.17*(P*x), an increase of 17%. The answer is E. #### E QUESTION:If x = 4 and y = −2, what is the value of (x − 2y)^y? options: A)−100 B)0.015 C)0.25 D)4 E)8 SOLUTION:Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE by inversing and squaring 0.015 Answer: B #### B QUESTION:Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE? options: A)1/15 B)1/14 C)1/12 D)1/13 E)1/17 SOLUTION:Explanation : Let two digit number that Shiwani thought be 'xy', where x and y are single digit number. Therefore, 10x+y=p(x+y)+3, where p is a natural number p=10x+y−3x+y. Also, y+x>3. Possible values of x and y for which p is a natural number are :- (x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9), (x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null), (x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4) There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits. Probability that Devesh thought of the same number as Shiwani = 1/14 Answer : B #### B QUESTION:In a business Ram invests Rs.60,000. After 6 months his uncle invests Rs.40,000. After one year they got a profit of Rs.12,000. Then uncle gets his share as options: A)Rs.2500 B)Rs.2000 C)Rs.1000 D)Rs.3000 E)Rs.4000 SOLUTION:ram=60,000(12months) uncle=(40000)(6months) 60000*12 : 40000*6 3 : 1 uncle share= (1/3+1)(12000)=3000 ANSWER:D #### D QUESTION:A train 100 m long pass a telegraph pole in 5 seconds. Find the speed of the train options: A)66 km/hr B)68.4 km/hr C)72 km/hr D)79.2 km/hr E)None SOLUTION:Sol. Speed = [100/5] m/sec = [20 * 18/5] km/hr = 72 km/hr. Answer C #### C QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested? options: A)Rs.20,000 B)Rs.20,028 C)Rs.20,298 D)Rs.20,029 E)Rs.20,291 SOLUTION:Let the second amount be Rs. x. Then, (12000 * 10 * 1)/100 + (x * 20 * 1)/100 = [(12000 + x) * 14 * 1] / 100 120000 + 20x = 16800 + 14x x = 8000 Total investment = 12000 + 8000 =Rs.20,000. Answer:A #### A QUESTION:If 2994 ÷ 14.5 = 171, then 29.94 ÷ 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.2 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ] = 171/10 = 17.1 Answer is A. #### A QUESTION:At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 30 other employees of Company K, how many employees does Company K have? options: A) 160 B) 120 C) 190 D) 200 E) 400 SOLUTION:Let the total number of employees in the company be x % of secretaries = 15% % of salespeople = 60% % of of employees other than secretaries and salespeople = 100 - 75 = 25% But this number is given as 30 so 25% of x = 30 x = 120 Therefore there a total of 120 employees in the company K Correct answer - B #### B QUESTION:A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? options: A)1/7 B)2/9 C)1/12 D)4/17 E)2/3 SOLUTION:Total number of balls = 7+2 = 9 n(S) = 9C3 = 9*8*7 / 3*2 = 84 n(E) = 2C2* 7C1 = 7 Probability = 7/84 = 1/12 Answer is C #### C QUESTION:The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there? options: A)24 B)30 C)36 D)42 E)48 SOLUTION:Let the number of pens be 5x and the number of pencils be 6x. 6x - 5x = 5 x = 5 The number of pencils is 30. The answer is B. #### B QUESTION:If 0 < m < 1 < n< 7, which of the following must be less than 1? I.m/n II. mn III. n - m options: A)II,III only B)I,III only C)I only D)III only E)II only SOLUTION:n > 1. So, option II, III is not possible. So, Option I is correct. Answer : C #### C QUESTION:In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase? options: A)$32 B)$50 C)$320 D)$400 E)$500 SOLUTION:Property tax as a percentage of its assessed value = 8% Increase in assessed value of the property = 24000 - 20000 = 4,000 $ Increase in property tax = (8/100)* 4000 = 320 $ Answer C #### C QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is? options: A)8118 B)8127 C)8618 D)8436 E)8128 SOLUTION:A = 7500(26/25)3 = 8436 Answer: D #### D QUESTION:Which of the number is odd one out ? options: A)84129 B)32418 C)47632 D)36119 E)67626 SOLUTION:C 47632 as 32*32 !=476 #### C QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4*side = 4* (3p/5) = 12p/5 Answer is C. #### C QUESTION:Depreciation applicable to an equipment is 20%.The value of the equipment 3 years from now will be less by options: A)48.8% B)47.8% C)46.8% D)49.8% E)45.8% SOLUTION:Value after 3 years will be 0.8^3 = 0.512 times the present value. so it will be less by 48.8%. ANSWER:A #### A QUESTION:The product of three consecutive numbers is 336. Then the sum of the smallest two numbers is ? options: A)13 B)15 C)20 D)38 E)56 SOLUTION:Product of three numbers = 336 336 = 6*7*8. So, the three numbers are 6, 7 and 8. And Sum of smallest of these two = 6+7 = 13. ANSWER : OPTION A #### A QUESTION:If x^2 + 1/x^2 = 3,what is the value of x^4 + 1/x^4 ? options: A)7 B)12 C)14 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 3 andSQUAREboth sides: (x² + 1/x²)²= 9 So, (x² + 1/x²)(x² + 1/x²) = 9 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 9 Simplify: x⁴ + 1/x⁴ = 7 Answer: A #### A QUESTION:A can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work? options: A)2 1/2days B)4 1/2days C)6 1/2days D)7 1/2days E)10 1/2days SOLUTION:The required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days Answer is B #### B QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 15% solution? options: A)A)5.8 B)B)1.3 C)C)9.6 D)D)12.5 E)E)7.9 SOLUTION:Amount salt in 100kg solution = 10*100/100 = 10 kg Let x kg of pure salt be added then(10+x)/(100+x)=15/100 200+20x=300+3x 17x = 100 x = 5.8 Answer is A #### A QUESTION:The sector of a circle has radius of 24 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)104.6 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 24) + 2(24) = 56.6 + 48 = 104.6 cm Answer:C #### C QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages options: A)30 B)35 C)37 D)41 E)42 SOLUTION:Explanation: Let A's age 10 years ago = x years. Then, B's age 10 years ago = 2x years. (x + 10) / (2x+ lO) = 3/4 => x = 5. So, the total of their present ages =(x + 10 + 2x + 10) = (3x + 20) = 35 years Option B #### B QUESTION:The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is options: A)0.4869 B)0.5904 C)0.6234 D)0.5834 E)0.2952 SOLUTION:P(winning prize atleast on one ticket) = 1 - P("Losing on all tickets") = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2) = (1.64)(0.36) = 0.5904 ANSWER:B #### B QUESTION:If w and y are positive integer and w/y is an even integer, which of the following can be an odd integer? options: A)x B)xy C)x−y D)x+2y E)w/3 SOLUTION:C w-Y Let says w =12 Y=3 iT BECOMES w-Y =9 This is odd True w = 12 Y = 6 THEN w-Y = 2, Which is even hence this is False. so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options. #### E QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}? options: A){6, 12} B){6, 15} C){21,28} D){9, 15} E){15, 24} SOLUTION:p/q= d=p/q+7 d= .75 q d= .6(q+7) we get d = 21 and q = 28. Answer = C. #### C QUESTION:A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.15 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost? options: A)1276 B)1200 C)2832 D)1800 E)1236 SOLUTION:Explanation: l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 15 = 1800 Answer: Option D #### D QUESTION:If n is a natural number, then 6n^2 + 6n is always divisible by? options: A)6 only B)6 and 12 C)12 only D)18 only E)20 only SOLUTION:6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Answer is B #### B QUESTION:What is the greatest positive integer T such that 3^T is a factor of 9^10? options: A)5 B)T=9 C)T=10 D)T=20 E)30 SOLUTION:What is the greatest positive integer T such that 3^T is a factor of 9^10? 9^10 = (3^2)^10 = 3^20 D. 20 #### D QUESTION:Here 10 programmers, type 10 lines within 10 minutes then 60 lines can type within 60 minutes. How many programmers are needed? options: A)16 B)10 C)6 D)60 E)50 SOLUTION:10 10 programmer 10 line 10 mins. 10 programmer 20 line 20 mins. . . . .10 programmer 60 line 60 mins. ANSWER:D #### D QUESTION:John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam four years ago? options: A)2 B)4 C)6 D)8 E)16 SOLUTION:j= 3s after 6 years j +6 = 2(s+6) j= 2s+6 2s +6 = 3s s= 6 four years ago s= 6-4= 2 A is the answer #### A QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ? options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours SOLUTION:Explanation: We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as Work done for 1 hour without leak = 1/3 Work done with leak = 3 1/2=7/2 Work done with leak in 1 hr=2/7 Work done by leak in 1 hr=1/3=2/7=1/21 So tank will be empty by the leak in 21 hours. ANSWER IS D #### D QUESTION:The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)40% D)62% E)80% SOLUTION:We need multipliers. multiplier for a 10% increases = 1 + 0.10 = 1.1 multiplier for a 20% decreases = 1 – 0.20 = 0.8 multiplier for a 50% increases = 1 + 0.50 = 1.5 Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3 (0.8)*(1.5) = (0.4)*(3) = 1.2 Now, multiply this by 1.1 1.2*1.1 = 1.32 Thus, the three percent changes combined produce a 32% increase. Answer = (B). #### B QUESTION:A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.) options: A)$15,360 B)$17,360 C)$25,560 D)$21,360 E)$27,360 SOLUTION:For every $3 earn above $9360, the recipient loses $1 of benefit. OR For every $1 loss in the benefit, the recipient earns $3 above $9360 If earning is; 9360+3x Benefit = 12000-x Or the vice versa If benefit is 12000-x, the earning becomes 9360+3x He lost 50% of the benefit; Benefit Received= 12000-0.55*12000 = 12000-6600 x=5400 Earning becomes 9360+3x=9360+3*5400=25560 Ans:C #### C QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:Can you deduce the pattern and find the next number in the series? 7, 15, 27, 99, __? options: A)276 B)277 C)278 D)279 E)None of these SOLUTION:Solution: 277 Explanation: 7 = (1^1 + 2^1 + 3^1) +1 15 = (1^2 + 2^2 + 3^2) +1 37 = (1^3 + 2^3 + 3^3) +1 99 = (1^4 + 2^4 + 3^4) +1 Thus the next number will be (1^5 + 2^5 + 3^5) +1 = 277 Answer B #### B QUESTION:Mixture A is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture A, how many kilograms of mixture A must be added to make a 70% material B in the new mixture? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Old mix has 20% oil. You add 2 kgs of 100% oil. You get new mix with 30% oil (70% material B). w1/w2 = (100 - 30)/(30 - 20) = 70/10 = 7/1 For every 7 parts of mix A, you have added 1 part of oil. Since you have added 2 kgs oil, mix A must be 7*2 = 14 kgs. You already had 8 kgs of mix A, so extra mix A added must be 14 - 8 = 6 kgs. Answer (A) #### A QUESTION:If (2/3)^n=(3/2)^3, what is the value of n? options: A)-3 B)-2 C)-1 D)0 E)1 SOLUTION:(2/3)^n = (3/2)^3 = (2/3)^-3 n = -3 (Answer = A) #### A QUESTION:A man can row upstream at 10kmph and downstream at 24 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)7 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(24 -10) kmph = 7 kmph. Answer C #### C QUESTION:The number of arrangements that can be made with the letters of the word LUCK so that the vowels occupy the even places? options: A)5 B)3 C)6 D)1 E)2 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways. Hence the total ways are 1 * 6 = 6. Answer:C #### C QUESTION:If a trader sold two cars each at Rs. 404415 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is ? options: A)1.44 % B)2.02 % C)1.04 % D)2.25 % E)3.40 % SOLUTION:Explanation: SP of each car is Rs. 404415, he gains 15% on first car and losses 15% on second car. In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (15)(15)/100 % = 2.25% ANSWER IS D #### D QUESTION:The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is: options: A)377 B)267 C)268 D)750 E)271 SOLUTION:Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 .Answer: D #### D QUESTION:Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride? options: A)28 B)30 C)32 D)34 E)36 SOLUTION:The cost of Annie's ride was 2.5+5+(0.25*14) = $11 Let x be the distance of Mike's ride. The cost of Mike's ride is 2.5+(0.25*x) = 11 0.25*x = 8.5 x = 34 miles The answer is D. #### D QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? options: A)8/35 B)34/35 C)27/35 D)21/32 E)33/35 SOLUTION:Solution: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)*P(B) = 2/5 * 4/7 = 8/35 ANSWER IS A #### A QUESTION:Two numbers N and 12 have LCM = 48 and GCF = 8. Find N. options: A)24 B)34 C)44 D)54 E)32 SOLUTION:The product of two integers is equal to the product of their LCM and GCF. Hence. 12 × N = 48 × 8 N = 48 × 8 / 12 = 32 correct answer E #### E QUESTION:what is the least number. which should be added to 221 to make it a perfect square? options: A)5 B)8 C)4 D)6 E)7 SOLUTION:221+4=225 15^2 ANSWER:C #### C QUESTION:Which of the following will give a non-integer on taking cube root? options: A)–64 B)–1 C)8 D)9 E)27 SOLUTION:all except 9, square root of 9 is 3 which is an integer but cube root is not an integer so answer is D #### D QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions? options: A)54 B)432 C)864 D)2,916 E)148,824 SOLUTION:We have the rectangle with dimensions 9*4 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis. Choose the (x,y) coordinates for vertex A: 9C1*4C1; Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A); Choose the y coordinate for vertex B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A). 9C1*4C1*8C1*3C1=864. Answer: C. #### C QUESTION:Tough and Tricky questions: Ratios 1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5 SOLUTION:let total no. of students be 30 students left on a field trip = 1/5(30) =6 thus 24 students left behind 1/3(24)=8 students did not want to go. thus 16 students want to go on the trip 1/2(16)=8 were able to join the other students on the field trip. thus total number of students that went on a field trip =6+8 =14 thus required fraction = 14/30 =7/15 C #### C QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)*(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)*(r+4)/(y+r+6) D)(y+3)/(y+r+7)*(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)12 B)45 C)77 D)88 E)51 SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer: B #### B QUESTION:what is the integer among the following that represents a sum of 3 consecutive even integers? options: A)200 B)303 C)400 D)554 E)588 SOLUTION:Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers) Divisibility of 3: Sum of the digits of the number must be divisible by 3 Divisibility of 2: Unit digit of the number must be divisible by 2 A. 200NOT A MULTIPLE OF 3 SO RULED OUT B. 303NOT A MULTIPLE OF 2 SO RULED OUT C. 400NOT A MULTIPLE OF 3 SO RULED OUT D. 554NOT A MULTIPLE OF 3 SO RULED OUT E. 588A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!! #### E QUESTION:In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is? options: A)14 years 8 months B)15 years C)13 years 8 months D)17 years 10 months E)17 years SOLUTION:Total decrease = (20 x 2) months = 3 years 4 months Age of the new boy = 17 years - 3 years 4 months. = 13 years 8 months. ANSWER:C #### C QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 9 minutes earlier. How far is the office from his house? options: A)3 2/5 Km B)3 1/5 Km C)4 1/5 Km D)5 1/5 Km E)None SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 17/6 = 24/2 * 17/60 = 17/5 = 3 2/5 Km A #### A QUESTION:A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere interest rate is increased by 8%, it would amount to bow mucb ? options: A)Rs 990 B)Rs 995 C)Rs 997 D)Rs 992 E)Rs 999 SOLUTION:S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _ . R = ((100 x 120)/(800*3) ) % = 5%. New rate = (5 + 3)% = 8%. New S.l. = Rs. (800*8*3)/100 = Rs. 192. :. New amount = Rs.(800+192) = Rs. 992 Answer is D. #### D QUESTION:In an election between two candidates, one got 55% of the total valid votes. 20% of the votes were invalid. If the total number of votes was 7500, what was the number of valid votes that the other candidate got? options: A)2800 B)2700 C)2100 D)2500 E)3000 SOLUTION:Total no of votes = 7500 20 % invalid =>80% valid tot valid votes = 7500*80/100 =>valid for 2nd candidate got 7500*80/100*45/100 =2700 ANSWER B #### B QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph? options: A)21.4 sec B)77 sec C)25 sec D)18 sec E)17 sec SOLUTION:D = 100 + 150 = 250 S = 42 * 5/18 = 11.7 mps T = 250/11.7 = 21.4 sec Answer:A #### A QUESTION:A man lent money of Rs. 2500 on simple interest for rate on interest being same as number of years. If he got Rs. 900 as interest amount at the end of the period then what is the rate of interest? options: A)6% B)4% C)5% D)3% E)2% SOLUTION:Explanation : SI = pnr SI = (2500*3r*3r)=900 r2 = 25 r = 5% Answer : C #### C QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre. options: A)$8250 B)$8350 C)$8650 D)$8450 E)$8500 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $400 Hence, total cost =5.5×3.75×400= $8250 A #### A QUESTION:On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 48 centimeters assuming that 1-inch is 2.54 centimeters? options: A)174.2 B)212 C)288.1 D)296 E)302 SOLUTION:1.5 inch = 2.54*1.5 cm. So, 2.54*1.5 represents 24 miles. So for 48 cm.: 48/(2.54*1.5) = x / 24 ---> x = 24*47/(3.81) = 302 Answer will be E. #### E QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested? options: A)$360 B)$380 C)$400 D)$420 E)$440 SOLUTION:S.I for 5 years = $680 - $480 = $200 The S.I. is $40/year S.I. for 2 years = $80 Principal = $480 - $80 = $400 The answer is C. #### C QUESTION:Excluding stoppages, the speed of a train is 55 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? options: A)82 B)16 C)12 D)82 E)18 SOLUTION:Explanation: T = 15/55 * 60 = 16 Answer: Option B #### B QUESTION:Three numbers are in the ratio 1:2:3 and their H.C.F is 62. The numbers are: options: A)62, 124, 186 B)60, 124, 186 C)10, 20, 30 D)62, 24, 186 E)12, 24, 186 SOLUTION:Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 62. The numbers are 62, 124, 186. ANSWER:A #### A QUESTION:A certain office supply store stocks 2 sizes of self-stick notepads, each in 8 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible? options: A)6 B)8 C)16 D)124 E)128 SOLUTION:Notepads of the same color = 8 (we have 8 colors). As we have two sizes then total for the same color=8*2=16 Notepads of the different colors = 8C3=56 (we should choose 3 different colors out of 8). As we have two sizes then total for the different color=56*2=112 Total=112+16=128 Answer: E. #### E QUESTION:If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due? options: A)8 months B)11 months C)10 months D)9 months E)12 months SOLUTION:Explanation : F = Rs. 498 TD = Rs. 18 PW = F - TD = 498 - 18 = Rs. 480 R = 5% TD = (PW × TR)/100 ⇒ 18 = (480 × T × 5)/100 ⇒ 18 = 24 × T ⇒ T = 18/24 = 3/4 years = (12×3)/4 months = 9 months Answer : Option D #### D QUESTION:Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive? options: A)20% B)17% C)4.0% D)3.3% E)2.8% SOLUTION:20/6 =3.33 Answer : D #### D QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)375 SOLUTION:Explanation: Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. ANSWER IS C #### C QUESTION:A car moves at 80 km/hr. What is the speed of the car in meters per second ? options: A)20 2/9m sec B)22 2/9m sec C)24 2/9m sec D)26 2/9m sec E)28 2/9m sec SOLUTION:Explanation: Speed=(80∗5/18)m/sec =200/9m/sec =22 2/9msec Option B #### B QUESTION:How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits? options: A) 48 B) 52 C) 66 D) 68 E) 84 SOLUTION:Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero: 0 1 1 1 2 2 2 3 3 2 5 5 Number of possibilities = 3*4*4 = 48. Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52. Answer: B #### B QUESTION:Jane and Ashley take 10 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ? options: A)10.2 Days B)15.2 Days C)16.2 Days D)18 Days E)20 Days SOLUTION:Let us assume that the work is laying 40 bricks. Jane = 4 bricks per day Ashley = 1 brick per day Together = 5 bricks per day Let's say first 8 days Ashley works alone, No of bricks = 8 Last 4 days Jane works alone, No. of bricks = 16 Remaining bricks = 40 - 24= 16 So together, they would take 16/5 = 3.2 Total no. of days = 8 + 4 + 3.2 = 15.2 Answer is B #### B QUESTION:In a 500 m race, the ratio of speeds of two runners P and Q is 3:5. P has a start of 200 m then the distance between P and Q at the finish of the race is: options: A)Both reach at the same time B)P wins by 100 m C)Q wins by 50 m D)Q wins by 100 m E)None of these SOLUTION:Explanation : When P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5. According to question P has already covered 200 m when Q is starting at starting point and Q needs to cove 300 m more mean while P covers this 300 m when Q can cover 500 m. So, both P and Q will reach the finishing point at the same time. Thus, Both reach at the same time. Answer : A #### A QUESTION:Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10? options: A)2140 B)2520 C)2980 D)3260 E)3680 SOLUTION:The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5. The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520 The answer is B. #### B QUESTION:Marge has C candies, where C is an integer such that 20 <C< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children? options: A) 0 B) 1 C) 2 D) 3 E) 4 SOLUTION:If Marge divides the candies equally among 5 children, she will have 2 candies remaining. This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47 If she divides the candies among 6 children, she will have 1 candy remaining. this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49 ONLY 37 is common, so candies are 37 in number.. if 37 is divided in 7 kids, remainder C= 2 C #### C QUESTION:When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number? options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these SOLUTION:Let the first and the second numbers be x and y respect then y + 30% of x = 140% of y or, y + 0.3x = 1.4y or, 0.3x = 0.4y ∴ x : y = 0.4 : 0.3 = 4 : 3 Answer B #### B QUESTION:If 4x = 8^y, which of the following expresses x in terms of y? options: A)2^(y-2) B)2^(y-1) C)2^(3y-2) D)2^(2y-3) E)2^y SOLUTION:By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: C #### C QUESTION:Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 3 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? options: A)1/24 B)1/8 C)1/4 D)1/3 E)3/8 SOLUTION:I hope you are familiar with basic probability fundas - Let's say you have just ONE letter and TWO envelopes ONE of which is correctly addressed and the other addressed incorrectly. What's the probability of putting the Letter in the correctly addressed envelope - To answer this question - we see IN HOW MANY WAYS can the letter be put into the envelope - you could put it (assuming you don't know which envelope is which) in either of the two - so in total you have TWO ways of shoving the letter in. However, there's only ONE way in which it can go into the correctly addressed envelope - so 1/2 is the prob of putting in correct envelope. This is easy. Now in our current problem - let's say we have just ONE letter but FOUR envelopes. Only one of these envelopes has the address corresponding to the letter. The remaining three envelopes are incorrectly addressed. So the probability that you will put the letter correctly is 1/4. Right? What happens if i ask you the reverse question? what is the prob for putting it in the incorrect envelope. Suddenly you have three envs that are incorrect so you can put the letter incorrectly with a prob of 3/4. Right? The whole problem can be broken down into Four Events that will fulfill the requirement of the question Event 1 - E1 We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the first letter goes into the correct envelope) we have the remaining THREE Letters and THREE envelopes. Event 2 - E2 Let's take letter number 2 now - what is the probability that it LANDS in the INCORRECT envelope. Again by the same logic as above - there are 3 envelopes remaining out of which ONLY ONE has the correct address for LETTER number 2. The remaining 2 have INCORRECT address and LETTER NUMBER 2 could go in either of these 2 to meet our condition. Thus the probability of this event is 2/3 So till now what we have done is - we have calculated the prob of shoving Letter number 1 in correct env -- 1/4 we have calculated the prob of shoving Letter number 2 in INcorrect env --- 2/3 Event 3 - E3 Now let's take letter number 3 - again according to question we want to shove this in the WRONG envelope. There are 2 remaining envelopes and hence the prob of shoving this in the wrong env (or equally in the RIght env) is 1/2. Finally we come to event E4 - the Letter number 4. This has only one way of going in so its probability of being put into the WRONG envelope is 1. ok so we can see that our grand event is actually a combination of FOUR EVENTS happening - each with a probability of its own. So to calculate the total probability of the Grand Event itself we just multiply the individual probabilities since each event happens INDEPENDENTLY of each other Egrand = 1/4 * 2/3 * 1/2 * 1/1 = 1/12 However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result. If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 and worked thru the remaining letters, we could have equally well started out with letter L2 or L3 or L4. Thus since each of these events ARE MUTUALLY EXCLUSIVE, meaning THEY CAN NEVER HAPPEN ALL THE SAME TIME BUT ONLY ONE LETTER AT A TIME, to calculate the TOTAL PROBABILITY of we will add the individual probabilities 1/12 + 1/12 + 1/12 + 1/12 which works out to 1/8. B #### B QUESTION:How many seconds will a 600 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ? options: A)48 B)36 C)26 D)11 E)18 SOLUTION:Explanation: Here distance d = 600 mts speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s time t = = 36 sec. Answer: B #### B QUESTION:Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 45 more revolutions than gear P? options: A)45 B)80 C)90 D)100 E)120 SOLUTION:Gear Q makes 30 more revolutions each 60 seconds. The time to make 45 = 30*1.5 more revolutions is 60*1.5 = 90 seconds. The answer is C. #### C QUESTION:A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.5 per sq m? options: A)6500 B)2779 C)2779 D)3900 E)2781 SOLUTION:Area = (l + b – d) d (80 + 60 – 10)10 => 1300 m2 1300 * 5 = Rs.6500 Answer:A #### A QUESTION:A train running at the speed of 36 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)286 B)278 C)90 D)150 E)287 SOLUTION:Speed=(36 * 5/18) m/sec = (10) m/sec Length of the train = (Speed x Time) = (10 * 9) m = 90 m. Answer:C #### C QUESTION:A coin is weighted so that the probability of heads on any flip is 0.2, while the probability of tails is 0.8. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 B)(0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2 C)(0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2 D)(0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.2 Probability of Tail, P(T) = 0.8 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2*(0.2)^3*(0.8)^2 1 Tail and 4 Heads, Probability = 5C1*(0.2)^4*(0.8)^2 0 Tail and 5 Heads, Probability = (0.2)^5 Required Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 Answer: option A #### A QUESTION:Pandiyan buys an old scooter for Rs. 6000 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is : options: A)20% B)12% C)9.09% D)5% E)None of these SOLUTION:Explanation : Solution: C.P. =Rs. (6000+600) =Rs. 6600; S.P. = Rs. 7200. Gain% = 7200-6600/6600*100 = 9.09% Answer : C #### C QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 6 rows or 4 rows or 8 rows, then no tree will be left. Find the least number of trees required options: A)24 B)60 C)28 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(6,4,8) = 24 Answer: A #### A QUESTION:Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y? options: A)15.5 sec B)8.4 sec C)33.6 sec D)31.11 sec E)16.8 sec SOLUTION:Z--------------------------------------|----------------------------Y Car A(20mps)------------------------->P<---------------Car B(15mps) Let 2 cars meet each other at point P in t seconds. Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t. From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further. so, 15t/20 = 10 So t=40/3 sec and total distance = (35*40)/3 Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx. Answer D #### D QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:6 B)7:3 C)7:4 D)7:2 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer: B #### B QUESTION:If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are the R odds that x^2+y^2>1? options: A)1. pi/4 B)2. R=pi/16 C)3. R=1-pi/4 D)4. 1-pi/16 E)5.4-pi SOLUTION:area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi. then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1) total outcomes = 4 therefore probability = (4-pi)/4 C #### C QUESTION:Two trains 200m and 250m long run at the speed of 72kmph and 18kmph in opposite directions in parallel tracks. The time which they take to cross each other is? options: A)5.6sec B)8.9sec C)10.8sec D)12.6sec E)18 sec SOLUTION:Relative speed = 72+18 = 90 kmph * 5/18 = 25 m/s Distance covered in crossing each other = 200+250 = 450m Required time = 450*1/25 = 18 sec Answer is E #### E QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100? options: A)33 B)67 C)25 D)66 E)81 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (100 - 75) = 25 points to C. Answer: C #### C QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)77 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:A person X working alone can complete a work in 5 days. A person Y completes the same amount of work in 10 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:The fraction of work completed in two days is 2/5 + 2/10 + 2/30 = 20/30 The fraction of work remaining is 1 - 20/30 = 10/30 The number of days required for Z is 10 days. The answer is E. #### E QUESTION:A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $2.05? options: A)980 B)1130 C)1440 D)1610 E)1820 SOLUTION:The charge is 65 cents for the first 250 grams. This leaves a charge of $2.05 - $0.65 = $1.40 The charge for the next 1300 grams is $1.30 which leaves a charge of $0.10 The weight is somewhere between 1550 and 1650. The answer is D. #### D QUESTION:There are 8 balls in a bucket, 4 balls are blue and 4 balls are red. If two ball chosen randomly , how many chances there are at least one blue ball will present? options: A)21 B)25 C)16 D)22 E)20 SOLUTION:Two ball will be chosen. At least 1 blue ball Total ways = 8C2 = 28 Total without any blue ball = 4C2 = 6 Hence ways in which at least one blue will be present = 28 - 6 = 22 Correct option: D #### D QUESTION:Which of the following is closest to (-6/7)^199？ options: A)-1 B)-1/2 C)0 D)1 E)2 SOLUTION:(-6/7)^4 = 1296/2401 which is already close to 1/2. For larger exponents, the expression will get closer and closer to zero. The answer is C. #### C QUESTION:(17)3.5 x (17)? = 178 options: A)2.29 B)2.75 C)4.25 D)4.5 E)None of these SOLUTION:Solution let (17)3.5 * (17)x = 178. then, (17)3.5 + x = (17)8. ∴ 3.5 + x = 8 ⇔ x = (8 - 3.5) ⇔ x = 4.5 Answer D #### D QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.79 B)5.71 C)5.76 D)5.79 E)5.73 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 Answer: C #### C QUESTION:If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream options: A)1.5kmph B)0.5kmph C)0.4kmph D)1.6kmph E)2.5kmph SOLUTION:Speed upstream = 32/4 = 8 kmph Speed down stream = 72/8 = 9 kmph Speed of stream = ½ (9-8) = 0.5kmph ANSWER:B #### B <<<Examples ends QUESTION:If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ? options: A)500 B)1000 C)1500 D)2000 E)3000 SOLUTION:Explanation: Let the cost of a table and that of a chair be Rs. x and Rs, y respectively. Then, 2x + 3y = 3500 ...(i) and 3x + 2y = 4000 .....(ii) solving (i) and (ii) we get x = 1000, y = 500 ANSWER IS B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be options: A)(1.5)^4 B)(1.05)^5 C)(1.05)^4 D)1 + (0.05)^4 E)1 + 4(0.05) SOLUTION:In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of . We'd have.... Answer :B #### B QUESTION:If n is an integer, which of the following CANNOT be a factor of 3n+4? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well. Answer: C. #### C QUESTION:Less than half of a committee that is to be formed out of certain group, are to be men. If there are 100 possible ways of forming the committee, then the number of men in the committee can be, options: A)2 B)3 C)4 D)5 E)cannot be determined SOLUTION:1. Let there be m men and w women out of which the committee is formed. 2. mCn * wCr = 100, where n is the number of men chosen and r is the number of women chosen 3. The possible products for LHS of (2) are, 100 * 1, 50 * 2, 25 * 4, 20 * 5, 10 * 10 4. Since the number of women is greater than the number of men, the first three products in (3) can be rejected as they would not satisfy this condition. 5. In the case of the fourth product, 20 * 5 may be given by 6C3 * 5C1. Though this may satisfy the condition with 3 women and 1 man, 1 man is not in the choices given. 6. The last product 10 * 10 may be given by 5C2 * 5C3 with 2 men and 3 women. This satisfies the condition and also 2 men is one of the choices given. Therefore the answer is choice A. #### A QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 14 x = 2 Mini’s age = 8 years And Minakshi’s age = 6 years Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7 ANSWER:C #### C QUESTION:A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount? options: A)21% B)25% C)69% D)31% E)12% SOLUTION:Let the price be 100. The price becomes 140 after a 40% markup. Now a discount of 20% on 140. Profit=112-100 12% answer E #### E QUESTION:What is the average of first 21 multiples of 7 ? options: A)49 B)77 C)66 D)57 E)50 SOLUTION:Required average = 7(1+2+....+21) / 21 (7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers) = 77 ANSWER IS B #### B QUESTION:The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square? options: A)277 B)268 C)287 D)480 E)281 SOLUTION:Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer:D #### D QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work? options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work .. Therefore, Y will do the remaining 1/10 th work alone.. As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job... ans 10 E #### E QUESTION:How many four letter words are formed using the letters of the word POLICE? options: A)280 B)321 C)330 D)360 E)370 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is 6P4 = 6 * 5 * 4 * 3 = 360. Answer: D #### D QUESTION:The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? options: A)4538 B)2778 C)2608 D)4530 E)2001 SOLUTION:Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs. 4530 Answer:D #### D QUESTION:What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive? options: A)90 B)80 C)100 D)105 E)110 SOLUTION:10 and 190 inclusive would mean there are 17 terms. No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170 The middle term is the average which is the tenth term = 80 B is the answer. #### B QUESTION:The product of three consecutive numbers is 336. Then the sum of the smallest two numbers is ? options: A)13 B)15 C)20 D)38 E)56 SOLUTION:Product of three numbers = 336 336 = 6*7*8. So, the three numbers are 6, 7 and 8. And Sum of smallest of these two = 6+7 = 13. ANSWER : OPTION A #### A QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)10 B)20 C)21 D)22 E)23 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days ANSWER : OPTION B #### B QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+99)=? options: A)7000 B)7250 C)7500 D)7750 E)6750 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 99=1+(n-1)2 => n=50 Use value of n in (1) then, Sn = (50/2)(1+99) = 2500 Ans:- 3(Sn) = 7500 Answer : C #### C QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? options: A)16cm B)18cm C)24cm D)Data inadequate E)None of these SOLUTION:Explanation: 2(l+b)/b=5/1 2l + 2b = 5b 3b = 2l b = 2/3 l Then, Area = 216 cm2 l x b = 216 l x (2/3)l = 216 l2 = 324. l = 18 cm. Answer: B #### B QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)4.1 B)3.6 C)2.6 D)5.0 E)5.5 SOLUTION:B 3.6 In this simple subtraction series, each number decreases by 0.4. #### B QUESTION:How much water must be added to 64 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)16 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 64 litres of milk = (1⁄4 × 64) litres = 16 litres. Answer A #### A QUESTION:Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered? options: A)17603 B)17608 C)17628 D)17600 E)176023 SOLUTION:Price at which the TV set is bought = Rs. 12,500 Discount offered = 20% Marked Price = 12500 * 100/80 = Rs. 15625 The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000 The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600 Answer: D #### D QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2000 B)2781 C)2278 D)2081 E)2721 SOLUTION:Explanation: (10*10)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer: A #### A QUESTION:If 144/0.144 = 14.4/x, then the value of x is: options: A)0.144 B)1.44 C)0.0144 D)0.014 E)0.00144 SOLUTION:=144/0.144 = 14.4/x =144 x 1000/144 =14.4/x =x = 14.4/1000 = 0.0144 Answer is C. #### C QUESTION:The rate of Interest on a sum of money is 11% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is options: A)1,000 B)2,000 C)2,100 D)2,250 E)2,540 SOLUTION:Explanation: I1 = (P x 3 x 11)/100 = P/3 I2 = (P x 4 x 4)/100 = 4P/25 I3 = (P x 1 x 5)/100 = P/20 P/3 + 4P/25 + P/20 = 540 27P/50 = 540 P = 1000 Answer: Option A #### A QUESTION:If 4 men working 10 hours a day earn Rs. 1000 per week, then 9 men working 6 hours a day will earn how much per week? options: A)Rs 840 B)Rs 1350 C)Rs 1620 D)Rs 1680 E)None of these SOLUTION:Explanation : (Men 4:9) : (Hrs/Day 10:6) :: 1000 : x hence 4 * 10 *x = 9 * 6 * 1000 or x = 9*6*1000/ 4*10 = 1350 Answer : B #### B QUESTION:A and B can do a piece of work in 12 days and 24days. Both starts the work together for some time, but B leaves the job 6 days before the work is completed. Find the time in which work is finished. options: A)10 days B)12 days C)14 days D)5 days E)6 days SOLUTION:Explanation: A & B completes the work in 12*24/12+24 = 12*24/36 = 8 days 2 days work = 2+1/8 = ¼ work Remaining work = 1-1/4 = ¾ A completes ¾ work in ¾*16 = 12 days Answer: Option B #### B QUESTION:A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)3/5 C)3/8 D)4/9 E)7/10 SOLUTION:The total possible choices are 10C3 = 120 The ways to choose 3 apples: 5C3 = 10 The ways to choose 2 apples: 5C2 * 5C1 = 50 P(at least 2 apples) = 60/120 = 1/2 The answer is A. #### A QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. options: A)1200 B)1400 C)2660 D)1600 E)1800 SOLUTION:A is a working member and for that, he receive 5% of the profit = 5% of 7400 = 5*7400/100 = 370 Remaining amount = 7400-370 = 7030 Ratio of their investments = 6500*6 : 8400*5 : 10000*3 = 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20 = 13 : 14 : 10 Share of B in the profit = 7030 * (14/37) = 190*14 = 2660 Answer is C #### C QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None SOLUTION:Explanation: 4/15A = 2/5B A = (2/5 x 15/4)B A = 3/2 B A/B = 3/2 A : B = 3 : 2. B's share = Sterling (1250 x 2/5) = Sterling 500. Answer: Option C #### C QUESTION:a, b, c, and d are positive consecutive even integers and a < b < c < d. If the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers? options: A)2 B)4 C)8 D)12 E)20 SOLUTION:We know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on. The product ad is 6 more than the sum bc. By testing some possible ad products (even numbers separated by two other even numbers), we can quickly see that the numbers have to be quite small: 6x12 is 72, much higher than any of the possible sums, and the products will go up much faster than the sums will. However, the lowest possible sequence gives an ad product of 2x8, or 16. And summing the middle numbers gives 10, exactly six less than the product. We have found the sequence: 2-4-6-8. The answer, then, is the product of the smallest two numbers, or 2x4, which is 8 (option C). #### C QUESTION:A square, with perimeter 40, is inscribed in a circle. What is the area of the circle? options: A)50π B)40π C)30π D)25π E)35π SOLUTION:Area of circuscribed circle = pi/2*area of square Area of square = (40/4)^2 = 10^2= 100 Area of circle = pi/2*100=50pi Answer : A #### A QUESTION:If U is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, U, 0, 1, 3, K, 7}? I. -1.5 II. -2 III. 0 options: A) I only B) II only C) III only D) I and III only E) None SOLUTION:If U is a negative integer and K is a positive integer, The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either.E #### E QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)5 B)6 C)9 D)7 E)3 SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 Answer: D #### D QUESTION:When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land twice on heads and once on tails? options: A)1/16 B)1/3 C)1/6 D)1/2 E)1/8 SOLUTION:Must be once on twice and once on tails 1/2*1/2*1/2 = 1/8 Answer: E #### E QUESTION:If 10 litres of an oil of Rs.55 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre? options: A)Rs.49.17 B)Rs.51.03 C)Rs.58.66 D)Rs.55.33 E)None of the above SOLUTION:55*10 = 550 66*5 = 330 880/15 = 58.66 ANSWER:C #### C QUESTION:The area of a triangle is with base 4m and height 5m? options: A)15 B)19 C)56 D)10 E)36 SOLUTION:Explanation: Area=1/2*b*h 1/2 * 4 * 5 = 10 m^2 Answer : D #### D QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 6 rows or 4 rows or 8 rows, then no tree will be left. Find the least number of trees required options: A)24 B)60 C)28 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(6,4,8) = 24 Answer: A #### A QUESTION:If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum? options: A)s.575 B)s.595 C)s.590 D)s.580 E)s.585 SOLUTION:80 = (450*4*R)/100 R = 5% I = (450*6*5)/100 = 135 450 + 135 = 585 ANSWER:E #### E QUESTION:The perimeter of one square is 48 cm and that of another is 36 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined? options: A)13√4 B)13√2 C)23√2 D)12√4 E)15√2 SOLUTION:4a = 48 4a = 36 a = 12 a = 9 a2 = 144 a2 = 81 Combined area = a2 = 225 => a = 15 d = 15√2 Answer: E #### E QUESTION:The average weight of a group of 30 friends increases by 2 kg when the weight of their football coach was removed. If average weight of the group after removing the weight of the football coach is 28 kg, what is the weight of their football coach? options: A)31 kg B)60 kg C)61 kg D)62 kg E)88 kg SOLUTION:let c=coach's weight original total weight=(30 friends)(30 kg avge)=900kg (900-c)/(30-1)=28 kg avge c=88 kg Answer - E #### E QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (5*27) - (4*25) = 135-100 = 35 Answer: Option A #### A QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum. options: A)800 B)700 C)600 D)500 E)None of them SOLUTION:Let the sum be Rs. x Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40 = (7x/20)-(3x/10)=40 x = (40 * 20) = 800. Hence, the sum is Rs. 800. Answer is A. #### A QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches were made? options: A)84 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 240 / 20 = 12 sandwiches in one part For bologna we have 7 parts so: 7 *12 = 84 Answer is A #### A QUESTION:In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase? options: A)16.67% B)25% C)20.45% D)31.56% E)40% SOLUTION:Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67% Answer is A #### A QUESTION:Complete the series: 16, 06 , 68 , 88 , ? , 98 options: A)L8 B)B6 C)S5 D)E8 E)M5 SOLUTION:A L8 To know why, just read the number series upside down and you will find that the numbers are 91, 90, 89, 88, __, 86 So L8 when read upside down reads as 87. #### A QUESTION:In a family 16 people eat only vegetarian, 9 people eat only non veg., 12 people eat both veg and non veg.. How many people eat veg in the family? options: A)28 B)26 C)22 D)31 E)21 SOLUTION:Total people eat veg = only veg + both veg and non veg Total= 16+12= 28 Answer = A #### A QUESTION:The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 6 years hence? options: A)22 B)77 C)70 D)98 E)72 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 6 years, their ages will be 46 and 26. Sum of their ages = 46 + 26 = 72. Answer: E #### E QUESTION:When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country? options: A)166 2/7 B)166 2/1 C)166 2/2 D)166 2/3 E)166 2/8 SOLUTION:5% - 2% = 3% 3% ---- 5 100% ---- ? => 166 2/3 Answer:D #### D QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,15 = 15/100 x= 80*15/100 x= 12 12/10 = 1,2 = 120%, Answer C #### C QUESTION:Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 4 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered? options: A)60 B)72 C)84 D)90 E)216 SOLUTION:E is the answer.... D = TS where D=distance, T=Time and S=Speed To travel half distance, (2+4T) = 9T ==> T = 2/5 ==> 24 minutes To travel double distance, 2(2+4T) = 9T ==> 4 ==> 240 minutes Difference, 216 minutes E #### E QUESTION:What approximate value should come in plce of question mark (?) in the following equations ? 728.038 x 54.978 - 72.016 x 85.250 = ? options: A)31400 B)32700 C)33900 D)34400 E)32400 SOLUTION:Explanation : ? = 728 x 55 - 72 x 85.25 = 40040 - 6138 = 339900 Answer : Option C #### C QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:A merchant purchased a jacket for $180 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale? options: A)$0 B)$3 C)$4 D)$12 E)$15 SOLUTION:Let selling price = x So, x = 180 + 25x/100 Calculating above, x = 240 Selling price =240 20% Discount on Selling price = 192 So, profit = 192-180 = 12 Answer = D #### D QUESTION:How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 3 can be used only once? options: A)20 B)150 C)225 D)250 E)316 SOLUTION:4 options for the first digit: 2, 4, 6, 8; 5 options for the second digit: 1, 3, 5, 7, 9; 4 options for the third digit: 2, 3, 5, 7; 4 options for the fourth digit: 0, 3, 6, 9. Four digit # possible without the restriction (about the digit 6): 4*5*4*4=320 Numbers with three 3-s, 3X3X3 4*1*1*1=4 Thus there are 320-4=316 such numbers. Answer: E. #### E QUESTION:A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $280. Find the original price of petrol? options: A)$11 B)$5 C)$45 D)$400 E)$6.2 SOLUTION:Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 280/45=$6.2 Answer: E. #### E QUESTION:Find the odd man out. 187, 264, 386, 473, 682, 781 options: A)386 B)187 C)781 D)682 E)564 SOLUTION:Explanation : In all numbers except 386, the middle digit is the sum of other two digits. Answer : Option A #### A QUESTION:If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 5 days. If he works at reduced efficiency, he can work without break and finish that same job in 5 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency? options: A)5/2 B)4/1 C)9/5 D)4/5 E)2/5 SOLUTION:We're told that there are 2 ways for Dale to complete a job: 1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 5 days. 2) Reduced Efficiency: 5 straight days with no days off. Working at Full Efficiency creates the following pattern: 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2= 5 days Totals: 4 days on, 1 days off Reduced Efficiency means that Dale will do 6 days of work in 5 days, thus those Reduceddaysare 4/1 of Full Efficiency. Answer : B #### B QUESTION:The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is? options: A)625 B)298 C)269 D)200 E)267 SOLUTION:Let the sum be Rs. x. Then, [x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x S.I. = (x * 4 * 2)/100 = 2x/25 51x/625 - 2x/25 = 1 or x = 625.Answer: A #### A QUESTION:A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? options: A)27 B)29 C)40 D)89 E)22 SOLUTION:1/8 - 1/x = 1/10 x = 40 Answer: C #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)25 B)15 C)18 D)47 E)26 SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? options: A)5 B)7 C)3 D)1/2 E)4 SOLUTION:Explanation: M = 4 S = 2 US = 4 - 2 = 2 D = 6 T = 6/2 = 3 Answer: C #### C QUESTION:Of the 100 athletes at a soccer club, 40 play defense and 62 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between options: A)10 to 20 B)10 to 40 C)22 to 40 D)30 to 70 E)40 to 70 SOLUTION:First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E. {Total} = {defense} + {midfield} - {both} + {neither} 100 = 40 + 62 - {both} + {neither} {both} = {neither} + 2. Since the least value of {neither} is given to be 20, then the least value of {both} is 20+2=22.Eliminate A and B. Answer: C. #### C QUESTION:Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters Look at this series: D12, H16, __, P24, T28, ... What number should fill the blank? options: A)H16 B)I17 C)J18 D)K19 E)L20 SOLUTION:E L20 In this series, the letters progress by 4, and the numbers increase by 4. #### E QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss? options: A)25 % B)50 % C)75 % D)85 % E)None of these SOLUTION:Explanation : Let the original expenditure = Rs. 100. New final expenditure = 150% of (50% of Rs. 100) = Rs.(150/10050/100100) = Rs. 75. Decrease = 100- 75 = 25 % Answer : A #### A QUESTION:In the number 10,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A? options: A)0 B)5 C)10 D)15 E)25 SOLUTION:You should notice that 55*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*5=15 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25). Answer: E. ! Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/ Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the mainMath forum. D #### D QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)22.4% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/53000 * 100 = 22.4% Answer: B #### B QUESTION:69 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? options: A)20 B)23 C)24 D)25 E)26 SOLUTION:According to the chain rule, M1 x T1 = M2 x T2 Therefore, 69 x 12 x 5 = 30 x 6 x X X = 23 Hence, the number of days = 23. ANSWER:B #### B QUESTION:Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take? options: A)40 B)50 C)70 D)80 E)90 SOLUTION:L+M=M+N-40 / N=2L+10 40=M+N-L-M 40=N-L 40=2L+10-L 30=L 2(30)+10=70 C #### C QUESTION:5216 × 51 = ? options: A)266015 B)266014 C)266016 D)266116 E)266226 SOLUTION:Normal way of multiplication may take time. Here is one alternative. 5216×51=(5216×50)+5216=(5216×1002)+5216=5216002+5216=260800+5216=266016 Answer is C. #### C QUESTION:If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars? options: A)3⁄20 B)11⁄60 C)9⁄40 D)1⁄5 E)2⁄15 SOLUTION:Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car. Half of them are men, and the other half are women, more precisely 60. It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total. Answer E #### E QUESTION:Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in? options: A)6 B)12 C)28 D)42 E)21 SOLUTION:The part of the tank filled by three pipes in one hour = 1/14 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/14= 1/21. The tank can be filled in 21 hours. Answer:E #### E QUESTION:What distance will be covered by a bus moving at 36 kmph in 30 seconds? options: A)287 B)600 C)289 D)300 E)207 SOLUTION:36 kmph = 36 * 5/18 = 10 mps D = Speed * time = 10 * 30 = 300 m. Answer:D #### D QUESTION:3x^2 + 5x - 2 = options: A)(3x-1)(x+2) B)(3x-4)(x+2) C)(3x-4)(x-2) D)(3x-2)(x+4) E)none of above SOLUTION:3x^2 + 5x - 2 = 3x^2 + 6x - x - 2 = 3x (x + 2) - (x+2) = (3x-1) (x+2) Option A #### A QUESTION:The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of R is? options: A)A)Rs.4078 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.6400 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10100 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv) Subtracting (i) from (iv), we get, P = 6400. P's monthly income = Rs.6400. Answer: E #### E QUESTION:A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper? options: A)140 B)388 C)238 D)119 E)112 SOLUTION:when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 14*10 = 140 sq cmV Answer: A #### A QUESTION:The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. options: A)179 B)208 C)210 D)223 E)229 SOLUTION:Explanation: Total runs scored by the batsman = 60*46 = 2760 runs Now excluding the two innings the runs scored = 58*44 = 2552 runs Hence the runs scored in the two innings = 2760 – 2552 = 208 runs. Let the highest score be x, hence the lowest score = x – 150 x + (x - 150) = 208 2x = 358 x = 179 runs ANSWER A #### A QUESTION:Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average score for all the three classes, taken together? options: A)81 B)81.5 C)82 D)84.5 E)None of these SOLUTION:Explanation : Let the number of students in classes X, Y and Z be a, b and c respectively. Then Total of X = 83a Total of Y = 76b Total of Z = 85c And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b. Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b. Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a. Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c). => 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a . => 978/12 => 81.5 Answer : B #### B QUESTION:Three clocks were set to true time and starts to run together, makes a beep sound at intervals of 8,10 and 12 minutes respectively. In 2 days, how many times do they will make the sound together ? options: A)12 B)15 C)25 D)30 E)35 SOLUTION:Explanation : The clocks make sound at intervals of 8, 10 and 12 minutes respectively. The LCM of 8,10 and 12 is 120. So, the clocks will make sound together after every 120 minutes. i.e., after every 2 hours. In 2 days(48 hours), they will make the sound together (48/2) = 24 times. At the end of 2nd day, they will make one more beep together. Therefore, totally (24+1) 25 times beep sound is made together. Hence the answer is 25 times. Answer : C #### C QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)40 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.78 B)5.79 C)5.76 D)5.74 E)5.721 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76.Answer: C #### C QUESTION:If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips? options: A)1/8 B)1/16 C)1/32 D)1/64 E)1/128 SOLUTION:P(HHHHTT) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64 The answer is D. #### D QUESTION:Walking across campus, a student interviewed a group of students. 35% of the students took a finance class last semester, 45% took a marketing class last semester, and 50% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? options: A)40% B)30% C)25% D)15% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 35 + 45 - {both} + 50 {both} = 30%. The answer is B. #### B QUESTION:The points A(0, 0), B(0, 4a - 4) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? options: A)88 B)98 C)108 D)78 E)90 SOLUTION:1/2bh=1/2(2a+1)(2a+6) Now 4a-4=2a+6 2a=10 , a=5 Therefore, A(0,0); B(0,16); C(11,16) 1/2*11*16=88 Answer: A #### A QUESTION:What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9? options: A)397 B)401 C)403 D)405 E)399 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=405. Answer: D. #### D QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)1687 B)1478 C)1480 D)14000 E)1500 SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 Answer: D #### D QUESTION:By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)20 kmph B)30 kmph C)87 kmph D)99 kmph E)77 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph. Answer:A #### A QUESTION:Sum of the numbers from 1 to 35 is options: A)630 B)660 C)670 D)450 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 35. So S20=35×36/2=630 Correct Option: A #### A QUESTION:What is the smallest positive integer x such that 108x is the cube of a positive integer? options: A)2 B)4 C)8 D)10 E)7 SOLUTION:Given 108x is a perfect cube so we will take 216 = 6*6*6 108x = 216 x = 216/108 = 2 correct option is A #### A QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 35%? options: A)600 B)887 C)256 D)654 E)675 SOLUTION:Cost price = Rs.500 profit = 35% of 500 = Rs.175 Selling price = Cost price + Profit = 500 + 175 = 675 Answer: E #### E QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)G.C.D.=0.18 D)0.2 E)0.21 SOLUTION:Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer: Option C #### C QUESTION:What is the leastvalue of x. So that 23x57 is divisible by 3? options: A)3 B)4 C)1 D)5 E)6 SOLUTION:The sum of the digits of the number is divisible by 3, then the number is divisible by3. 2 + 3 + x + 5 + 7 = 17 + x Least value of x may be 1 Therefore 17 + 1 = 18 is divisible by 3. C #### C QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly? options: A)4 B)6 C)10 D)12 E)24 SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5∗150=90 2nd Question : four fifths of the remainder answered the second question correctly so 4/5∗(150−90)=4/5∗60=48 total students who answered at least one Q correct =90+48=138 so students who answered BOTH incorrectly = 150−138=12 ANSWER:D #### D QUESTION:If a certain number X is divided by 62, the reminder is 7. what is the reminder when X+11 is divided by 31? options: A)3 B)5 C)18 D)6 E)8 SOLUTION:X can be written as 62K + 7 or X = 7,69,131,etc. X + 11 = 62K + 7+11= 62K +18 or X + 11 = 18,80,142 etc. When divided by 31, we will get the remainder 18. C #### C QUESTION:Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number? options: A)7 B)9 C)11 D)13 E)15 SOLUTION:Let the three numbers be x, x+2, and x+4. 3x = 2(x+4) + 3 x = 11 and then the third number is x+4 = 15. The answer is E. #### E QUESTION:A bike covers a certain distance at the speed of 65km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)85 km/h B)85.34 km/h C)86.66 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(C) Sol. Total distance = 65 × 8 = 520 km Now speed = 520/6 = 86.66 km/h #### C QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 * (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 650 = 13 Answer: E #### E QUESTION:Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)491 B)481 C)471 D)441 E)445 SOLUTION:Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 3*7/100*2100 = 441. D #### D QUESTION:There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women? options: A)8/12 B)6/16 C)4/16 D)6/10 E)4/10 SOLUTION:w = m+4 w+m = 20 m+4+m = 20 2m = 16 m = 8 w = 12 ratio:8:12 Ans: A #### A QUESTION:Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is? options: A)10 B)30 C)40 D)50 E)60 SOLUTION:Let the numbers be 3x,4x and 5x their L.C.M. = 60x 60x =600 x = 10 The numbers are 3*10 , 4*10 , 5*10 Hence required H.C.F. = 10 Answer is A #### A QUESTION:What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x options: A)35678 B)73205 C)75653 D)86554 E)87565 SOLUTION:(B) 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205 #### B QUESTION:If a < b < c , which of the following must be true? (I) a < b^2 (II) a < c - b (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:What is the greatest positive integer x such that 7^x is a factor of 343^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:343^10 = (7^3)^10 = 7^30 ANSWER:E #### E QUESTION:The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ? options: A)148 B)134 C)156 D)144 E)None SOLUTION:Solution: Ratio of Ducks and Frogs in Pond, = 37 : 39. Average of Ducks and Frogs in Pond, = 132. So, total number of Ducks and Frogs in the Pond, = 2* 132 = 262. Therefore, Number of Frogs, = (262*39)/76 = 134. Answer: Option B #### B QUESTION:A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 63 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:1 percent for 3 years= 63 1 percent for 1 year = 21 => 100 percent = 2100 ANSWER:B #### B QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A? options: A)240 B)288 C)266 D)216 E)123 SOLUTION:(3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 630 = 240 Answer: A #### A QUESTION:A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 2 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x? options: A)x/70 B)2x/63 C)3x/70 D)3x/10 E)3x/7 SOLUTION:cost of boat per day = x cost per person =x/7 if three more persons afre there, cost =x/9 difference = x/7-x/9 =2x/63 Ans B #### B QUESTION:How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane? options: A)03 B)4 C)5 D)1 E)7 SOLUTION:You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines. AB , AC BA , BC CA , CB There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB. The lines are: AB, BC and AC ; 3 lines only. So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important. Answer:A #### A QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)? options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5 SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57) 4.5/(4.5 - 2) = 9/5 (1.8) 3.5/(3.5 - 2) = 7/3 (~2.33) 2.5/(2.5-2) = 5 1.5/(1.5 - 2) = -3 Thus, the answer is D. #### D QUESTION:There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems options: A)36 minutes B)60 minutes C)72 minutes D)100 minutes E)None of these SOLUTION:Explanation : Let x = minutes spent on a non-math problem then 2x = minutes spent on a math problem x(200-50) + 2x(50) = 180 x(150) + 2x(50) = 180 150x + 100x = 180 250x = 180 x = 0.72 minutes Time to spend on math problems: 2x(50)=100x = 100(0.72) = 72 minutes Answer : C #### C QUESTION:In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 240 vote’s majority. What is the total number of votes polled? options: A)600 B)700 C)800 D)850 E)None of these SOLUTION:Explanation: Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %) 40 % = 70 % - 30 % 40% -----> 280 (40*6 = 240) 100% -----> 600 (100*6 = 600) Answer: Option A #### A QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)767 E)408 SOLUTION:1h ----- 2 ? ------ 60 12 h RS = 16 + 18 = 34 T = 12 D = 34 * 12 =408 Answer: E #### E QUESTION:If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is options: A)Rs.1820 B)Rs.1040 C)Rs.1120 D)Rs.1680 E)None of these SOLUTION:Explanation: Let the sum of money be x then (x × 4 × 8)/100 = (560 × 12 × 8)/100 x × 4 × 8 = 560 × 12 × 8 x × 4 = 560 × 12x = 560 × 3 = 1680 Answer: Option D #### D QUESTION:Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 75 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains? options: A)93% B)97% C)100% D)107% E)99% SOLUTION:Say Arthur's fortune was $100. Then: A = 20*1.5*1.1 = 33 B = 20*1.5*1.1 = 33 C = 20*1.5*0.4 = 12 D = 20*0.6*1.75 = 21 E = 0 Total 33 + 33 + 12 + 21 = 99. Answer: E. #### E QUESTION:A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? options: A)8 B)12 C)15 D)21 E)27 SOLUTION:As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain: A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15 B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12 A+B=15+12=27 Answer: E. #### E QUESTION:At 6'o clock clock ticks 6 times. The time between first and last ticks was 30sec. How much time it takes at 10'o clock. options: A)60sec B)62sec C)66sec D)64sec E)54sec SOLUTION:At 6'0 clock, clock ticks 6 times. So, there must be 5 intervals between clock ticks. Time Between first and last ticks = 30sec So, 1 interval = 30/5 = 6sec So 6'o clock 5 *6=30sec 7'o clock 6 *6=36sec . . 9'o clock 8 *6=48sec 10'o clock 9 *6=54sec So, 54sec at 10'o clock. ANSWER:E #### E QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)5.14 SOLUTION:Time taken by First tank Fill 1/2 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank =12 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours Answer: option E #### E QUESTION:A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip? options: A)36 mph B)40 mph C)44 mph D)52 mph E)58 mph SOLUTION:So The Answer is Plainly A.... we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance) for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour.... #### A QUESTION:Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income? options: A)$40,000 B)$56,000 C)$64,000 D)$66,667 E)$80,000 SOLUTION:Equation is correct, so math must be a problem. 0.12*40,000+0.2*(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000. Answer: B. #### B QUESTION:Sophika can buy watches at a price of P dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of P and X and Y, what is the percent of the markup from her buy price to her sell price? options: A)(YP)/100X B)100X/(YP) C)(YP)+100X D)(YP)-100X E)(YP)*100X SOLUTION:Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/P *100 = 100X/(YP) Answer : B #### B QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race? options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m SOLUTION:C 111.12 m X runs 1000 m while Y runs 900 m and Z runs 800 m. The number of meters that Z runs when Y runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. Y can give Z = 1000 - 888.88 = 111.12 m. #### C QUESTION:John began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after John? options: A)35 B)55 C)39 D)40 E)60 SOLUTION:Carla starts 30 minutes later and it takes 3 hr for carla to meet John So John total time travelled = 3hr + 30 minutes John distance = 30 * (3 1/2) = 105 so carla need to travle 105 to meet John in 3 hrs speed of carla = 105/3 = 35 miles per hour Answer is A #### A QUESTION:117 x 217 + 83 x 83=? options: A)79698 B)20578 C)80698 D)81268 E)None of them SOLUTION:=(117)^2 + (83)^2 =(100+17)^2 + (100-17)^2 =2[(100)^2+(17)^2] =2[10000+289] =2 x 10289 = 20578 Answer is B #### B QUESTION:A factory produces 6000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? options: A)4436 toys B)1500 toys C)6113 toys D)2354 toys E)1375 toys SOLUTION:To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4. 6000 /4 = 1500 toys correct answer B #### B QUESTION:The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area? options: A)288 B)240 C)267 D)299 E)162 SOLUTION:4a = 68 => a = 17 172 – 82 = 152 1/2 * 16 * 30 = 240 Answer:B #### B QUESTION:In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water? options: A)3:1 B)3:5 C)7:8 D)7:9 E)9:11 SOLUTION:First mixture: milk and water in the ratio of 3x:4x. Second mixture: milk and water in the ratio 5y:2y. We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3. Answer: A. #### A QUESTION:WHEN A PERSON SELLS TWO ITEMS $1656 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURS A LOSS OR GAIN OF: options: A)no loss no gain B)20 % profit C)4% loss D)2% profit E)2% loss. SOLUTION:The 2 items are sold at 1656 each , one at a profit of 20% and the other at a loss of 20% So the original rates of the items are 1380 and 2070 respectively So the total he spend for those 2 items is 3450 but he ended up in selling them with (1656*2) 3312 So the loss is 3450 - 3312 = 138 The loss percentage is (138/3450) *100 = 4% loss - Answer C #### C QUESTION:If x is an even integer and y = 5x + 1, which of the following CANNOT be a divisor of y? options: A)11 B)31 C)21 D)41 E)30 SOLUTION:x takes even values as 2,4,6,8., y=5x+1 x is an even term so 5x must be an even term when it adds with 1 so it must be a odd integer 30 didn't follows this condition ans is E #### E QUESTION:When the positive integer k is divided by the positive integer n , the remainder is 13. If k/n = 81.2 , what is the value of n? options: A)9 B)20 C)55 D)70 E)81 SOLUTION:Here's an approach that's based on Number Properties and a bit ofbrute forcemath: We're told that K and N are both INTEGERS. Since K/N = 81.2, we can say that K = 81.2(N) N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E. With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11) Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH. Final Answer: B #### B QUESTION:The average of first 10 odd numbers is? options: A)22 B)10 C)98 D)66 E)88 SOLUTION:Sum of 10 odd no. = 100 Average = 100/10 = 10 Answer:B #### B <<<Examples ends QUESTION:Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: options: A)175.5 B)170 C)169.5 D)180 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. average price = 126+135/2 = 130.50 o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x - 153 = 22.50 x = 175.50 ANSWER A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n? options: A)-200 B)-130 C)-104 D)51 E)305 SOLUTION:2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151: -51 < c < 151 -51 < n < 151 -102 < c+n < 302. Only option D is in this range. Answer: D. #### D QUESTION:If a is a number such that –2 ≤ a ≤ 2, which of the following has the largest possible absolute value? options: A)3a – 1 B)x^2 + 1 C)3 – x D)x – 3 E)x^2 – x SOLUTION:Ans is A .. leads to the max value of 7 for a = -2 #### A QUESTION:The mean of 1^3,2^3,3^3,4^3,5^3 is? options: A)30 B)45 C)50 D)60 E)75 SOLUTION:1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2 1^3+2^3+3^3+-----+5^3 = (5*6/2)^2 = 225 Required average is = 225/5 = 45 Answer is B #### B QUESTION:An seller earns an income of Re 3 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 15th day of business, he earns an income of: options: A)19 B)22 C)25 D)20 E)36 SOLUTION:2nd day he earns = 3(2 – 3) 3rd day he earns = 3(3 – 3) On 15th day he earns 3(15 -3) = 36 rupees ANSWER:E #### E QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)8 B)twelve (12) C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern? options: A)90 min B)100 min C)110 min D)120 min E)None SOLUTION:Solution Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75) = (1/50 - 3/100) = -1/100. Therefore, the third pipe alone can empty the cistern in 100 min. Answer C #### C QUESTION:Three years ago, the average age of M and N was 18 years. With P joining them, the average age becomes 22 years, How old is P now? options: A)24 years B)27 years C)28 years D)30 years E)40 years SOLUTION:Explanation : Present age of (M + N) = (18 x 2 + 3 x 2) years = 42 years. Present age of (M + N + P) = (22 x 3) years = 66 years. P's age = (66 - 42) years = 24 years. Answer : A #### A QUESTION:60 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)8 days B)6 days C)7 days D)9 days E)12 days SOLUTION:1 women's 1 day work = 1/420 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/420 + 10/140) = 1/12 5 women and 10 children will complete the work in 12 days. Answer: E #### E QUESTION:On a certain day, Tim invested $600 at 10 percent annual interest, compounded annually, and Lana invested 800 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$44 D)$100 E)$105 SOLUTION:Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 600(1.10)^2 = 600(1.21) = 726 and Lana would have 800(1.05)^2 = 800(1.1025) = 882 Thus, Tim earned 126 dollars, while Lana earned 82 dollars The difference is $44 and the answer is C. #### C QUESTION:In an examination, 34% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both? options: A)975 B)1150 C)1175 D)1243 E)1525 SOLUTION:Failed in 1st subject = 34*2500/100 = 850 Failed in 2nd subject = 42*2500/100 = 1050 Failed in both = 15*2500/100 = 375 Failed in 1st subject only = 850-375 = 475 Failed in 2nd subject only = 1050-375 = 675 Passed in either subject but not in both = 675+475 = 1150 Answer is B #### B QUESTION:If it takes a machine 1⁄3 minute to produce one item, how many items will it produce in 2 hours? options: A)1⁄3 B)4⁄3 C)80 D)120 E)360 SOLUTION:1 item takes 1/3 min so it takes 120 min to produce x x/3=120 the x=360 Answer:E #### E QUESTION:X can do 1/4 of a work in 10 days, Y can do 40% of work in 40 days and Z can do 1/3 of work in 13 days. Who will complete the work first? options: A)D B)F C)X D)Z E)W SOLUTION:Whole work will be done by X in 10*4 = 40 days. Whole work will be done by Y in (40*100/40) = 100 days. Whole work will be done by Z in (13*3) = 39 days Therefore, Z will complete the work first. The answer is D. #### D QUESTION:By selling 20 pens for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%? options: A)8.76 B)10.76 C)8.76 D)9.76 E)5.76 SOLUTION:70% --- 20 130% --- ? 70/130 * 20 = 10.76 Answer: B #### B QUESTION:We made a down payment of $80 and borrowed the balance on a new cello which cost $500. The balance with interest was paid in 23 monthly payments of $19 each and a final payment of $4. The amount of interest paid was what percent of the amount borrowed? options: A)3.5% B)4% C)4.5% D)5% E)5.5% SOLUTION:We borrowed $420. To pay back this loan, we paid 23*$19 + $4=$441. The interest was $441-$420=$21. The percentage was $21/$420=0.05=5%. The answer is D. #### D QUESTION:If B and C are digits and 8BC is a 3-digit number that is divisible by 5, which of the following is a possible product of B and C? options: A)1 B)2 C)5 D)7 E)14 SOLUTION:Try with the options - A. If BC = 1 , both B and C must be 1 B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3 C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3 D. If BC = 6 , then we can have the following possibilities i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3 ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3 E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 5 Thus answer is (D) #### D QUESTION:What is the speed required for a car to cover a distance of 600 km in 5 hours? options: A)160 kmh B)140 kmh C)150 kmh D)130 kmh E)120 kmh SOLUTION:Speed= Distance / Time Speed = 600 / 5 = 140 Answer: B #### B QUESTION:The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)75 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 2.5) kg = 25 kg. Weight of new person = (50 + 25) kg = 75 kg. Answer: C #### C QUESTION:If the sum of 5 consecutive integers is y, which of the following must be true? I. y is an even number II. y is an odd number III. y is a multiple of 5 options: A) I only B) II only C) III and II only D) I and III E) III only SOLUTION:I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true. II. Same as above. This need not be always true. III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4) = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases. Therefore E is the answer. #### E QUESTION:If n is an integer greater than 8, which of the following must be divisible by 3? options: A)1. n (n+1) (n-4) B)2. n (n+2) (n-1) C)3. n (n+3) (n-5) D)4. n (n+4) (n-2) E)5. n (n+5) (n-6) SOLUTION:We need to find out the number which is divisible by three, In every 3 consecutive integers, there must contain 1 multiple of 3. So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three 1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1) 2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1) 3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n) 4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1) 5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2) from the above onlyoption Ais product of consecutive three numbers. C #### C QUESTION:Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work? options: A)6 days B)7.2 days C)9.5 days D)12 days E)13 days SOLUTION:EXPLANATION: Hint: A's one day work = 1/12 B's one day work = 1/18 (A + B)'s one day work = 1/12 + 1/18 = (18 + 12)/(12 x 18)= 30/216= 1/7.2 Together, A & B will finish the work in 7.2 days. ANSWER IS B #### B QUESTION:If the speed of X meters per second is equivalent to the speed of Y kilometers per minute, what is Y in terms of X? (1 kilometer=1000 meters) options: A)0.06x B)6x/5 C)18x/5 D)60x E)3600000x SOLUTION:x=1000y/60 y = 0.06x Answer : A #### A QUESTION:Lorna invests $6000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/100*6000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose? options: A)5 B)8 C)11 D)15 E)17 SOLUTION:Explanation : Let a, b, c be the Englishmen and d, e, f be the Frenchmen. Let a be the Englishman who knows French. 'a' calls 'b & c' and now knows the secret of both of them. So now 'a' knows 'abc' secrets. 'd' calls 'e & f' and now knows the secret of both of them. So now 'd' knows 'def' secrets. 'a' now calls 'd', and exchange all secrets in French, so now 'a' and 'd' know all the 6 secrets. Now 'a' calls 'b & c' again, and 'd' calls 'e & f' again and tell all the secrets. So, totally 9 calls. Answer : B #### B QUESTION:A car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+336*6=448c =>c=336*6/112=18 Answer B. #### B QUESTION:Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n? options: A)50 years B)25 years C)12 years 6 months D)37 years 6 months E)75 years SOLUTION:Explanatory Answer Let us say Braun invested $100. Then, at the end of 'n' years he would have got back $700. Therefore, the Simple Interest earned = 700 - 100 = $600. We know that Simple Interest = (Principal * number of years * rate of interest) / 100 Substituting the values in the above equation we get 600 = (100 * n * 8) / 100 Or 8n = 600 Or n = 75 years. correct choice is (E) #### E QUESTION:If 20% of a = b, then b% of 20 is the same as: options: A)4% of a B)5% of a C)6% of a D)3% of a E)2% of a SOLUTION:Here, 20% of a=b i.e.,(20/100)a=b then, b% 20 i.e.,(b/100)x20---I then sub b=(20/100)a in I we get, =(20/100)a x (1/100) * 20 =(20/100)a x (20/100) =(400/10000)a =(4/100)a = 4% of a ANSWER :A #### A QUESTION:The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. options: A)179 B)208 C)210 D)223 E)229 SOLUTION:Explanation: Total runs scored by the batsman = 60*46 = 2760 runs Now excluding the two innings the runs scored = 58*44 = 2552 runs Hence the runs scored in the two innings = 2760 – 2552 = 208 runs. Let the highest score be x, hence the lowest score = x – 150 x + (x - 150) = 208 2x = 358 x = 179 runs ANSWER A #### A QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)11 2/3% loss C)66 2/3% loss D)12 2/3% loss E)17 2/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss Answer: A #### A QUESTION:A committee of 7 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed? options: A)308 B)700 C)1404 D)2620 E)3510 SOLUTION:The only cases possible are : 1. 2 men and 5 women : 8C2 * 5C5 = 28 2. 4 men and 3 women: 8C4*5C3 = 280 Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed) Total possible combinations = 28+280 = 308. Thus A is the correct answer. #### A QUESTION:A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? options: A)10.18 p.m B)10.29 p.m C)10.30 p.m D)10.38 p.m E)10.32 p.m SOLUTION:D = 70 * 1 ½ = 105 km RS = 85 – 70 = 15 T = 105/15 = 7 h 3.30 + 7 h = 10.30 p.m. Answer:C #### C QUESTION:if log 2 = 0.30103, the number of digits in 2128 is options: A)22 B)39 C)88 D)28 E)11 SOLUTION:Explanation: log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4 ie, its characteristic = 38 Hence, number of digits in 2128 = 38+1 = 39 Answer: Option B #### B QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 35%? options: A)600 B)887 C)256 D)654 E)675 SOLUTION:Cost price = Rs.500 profit = 35% of 500 = Rs.175 Selling price = Cost price + Profit = 500 + 175 = 675 Answer: E #### E QUESTION:A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? options: A)35 B)20 C)47 D)36 E)30 SOLUTION:1: 2/5 = 5: 2 2/7 * 70 =20 Answer:B #### B QUESTION:In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was options: A)548 B)9674 C)2397 D)2700 E)3000 SOLUTION:Explanation: Number of valid votes = 80% of 7500 = 6000. Valid votes polled by other candidate = 45% of 6000 =(45/100*6000)=2700 Answer: D #### D QUESTION:George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is options: A)28 B)H C)27 D)29 E)271 SOLUTION:Answer:B #### B QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was? options: A)160000 B)228788 C)266891 D)267689 E)127791 SOLUTION:X * (105/100) * (105/100) * (105/100) = 185220 X = 185220/1.157625 X = 160000 Answer:A #### A QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? options: A)12/489 B)12/452 C)12/455 D)12/429 E)12/292 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When three marbles are drawn, the probability that one is yellow and two are red = (²C₁)(⁴C₂)/¹⁵C₃ = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455 Answer: C #### C QUESTION:A searchlight on top of the watchtower makes 4 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds? options: A)5/6 B)4/5 C)3/4 D)2/3 E)1/2 SOLUTION:The searchlight completes one revolution every 15 seconds. The probability that the man's area will be lit up is 5/15=1/3. The probability that he will stay in the dark is 1-1/3=2/3 The answer is D. #### D QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share? options: A)8239 B)2900 C)2000 D)2393 E)2009 SOLUTION:Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively. Then, 4x - 3x = 1000 => x = 1000. B's share = Rs. 2x = 2 * 1000 = Rs. 2000. Answer: C #### C QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.180 only. Men’s wages are? options: A)6Rs B)2Rs C)4Rs D)9Rs E)12Rs SOLUTION:5M = xW = 8B 5M + xW + 8B ----- 180 Rs. 5M + 5M + 5M ----- 180 Rs. 15M ------ 180 Rs. => 1M = 12Rs. Answer: E #### E QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:What percent of a day is 15 hours? options: A)37×1/2% B)16×1/2% C)18×2/3% D)22×1/2% E)None SOLUTION:Solution Required percentage = (15/24×100)% = (75 / 2)%. = 37×1/2%. Answer A #### A QUESTION:If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be . options: A)90 seconds B)150 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B #### B QUESTION:Which of the following MUST yield an integer when divided by 11? options: A)The sum of eleven consecutive positive integers. B)The square of a prime number. C)The sum of two odd integers. D)The product of three consecutive odd numbers. E)The difference between a multiple of 8 and a multiple of 3. SOLUTION:For option A: Let the numbers be (x-5), (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4), (x+5). Now, (x-5)+(x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4)+(x+5) = 11(x). Hence A is true. No need to check other answers since there can only be one correct answer. So, Ans(A). #### A QUESTION:A man purchased 3 blankets @ Rs.100 each, 4 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)600 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 A #### A QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:If the population of a certain country increases at the rate of 1 person every 60 seconds, by how many persons does the population increase in 2 Hours? options: A)120 B)80 C)100 D)150 E)140 SOLUTION:Answer = 1 * 120(2 hour = 120 minutes)= 120 Answer = A #### A QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)Rs.6620 B)3378 C)2768 D)2999 E)2771 SOLUTION:A = 20000(11/10) 3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period. options: A)5113 B)5117 C)5120 D)8119 E)10115 SOLUTION:Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, D,E The answer to be C Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year. If x = initial number of trees = 5120 Year 1 = 5/4x Year 2 = (5/4)(5/4)x Year 3 = (5/4)(5/4)(5/4)x Year 4 = (5/4)(5/4)(5/4)(5/4)x Only for Answer D: (5/4)(5/4)(5/4)(5/4) 5120 = 12500 Hence, correct answer = C #### C QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15 options: A)3 B)5 C)7 D)8 E)9 SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Answer: Option A #### A QUESTION:385, 462, 572, 396, 424, 671, 264 options: A)385 B)424 C)671 D)264 E)None of these SOLUTION:Solution In each number except 424,the middle digit is the sum of the other two. Answer B #### B QUESTION:Jerry, an electrician, worked 5 months out of the year. What percent of the year did he work? (round answer to the nearest hundredth) What percent 12 is 5? 12 months = 1 year options: A)58.33% B)68.33% C)78.33% D)88.33% E)41.66% SOLUTION:1. Multiply the opposites 5 x 100 = 500 100=5/12 Divide by the remaining number 41.66% (rounded to hundredth) correct answer E #### E QUESTION:If y is an integer, then the least possible value of |23 - 4y| is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We know that 4y is a multiple of 4, so let’s first look at the multiples of 4 closest to 23. We have “20” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 4y = 20, y is 5 and when 4y = 24, y is 5. Let’s start with letting y = 4. |23-4(5)| |23-20| |3| = 3 Next, let’s let y equal 5. |23-4(6)| |23-24| |-1| = 1 We see that the smallest possible value of |23-4y| is 1. Answer A. #### A QUESTION:Which of the following is closer to √0.8+√0.05? options: A)0.5 B)0.7 C)0.9 D)1.1 E)1.2 SOLUTION:√0.8+√0.05=approximately √0.81+√0.04=0.9+0.2=1.1. Hence, the correct answer is D. #### D QUESTION:12.5 * 6.2 * 8.8 = ? options: A)352 B)435 C)224 D)682 E)742 SOLUTION:D 682 ? = 12.5 * 6.2 * 8.8 = 682 #### D QUESTION:The present worth of Rs.676 due in 2 years at 4% per annum compound interest is options: A)Rs.150.50 B)Rs.154.75 C)Rs.156.25 D)Rs.625 E)None SOLUTION:Solution Present Worth = Rs.[676/(1+4/100)²] = Rs.(676x25/26x25/26) = Rs.625 Answer D #### D QUESTION:If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 280, 511, 1023 and x? options: A)395 B)375.8 C)355 D)415 E)365 SOLUTION:The mean of numbers 28, x, 42, 78 and 104 is 62: 28+x+42+78+104=62*5 --> x=58; So, the mean of 128, 255, 511, 1023 and x is (128+255+280+511+1023+58)/6=375.8. Answer: B. #### B QUESTION:The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)40% D)62% E)80% SOLUTION:We need multipliers. multiplier for a 10% increases = 1 + 0.10 = 1.1 multiplier for a 20% decreases = 1 – 0.20 = 0.8 multiplier for a 50% increases = 1 + 0.50 = 1.5 Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3 (0.8)*(1.5) = (0.4)*(3) = 1.2 Now, multiply this by 1.1 1.2*1.1 = 1.32 Thus, the three percent changes combined produce a 32% increase. Answer = (B). #### B QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261? options: A)8000 B)8077 C)2776 D)2976 E)2971 SOLUTION:8820 ---- 441 100 ---- ? => 5% x *105/100 * 105/100 = 8820 x*1.1025=8820 x=8820/1.1025 => 8000.Answer: A #### A QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? options: A)700 B)666 C)600 D)400 E)800 SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C #### C QUESTION:The missing term in the sequence 2, 3, 5, 7, 11, ... 17, 19 is options: A)11 B)13 C)15 D)17 E)18 SOLUTION:Sequence is contain prime numbers. Final sequence : 2,3,5,7,11,13,17,19 ANSWER:B #### B QUESTION:70,76, 74,85,90,105,105,130,130,130 The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD. We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74. Answer: C. #### C QUESTION:If x^2=3x+2, then x^3 = ? options: A)3x+2 B)6x+2 C)11x+6 D)8x-3 E)5x+4 SOLUTION:x^2 = 3x+2 x^3 = x*x^2 = x*(3x+2) = 3x^2 + 2x = 3(3x+2)+2x = 11x+6 The answer is C. #### C QUESTION:Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X? options: A)25% B)40% C)50% D)60% E)75% SOLUTION:34% is 9%-points above 25% and 6%-points below 40%. Thus the ratio of mixture Y to mixture X is 2:3. The percent of mixture X is 3/5 = 60%. The answer is D. #### D QUESTION:Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? options: A)654 B)655 C)656 D)588 E)658 SOLUTION:total cost 840 840*30/100=252 so the cut in amount is 252 the less amount to be spend is 840-252=588 ANSWER:D #### D QUESTION:For a certain set of numbers, if x is in the set, then x - 4 is also in the set. If the number 1 is in the set , which of the following must also be in the set ? a) 4 b) -3 c) -6 options: A)a only, B)b only, C)c only, D)a and b only E)b and c only SOLUTION:Notice that the question asks which of the following MUST be in the set, not COULD be in the set. Since 1 is in the set, then so must be 1-4=-3. Similarly, since -3 is in the set, then so must be -3-3=-6. Could 4 and -1 be in the set? Certainly, but we don't know that for sure. Answer: E. Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set. #### E QUESTION:An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Total Employees: 6 Female: 5 Male: 1 committee of 3 with inclusion of Male Number of ways Female can be selected : 5C2 = 10 For male it should be 6C1 or 6C6 6C1= 6 6C6= 1 ANS= 10 B #### B QUESTION:If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r? options: A)2 B)3 C)4 D)5 E)Cannot be determined SOLUTION:\frac{15^r( 1+ 15)}{4^y} = 15^y (15^r . 4^2 ) / 4^y = 15^y. 4^0 15^r . 4^(2-y) = 15^y. 4^0 Equating the powers, r = y; 2-y = 0; So r = y = 2=A #### A QUESTION:The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)265 m B)755 m C)245 m D)127 m E)156 m SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer:C #### C QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rajan? options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000 =>4:5:3 =>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...] => 12:5:6 Share of Rajan => 4600*12/23 = 2400 ANSWER:E #### E QUESTION:A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:14x + 75 = 15(x + 3) x = 30 + 3 = 33 Answer:C #### C QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A QUESTION:Which number should replace both the asterisks in (* /21) x (*/84) = 1 ? options: A)21 B)42 C)63 D)72 E)168 SOLUTION:Let (y/21) x (y/84) = 1 y^2 = 21 x 84 = 21 x 21 x 4 y = (21 x 2) = 42 The answer is B. #### B QUESTION:A box contains 4 chocobars and 4 ice creams. Tom eats 3 of them, by randomly choosing. What is the probability of choosing 2 chocobars and 1 icecream? options: A)9/3 B)1/7 C)2/8 D)2/7 E)4/7 SOLUTION:Probability of choosing 1 chocobar = 4/8 = 1/2 After taking out 1 chocobar, the total number is 7. Probability of choosing 2nd chocobar = 3/7 Probability of choosing 1 icecream out of a total of 6 = 4/6 = 2/3 So the final probability of choosing 2 chocobars and 1 icecream = 1/2 * 3/7 * 2/3 = 1/7 B #### B QUESTION:Insert the missing number 3, 7, 6, 5, 9, 3, 12, 1, 15, ... options: A)18 B)33 C)-1 D)3 E)-3 SOLUTION:3, 7, 6, 5, 9, 3, 12, 1, 15, ... has two different series 1) 3, 6, 9, 12, 15..... 2) 7, 5, 3, 1, ..... -1 is the next number ANSWER:C #### C QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:Set X consists of 10 integers and has median of 30 and a range of 20. What is the value of the greatest possible integer that can be present in the set? options: A)32 B)37 C)C.40 D)43 E)50 SOLUTION:Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle. Quick check of each option starting from the largest: (E) 50 Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median. (D) 43 Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median. (C) 40 Range of 20 means the smallest integer will be 20. 20 can lie in between such as: 20, 20, 20, 20, 20, 20, 20, 20, 20, 50 This is possible. Hence it is the greatest such number. Answer (E) #### E QUESTION:What Is The Next Number 12 13 15 17 111 113 117 119 ? options: A)123 B)220 C)129 D)428 E)224 SOLUTION:123. These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1 Answer : A #### A QUESTION:The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most? options: A)3 B)1 C)0 D)19 E)20 SOLUTION:Average of 20 numbers = 0 Sum of 20 numbers / 20=0 => Sum of 20 numbers = 0 Hence at the most, there can be 19 positive numbers. (Such that if the sum of these 19 positive numbers is x, 20th number will be -X) ANSWER:C #### C QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)3 B)3.3 C)3.5 D)3.6 E)None SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4. Answer: Option D #### D QUESTION:An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? options: A)520 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (240 x 5) = 1200 km. Speed = Distance/Time Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours] Required speed = 1200 x 3 km/hr = 720 km/hr. 5 E #### E QUESTION:The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be social teachers? options: A)2/3 B)1/12 C)2/9 D)1/2 E)1/24 SOLUTION:Probability of first member an English teacher = 3/9 Probability of second member an English teacher = 2/8 Probability of both being english teacher = 3/9 x 2/8 =1/12 (B) #### B QUESTION:One of the longest sides of the triangle is 20 m,the other side is 10 m.Area of the triangle is 80m^2.What is the another side of the triangle? options: A)2sqrt(61) B)2sqrt(62) C)2sqrt(63) D)2sqrt(64) E)2sqrt(65) SOLUTION:base of triangle is 20 and area is 80 therefore height=2*80/20=8. now one side of triangle is of 10. so we can get the point were the base is divided by applying Pythagoras therm so division pt =sqrt(10^2-8^2)=sqrt(36)=6 threfore other half is 14. now second side=sqrt(14^2+8^2)=sqrt(260)=2sqrt(65) ANSWER:E #### E QUESTION:A and B together can do a work In 4 days. A alone can do it in 12 days. What time B will take to do the work alone? options: A)6 days B)8 days C)12 days D)10 days E)5 days SOLUTION:Explanation: A and B 1day's work = 1/6 A alone can do 1day's work = 1/12 what time B will take to do the work alone? B = (A+B) - A = (1/6) - (1/12) = 12 Days Answer: Option C #### C QUESTION:Three distinct single-digit numbers. A,B,C are in GP. If abs(x) for real x is the absolute value of x(x if x is +ve or 0 and -x if x is -ve), then the number of different possible values of abs(A+B+C) is options: A)5 B)6 C)3 D)4 E)7 SOLUTION:A,B,C may be (1,2,4) & (4,2,1) (1,3,9) & (9,3,1) (2,4,8) & (8,4,2) (4,6,9) & (9,6,4) find abs(A+B+C) for these 8 GPs 7,13,15,19 So,we get 4 different values ANSWER:D #### D QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)25 SOLUTION:Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER IS A #### A QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12 SOLUTION:6a/100 = 12 a = 200 12b/100 = 6 b = 50 c = b/a = 50 / 200 = 1/4 The answer is C. #### C QUESTION:What distance will be covered by a bus moving at 36 kmph in 30 seconds? options: A)287 B)600 C)289 D)300 E)207 SOLUTION:36 kmph = 36 * 5/18 = 10 mps D = Speed * time = 10 * 30 = 300 m. Answer:D #### D QUESTION:On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done? options: A)2880 B)2778 C)2682 D)8222 E)6282 SOLUTION:Explanation: There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways. Further, in each category (subject), books are to be arranged in different order, we get, Required number of ways: 3! * [2! * 2! * 5!] = 2880 ANSWER: A #### A QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 25,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 25,000 is made = 96,000 + 25,000 = Rs. 1,21,000 ANSWER:D #### D QUESTION:16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work? options: A)26.7 days B)77 days C)20 days D)88 days E)44 days SOLUTION:16 * 25 = 15 * x => x = 26.7 days Answer: A #### A QUESTION:There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women? options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35 SOLUTION:METHOD- 1: Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36 Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70 Probability = 36/70 = 18/35 A METHOD-2:Also see the mistake done by the person who posted this question Probability of First selected person being Man = 4/8 Probability of Second selected person being Man = 3/7 Probability of First selected person being Woman = 4/6 Probability of Second selected person being Woman = 3/5 i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35 The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2! A #### A QUESTION:The percentage increase in the area of rectangle , if each of its side is increased by 20% is? options: A)30% B)44% C)50% D)55% E)60% SOLUTION:Let original length = x meters original breadth = y meters original area = xy m^2 New length = 120x/100 New breadth = 120y/100 = 6y/5 New area = 6x/5 * 6y/5 = 36xy/25 m^2 Increase percent = 11xy/25 * 1/xy *100 = 44% Answer is B #### B QUESTION:The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half? options: A)44.2 B)47.8 C)50.5 D)53.6 E)56.9 SOLUTION:The average of this half is 154.4/4 = 38.6 This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8 The answer is B. #### B QUESTION:Sagar was riding bike towards north,turned left road 1 km turnes towrds left &road 2km found himself 1km west of starting how far did he road north? options: A)2km in north. B)2km in south. C)2km in east. D)2km in west. E)4km in north. SOLUTION:He travelled total distance of 3km. From which he travelled 1km in west. Hence in all he travelled total 2km in north. ANSWER:A #### A QUESTION:If every 2 out of 3 readymade shirts need alterations in the sleeves, and every 4 out of 5 need it in the body, how many alterations will be required for 60 shirts ? options: A)88 B)123 C)133 D)143 E)153 SOLUTION:no.of Alteration required in 1 shirt is (2/3)+(4/5)+(3/4)=133/60 for 60 shirts it will 60*(133/60)=133 ANSWER:C #### C QUESTION:A company organzied a help desk.there have been done 24 hrs work on software,17 hrs on help user nd 40% on other services.find the total no. of hrs have been worked on that day? options: A)68 B)69 C)70 D)67 E)76 SOLUTION:let total no of hrs = x they have done 24+17=41 40% of x is 40/100=2/5 x=41+2x/5 x=68.3 ANSWER:A #### A QUESTION:. The average of first ten prime numbers which are odd is? options: A)22.9 B)28.1 C)12.9 D)15.8 E)11.2 SOLUTION:Explanation: Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members 51* 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ? options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:Just putting values, the LHS becomes n=0 --> 11 n=-1 --> 11/10 n=-2 --> 11/100 n=-3 --> 11/1000 Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3. Answer is B. #### B QUESTION:Convert the 11/36 m/s into kilometers per hour? options: A)2.9 kmph B)1.1 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:11/36 m/s = 11/36 * 18/5 = 11/10 = 1.1 kmph. Answer: B #### B QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam. options: A)15 B)25 C)30 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 92(x - 5) 80x - (5 * 20) = 92(x - 5) 360 = 12x => x = 30 ANSWER:C #### C QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings? options: A)Rs.3600 B)Rs.3629 C)Rs.3279 D)Rs.3629 E)Rs.3283 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 18000 => x = 3600 Savings = Income - expenditure = 5x - 4x = x So, savings =Rs.3600. Answer: A #### A QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1232? options: A)1000 B)2217 C)1100 D)2777 E)2991 SOLUTION:1232 = P [1 + (5*12/5)/100] P= 1100 Answer: C #### C QUESTION:"A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap? options: A)90 seconds B)54.44 seconds C)110 seconds D)63 seconds E)77 seconds SOLUTION:A is faster than B. Every second he increases distance between A and B. They will meet for the first time again when he increases distance between them by one full circle. (Say the lap is of 100m. He keeps increasing distance between them. When he is 90 m ahead of him, it is the same as 10 m behind him because they are moving in a circle. Finally when he is 100 m ahead of him, he is exactly 1 lap ahead and hence both are at the same point). A takes 70 secs for one full lap. So he covers 4.5 laps in exactly 70*4.5 = 315 seconds. In 315 secs, B completes 3.5 laps. So for each lap, he takes 315/3.5 = 90 secs Answer (A) #### A QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D QUESTION:If a committee of 2 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? options: A)24 B)40 C)50 D)80 E)120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 4C2=6. But these 2 chosen couples can send two persons (either husband or wife): 2*2=2^2=4. Total # of ways: 4C2*2^2=24. Answer: A #### A QUESTION:In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday? options: A)Thursday B)Friday C)Saturday D)Sunday E)Monday SOLUTION:Day of week after 64 days after Arman's birthday = 7*9 + 1 Saturday as the period will have 9 weeks and 1 days . The 1 days in the end will be Friday . Answer B #### B QUESTION:When positive integer F is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when F is divided by B? options: A) 13 B) 14 C) 15 D) 16 E) 17 SOLUTION:the remainder will be obtained from the decimal part when F is divided by B i.e. 0.35 0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this PS: for B-14 F=174 and B=40 #### B QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 24*5= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 24*5 + 2y =124 then y=2 24*4 + 2y = 124 then y=14 24*3 +2y = 124 then y= 26 24*2 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:Out of 470 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ? options: A)80 B)150 C)100 D)180 E)220 SOLUTION:n(A)=325,n(B)=175,n(AuB)=470-50=420. Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80. Answer is A #### A QUESTION:The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $95 per day. What was his wage on the 8th day? options: A)$76 B)$90 C)$92 D)$97 E)$104 SOLUTION:Average daily wage of a worker for 15 consecutive working days = 90$ During the first 7 days , the daily average daily wage = 87$ During the last 7 days , the daily average daily wage = 95$ Wage on 8th day = 90*15 -( 87*7 + 95 *7) = 1350 - (609 + 665) =1350 - 1274 = 76 Answer A #### A QUESTION:If 6 (A's capital) = 8 (B's capital) = 8 (C's capital). Then the ratio of their capitals is? options: A)4:15:16 B)4:15:68 C)4:3:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 8 C A:B:C = 1/6:1/8:1/8 = 4:3:3 Answer: C #### C QUESTION:A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? options: A) 7! – 2!3!2! B) 7! – 4!3! C) 7 × 2!3!2! D) 7! – 5!3! E) 2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 7 is 7!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!5!. # of arrangements when 3 boys do not sit together would be: 7!-3!5!. Answer: D). #### D QUESTION:A train 300 m long passed a pole in 30 sec. How long will it take to pass a platform 650 m long? options: A)28 sec B)89 sec C)85 sec D)16 sec E)95 sec SOLUTION:Speed = 300/30= 10 m/sec. Required time = (300 + 650)/10 = 95 sec. Answer:E #### E QUESTION:The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)44% D)62% E)80% SOLUTION:Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 . So overall increase is from 100 to 144 is 44% Answer C #### C QUESTION:The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? options: A)81 : 121 B)81 : 127 C)81 : 191 D)81 : 161 E)81 : 182 SOLUTION:Explanation: Ratio of the sides = ³√729 : ³√1331 = 9 : 11 Ratio of surface areas = 92 : 112 = 81 : 121 Answer: Option A #### A QUESTION:A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)28 sec B)16 sec C)36 sec D)18 sec E)17 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 240 + 120 = 360 m. Time taken = 360/10 = 36 sec. Answer:C #### C QUESTION:Ajay, Bhavan and Chetan started a business together. Thrice the investment of Ajay, twice the investment of Bhavan and the investment of Chetan are equal. Find the ratio of their respective profits at the end of the year? options: A)1:2:1 B)2:3:6 C)3:2:1 D)1:2:3 E)1:4:3 SOLUTION:Let the investments of Ajay, Bhavan and Chetan be Rs,a, Rs.b and Rs.c respectively. 3b = 2b = c. a = c/3. b = c/2. Ratio of profits of Ajay, Bhavan and Chetan at the end of one year = Ratio of their respective investments = 2:3:6. ANSWER:B #### B QUESTION:Some of the 50% solution of acid was removed and this was replaced with an equal amount of 14% solution of acid. As a result, a 23% solution of acid was obtained. What fraction of the original solution was replaced? options: A)1/2 B)1/3 C)2/3 D)3/4 E)4/5 SOLUTION:Let x be the fraction of the original solution that was replaced. 0.5*(1-x)+0.14(x)=0.23 0.36x=0.27 x=3/4 The answer is D. #### D QUESTION:If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be options: A)2 B)4 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 4*11025 = 44, 100, which is a square of 210 B #### B QUESTION:In how many ways can you seat 8 people on a bench if one of them does not want to sit in one of the two middle seats or at either end? options: A)17,540 B)18,360 C)19,320 D)20,160 E)21,480 SOLUTION:One person can choose 4 possible chairs to sit. The remaining 7 people can sit in 7! ways. The number of arrangements is 4*7! = 20,160. The answer is D. #### D QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? options: A)13680 B)13885 C)14005 D)14280 E)14680 SOLUTION:dana borrows 6000 and returns 2% per month. so returns 120 per month. and 1440 per year. so dana owes 6000-1440=4560 per year. after 3 years she will owe 13680. Ans (A) #### A <<<Examples ends QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Find the value of a from (15)^2 x 8^3 ÷ 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 ÷ 256 = a = 225 x 512 ÷ 256 = 450 E #### E QUESTION:A sum 's' is divided into 4 parts. second person gets Rs 10 more than first.3rd person is Rs 10 more than second,4th is 10 more than 3rd.how much amount do 1st person get.? options: A)x = (s-60)/4 B)x = (s-60)/5 C)x = (s-60)/3 D)x = (s-60)/2 E)x = (s-60)/6 SOLUTION:let x be amount getting by first person, second person gets x +10,third person gets x + 20,fourth person gets x + 30, now s = (x)+(x+10)+(x+20)+(x+30) s = 4x + 60 s - 60 = 4x or x = (s-60)/4 ANSWER:A #### A QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)? options: A)2 B)4 C)7 D)9 E)10 SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3. Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9. The answer is D. #### D QUESTION:A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist? options: A)9km/hr B)7km/hr C)12km/hr D)15km/hr E)18km/hr SOLUTION:Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr Ans:E #### E QUESTION:If 3 women can color 180 m long cloth in 2 days, then 5 women can color 300 m long cloth in? options: A)2 days B)3 days C)5 days D)1 day E)4 days SOLUTION:The length of cloth painted by one woman in one day = 180/ 3× 2 = 30 m No. of days required to paint 300 m cloth by 5 women = 300/ 5 × 30 = 2 days Answer : A #### A QUESTION:What is the average of first 21 multiples of 7 ? options: A)49 B)77 C)66 D)57 E)50 SOLUTION:Required average = 7(1+2+....+21) / 21 (7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers) = 77 ANSWER IS B #### B QUESTION:19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)286 B)342 C)422 D)540 E)618 SOLUTION:2*19C2 = 2*171 = 342 The answer is B. #### B QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:What is the units digit of (493) (915) (381) (756) (22) options: A)0 B)1 C)4 D)5 E)6 SOLUTION:Just multiply the digits in the units place for each term and you will get the answer. It should be 0. you got a 5 as a unit digit and an even number term. so the multiplication of this will definitely yield a 0. Answer has to be 0. I also tried it using the calculator and the answer is 1. IMO B. #### B QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 10 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 50 will be in team A 50 will be in team B The larger diff is 70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10. Answer choice C #### C QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? options: A)12/489 B)12/452 C)12/455 D)12/429 E)12/292 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When three marbles are drawn, the probability that one is yellow and two are red = (²C₁)(⁴C₂)/¹⁵C₃ = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455 Answer: C #### C QUESTION:A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done? options: A)14 days B)21 days C)22 days D)11 days E)43 days SOLUTION:D 11 days x/24 + x/30 + x/40 = 1 x = 11 days #### D QUESTION:A sum of money when distributed among friends is in the ratio of 3:4:5, if the amount is the larger 3digit number divisible by 24, what is the share of 3rd person? options: A)400 B)410 C)420 D)430 E)440 SOLUTION:Largest 3 digit number divisible by 24= 984 So their shares are (984*3/12=246) , (984*4/12=328) , (984*5/12=410) ANSWER:B #### B QUESTION:How many digits are required to number a book containing 260 pages? options: A)784 B)672 C)492 D)372 E)300 SOLUTION:9 pages from 1 to 9 will require 9 digits. 90 pages from 10 to 99 will require 90*2=180 digits. 260-(90+9)=161 pages will require 161*3=483 digits. The total number of digits is 9+180+483=672. The answer is B. #### B QUESTION:The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is? options: A)10 years B)11 years C)12 years D)13 years E)14 years SOLUTION:Total age of 3 boys = 24*3 =72 ratio of their ages = 1:2:3 Age of the youngest = 72*1/6 = 12 years Answer is C #### C QUESTION:The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000 SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=4500pi r=15 so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx) E #### E QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m? options: A)1350 B)1357 C)2025 D)2052 E)2122 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 => 675 675 * 3 = Rs.2025 Answer:C #### C QUESTION:An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is: options: A)2/91 B)1/22 C)3/22 D)2/77 E)None of these SOLUTION:Explanation : Let S be the sample space. Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455 Let E = event of getting all the 3 questions from simple mathematics section. n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10 P(E) = n(E)/n(S) = 10/455 = 2/91 . Answer : A #### A QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4*side = 4* (3p/5) = 12p/5 Answer is C. #### C QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 54 km/hr? options: A)2.5 B)2.9 C)6.67 D)2.8 E)2.1 SOLUTION:Speed = 54 * 5/18 = 15 m/sec Time taken = 100/15 = 6.67 sec. Answer:C #### C QUESTION:Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min. options: A)8 min B)3 min C)21 min D)23 min E)24 min SOLUTION:3/4 tank is filled by A in 18 mins. then balance 1/4 tank is filled by B in 32*1/4 = 8 mins. ANSWER:A #### A QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:If P represents the product of the first 13 positive integers, which of the following must be true? I. P is an odd number II. P is a multiple of 24 III. P is a multiple of 23 options: A)I only B)II only C)III only D)None of the above E)All of the above SOLUTION:The correct answer is B. #### B QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B QUESTION:A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested? options: A)25 B)37 C)36 D)29 E)21 SOLUTION:Explanation: From the information provided we know that, Principal + 8% p.a. interest on principal for n years = 180 …….. (1) Principal + 4% p.a. interest on principal for n years = 120 ……… (2) Subtracting equation (2) from equation (1), we get 4% p.a. interest on principal for n years = Rs.60. Now, we can substitute this value in equation (2), i.e Principal + 60 = 120 = Principal = Rs.60. We know that SI = , where p is the principal, n the number of years and r the rate percent of interest. In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60. Therefore, 60 =(60*n*4)/100 => n = 100/4 = 25 years. Answer: A) 25years #### A QUESTION:Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(a + y) / t B)2(a + t) / ay C)2ayt / (a + y) D)2(a + y + t) / ay E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for a 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (4,-3), (4, 7), (12, 2), (12,-7)? options: A)64 B)68 C)72 D)76 E)80 SOLUTION:By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is: Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides. We can now determine the area of the quadrilateral: Area = 1/2 × (10 + 9) × 8 = 76. The answer is D. #### D QUESTION:Which number is the odd one out? 159 248 963 357 951 852 options: A)154 B)248 C)536 D)645 E)135 SOLUTION:B 248 In the rest there is the same difference between each digit, eg: 8 (–3) 5 (–3) 2. #### B QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube. options: A)36 B)48 C)45 D)360 E)55 SOLUTION:16200 = 23 * 34 * 52 A perfect cube has a property of having the indices of all its prime factors divisible by 3. Required number = 32 * 5 = 45. ANSWER:C #### C QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00? options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00 SOLUTION:For retail price = $25 First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5 Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14 Answer: Option A #### A QUESTION:The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is options: A)51:53 B)52:53 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (102% of x) / (106% of x) =102/106 =51/53 = 51:53. Answer: A #### A QUESTION:In how many ways can the integer 120 be expressed as a product of two different positive integers? options: A)10 B)8 C)5 D)4 E)2 SOLUTION:120=(2^3)*3*5 Since 120 is not a perfect square, no of ways=5 Answer C #### C QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? options: A)12 B)15 C)16 D)18 E)14 SOLUTION:Draw a Venn Diagram yourself ! B + C - BC = Number of students that play either Basketball or Cricket 10 +8 - 4 = 14 E) #### E QUESTION:Martins made a part payment of $650 toward buying a brand new washing machine, which represents 15% of the total cost of the washing machine, how much remains to be paid? options: A)$1116.3 B)$3583.3 C)$3283.3 D)$3683.3 E)$2683.3 SOLUTION:Explanation: Let's start with what the total price of the washing machine would be. If 15% is equal to $650 then 100% equals $x. We just have to multiply $650 by 6.67 to get total amount=$4333.3. Out of this amount we then need to deduct the amount already paid which was $650 so we have $4333.3-$650=$3683.3 Answer: Option D #### D QUESTION:What positive number, when squared, is equal to the cube of the positive square root of 17? options: A)64 B)32 C)8 D)4 E)2 SOLUTION:Let the positive number be x x^2 = ((17)^(1/2))^3 =>x^2 = 4^3 = 64 => x = 8 Answer C #### C QUESTION:A man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey ? options: A)1 kmph B)5 kmph C)5.5 kmph D)4 kmph E)7 kmph SOLUTION:Explanation: Speed of Man = 6.5 kmph Speed of stream = 2.5 kmph Speed in DownStream = 9 kmph Speed in UpStream = 4 kmph Average Speed = (2 x 9 x 4)/13 = 5.5 kmph. Answer: C #### C QUESTION:When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y? options: A)96 B)75 C)50 D)25 E)12 SOLUTION:Guys, one more simple funda. 5/2= 2.5 now .5 x2 =1 is the remainder 25/4 = 6.25 now .25x4=1 is the remainder 32/5=6.4 now.4x5 = 2 is the remainder given x/y = 6.12 and remainder is 6 So .12 X y = 6 hence y= 50 Ans C #### C QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)22 B)73 C)99 D)42 E)11 SOLUTION:Explanation: Just go in reverse order. Check the options with th subtracting 18 from each option for getting reverse number. 42 – 18 = 24 (which is in reverse). So answer is 42. Answer D #### D QUESTION:How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. options: A)106 B)109 C)108 D)101 E)104 SOLUTION:(18 × 15 × 12)/(5 × 3 × 2) = 108 Answer is C. #### C QUESTION:The probability of having a girl is identical to the probability of having a boy. In a family with two children, what is the probability that all the children are of the same gender? options: A)1/2 B)1/16 C)1/9 D)1/4 E)1/25 SOLUTION:There are two cases. All boys and all girls. case 1. all boys. 1/2*1/2= 1/4 case 2 .all girls. 1/2*1/2=1/4 We will add the cases to get 1/2 #### A QUESTION:Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters Look at this series: D12, H16, __, P24, T28, ... What number should fill the blank? options: A)H16 B)I17 C)J18 D)K19 E)L20 SOLUTION:E L20 In this series, the letters progress by 4, and the numbers increase by 4. #### E QUESTION:Mary works in a restaurant a maximum of 60 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week? options: A)300 B)420 C)560 D)320 E)400 SOLUTION:Mary receives $8(20)=$160 for the first 20 hours. For the 40 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(40)=$400. The total amount is $160+$400 = $560 Answer C 560. #### C QUESTION:12 welders work at a constant rate they complete an order in 3 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)6 SOLUTION:1. We need to find out the time taken by 3 workers after day 1. 2. total no.of wokers * total time taken = time taken by 1 worker 3. Time taken by 1 worker = 12*3 = 36 days 4. But on day 1 twelve workers had already worked finishing 1/3 of the job. So 3 workers have to finish only 2/3 of the job. 5. Total time taken by 3 workers can be got from formula used at (2). i.e., 3* total time taken = 36. Total time taken by 3 workers to finish the complete job is 36/ 3 = 12 days. 6. Time taken by 6 workers to finish 2/3 of the job is 2/3 * 12 =8 days. The answer is choice C #### C QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is? options: A)39yr B)42yr C)45yr D)32yr E)50yr SOLUTION:Let B's present age = x years Then A's present age = x+9 years x+9+10 = 2(x-10) x + 19 = 2x - 20 x = 39years Answer is A #### A QUESTION:A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? options: A)A B)B C)C D)all alike E)None of these SOLUTION:Let B = 100 A = 50 C * (150/100) = 50 3C = 100 C = 33.3 then 'C' Cheapest ANSWER:C #### C QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is? options: A)6 days B)8 days C)10 days D)12 days E)14 days SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 10 × 40/50 = 8 days B) #### B QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 * 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other? options: A)1.5 hours B)1.27 hours C)1.73 hours D)2 hours E)1.69 hours SOLUTION:The cars travel (145+150=295) miles in one hour. 500 miles/295 miles/hour= 1.69 hours Answer is E #### E QUESTION:What is the remainder when 1014*1047*1050*1053 is divided by 33? options: A)3 B)6 C)30 D)21 E)18 SOLUTION:OA is 'C'. OE: take the remainder from each of 1044/33, 1047/33 and so on.. 1014/33 gives remainder = 24 1047/33 gives remainder = 24 1050/33 gives remainder = 27 1053/33 gives remainder = 30 the net remainder is the product of above individual remainders. i.e = 24*24*27*30 break them into pairs 24*24/33 gives remainder 15 and 27*30/33 gives remainder 18 so 15*18/33 gives remainder 6. B #### B QUESTION:If 18!/3^x is an integer, what is the greatest possible value of x? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:18 - 3*3*2 15 - 5*3 12 - 4*3 9 - 3*3 6 - 2*3 3 - 1*3 Hence max of 3^8 is allowed. IMO E. #### E QUESTION:Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? options: A)A)7 B)B)6 C)C)8 D)D)9 E)E)4.74 SOLUTION:1/5 + 1/15 - 1/x = 1/18 x = 4.74 Answer:E #### E QUESTION:A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)29 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 180, so from 2003 to 2005 it increased by (180-140)/140=40/140=2/7=~29%. Answer: E. #### E QUESTION:SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS: options: A)15 B)16 C)18 D)25 E)NONE OF THESE SOLUTION:RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4 SUPPOSE TANYA TAKES X DAYS TO DO THE WORK; 5:4::20:X, X=(4x20/5), X=16 DAYS. CORRECT OPTION: B #### B QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)78% D)48% E)11% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture? options: A)2 B)2 1/2 C)3 D)3 1/2 E)4 SOLUTION:Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. B #### B QUESTION:The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made? options: A)Rs. 120,002 B)Rs. 1,20,000 C)Rs. 1,20,00 D)Rs. 1,20,028 E)Rs. 1,20,011 SOLUTION:Explanation: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000 Answer: B #### B QUESTION:A work can be finished in 15 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is options: A)4:3 B)3:4 C)2:3 D)3:2 E)5:4 SOLUTION:Work done by 20 women in 1 day = 1/15 Work done by 1 woman in 1 day = 1/(15×20) Work done by 16 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×16) Ratio of the capacity of a man and woman =1/(15×16) : 1/(15×20) = 1/16 : 1/20 = 1/4 :1/5 = 5:4 Answer is E. #### E QUESTION:A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. options: A)40 B)50 C)62 D)45 E)56 SOLUTION:Let the average after 11th inning = x Then, average after 10th inning = x-5 10(x-5)+100 = 11x x = 100-50 = 50 Answer is B #### B QUESTION:In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 272 runs? options: A)6.25 B)6.22 C)6.29 D)6.39 E)6.0 SOLUTION:Required run rate = [272 - (3.2 * 10)]/40 = 240/40 = 6.00 Answer: E #### E QUESTION:Five men and five women have to sit around a circular table so that no 2 women are together. In how many ways can that be done? options: A)4!*5! B)6!*6! C)5!*7! D)6!*7! E)7!*7! SOLUTION:The number of arrangements of n distinct objects in a row is given by n!. The number of arrangements of n distinct objects in a circle is given by (n-1)!. The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)! Now, 5 men in a circle can be arranged in (5-1)! ways and if we place 5 women in empty slots between them then no two women will be together. The # of arrangement of these 5 women will be 5! and not 4! because if we shift them by one position we'll get different arrangement because of the neighboring men. So the answer is indeed 4!*5!. A #### A QUESTION:A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x? options: A)7 B)8 C)9 D)6 E)5 SOLUTION:(3+11+7+9+15+13+8+19+17+21+14+x)/12 =12 ⇒(137+x)/12=12 ⇒137+x=144 ⇒x=144−137=7 Answer is A. #### A QUESTION:The distance between A&B is 450km. A person is traveling from A to B at 70km/hr started at 9AM and another person is traveling from B to A at 80km/hr and started at same time. Then at what time they meet together.? options: A)A)12PM B)B)4PM C)C)1PM D)D)3PM E)E)5PM SOLUTION:Let x hours be they will meet together distance covered by 1st person+distance covered by 2nd person = 450km 70x+80x = 450 x= 3 hr They will meet = 9AM +3hr = 12PM Answer is A #### A QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)95 SOLUTION:number of handshakes = 10C2= 10*9/2 = 45 ANSWER:B #### B QUESTION:Given two fair dice, what is the probability G that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. G=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:The ratio 3 : 5 expressed as a percent equals options: A)60% B)40% C)80% D)125% E)None SOLUTION:Solution 3 : 5 = 3/ 5 = (3 / 5 x 100)%. = 60 %. Answer A #### A QUESTION:Find the missing number: 6 9 12 ? 6 options: A)6 B)7 C)8 D)9 E)5 SOLUTION:6 9 12 9 6 palindrome ANSWER:D #### D QUESTION:There are two inlets and one outlet to a cistern. One of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full? options: A)2 hours B)2.5 hours C)3 hours D)3.5 hours E)8 hours SOLUTION:The combined inflow rate of the two inlets is 1/4 + 1/8 = 3/8 cistern/hour. Thus, working together, it takes 8/3 hours (time is reciprocal of rate) to fill the cistern. From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) =2*3/8 = 3/4 th of the cistern . Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour. Letting x to be the rate of the outlet, we would have: 3/8 - x = 1/4 --> x = 1/8 cistern/hour, which means that it takes 8 hours the outlet working alone to empty the cistern. Answer: E. #### E QUESTION:The ratio of flour to water to sugar in a recipe is 11:8:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 4 cups of water, how much sugar is required? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:The ratio of flour to water is 22:8=11:4. The ratio of flour to sugar is 5.5:1=11:2. The new ratio of flour to water to sugar is 11:4:2 If we need 4 cups of water, then we need 2 cups of sugar. The answer is D. #### D QUESTION:A certain kind of necklace is made from 9 gold, 6 blue, and 3 white beads. What is the maximum number of these necklaces that can be made from 36 beads of each color ? options: A)8 B)4 C)6 D)5 E)4 SOLUTION:Atleast 9 gold breads are needed to make a necklace, so irrespective of the combinations of blue and white beads, the number of necklaces that can be formed will be 36/9 =4 Answer:- E #### E QUESTION:The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle? options: A)8m. B)6m. C)4m. D)2m. E)5m. SOLUTION:Explanation: Let the sides of the rectangle be l and b respectively. From the given data, (√l2 + b2) = (1 + 108 1/3 %)lb => l2 + b2 = (1 + 325/3 * 1/100)lb = (1 + 13/12)lb = 25/12 lb => (l2 + b2)/lb = 25/12 12(l2 + b2) = 25lb Adding 24lb on both sides 12l2 + 12b2 + 24lb = 49lb 12(l2 + b2 + 2lb) = 49lb but 2(l + b) = 28 => l + b = 14 12(l + b)2 = 49lb => 12(14)2 = 49lb => lb = 48 Since l + b = 14, l = 8 and b = 6 l - b = 8 - 6 = 2m. Answer: Option D #### D QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100 x 3000)/(12500 x 4)% = 6% answer :D #### D QUESTION:What is the average of xx,2x2x,and 66? options: A)x+2 B)x+2x C)x+2x+2 D)2x+2 E)x+2x-2 SOLUTION:By the definition of an average, we get: x+2x+63=3x+63x+2x+63=3x+63 =3(x+2)3=x+2.=3(x+2)3=x+2. Hence, the answer is x+2x+2 or Option C #### C QUESTION:If, 1 * 3 * 5 = 16 3 * 5 * 7 = 38 Then find, 15 * 17 * 19 =? options: A)89 B)49 C)68 D)38 E)338 SOLUTION:E 338 (19 * 17) + 15 = 338 #### E QUESTION:A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen? options: A)119 B)1,200 C)3,240 D)3,600 E)14,400 SOLUTION:To meet the conditions we can have only 2 cases: 2 officers and 3 civilians: C25∗C39=840 3 officers and 2 civilians: C35∗C29=360 Total: 840+360=1,200. Answer: B. #### B QUESTION:Mother,her daughter and her grand child weighs 160 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter? options: A)46 B)47 C)48 D)49 E)40 SOLUTION:mother + daughter + child = 160kg daughter + child = 60kg mother = 160 - 60 = 100kg child = 1/5th of mother = (1/5)*100 = 20kg So now daughter = 120 -(mother + child) = 160 - (100+20) = 40kg ANSWER:E #### E QUESTION:Evaluate 35 / .07 options: A)400 B)500 C)505 D)None of these E)506 SOLUTION:Explanation: 35/.07 = 3500/7 = 500 Option B #### B QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 253 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)23 D)33 E)22 SOLUTION:E 22rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 = 253 Thus our anniversary falls on the 22rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### E QUESTION:How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 30% iodine solution? options: A)30.5 B)49 C)100 D)105 E)140 SOLUTION:Solution 1: Assume the iodine solution to be mixed = x lts. Iodine = 0.4x lts, Water = 0.6x lts. Solution 2: 35 liters of a 20% iodine solution Iodine = 7 lts, Water = 28 lts. Total iodine = 0.4x + 7 Total water = 0.6x + 28 The resultant is a 35% idoine solution. Hence (0.4x + 7) / (x + 35) = 30/100 40x + 700 = 30x + 1050 10x = 305 x = 30.5 lts Correct Option: A #### A QUESTION:During a trip, joe traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francine's average speed for the entire trip? options: A)(180-x)/2 B)(x+60)/4 C)(300-x)/5 D)600/(115-x) E)12000/x+300 SOLUTION:total distance =100 ;total time = T t1 = x/30 t2 = 100-x /40 T =t1+t2 = x/30 + 100-x/40 = (40x + 3000- 30x)/1200 = (10x+3000)/1200 = x+300/120 av speed = 100*120/x+300 = 12000/x+300 E #### E QUESTION:Diana picked a number of pears, each of which she sold, canned, or poached. If she canned 60 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 115 pears, then how many pears did she sell? options: A)41 B)44 C)47 D)50 E)53 SOLUTION:Let x be the amount of pears that she sold. Then she poached 0.5x. Then she canned 1.6*0.5x=0.8x. The total amount of pears is x+0.5x+0.8x=2.3x The fraction of pears that she sold is 1/2.3=10/23. The number of pears she sold is (10/23)*115=50. The answer is D. #### D QUESTION:A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? options: A)3 B)4 C)5 D)8 E)2 SOLUTION:M = 4 S = 2 US = 4 - 2 = 2 D = 6 T = 6/2 = 3 Answer: A #### A QUESTION:A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work? options: A)30 days B)20 days C)25 days D)35 days E)45 days SOLUTION:Work done by A in 10 days = 10/80 = 1/8 Remaining work = (1 - (1/8)) = 7/8 Now, work will be done by B in 42 days. Whole work will be done by B in (42 x 8/7) = 48 days Therefore, A’s one day’s work = 1/80 B’s one day’s work = 1/48 (A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30 Hence, both will finish the work in 30 days. ANSWER:A #### A QUESTION:Whats the reminder when 58,458,965,231,457,895,684,525,465,985,445 is divided by 16 options: A)5 B)7. C)2. D)3 E)9 SOLUTION:A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16. Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it. 58,458,965,231,457,895,684,525,465,985,445 = 58,458,965,231,457,895,684,525,465,980,000+5,445 The first number is divisible by 16. You just have to find the remainder when you divide 5445 by 16. That will be the remainder when you divide the original number by 16. 5445/16 gives remainder 5. Answer (A) #### A QUESTION:If 0 < n < 1, what is the median of the values n, n^-1, n^2, n^1/2 and n^3? options: A)n B)n^-1 C)n^2 D)n^1/2 E)n^3 SOLUTION:A. To make the problem less confusing, I picked a number between 0 and 1 such as n = 1/4 and calculate: n = 1/4 n^-1 = 4 n^2 = 1/16 n^(1/2) = 1/2 n^3 = 1/8. From this, rearrange the number and the median is 1/4, which is n. Answer A #### A QUESTION:What should come in place of the question mark (?) in the following equation? 5978 + 6134 + 7014 = ? options: A)19226 B)16226 C)19216 D)19126 E)None of these SOLUTION:? = 5978 + 6134 + 7014 = 19126 Answer D #### D QUESTION:If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is? options: A)20 B)98 C)66 D)54 E)12 SOLUTION:Let C.P. of each article be Re. 1. Then, C.P. of 50 articles = Rs. 50; S.P. of 50 articles = Rs. 40. Loss % = 10/50 * 100 = 20% Answer: A #### A QUESTION:A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system correct answer D #### D QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 20 years = (20 + 20) years =40 years. Answer : C #### C QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 7*1+1 (7*1+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:Three faces of a fair die are Yellow, two faces red and two blue.The die is tossed three times. The probability that the colours, yellow, red and blue appear in the first, second and third tosses respectively is options: A)1/36 B)1/18 C)1/32 D)1/37 E)None of these SOLUTION:Probability of getting yellow color = P(Y) = 3/6 = 1/2 Probability of getting red color = P(R) = 2/6 = 1/3 Probability of getting blue color = P(B) = 2/6=1/3 So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/2 x 1/3 x 1/3 = 1/18 ANSWER:B #### B QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: options: A)27% B)87% C)15% D)66% E)88% SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900. Face value = Rs. (50 x 20) = Rs. 1000. Dividend = Rs. 27 x 1000 = Rs. 135. 2 100 Interest obtained = 135 x 100 % = 15% 900 View Answer Discuss in Forum Answer: C #### C QUESTION:Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income? options: A)$40,000 B)$56,000 C)$64,000 D)$66,667 E)$80,000 SOLUTION:Equation is correct, so math must be a problem. 0.12*40,000+0.2*(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000. Answer: B. #### B QUESTION:For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution? options: A)12 B)9 C)3 D)7.5 E)2.5 SOLUTION:we have 2 equations 1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36 2. kx + 12y = 30 substract 1-2, we get (9-K)x = 6 i.e. x = 6/(9-k) then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B #### B QUESTION:In a sports club with 27 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence, (17-x)+(19-x)+x+2=27 38-2x+x=27 38-x=27 x=11 So 8 members play both badminton and tennis. E #### E QUESTION:A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? options: A)600 B)2877 C)208 D)1882 E)191 SOLUTION:Explanation: Cost price = Rs.500 profit = 20% of 500 = Rs.100 Selling price = Cost price + Profit = 500 + 100 = 600 Answer:A #### A QUESTION:Set A = {1, 2, 3, 4, 5, 6, q} Which of the following possible values for q would cause Set A to have the smallest standard deviation? options: A) 1 B) 2.5 C) 3 D) 3.5 E) 7 SOLUTION:I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice. Answer D. #### D QUESTION:The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is ? options: A)87 B)95 C)99 D)100 E)103 SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: C. #### C QUESTION:Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 12:10 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of water to milk ? options: A)547/398 B)392/598 C)598/392 D)210/279 E)398/547 SOLUTION:12:10=>12x+10x=22x 2:1=>2y+1y=3y 3:2=>3z+2z=5z 22x=3y=5z Take LCM of 22,3,5=330 Or simply; x=15 y=110 z=66 So, Ratio of Water:Milk=(10x+y+2z)/(12x+2y+3z)=392/598 Ans:B #### B QUESTION:Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? options: A)35 B)36 C)37 D)43 E)39 SOLUTION:James worked for 41 hours hence he earned 40*x+5*2x=50x dollars; We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours. Answer: D. #### D QUESTION:A can complete a work in 12days and B can do the same work in 8days. If A after doing 2days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4 1/2days C)6 1/2 days D)7 3/4days E)10days SOLUTION:The required answer = (12-2)*8 / 12 = 80/12 = 6 1/2days Answer is C #### C QUESTION:The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is: options: A)89.25 km/hr. B)77 km/hr. C)90.25 km/hr. D)94.25 km/hr. E)96.25 km/hr. SOLUTION:Let the speed of two bullet trains be 7x and 8x km/hr. Then, 8x = (440/5) = 88 x = (88/8) = 11 Hence, speed of first bullet train = (7 x 11) km/hr = 77 km/hr. B #### B QUESTION:Carol spends 1/4 of her savings on a stereo and 1/2 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? options: A)1/4 B)2/7 C)5/12 D)3/8 E)7/12 SOLUTION:Total Savings = S Amount spent on stereo = (1/4)S Amount spent on television = (1-1/2)(1/4)S = (1/2)*(1/4)*S = (1/8)S (Stereo + TV)/Total Savings = S(1/4 + 1/8)/S = 3/8 Answer: D #### D QUESTION:The sale price sarees listed for Rs.400 after successive discount is 15% and 5% is? options: A)338 B)323 C)342 D)882 E)212 SOLUTION:400*(85/100)*(95/100) = 323 Answer: B #### B QUESTION:A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 kmph B)7.5 kmph C)8 kmph D)9 kmph E)4 kmph SOLUTION:US = 20 DS = 35 M = (35 - 20)/2 = 7.5 Answer:B #### B QUESTION:A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 90 minutes later? options: A)2(10^5) B)9(10^5) C)(2^9)(10^5) D)(10^9)(10^5) E)(10^5)^9 SOLUTION:Every 10 minutes, the population is double the previous population. In 90 minutes, the population doubles 9 times. The population then is 2^9*10^5. The answer is C. #### C QUESTION:A train 350 m long, running with a speed of 63 km/hr will pass a tree in? options: A)15 sec B)16 sec C)18 sec D)20 sec E)25 sec SOLUTION:Speed = 63 * 5/18 = 35/2 m/sec Time taken = 350 * 2/35 = 20 sec ANSWER: D #### D QUESTION:The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ? options: A)20 years B)21 years C)22 years D)34 years E)24 years SOLUTION:The average age of the 5 members is 20 years => The sum of the ages of the 5 members is 20*5 = 100 years Once the new member joins, the average age becomes 24 years. Let the age of the new member be x. Then (110+x)/6 = 24 => x = 34 years Answer D #### D QUESTION:Dacid obtained 45, 35, 52, 47 and 55 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)79 B)99 C)47 D)89 E)45 SOLUTION:Average = (45+35+ 52+ 47+55)/5 = 234/5 = 47. Answer:C #### C QUESTION:One student to pass the subject as probability 1/4. another man to get driving licence and student passed subject probability 1/6. find the probability man get driving licence. options: A)1/3 B)2/3 C)4/3 D)5/3 E)1/4 SOLUTION:Let the probability of the man get driving licence is x. so, 1/4 * x = 1/6 x = 2/3. ANSWER:B #### B QUESTION:A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? options: A)63 B)336 C)567 D)3024 E)5040 SOLUTION:All the cordinates are integer hence, possible AT values are {-1,0}, {-1,1} ....{-1,7}: 8 ways .... {7,-1}, {7,0} ......{7,6}: 8 ways 9*8 ways = 72 for AC values can be {1,2}, {1,3} .... {1,7} : 6ways ...... {7,1}, {7,2} ..... {7,6} : 6 ways 7*6 = 42 Total = 72 * 42 = 3024 hence D #### D QUESTION:Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24 options: A)22 B)62 C)28 D)16 E)11 SOLUTION:Answer:B #### B QUESTION:6x − 12 = 6y 5y + 5x = 10 Which of the following is the number of solutions to the system of equations shown above? options: A)More than three B)Exactly three C)Exactly two D)Exactly one E)None SOLUTION:6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 5y + 5x = 10 =>x + y = 2 -- 2 From equation 1 and 2 , we get 2x = 4 => x=2 y=0 Therefore , the given system will have Exactly one solution D #### D QUESTION:Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm. options: A)221 cm2 B)211 cm2 C)231 cm2 D)236 cm2 E)241 cm2 SOLUTION:Given: length = 17 cm, breadth = 13 cm Perimeter of rectangle = 2 (length + breadth) = 2 (17 + 13) cm = 2 × 30 cm = 60 cm We know that the area of rectangle = length × breadth = (17 × 13) cm22 = 221 cm2 ANSWER :A #### A QUESTION:Vijay bought 160 shirts at the rate of Rs. 220 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? options: A)s.225 B)s.288 C)s.485 D)s.279 E)s.282 SOLUTION:Total CP per shirt = 220 + 1400/160 + 1.75 + 320/160 = Rs. 232.5 SP = CP[(100 + profit%)/100] = 232.5 * [(100 + 20)/100] = Rs.279. Answer:D #### D QUESTION:The average of two numbers is P. If one number is Q, then the other number is options: A)2Q B)2P C)P - Q D)2P-Q E)None of these SOLUTION:Explanation : Let the other number be x, According to the question, => ( x + Q ) / 2 = P. => x + Q = 2P. => x = 2P - Q. Hence, the required number is 2P - Q. Answer : D #### D QUESTION:In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 1 people every two seconds. Estimate the size of the population net increase that occurs in one day. options: A)32,300 B)172,800 C)468,830 D)338,200 E)259,200 SOLUTION:Every 2 seconds, 6 persons are added (7-1). Every second 3 persons are added. In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds. 86400 * 3 = 259200 Option E #### E QUESTION:A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5% options: A)Rs 6.56 B)Rs 9.56 C)Rs 10.56 D)Rs 11.56 E)None of these SOLUTION:Explanation: 80 : 5 = 105 : x x= (5×105/80) = Rs 6.56 Option A #### A QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt? options: A)16.67 B)30 C)50 D)60.33 E)150 SOLUTION:let x=ounces of 60% salt solution to be added .2*50+.6x=.5(50+x) x=150 Answer E #### E QUESTION:A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting? options: A)12 B)22 1/2 C)37 1/2 D)88 E)80 SOLUTION:(16/2) ( 2+3) * 2 = 80=E #### E QUESTION:There are 6 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)3/5 D)4/9 E)2/3 SOLUTION:total 10 from take one. 10c1=10 red 6 from one 6c1=6 6/10= 3/5 ANSWER:C #### C QUESTION:Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L options: A)1/3. B)1/2. C)3. D)2. E)6. SOLUTION:Difference = Average H - L = (H + L)/2, Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2 C #### C QUESTION:A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number? options: A)297 B)187 C)278 D)200 E)267 SOLUTION:25 + 25 = 50 25% ------ 50 100% ----- ? => 200 Answer:D #### D QUESTION:Which of the following points is closest to line y=x options: A)(2, -1) B)(-2, -4) C)(-1, 1) D)(-2, 1) E)(-2, 0) SOLUTION:Attachment: m12-20.pngAs you can see point (-2, -4) is the closest to line y=x. Answer: B. #### B QUESTION:A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? options: A)1/3 B)2by3 C)2/5 D)3/5 E)4/5 SOLUTION:Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol. Let x ml be the amount removed ---> total alcohol left = 4-0.4x New quantity of whiskey added = x ml out of which 0.19 is the alcohol. Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml. Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3. Hence, B is the correct answer. #### B QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7 SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144. Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520. P = favorable/total = 2520/144 = 35/2. Answer: B. #### B <<<Examples ends QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these SOLUTION:Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: C #### C QUESTION:How many integers between 323,700 and 458,600 have tens digit 1 and units digit 3? options: A)10,300 B)10,030 C)1,353 D)1,352 E)1,349 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ... The difference between 323,700 and 458,600 is 458,600-323,700=134,900 - one number per each hundred gives 134,900/100=1,349 numbers. Answer: E. #### E QUESTION:The price of a T.V. set worth Rs. 30000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)22678 B)26699 C)29000 D)19000 E)26711 SOLUTION:Money paid in cash = Rs. 1000 Balance payment = (30000 - 1000) = Rs. 29000 Answer: C #### C QUESTION:The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is options: A)35.22 B)36.12 C)36.22 D)36.42 E)None SOLUTION:Solution Correct sum = (36x50+44-23) = 1821. ∴ Correct mean = 1821 / 50 = 36.42. Answer D #### D QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 4 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.22 B) 0.44 C) 0.55 D) 22 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/12*33 = 22 cents. Answer: D. #### D QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)63 B)30 C)36 D)45 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 14) = (x + 7) or x = 21. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63. Answer: A #### A QUESTION:There are 4 copies of 5 different jeans. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different jeans.20!/((4!)^5) Answer - C #### C QUESTION:If each side of a square is increased by 20%, find the percentage change in its area? options: A)40% B)42% C)46% D)44% E)38% SOLUTION:let each side of the square be a , then area = a x a New side = 120a / 100 = 6a / 5 New area =(6a x 6a) / (5 x 5) = (36a²/25) increased area== (36a²/25) - a² Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44% answer :D #### D QUESTION:If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute). options: A)2 hours 2 minutes B)3 hours 5 minutes C)4 hours 6minutes D)5 hours 7 minutes E)7 hours 9 minutes SOLUTION:In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill 1/5 + 1/8 = 13 / 40 of a tank Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving (13/40) t = 1 t = 40 / 13 = 39/13 + 1/13 hours = 3 hours and (1/13)*60 minutes = 3 hours 5 minutes (rounded to the nearest minute) correct answer B #### B QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. options: A)220 B)222 C)223 D)224 E)225 SOLUTION:distance = speed x time Let time taken to travel the first half = x hr then time taken to travel the second half = (10 - x) hr Distance covered in the the first half = 21x Distance covered in the the second half = 24(10 - x) But distance covered in the the first half = Distance covered in the the second half => 21x = 24(10 - x) => 21x = 240 - 24x => 45x = 240 => 9x = 48 => 3x = 16 ⇒x=16/3 Hence Distance covered in the the first half = 21x=21×16/3=7×16=112 km Total distance = 2×112=224 km Answer is D. #### D QUESTION:If r and s are positive integers and r-s=6, which of the following has the greatest value M? options: A)2r B)2s C)r +s D)2r-s E)2s-r SOLUTION:You can answer this question by using Number Properties and logic or by TESTing VALUES. We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value. IF.... R = 8 S = 2 Answer A: 2R = 2(8) = 16 Answer B: 2S = 2(2) = 4 Answer C: R+S = 8+2 = 10 Answer D: 2R-S = 2(8) - 2 = 14 Answer E: 2S-R = 2(2) - 8 = -4 Final Answer: A #### A QUESTION:Find the odd man out 2, 5, 10, 17, 26, 37, 50, 64 options: A)50 B)26 C)64 D)27 E)17 SOLUTION:Difference is series of ODD numbers 2+3 = 5 5+5 =10 10+7=17 17+9=26 26+11=37 37+13=50 50+15=65 ANSWER:C #### C QUESTION:Three different containers contain 496 litres, 403 litres and 713 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ? options: A)29 litres B)31 litres C)35 litres D)19 litres E)26 litres SOLUTION:M1 = 496 litres M2 = 403 litres M3 = 713 litres Required measurement = H.C.F. of M1,M2,M3 = 31 litres Answer is B #### B QUESTION:There are 9 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played? options: A)24 B)25 C)28 D)32 E)36 SOLUTION:9C2 = 36 The answer is E #### E QUESTION:A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work? options: A)6 days B)2 days C)4 4/5 days D)3 days E)9 days SOLUTION:Work done by A in 2 days = 2/10 = 1/5 Remaining work = 4/5 Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6 Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days. Answer: C #### C QUESTION:In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:If 0.6 : x :: 5 : 8, then x is equal to: options: A)A)0.96 B)B)1.2 C)C)1.25 D)D)1.3 E)E)0.8 SOLUTION:(x * 5) = (0.6 * 8) x = 4.8/5 x = 0.96 Answer = A #### A QUESTION:The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y? options: A)7/9 B)14/9 C)7/18 D)11/13 E)It Cannot Be Determined SOLUTION:Ratio = 7k/9k = 7/9, 14/18, etc. v and y are increased by 4 --> (7k + 4)/(9k + 4) New ratio can be 11/13, 18/22, etc. Answer: E #### E QUESTION:After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day? options: A)$1.25 million B)$80,000 C)$750,000 D)$27,000 E)$10,000 SOLUTION:Let sales in previous month = X 1.25 X=2,000,000 5/4 X= 2,000,000 ..........> X=2,400,000 sales per day= 2,400,000/30= less than 80,000 Answer:B #### B QUESTION:If 9^y = 3^14, what is y? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:9^y = 3^2y = 3^14 2y=14 y = 7 The answer is E. #### E QUESTION:James took a 3-hour bike ride. In the second hour he traveled 6 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride? options: A)54.0 B)54.9 C)18.5 D)57.0 E)63.0 SOLUTION:Let the distance travelled in the first hour be x. Thus, 1.2x = 6, x = 5. Now, the distance travelled in the 3rd hour = 6+1/4∗6=7.5 The only option ending with a 0.5 in the decimal place is C. ANSWER:C #### C QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:If 4a = 16b and 8b = 13c, Find a:b:c? options: A)52:13:8 B)13:7:52 C)7:13:52 D)7:13:54 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (8b = 13c ==> b/c = 13/8) ==> a:b = 16:4 and b:c = 13:8 a:b:c = 52:13:8 Answer: Option A #### A QUESTION:At a game of billiards,A can give B 15 points in 60 and A can give C 20 points in 60.How many points can B give C in a game of 90 ? options: A)30 points B)20 points C)10 points D)12 points E)None of these SOLUTION:Solution A : B = 60 : 45 and A : C = 60 : 40. ∴ B/C =( B/A x A/C) = (45/60 x 60/40) = 45/40 =90/80= 90 : 80 ∴ B can give C 10 points in a game of 90. Answer C #### C QUESTION:Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet? options: A) On the Columbia side, 4 miles away from the bridge B) On the Sumter side, 6 miles away from the bridge C) On the Columbia side, 6 miles away from the bridge D) On the Sumter side, 4 miles away from the bridge E) On the bridge SOLUTION:Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location. In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same. Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle. Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate. The correct answer is (E). #### E QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:A trader bought a car at 30% discount on its original price. He sold it at a 50% increase on the price he bought it. What percent of profit did he make on the original price? options: A)7% B)62% C)12% D)19% E)5% SOLUTION:Original price = 100 CP = 70 S = 70*(150/100) = 105 100 - 105= 5% Answer: E #### E QUESTION:John has taken four (4) tests that have an average of 81. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade? options: A)87 B)90 C)92 D)94 E)99 SOLUTION:87-81=6*4=24 points 2*87=174 174+24=198 points to be scored in the 2 tests. Avg of 2 tests = 198/2=99 Answer: E Traditional Method: Total scored till now 81*4=324 Total score to avg 87 in 6 tests = 87*6=522 Total to be scored on 2 tests = 522-324=198 Avg on 2 tests = 198/2 = 99 Answer E #### E QUESTION:If P represents the product of the first 13 positive integers, which of the following must be true? I. P is an odd number II. P is a multiple of 24 III. P is a multiple of 23 options: A)I only B)II only C)III only D)None of the above E)All of the above SOLUTION:The correct answer is B. #### B QUESTION:If the product of 2 integers is negative, at most how many of the integers can be negative? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The product of 2 integers is negative Thus an odd number of integers need to be negative to have a negative product We are asked at most how many are required. So, the highest odd integer before 6,i.e. 1 Correct Option : A #### A QUESTION:. A car covers a distance of 390 km in 4 hours. Find its speed? options: A)104 B)55 C)66 D)98 E)100 SOLUTION:390/4 = 98 kmph Answer: D #### D QUESTION:2+2+2²+2³ ... +2^9 options: A)2^9 B)2^10 C)2^16 D)2^35 E)2^37 SOLUTION:2+2=2^2 2^2+2^2=(2^2)*(1+1)=2^3 2^3+2^3=(2^3)*(1+1)=2^4 so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10 Answer B #### B QUESTION:Which of the following inequalities is equivalent to −1 < x < 5? options: A)|x - 1| < 7 B)|x + 2| < 3 C)|x + 3| < 5 D)|x - 2| < 3 E)None of the above SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -1 < x < 5, let's say by adding y to this inequality we will get into the above format -1+y < x+y < 5+y Now, to move this into the mod format, we need to have (-1+y) + (5+y) = 0 => y = -2 Thus, -3< x-2 < 3 => |x-2| < 3. Hence, answer is D #### D QUESTION:Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next? options: A)4.7 B)4.5 C)6.7 D)8.9 E)9.2 SOLUTION:In this simple addition series, each number increases by 0.8. ANSWER A #### A QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads? options: A)1 B)2 C)8 D)31 E)30 SOLUTION:Total outcome is 2^3 = 8 Favourable cases = H_ H The second place can be occupied by either H or T There are 2^1 =2 ways that can be done. Hence, the correct option is B #### B QUESTION:Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops? options: A)white − wheat − wheat B)wheat − wheat − rye C)rye − white− wheat D)rye − rye − rye E)rye − rye − white SOLUTION:In a single round Lucy drops 6 morsels. Remainder (2000/6) = 2 Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated Answer: A #### A QUESTION:A and B together have Sterling 1250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)Sterling 460 B)Sterling 484 C)Sterling 500 D)Sterling 664 E)None SOLUTION:Explanation: 4/15A = 2/5B A = (2/5 x 15/4)B A = 3/2 B A/B = 3/2 A : B = 3 : 2. B's share = Sterling (1250 x 2/5) = Sterling 500. Answer: Option C #### C QUESTION:A certain galaxy is known to comprise approximately 5 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun? options: A)800 B)1,250 C)8,000 D)12,000 E)10,000 SOLUTION:Total no. of stars on galaxy = 5 * 10^11 Of every 50 million stars, 1 is larger than sun. 1 million = 10^6 therofore, 50 million = 50 * 10^6 total no. of stars larger than sun = 5 * 10^11 / 50 * 10^6 =50 * 10^3 /5 = 10000 therefore answer is E #### E QUESTION:If the length of an edge of cube M is thrice the length of an edge of cube N, what is the ratio of the volume of cube N to the volume of cube M? options: A)2/13 B)1/27 C)1/5 D)1/9 E)1/8 SOLUTION:The length of cube N = 1; The length of cube M = 3; The ratio of the volume of cube N to the volume of cube M = 1^3/3^3 = 1/27 Answer : B #### B QUESTION:In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent X of his family’s total income? options: A) 15% B) 17% C) 24% D) 30% E) 33% SOLUTION:Lets suppose the Total Family income in Feb = 100x Wilson's earning in Feb = 40% of 100x = 40x Earnings of remaining family in Feb = 100x - 40x = 60x Wilson's earning in March = 75% of Wilson's Feb earnings = 75% of 40x = 30x Earnings of remaining family in March = Earnings of remaining family in Feb = 60x Thus Wilson's earning as % of Total family income in March X= 30x/ (30+60)x = 30x/90x = 33.33% Thus Answer is E #### E QUESTION:If x is negative and y is positive, which of the following cannot be positive? options: A)x/y B)-x*y C)-x/y D)x^2+y E)x^6+y SOLUTION:- /+ = - x/y is negative. Answer : A #### A QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)*28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? options: A)2100 B)1800 C)1245 D)3210 E)4521 SOLUTION:5 subjects can be arranged in 6 periods in 6P5 ways. Any of the 5 subjects can be organized in the remaining period (5C1 ways). Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting. Total number of arrangements = 6P5× 5C1 /2!=1800 Ans: B #### B QUESTION:If 6 (A's capital) = 8 (B's capital) = 16 (C's capital). Then the ratio of their capitals is? options: A)8:15:16 B)8:15:68 C)8:6:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 16 C A:B:C = 1/6:1/8:1/16 = 8:6:3 Answer: C #### C QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true? options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6 SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) . ans B #### B QUESTION:Anitha had 80 currency notes in all, some of which are of Rs 95 denomination and the remaining of Rs 45 denomination. The total amount of all these currency notes was Rs. 4000. How much amount (in Rs) did she have in the denomination of Rs 45? options: A)3500 B)72 C)2000 D)3000 E)4000 SOLUTION:Let the number of 45-rupee notes = x Then, the number of 95-rupee notes = (80 – x) 45x + 95(80 – x) = 4000 or x + 2(80 – x) = 95 or x = 72. ANSWER:B #### B QUESTION:Find the value of 72519 x 9999 = m. options: A)233243413 B)354545451 C)343435451 D)565656767 E)725117481 SOLUTION:72519 x 9999 = 72519 x (10000 - 1) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 E #### E QUESTION:An airplane flies along the four sides of a square field at the speeds of 200, 400, 600 and 800 km/h. The average speed of the plane around the field in km/h is options: A)384 B)400 C)500 D)284 E)None of these SOLUTION:Explanation : Let each side of the square field be x km. So, average speed of the plane = 4x/((x/800)+(x/600)+(x/400)+(x/200)) = (4*2400)/(3+4+6+12) = 9600/25 = 384 Answer : A #### A QUESTION:A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)95 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)56 km/hr SOLUTION:Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr. ANSWER: A #### A QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y? options: A)(320 - y)/(5x) B)(y +220)/(5x) C)5(80 - y)/(4x) D)(y + 400)/(4x) E)(4y + 320)/(5x) SOLUTION:Ans B Plug some numbers Let y = 40 houses and x = 20 then they painted 20 houses per week as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20 = 65 houses per week total time they took = (40/20) + (40/65) = 2.6 weeks Putting the values of x and y in equation B (y +220)/(5x) = (40+220)/5*20 = 260/100 = 2.6 #### B QUESTION:In Town X, 120 percent of the population are employed, and 80 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)33% D)40% E)52% SOLUTION:Total employed people 12%, out of which 80 are employed males, hence 40% are employed females. (employed females)/(total employed people)=40/120=1/3=33% Answer: C. #### C QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate? options: A)Cannot be determined B)43 C)3 D)6 E)10 SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position. Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A QUESTION:The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year? options: A)40 B)42 C)45 D)48 E)54 SOLUTION:1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer)) 2ndyear : 1-2 (age), we take age = 1 3rd year : 2-3 (age), we take age = 2 4th year : 3-4 (age), we take age = 3 5th year : 4-5 (age), we take age = 4 6th year : 5-6 (age), we take age = 5 Thus for the 5th year = 50, 6th year = 50-5 = 45. The correct answer is C. #### C QUESTION:Two hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:Two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have ALL even (being multiple of 8) Probability of number selected being odd = Total Odd Numbers / Total available numbers Probability = 100/500 = 0.2 = 20% Answer: Option A #### A QUESTION:A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ? options: A)5 sec B)6 sec C)7 sec D)10 sec E)None SOLUTION:Solution Speed of train relative to man =(60+6) km/hr= 66km/hr =(66x5/18) m/sec =(55/3) m/sec ∴ Time taken to pass the man = (110x3/55)sec = 6sec Answer B #### B QUESTION:Two letters from the word KYANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant? options: A)14/27 B)15/28 C)27/28 D)16/28 E)30/28 SOLUTION:There are 6 consonants and 2 vowels in KYANTKAR . probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels) Probability of both vowels = 2C2/8C2 = 1/28 So,Answer is 1 - 1/28 = 27/28 Answer : C #### C QUESTION:A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in options: A)18 sec B)12 sec C)15 sec D)20 sec E)13.5 sec SOLUTION:Length of train = 12 × 15 = 180 m. Then, speed of train = 180⁄18 = 10 m/s Now, length of train = 9 × 15 = 135m ∴ Required time = 135⁄10 = 13.5 sec. Answer E #### E QUESTION:A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: options: A)4 mph B)2.5 mph C)3 mph D)2 mph E)None of these SOLUTION:Explanation : Speed of the boat in still water = 10 mph Let speed of the stream be x mph Then, speed downstream = (10+x) mph speed upstream = (10-x) mph Time taken to travel 36 miles upstream - Time taken to travel 36 miles downstream = 90/60 hours =>36/(10−x) − 36/(10+x) = 3/2 =>12/(10−x) − 12/(10+x) = 1/2 =>24(10 + x) − 24(10 − x) = (10 + x)(10 − x) =>240 + 24x − 240 + 24x = (100−x2) =>48x = 100 − x2 =>x2 + 48x − 100 =0 =>(x+50)(x−2)=0 => x = -50 or 2. Answer : Option D #### D QUESTION:The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is options: A)3x + y + 15 = 0 B)y + 3x - 1 = 0 C)-3x + y - 16.5 = 0 D)-2x - y - 7 = 0 E)-3x + y + 13.5 = 0 SOLUTION:The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant). In options B , if you put x = -5, you get -ve value for y co-ordinate. Answer must be (B) #### B QUESTION:A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area T covered by the two roads? options: A)400 B)1550 C)1575 D)1600 E)1625 SOLUTION:Area Covered by Road Along the Length = 5*200 = 1000 Square Meter Area Covered by Road Along the Width = 5*120 = 600 Square Meter Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 5*5 = 25 Total Area of the Roads T= 1000+600-25 = 1575 Answer: option C #### C QUESTION:A tank can supply water to a village for 30 days. If a leak at the bottom of the tank drains out 15 liters per day, the supply lasts for 20 days only. For how many days will the supply last if the leak drains out 20 liters per day? options: A)12 B)14 C)15 D)16 E)18 SOLUTION:Losing 15 liters per day results in a loss of 300 liters in 20 days. So, those 300 liters were for 10 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*30 = 900 liters. Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 900/50 = 18 days. The answer is E. #### E QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? options: A)3 B)5 C)4 D)2 E)6 SOLUTION:A rate = 1/8 B rate = 1/24 (A+B) rate = (1/8)+(1/24) = 1/6 A & B finish the work in 6days correct option is E #### E QUESTION:There are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated? options: A)120. B)132. C)141 D)154. E)166. SOLUTION:Let the foam generators capacity be - A = 12 lit/hr B = 12 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate 42 + 21 => 63 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 12 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 60 litres {2 (12+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 12 => 18 litres So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C) #### C QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5 options: A)134 B)136 C)140 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:A family pays $700 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? options: A)$1,000 B)$1,200 C)$1,500 D)$1,800 E)$2,200 SOLUTION:Assuming the medical expenses are $1000 or more, the family pays $700 + $400 = $1100. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $500 when the medical expenses are $1500. The answer is C. #### C QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 6? options: A)1/4 B)5/36 C)2/11 D)3/13 E)1/5 SOLUTION:n(S) = 6*6 = 36 E = {(1,5),(2,4),(3,3),(4,2),(5,1)} Probability = 5/36 Answer is B #### B QUESTION:A 180 meter long train crosses a man standing on the platform in 9 sec. What is the speed of the train? options: A)72 B)108 C)1266 D)188 E)211 SOLUTION:S = 180/9 * 18/5 = 72 kmph Answer: A #### A QUESTION:The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year? options: A)12300 B)12350 C)12000 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 120/100 = 12000 C #### C QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)25 SOLUTION:Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER IS A #### A QUESTION:if remainder is 8 , quotient is 43 and dividend is 997 then what is divisor ? options: A)21 B)20 C)23 D)27 E)31 SOLUTION:we know dividend = divisor * quotient + remainder===> 997 = divisor * 43 + 8 =====> 989/43 = divisor ===> divisor = 23 Ans - C #### C QUESTION:Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? options: A)87 B)89 C)90 D)93 E)95 SOLUTION:Total score on 3 tests = 81*3 = 243 Jerry wants the average to be = 83 Hence total score on 4 tests should be = 83*4 = 332 Score required on the fourth test = 332 - 243 = 89 Option B #### B QUESTION:An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled options: A)50% B)40% C)33.5% D)37.5% E)None of these SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8 ∴ required% = 3A⁄ (8 × A) × 100 = 37.50% Answer D #### D QUESTION:Felix earned 30% more per month than Oscar. If Felix’s salary is decreased 10% and Oscar’s salary is increased by 10%, then Felix would be earning what percent more than Oscar? options: A)10% B)9.09% C)7% D)6.36% E)It cannot be determined from the information given. SOLUTION:the very first step requires taking some numbers for each.. ONE should be 100... it is easy to take 70 and 100 here.. but the BASE is 100 here, so the salary can be 100 and 130.. 100 increases 10% =110.. 130 decreases 10%=117.. so the increase is 7.. again the BASE is 110, so answer 7/110 * 100= 6.36% D without calculations, answer cannot be equal to or greater than 7, as 7 is on 110.. so D is the only one left ANSWER:D #### D QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:13 C)23:12 D)11:9 E)11:10 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only. A : B 8000*18 : (8000*8) + (4000*10) 144000 : 104000 A:B = 18:13 ANSWER:B #### B QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:Four hundred multiples of seven are chosen at random, and 100 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(400) / 500 = 40% The answer is C. #### C QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share twice, no apples were left.How many apples were there? options: A)62 B)63 C)64 D)65 E)66 SOLUTION:Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 6 times. So answer is (2^6)-1=63. ANSWER:B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)210m B)240m C)963m D)874m E)578m SOLUTION:Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B)240m #### B QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 14 years? options: A)30 B)34 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 14 years = (20 + 14) years =34 years. Answer : B #### B QUESTION:On a ferry, there are 27 cars and 13 trucks. The cars have an average mass of 1100 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1515.5 B)1616.5 C)1717.5 D)1818.5 E)1919.5 SOLUTION:The total mass of the vehicles is 27*1100+13*3000=68700 The average mass is 68700/40=1717.5 The answer is C. #### C QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/10 * 480 =48 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 48-68 =20>>> therfore answer is 20 greater A #### A QUESTION:If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)? options: A)85/365∗84/364 B)13/65∗13/64 C)1 - 85!/365! D)1 - {365!}/{280!(365^8^5)} E)1 - 85!/(365^8^5) SOLUTION:Probability(At Least 2 share a bday) = 1 - Probability(All 85 have distinct birthdays) total ways to pick 85 birthdays = 365^85 Ways to pick distinct 85 out of the 365 & distribute it to 85 people = C(365,85)*85! Hence Probability = 1−365!/280!36585 ANswer is D #### D QUESTION:When positive integer N is divided by positive integer P, the quotient is 20, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 2. What is the value of N? options: A)107 B)331 C)511 D)691 E)871 SOLUTION:N/P=10 7/P= 20P+7 N/(P+2)=15 2/(P+2)=15P+30+2 solving these two equations we get P=5 N= 107 answer is A. #### A QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue? options: A)33/95 B)33/91 C)33/94 D)33/16 E)33/17 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:B #### B QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A? options: A)240 B)288 C)266 D)216 E)123 SOLUTION:(3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 630 = 240 Answer: A #### A QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible? options: A)30 B)42 C)120 D)360 E)720 SOLUTION:5 people ,7 seats, only 2 can drive if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways since any one can drive total ways = 24 *2= 48 ways 4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways 48*15=720 ANSWER:E #### E QUESTION:In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is: options: A)24 B)26 C)42 D)46 E)48 SOLUTION:Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2. Sum of digits = x + (x + 2) = 2x + 2. (11x + 2)(2x + 2) = 144 22x2 + 26x - 140 = 0 11x2 + 13x - 70 = 0 (x - 2)(11x + 35) = 0 x = 2. Hence, required number = 11x + 2 = 24. Answer:A #### A QUESTION:In a manufacturing plant, it takes 48 machines 4 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders? options: A)3 B)6 C)8 D)9 E)12 SOLUTION:the choices give away the answer.. 48 machines take 4 hours to fill 8 standard orders.. in next eq we are doubling the machines from 48 to 72, but the work is not doubling(only 1 1/2 times), = 4*48/72*12/8 =4 Ans A #### A QUESTION:Find the median of the data 25, 37, 47, 18, 19, 26, 36. options: A)22 B)23 C)24 D)25 E)26 SOLUTION:Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47 Here, the number of observations is odd, i.e., 7. Therefore, median = (n + 1/2)th observation. = (7 + 1/2)th observation. = (8/2)th observation = 4th observation. 4th observation is 26. Therefore, median of the data is 26. ANSWER :E #### E QUESTION:2 friends A n B running up hill and then to get down length of road 440 yads A on his return journey met B going up at 20 yards from top if A has finished race 5 minute earlier than B then how much time A had taken to complete the race ? options: A)100 minute B)110 minute C)120 minute D)130 minute E)140 minute SOLUTION:total journey= 440*2=880 A meet B 20 yards from top in getting down it means he has covered 440+20=460 yards while B is 420 yards.so he is 40 yards ahead of B which is equals to 5 minute. so 40 yards in 5 min 880 yards will be in 5*880/(40)=110 minute ANSWER:B #### B QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/6. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)25. B)24. C)23. D)20. E)16. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 6,5 and 10 Lets take LCM of three balls 6,5 and 10 = 30. The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS. Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls. IMO option E is correct. #### E QUESTION:The ratio, by weight, of coffee to mate to water in a certain cup of coffee is 6:2:15. The coffee is altered so that the ratio of coffee to mate is halved while the ratio of coffee to water is doubled. If the altered coffee will contain 16 grams of mate, how many grams of water does it contain after alteration? options: A)12 B)15 C)30 D)60 E)100 SOLUTION:c:m:w = 6:2:15 new c:m = 1/2(6/2) = 3:2 new c:w = 2(6:15) = 12:15 = 4:5 so new m:c:w = 2:3 4:5 = 8:12:15 ( notice how i combined the two ratios by multiplication by 3 and 4 of respective ratios) m = 16 g Let T = total amount of c + m + w then 8 / (8+12+15)T = 16 x 35/8 = 70g then w = 15/35 x 70 = 30g Answer C #### C QUESTION:Divide Rs. 1300 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)346 B)368 C)375 D)337 E)325 SOLUTION:A+B+C = 1300 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1300 => 325 Answer:E #### E QUESTION:how many square are there between 2001....2300 I don't remember the exact series. options: A)1 B)4 C)2 D)3 E)5 SOLUTION:series was from 2001 to 2300 45^2=2025 46^2=2116 47^2=2209 48^2=2304 (so exclude 48) so ans is 3 (45,46 and 47) ANSWER:D #### D QUESTION:In the quadratic equation ax2 - x - 12 = 0, if the sum of two roots is 1, what is the product of the two roots? options: A)-12 B)-6 C)12 D)6 E)24 SOLUTION:Explanation: The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a). Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 1 and c = -12. we get, sum of the roots = 1 / a = 1 a = 1 Product of the roots = -12 / 1 =-12 ANSWER: A #### A QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $25. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet) options: A)9/(25xy) B)xy/225 C)225/(xy) D)225xy E)25xy/9 SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 9. The price per square yard is 25 / (xy/9) = 225/(xy). The answer is C. #### C QUESTION:Find the average of all numbers between 1 and 76 which are divisible by 5 options: A)40 B)20 C)25 D)30 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75)/15=600/15=40 Answer: Option A #### A QUESTION:9 friends went to a super market, and everyone decided to contribute equally to the total bill of $900. If one of the friends had a coupon for 10% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay? options: A)30 B)60 C)80 D)90 E)95 SOLUTION:At the non-discounted price, each friend would pay $100, as $900 divided by 9 friends is $100 per friend. But if the bill is 10% off, then each friend would pay 10% less. 10% of $100 is $10, so each friend saves $10 and pays the remaining $90 CORRECT OPTION:OPTION D #### D QUESTION:In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes? options: A)25 B)43 C)64 D)78 E)98 SOLUTION:Ans.(C) Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways #### C QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 52 years now, the son's age five years back was? options: A)16 years B)14 years C)18 years D)21 years E)15 years SOLUTION:Let the son's present age be x years. Then, (52 - x) = x 2x = 52 => x = 26 Son's age 5 years back = (26 - 5) = 21 years. Answer: D #### D QUESTION:A family has two children. find the probability that both the children are girls given that at least one of them is a girl? options: A)1/3 B)1/5 C)1/7 D)1/9 E)2/3 SOLUTION:Let b stand for boy and g for girl. The sample space of the experiment is S = {(g, g), (g, b), (b, g), (b, b)} Let E and F denote the following events : E : ‘both the children are girls’ F : ‘at least one of the child is a girl’ Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)} Now E n F = {(g,g)} Thus P(F) = 3/4 and P (E n F )= 1/4 Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3 A) #### A QUESTION:The workforce of Company Samsung is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers? options: A)180 B)170 C)160 D)150 E)145 SOLUTION:let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added 06x/(0.4x +20) = 50/100 or 60x = 50*( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125 total worker = 125+20= 145 E #### E QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these SOLUTION:Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.150 15x + 5x = Rs.150 X = 150/20 = 7.50 :. Cost of 1 pen = 5x = 5 x 7.50 = 37.50 :. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450 Answer: Option D #### D QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:Two whole numbers whose sum is 72 cannot be in the ratio options: A)3 : 4 B)3 : 5 C)4 : 5 D)5 : 7 E)None SOLUTION:Sol. The sum of the ratio terms must divide 72. So, the ratio cannot be 3 : 4. Answer A #### A QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:3^7+3^7+3^7=? options: A)a) 81^2 B)b) 81^4 C)c) 81^5 D)d) 81^6 E)e) 81^15 SOLUTION:The correct answer is A 81^2 #### A QUESTION:Evaluate: 20 - 12÷12×2 = options: A)A)4 B)B)8 C)C)12 D)D)16 E)E)20 SOLUTION:According to order of operations, 12÷12×2 (division and multiplication) is done first from left to right 12÷12×2 = 1 × 2 = 2 Hence 20 - 12÷12×2 = 20 - 12 = 8 correct answer is B) 8 #### B QUESTION:When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number? options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these SOLUTION:Let the first and the second numbers be x and y respect then y + 30% of x = 140% of y or, y + 0.3x = 1.4y or, 0.3x = 0.4y ∴ x : y = 0.4 : 0.3 = 4 : 3 Answer B #### B QUESTION:For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N? options: A)8/5 B)5/2 C)3 D)33/25 E)4 SOLUTION:Let monthly salary for each of the 11 months except December was x, then 11x*1/10 + Nx*1/3 = 1/8(11x + Nx); 11/10 + N/3 = 1/8(11 + N) 33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66 N = 66/50=33/25 Answer: D. #### D QUESTION:What least no. must be subtracted from 5026 so that remaining no.is divisible by 5? options: A)3 B)4 C)5 D)6 E)1 SOLUTION:Explanation: On dividing 5026 by 5 we get the remainder 1, so 1 should be subtracted Option E #### E QUESTION:what is next number in sequence 212 427 303 336 394 ? options: A)123 B)345 C)560 D)567 E)245 SOLUTION:E 245 space them properly as 21 24 27 30 33 36 39 42 45 ? #### E QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good. options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980 SOLUTION:Let actual price was 100. After three successive discount this will become, 100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4 Now Compare, 68.4 = 6400 1 = 6400/68.4 100 = (6400*100)/68.4 = Rs. 9357. Answer: Option D #### D QUESTION:he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)10 D)19 E)8 SOLUTION:Average of 20 numbers = 0. Sum of 20 numbers (0 x 20) = 0. It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a). Answer: Option D #### D QUESTION:The income tax in country X is 8% of any income up to $5000. For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? options: A)$10,500 B)$11,000 C)$13,000 D)$13,500 E)$14,000 SOLUTION:Given : For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? for first 5000 , 8% tax then we get 400$ as tax. Now Perry paid 950$ tax... we need to check which option is going to yield 550$ on the remaining amount. A. $10,500 - 5000 = 5500 , then we get 10% tax , we get 550$... ( $10,500 - 5000 - here already for 5000$ we have calculated the tax and we need to tally for the remaining amount) 550+400 = 950$...hence this is the option. ANSWER :option A. #### A QUESTION:For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.988] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ? options: A)0 B)1 C)27 D)54 E)Cannot be determined SOLUTION:It cannot be determined.As we do not know the actual value of K. however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer K=[lCM of 80 and 45] * (any integer) for value of k(60) * any integer unit value will be always zero . A #### A QUESTION:Marie has 248 $ in her account of the bank. She has to buy presents for her 7 children and wants to distribute the money fairly. How much he will once have the money shared fairly? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(248$ / 7children) = 35.42 Took the lowest number = 35 * 7 children = $245 $248 - $245 = staying $3 Correct option: C) 3$ #### C QUESTION:What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-99)*(50-100)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour? options: A)15 kmph B)5 kmph C)10 kmph D)Data inadequate E)None of these SOLUTION:Here downstream speed = 15 km/hr and upstream speed = 5 km/hr ∴ Speed of the boat = 15+5/2=10km/h Answer C #### C QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:Find a a prime number the options below. options: A)78 B)80 C)81 D)82 E)83 SOLUTION:Clearly, 83 is a prime number. E #### E QUESTION:The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? options: A)c is not changed. B)c is halved. C)c is doubled. D)c is multiplied by 4. E)c is multiplied by 16. SOLUTION:a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. E c is multiplied by 16. #### E <<<Examples ends QUESTION:If 0.75: x :: 5:9, then x is equal to: options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *9) X=6.75/5 = 1.35 Answer: D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)11*10! B)9*8! C)8*7! D)7*6! E)6*5! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=11*10! Ans:A #### A QUESTION:P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days? options: A)12 days B)12.5 days C)13 days D)13.5 days E)15.5 days SOLUTION:Both together worked for 3 days. In 3 days , P can do = 3 x 1 18 = 1 6 th work In 3 days, Q can do = 3 x 1 15 = 1 5 th work In 3 days , work finished = 1 6 + 1 5 = 11 30 Balance work = 19 30 Balance work finished by Q => Time taken by Q to finish the balance work = 19 30 x 15 = 9.5 days The whole work was completed in 9.5 + 3 = 12.5 days B #### B QUESTION:On a certain day, mangrov farm harvested 4267 apples. If mangrov distributes his apples evenly across 7 different retail shops, how many apples would remain with him. Options: options: A)1 apple B)2 apple C)3 apple D)4 apple E)5 apple SOLUTION:This is equivalent to finding the first number that is divisible by 7 that occurs before 4267. In order to divide the sum in 7 parts, the amount must be divisible by 7 Divisibility rule of 7: The sum of the digits must be divisible by 7 Sum of digits of 4267 = 19 and 7 is divisible by 7. Hence, we need to remove 5 to this number for it to be divisible by 7 Correct Option:E #### E QUESTION:If the sum of the interior angles of a regular polygon measures up to 1440 degrees, then how many sides does the polygon have? options: A)10 B)16 C)12 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1440 180n - 360 = 1440 180n = 1800 n = 1800/180 = 10 ANSWER:A #### A QUESTION:If “*” is called “+”, “/” is called “*”, “-” is called “/”, “+” is called “-”. 240*80 / 60 + 40 / 10 = ? options: A)-2305 B)-2407 C)2509 D)-2101 E)None of these SOLUTION:Explanation: Given : 240*80 / 60 + 40 / 10 = ? Substituting the coded symbols for mathematical operations, we get, 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = -2407 ANSWER : B #### B QUESTION:A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees? options: A)$20,200 B)$20,500 C)$20,800 D)$21,000 E)$21,400 SOLUTION:average = 2(19000)+(21000)+3(22000) / 6 = $20,833 The answer is C. #### C QUESTION:Lionel left his house and walked towards Walt's house, 48 miles away. Four hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt? options: A)12 B)16 C)20 D)24 E)28 SOLUTION:In the first 4 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=4*3=12 miles. So, the distance between him and Walt was 48-12=36 miles when Walt left his house. Now, their combined rate to cover this distance was 3+6=9 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=36/9=4 hours. Total time that Lionel was walking is 4+4=8 hours, which means that he covered in that time interval distance=rate*time=3*8=24 miles. Answer: D. #### D QUESTION:If -2/(a - 6) = 4/(a + 4), then a = ? options: A)2/3 B)1/2 C)5/3 D)8/3 E)7/3 SOLUTION:Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve (a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ] - 2 (a + 4) = 4 (a - 6) a = 8/3 correct answer D #### D QUESTION:A sum of money when distributed among friends is in the ratio of 3:4:5, if the amount is the larger 3digit number divisible by 24, what is the share of 3rd person? options: A)400 B)410 C)420 D)430 E)440 SOLUTION:Largest 3 digit number divisible by 24= 984 So their shares are (984*3/12=246) , (984*4/12=328) , (984*5/12=410) ANSWER:B #### B QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12 SOLUTION:6a/100 = 12 a = 200 12b/100 = 6 b = 50 c = b/a = 50 / 200 = 1/4 The answer is C. #### C QUESTION:If x is an integer and y = 3x + 5, which of the following CANNOT be a divisor of y? options: A)4 B)12 C)2 D)7 E)6 SOLUTION:For any value of x, the expression 3x + 5 would never be divisible by 3,6,9...... onwards So answer = 6 = E #### E QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4 Total factors = (4+1)*(4+1) = 6*4 = 24 Answer C. #### C QUESTION:The speed of a boat in still water in 65 km/hr and the rate of current is 15 km/hr. The distance travelled downstream in 25 minutes is: options: A)55.55 km B)44.44 km C)33.33 km D)22.22 km E)11.11 km SOLUTION:Explanation: Speed downstream = (65 + 15) = 80 kmph Time = 25 minutes = 25/60 hour = 5/12 hour Distance travelled = Time × speed = (2/5)×80 = 33.33 km Answer: Option C #### C QUESTION:How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 15% solution? options: A)A)5.8 B)B)1.3 C)C)9.6 D)D)12.5 E)E)7.9 SOLUTION:Amount salt in 100kg solution = 10*100/100 = 10 kg Let x kg of pure salt be added then(10+x)/(100+x)=15/100 200+20x=300+3x 17x = 100 x = 5.8 Answer is A #### A QUESTION:A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes? options: A)100 m B)150 m C)190 m D)200 m E)220 m SOLUTION:Explanation: Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr Distance covered in 6 minutes =1/60X6km=1/10km=100m Distance between the thief and policeman = (200 – 100) m = 100 m. ANSWER IS A #### A QUESTION:A $84.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased? options: A)15% B)20% C)25% D)29% E)80% SOLUTION:Listed selling price of chair = 84.95 $ Discounted selling price of chair = 59.95 $ Discount = 84.95 - 59.95 = 25 $ % decrease in price of chair = (25/84.95) * 100% = 29 % approx Answer D #### D QUESTION:Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities? options: A)3 B)6 C)8 D)9 E)12 SOLUTION:3! = 6 M L S C M S L C L M S C L S M C S M L C S L M C She can visit the cities in any order. Number of ways of arranging the three cities is 3! = 6 ways. Hence B. #### B QUESTION:The total cost of 100 paper plates and 200 paper cups is $7.50 At the same rates what is the total cost of 20 of the plates and 40 of the cups? options: A)$.90 B)$1.00 C)$1.20 D)$1.50 E)$1.60 SOLUTION:U dont need to go through all this What u have with u is 100 P + 200 C = $7.50 Just divide the equation by 5 and you will get what u are looking for 20P + 40 C = $1.50 Therefore OA is D #### D QUESTION:A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:14 To be divisible by three the sum of the digits must be divisible by 3. Highest number made by these digits is 75 that is divisible. We count down the selections from there and see what is feasible. 75-yes 72 -yes 69 and 66 -no 63 - yes 60 -no 57, 54, and 51 -yes 48 - no 45 and 42 - yes 39 - no 36 - yes 33 and 30 - no 27, 24, and 21 - yes 18 -no 15 and 12 yes Correct answer is E. #### E QUESTION:How many factors of 60 are odd numbers greater than 1? options: A)3 B)4 C)5 D)3 E)7 SOLUTION:prime factors of 60 are 2^2,3^1,5^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,) = (1+1)(1+1)=4 since we need odd divisors other than 1 =>4-1 = 3 odd divisors D is the answer #### D QUESTION:Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?. options: A)Rs. 10000 B)Rs. 20000 C)Rs. 30000 D)Rs. 40000 E)Rs. 50000 SOLUTION:Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajeev’s share = Rs.(150000×2/6) = Rs. 50000 Answer E #### E QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 years B)9 years C)4 years D)6 years E)2 years SOLUTION:Explanation: 100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer: Option D #### D QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33*100 = 180% of 3.33. Answer: E. #### E QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? options: A)s.2.04 B)s.2.08 C)s.3.67 D)s.2.83 E)s.2.42 SOLUTION:C.I. when interest is compounded yearly = [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100] = 9000 * 26/25 * 51/50 = Rs. 9547.2 C.I. when interest is compounded half-yearly = [9000 * (1 + 2/100)2] = (9000 * 51/50 * 51/50 * 51/50) = Rs. 9550.87 Difference = (9550.87 - 9547.2) = Rs.3.67. Answer: C #### C QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is options: A)51:52 B)52:54 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (104% of x) / (108% of x) =104/108 =52/54 = 52:54. Answer: B #### B QUESTION:There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)410 B)490 C)493 D)455 E)445 SOLUTION:Answer: A. #### A QUESTION:How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ? options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters SOLUTION:Let x ltr water to be added 2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x))) 2=5%*(13+x)-------->x=27 Ans B #### B QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A QUESTION:A tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 9.33% D) 10.67% E) 11.7% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 700 gallons (7% of initial solution of 10,000 gallons) then sodium chloride is 700/7,500*100=~9.33% of the remaining solution of 7,500 gallons. Answer: C. #### C QUESTION:A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)75 ways B)87 ways C)66 ways D)108 ways E)21 ways SOLUTION:Explanation: The boy can select one trouser in five ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 5 * 15 = 75 ways. Answer: A #### A QUESTION:A certain office supply store stocks 2 sizes of self-stick notepads, each in 8 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible? options: A)6 B)8 C)16 D)124 E)128 SOLUTION:Notepads of the same color = 8 (we have 8 colors). As we have two sizes then total for the same color=8*2=16 Notepads of the different colors = 8C3=56 (we should choose 3 different colors out of 8). As we have two sizes then total for the different color=56*2=112 Total=112+16=128 Answer: E. #### E QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C? options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480 SOLUTION:Explanation : Amount of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400 Answer : Option D #### D QUESTION:Pavan travelled for 15 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:(X+2) is an even number and Y is a positive odd number. Which of the following expressions cannot be even? options: A)(X+2)Y B)(X+2)Y^2 C)(X+2)Y^3 D)Y^4 E)(X+2) SOLUTION:Y^4 D #### D QUESTION:If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream options: A)1.5kmph B)0.5kmph C)0.4kmph D)1.6kmph E)2.5kmph SOLUTION:Speed upstream = 32/4 = 8 kmph Speed down stream = 72/8 = 9 kmph Speed of stream = ½ (9-8) = 0.5kmph ANSWER:B #### B QUESTION:A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars? options: A)500 000 B)1 000 000 C)2 000 000 D)5 000 000 E)250 000 SOLUTION:The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is. 5+3+2 = 10 10/2 = X/100 000 5*100 000 = X 500 000 = X Answer: A) #### A QUESTION:A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 12 cups of tea are prepared, 6 in one way and 6 in other. Find the different possible ways of presenting these 12 cups to the expert. options: A)252 B)240 C)300 D)924 E)None SOLUTION:Solution: Since, there are 6 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is, [12!/(6!x 6!)]= 924 Answer: Option D #### D QUESTION:Two trains 200 m and 800 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? options: A)10.6 B)10.9 C)36 D)10.8 E)10.1 SOLUTION:Relative speed = 60 + 40 = 100 km/hr. = 100 * 5/18 = 250/9 m/sec. Distance covered in crossing each other = 200 + 800 = 1000 m. Required time = 1000 * 9/250 = 36 sec. Answer: C #### C QUESTION:If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: options: A)0 B)1 C)2 D)3 E)None of these SOLUTION:(5+1+7+A+3+2+4)=(22+A)MUST BE DIVISIBLE BY 3. HENCE THE SMALLEST WHOLE No. must be 2 ANSWER:B #### B QUESTION:In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/2 of the absentee ballets were thrown out and 1/2 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000 SOLUTION:1/2 * 1/2 (total absentee votes) = 1/4 (total votes)=1/4*12000=3000 Answer is B #### B QUESTION:Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3. options: A)131 B)197 C)207 D)219 E)227 SOLUTION:Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3. Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1) = 131. ANSWER:A #### A QUESTION:How many digits are in (8×10^10)(10×10^5)? options: A)17 B)25 C)26 D)27 E)28 SOLUTION:The question simplfies to (8×10^10)(10^6) => 8*10^16 => Will contain 16 zeros +1 digit 8 =>17 Ans A #### A QUESTION:The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ? options: A)12 B)14 C)15 D)16 E)20 SOLUTION:HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D #### D QUESTION:Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying science? options: A)52 B)65 C)115 D)158 E)168 SOLUTION:Given, boys and girls are in the ratio of 7 : 6, So, Number of boys = 7/13 x 390 = 210 Number of girls = 390 - 210 = 180 Students studying Arts and Science are in the ratio of 3 : 7, Number of students studying Arts = 3/10 x 390 = 117 Number of students studying Science = 390 - 117 = 273 Also boys and girls studying Arts are in the ratio of 4 : 5, Number of boys studying arts = 4/9 x 117 = 52 Number of boys studying science = 210 - 52 = 158 ANSWER:D #### D QUESTION:The area of a triangle is with base 5.5m and height 6m? options: A)11 m2 B)16.5 m2 C)18.5 m2 D)19.5 m2 E)12 m2 SOLUTION:1/2 * 5.5* 6 = 16.5 m2 Answer: B #### B QUESTION:The average of four positive integers is 67. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers? options: A)72 B)78 C)80 D)82 E)84 SOLUTION:Let the four integers be A, B, C and D where A > B > C > D. (A + B + C + D)/4 = 67 => A + B + C + D = 268 ---> (1) A = 93, D = 39 and B - C = 28 (1) => B + C = 268 - (A + D) = 268 - 132 = 136. B + B -28 = 136 B = (136 + 28)/2 = 82 ANSWER:D #### D QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 4 candidates are there to fill the 4 positions? options: A)420 B)770 C)840 D)165 E)315 SOLUTION:1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer None of the 4 chosen people can be in more than one departments. We can choose any of the 7 candidates for the math dep., which gives as 7 selections. We can choose 3 of the 10 candidates for the computer dep., which gives us 3 selections and 7 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /3!*7!= 120 We are multiplying our individual selections: 7*120 = 840 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans C #### C QUESTION:In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? options: A)7⁄19 B)2⁄3 C)3⁄4 D)9⁄21 E)None of these SOLUTION:If the drawn ball is neither red nor green, then it must be blue, which can be picked in 7C1 = 7 ways. One ball can be picked from the total(8 + 7 + 6 = 21) in 21C1 = 21 ways. ∴ Reqd probability = 7⁄21 = 1⁄3 Answer E #### E QUESTION:What is the greatest prime factor of (11!10!) + (11!12!)? options: A)11 B)17 C)19 D)23 E)29 SOLUTION:11!10! + 11!12! = 11!10! (1+11*12) = 12!11!(133) = 12!11!(7*19) The greatest prime factor is 19. The answer is C. #### C QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)9 C)4 D)1 E)3 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:If A= {2, 4, 6}, B= {1, 2, 5, 7}, and C= {2, 3, 4, 6}. Find A-(B U C) options: A){1 , 2} B){2 ,3 ,5 } C){ } D){5 } E)None of these SOLUTION:Explanation : A= {2, 4, 6}, B= {1, 2, 5, 7}, C = {2, 3, 4, 6} Now,(B U C) = {1, 2, 5, 7} U {2, 3, 4, 6} = {1,2,3,4,5,6,7} A-(B U C) = {2, 4, 6} - {1,2,3,4,5,6,7} = { } Hence (C) is correct answer. Answer : C #### C QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)*(100%-19%) = 1.07*.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D QUESTION:A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth? options: A)80 B)28 C)90 D)26 E)11 SOLUTION:Explanation: SP of 1m of cloth = 8925/85 = Rs. 105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 105 - Rs. 25 = Rs. 80. Answer: A #### A QUESTION:If n is an integer and 102n^2 is less than or equal to 8100, what is the greatest possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:102 * n^2 <=8100 n^2 <=8100/102 which will be less than 81 since 8100/100 = 81 which is the square of 9 Next closest value of n where n^2<=81 is 8 Ans B #### B QUESTION:If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15%, the gain is: options: A)16(2/3)% B)13(1/3)% C)15 (1/6)% D)15% E)None of these SOLUTION:Let C.P.=Rs. 100. First S.P.=Rs. 120 Now, S.P. =Rs. 120, commission=10% Therefore, Marked Price=[(100/90)X120]=Rs. 400/3. No, marked price=400/3, commission=15% Therefore, S.P.=85% of 400/3=[(85/100)X(400/3)]=340/3. Therefore, Gain%=[(340/3)-100]=40/3=13(1/3)%. ANSWER:B #### B QUESTION:Mangala completes a piece of work in 10 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is? options: A)8 days B)10 days C)20/3 days D)14 days E)16 days SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 10 × 20/30 = 20/3 days C) #### C QUESTION:What comes next in the series? 16 72 38 94 50 __ options: A)11 B)25 C)17 D)19 E)16 SOLUTION:E 16 Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit. #### E QUESTION:How many integers between 5000 and 6000 that have distinct digits and increase from left to right ? options: A)10 B)48 C)60 D)20 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 545_ --> 4 546_ --> 3 547_ --> 2 548_ --> 1 556_ --> 3 557_ --> 2 558_ --> 1 567_ --> 2 568_ --> 1 578_ --> 1 Number of integers =20 D #### D QUESTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (4x - 2y) is odd II. xy^2 is an even negative integer III. (y^2 - x) is an odd negative integer options: A)I only B)I,II,III NOT TRUE C)I and II D)I and III E)II and III SOLUTION:If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 2y) is odd 4x - is always negative and EVEN 2y - can be 0, when y=0, or always even integer (positivie or negative) odd integer +/- even integer = always EVEN I statement is always true II. xy^2 is an even negative integer y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true III. (y^2 - x) is an odd negative integer y can be 0 => -x will be positive => III statement is not true basing on above, only I statement will always be true answer is B #### B QUESTION:In a mixture of 60 liters, the ratio of milk and water is 4:1. What amount of water must be added to make the ratio of milk and water as 1:4? options: A)60 liters B)42 liters C)68 liters D)65 liters E)62 liters SOLUTION:4:1 --- 60 1:4 2:8 --------------- 5 5 ----------- 60 5 ----------- ? => 60 liters ANSWER:A #### A QUESTION:A high school has 400 students 1/2 attend the arithmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 3/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs. options: A)35 B)45 C)55 D)60 E)50 SOLUTION:A-Club has 200 members (1/2 of 400) B-Club has 250 members (5/8 of 400) C-Club has 300 members (3/4 of 400) We can create an equation to solve this: 200+250+150 = n + x + 2y where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs. The question provides y for us (150). 750 = 400 + x + 300 x = 50 E #### E QUESTION:The ages of Smirthi and Samantha vary by 16 years, Six years ago, Deepika’s age was three times as that of Smirthi’s, find their current ages. options: A)20 B)50 C)40 D)30 E)45 SOLUTION:D 30 Let Smirthi’s age = A years So, Deepika’s age = (A + 16) years Also, 3(A – 6) = A + 16 – 6 or, A = 14 Smirthi’s age = 14 years and, Deepika’s age = 14 + 16 = 30 years #### D QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)k(n+m+mn)+ k B)(1+n+m+mn)(k+1) C)k^2(mn+n/m) D)kmn(k+m+n) E)None of the above SOLUTION:The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together: (mn + m + n + 1)(k + 1). ANSWER:B #### B QUESTION:If the height of a cone is increased by 100% then its volume is increased by? options: A)200% B)300% C)100% D)500% E)350% SOLUTION:Height of=>100% so increased by 100% ANSWER C #### C QUESTION:6% of customers that enter a store on any given day must not pay tax. If 1000 people shop every day, how many people pay taxes in the store every week options: A)6500 B)6580 C)7200 D)7120 E)6800 SOLUTION:6% of customers do not pay taxes. 6/100 * 1000 customers do not pay taxes. 6/100 * 1000 = 60 Therefore 1000 - 60 customers do pay taxes. 1000 - 60 = 940 940 * 7 days per week = 6580 B) #### B QUESTION:If a and b are integers and (2^a)(3^b) is a factor of 900^40, what is the largest possible value of ab? options: A)2a B)5a C)20a D)40a E)80a SOLUTION:(2^a)(3^b) is a factor of 900^40 We need to find the largest possible value of ab. We know that 900 = 2^2*5^2*3^2 Therefore 900^40 will have 2 powers of 3 in it. Hence in (2^a)(3^b), b has to 2 Therefore value of ab = 2a Correct Option: A #### A QUESTION:How many keystrokes are needed to type numbers from 1 to 1000? options: A)2704 B)2890 C)2893 D)3001 E)None of these SOLUTION:1-9 9 digits 10-99 There are 90 2-digit numbers (90)(2) = 180 digits 100-999 There are 900 3-digit numbers (900)(3) = 2700 digits 1000 4 digits 9 + 180 + 2700 + 4 = 2893 Answer: C #### C QUESTION:If 15648 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box? Options: 8 options: A)12 books B)6 books C)24 books D)18 books E)5 books SOLUTION:The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 15648. In order to divide the sum in 9 parts, the amount must be divisible by 9 Divisibility rule of 9: The sum of the digits must be divisible by 9 Sum of digits of 15648 =24 and 18 is divisible by 9. Hence, we need to remove 6 to this number for it to be divisible by 9 Correct Option:B #### B QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots? options: A)4/M B)4M C)900M D)M/900 E)M/4 SOLUTION:The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours. The answer is E. #### E QUESTION:The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class. options: A)47.55 kg B)48 kg C)48.55 kg D)49.25 kg E)59.25 kg SOLUTION:16*50.25+8*45.15/24=48.55 ANSWER:C #### C QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Tuesday, what was the expected day when both the brothers were to return home and when did Rohit Return? options: A)Wednesday, Sunday B)Thursday, Monday C)Friday, Tuesday D)Monday, Friday E)none SOLUTION:Rajat returned on Tuesday -i.e. 3 days earlier so actual day to return home is Friday. Rohit returned after days so Tuesday. ANSWER:C #### C QUESTION:I. m-14, m, m, m, m+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A QUESTION:Find 60/42*4 options: A)14.7653 B)0.5897 C)3.6974 D)0.3571 E)1.2587 SOLUTION:Answer=60/42*4 =60/168=0.3571 Option D is correct #### D QUESTION:12,31,68,129,220,? options: A)129 B)220 C)387 D)347 E)520 SOLUTION:2*2*2 + 4 = 12 3*3*3 +4 = 31 4*4*4 + 4 = 68 5*5*5 + 4 = 129 6*6*6 + 4 = 220 7 *7 *7 + 4 = 347 ANSWER : D #### D QUESTION:The area of a circle is increased by 300%. By what percent has the radius of the circle increased? options: A) 400% B) 200% C) 100% D) 600% E) 800% SOLUTION:The area of the circle is increased by 300%, thus the area is increased 4 times. The area of a circle it proportional to the square of the radius (area=πr^2), therefore the radius must increase 2 times (diameter increase 2 times = area increase 4 times), which is increase by 100%. Answer: C #### C QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is? options: A)35 B)50 C)88 D)66 E)22 SOLUTION:Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr. Answer:A #### A QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 2. Find his average after 17th inning. options: A)36 B)39 C)42 D)45 E)None of the above SOLUTION:Let the average after 17th inning = x. Then, average after 16th inning = (x – 2). ∴ 16(x – 2) + 87 = 17x or x = (87 – 32) = 55. Answer E #### E QUESTION:A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters, at 10 meters per minute. However, the toy train is defective and it now produces only two different tunes at random. What is the probability that the toy train produces 3 music tunes of the same type (1 in _____ ) ? options: A)3 B)9 C)8 D)4 E)5 SOLUTION:1/2^3=1/8 but here der r two types of tone and we need to find the odds of d train of two tones to form 3 tones consequently so 2*1/8= 1/4 so ans is 4 ANSWER:D #### D QUESTION:A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back? options: A)$4,040 B)$4,120 C)$1,960 D)$4,920 E)$1,400 SOLUTION:In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost. So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost. Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $5,000-$880=$4,120. Answer: B. #### B QUESTION:A person can swim in still water at 8 km/h. If the speed of water 4 km/h, how many hours will the man take to swim back against the current for 8km? options: A)2 B)4 C)5 D)6 E)7 SOLUTION:M = 8 S = 4 US = 8 - 4 = 4 D = 4 T = 8/4 = 2 Answer:A #### A QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer C #### C QUESTION:6.513/10.02 = options: A) 0.35 B) 0.3505 C) 0.3509 D) 0.65 E) 0.3527 SOLUTION:6.513 / 10.02 6.513 / 1002 = 6.5 move the comma two places to the left as we have 2 decimal places from the divisor: 0.65. Answer: D #### D QUESTION:A tap can fill a tank in 12 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely? options: A)5 hr 30 mins B)7 hr 30 mins C)4hr 30 mins D)2 hr 30 mins E)3 hr 30 mins SOLUTION:Explanation: A tap can fill a tank in 12 hours. Therefore the tap can fill half the tank in 6 hours. One tap take time to fill half of the tank = 6 hrs 4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins Answer : B #### B QUESTION:A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? options: A)37 B)38 C)30 D)77 E)27 SOLUTION:US = 25 DS = 35 M = (35 + 25)/2 = 30 Answer:C #### C QUESTION:A car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment? options: A)$503 B)$504 C)$505 D)$506 E)$507 SOLUTION:Explanation: Cash price = $21 000 Deposit = 10% × $21 000 = $2100 Loan amount = $21000 − $2100 = $18900 I=p*r*t/100 I=11340 Total amount = 18900 + 11340 = $30240 Regular payment = total amount /number of payments Answer: B #### B QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 guards will be available to patrol the fairgrounds on the following Saturday night? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:For any given day, only the guards patrolling on the previous day won't be available. So, 3 guards who patrolled on Friday won't be available. We are thus left with 4 guards. To choose 3 out of 4, we will have 4C3 = 4 different groups. The answer is B. #### B QUESTION:If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many C such committees are possible? options: A)20 B)40 C)C=50 D)C=80 E)C=120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10. But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8. Total # of ways: 5C3*2^3=80. Answer: D. #### D QUESTION:Obra drove 140π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive? options: A)6.67% B)12.5% C)18.75% D)29.16% E)33.3% SOLUTION:area enclosed by the circular track on which she drove is 57,600π square meters So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240 Circumference of the circular track = 2πr = 480π Therefore, part of circumference covered = 140π/480π =29.16% Hence, answer is D. #### D QUESTION:The average height of 50 pupils in a class is250 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is __________ . options: A)151 cm B)351 cm C)241 cm D)251 cm E)261 cm SOLUTION:Total height = 250 * 50 = 12500 cm. New average = [12500 - 5 * 146 + 5 * 156 ] / 50 =251 cm. ANSWER:D #### D QUESTION:a, b, c and d are four consecutive numbers. If the sum of a and dis 111, what is the product of b and c? options: A)2652 B)2578 C)2534 D)3080 E)4234 SOLUTION:Here d = a + 3 a + a + 3 = 111 2a = 108 a = 54 So, numbers are 54, 55, 56 and 57 ∴ b × c= 55 × 56 = 3080 D #### D QUESTION:In May Mrs Lee's earnings were 50 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ? options: A)55 B)56 C)34 D)78 E)23 SOLUTION:Lets say the Family Income is 100 In May, lee earned 50Family income is 50 In june, Lee earned 20% more than May, so it is (50+20*50/100 = 60) Family Income is same 50 In June Lee's Income percent is 60*100/110 ~ 55 Ans is A #### A QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent? options: A)200 B)992 C)772 D)662 E)552 SOLUTION:Profit on first article = 20% of 1000 = 200. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: A #### A QUESTION:A sum of money becomes 7/6 of itself in 6 years at a certain rate of simple interest. The rate per annum is? options: A)50/9 B)50/13 C)50/17 D)25/9 E)5 5/1 SOLUTION:Let sum = x. Then, amount = 7x/6 S.I. = 7x/6 - x = x/6; Time = 6 years. Rate = (100 * x) / (x * 6 * 6) = 25/9 %. Answer:D #### D QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Method #1: Using the permutation formula # of 5 letter code words: nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6 # of 4 letter code words: nPr = 10! / (10 – 4)! = 10*9*8*7 # of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7) = 6 = 6/1 Answer is E. #### E QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required ? options: A)34 B)40 C)68 D)88 E)None of these SOLUTION:Solution We have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. ∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D #### D QUESTION:The ratio 3 : 5 expressed as a percent equals options: A)60% B)40% C)80% D)125% E)None SOLUTION:Solution 3 : 5 = 3/ 5 = (3 / 5 x 100)%. = 60 %. Answer A #### A QUESTION:Find the value of 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] options: A)800 B)3200 C)900 D)1600 E)None SOLUTION:Answer 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] = 4 x [(36 x 48 x 250) / (12 x 9 x 5)] = 4 x 4 x 4 x 50 = 3200 Correct Option: B #### B QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00? options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00 SOLUTION:For retail price = $25 First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5 Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14 Answer: Option A #### A QUESTION:What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive? options: A)90 B)80 C)100 D)105 E)110 SOLUTION:10 and 190 inclusive would mean there are 17 terms. No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170 The middle term is the average which is the tenth term = 80 B is the answer. #### B QUESTION:1 quarter Kg of potatoes cost 60 paise. Calculate the cost of 200 grams options: A)48 paise B)77 paise C)96 paise D)66 paise E)55 paise SOLUTION:Explanation: Let 200 gm potato cost X paise According to question, Cost of 1/4 Kg potato = 60 Paise => Cost of 250 gm potato = 60 Paise => 1 Kg = 1000 gm => 1/4 Kg = 1000/4 gm = 250 gm By direct proportion, more quantity, more cost 200 grams : 250 grams = X : 60 => 200*60 = 250 X => 12000 = 250 X => X = 48 => Thus, the cost of 200 grams is 48 paise. ANSWER: A #### A QUESTION:Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? . options: A)20 B)30 C)50 D)80 E)100 SOLUTION:150 employees 80 are full-time 100 have worked at company X for at least a year 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? 150-80=70 employees not full time 70-20= 50 employees not full time who worked over a year 100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year ANSWER:C #### C QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 . Number of pages typed by Kumar in 1 hour = 40/5 = 8. Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 . Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours = 8 hours 15 minutes. ANSWER : E #### E QUESTION:A bowl of fruit contains 14 apples and 23 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples? options: A)3 B)6 C)14 D)17 E)20 SOLUTION:Number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70% of pieces of fruit in bowl will be apples = x Total number of fruits after x oranges are removed = 14+(23-x) = 37-x 14/(37-x) = 7/10 =>20 = 37-x =>x= 17 Answer D #### D QUESTION:Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride? options: A)14 mph B)20 mph C)70/3 mph D)80/3 mph E)30 mph SOLUTION:Average speed for first two hours, S1 = 30 mph Distance travelled in these two hours, D1 = 60 miles Average speed for the entire 5 hour ride, S = 30 mph Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles. Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90 Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30 Hence, the correct answer is E #### E QUESTION:A man sells two articles for Rs.3600 each and he gains 40% on the first and loses 40% on the next. Find his total gain or loss? options: A)16% loss B)400 C)4000 D)324 E)8% LOSS SOLUTION:(40*40)/100 = 16%loss ANSWER:A #### A QUESTION:3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last? options: A)6 B)9 C)12 D)15 E)18 SOLUTION:2 oxen = 3 buffaloes = 4 cows Also: 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen There is enough fodder for 1 oxen for 30*24 days. 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen The new total is equal to 80 oxen instead of 30 oxen. 30*24 / 80 oxen = 9 days The answer is B. #### B QUESTION:A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? options: A)10.18 p.m B)10.29 p.m C)10.30 p.m D)10.38 p.m E)10.32 p.m SOLUTION:D = 70 * 1 ½ = 105 km RS = 85 – 70 = 15 T = 105/15 = 7 h 3.30 + 7 h = 10.30 p.m. Answer:C #### C QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)24 B)66 C)55 D)88 E)61 SOLUTION:(15*18)/12 = 24 Answer:A #### A QUESTION:A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: options: A)4 mph B)2.5 mph C)3 mph D)2 mph E)None of these SOLUTION:Explanation : Speed of the boat in still water = 10 mph Let speed of the stream be x mph Then, speed downstream = (10+x) mph speed upstream = (10-x) mph Time taken to travel 36 miles upstream - Time taken to travel 36 miles downstream = 90/60 hours =>36/(10−x) − 36/(10+x) = 3/2 =>12/(10−x) − 12/(10+x) = 1/2 =>24(10 + x) − 24(10 − x) = (10 + x)(10 − x) =>240 + 24x − 240 + 24x = (100−x2) =>48x = 100 − x2 =>x2 + 48x − 100 =0 =>(x+50)(x−2)=0 => x = -50 or 2. Answer : Option D #### D QUESTION:In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ? options: A)8% B)5% C)7% D)12% E)19% SOLUTION:A 8% of student hate all four subjects. #### A QUESTION:1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4.... options: A)7 B)6 C)3 D)4 E)1 SOLUTION:First if we count 1223334444. they are 10 In the next term they are 20 Next they are 30 and so on So Using n(n+1)2×10≤2888 For n = 23 we get LHS as 2760. Remaining terms 128. Now in the 24th term, we have 24 1's, and next 48 terms are 2's. So next 72 terms are 3's. The 2888 term will be “3”. Answer:B #### B QUESTION:A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train? options: A)94 kmph B)58 kmph C)54 kmph D)180 kmph E)59 kmph SOLUTION:D = 100 + 250 = 350 T = 7 S = 350/7 * 18/5 = 180 kmph Answer:D #### D QUESTION:Out of 470 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ? options: A)80 B)150 C)100 D)180 E)220 SOLUTION:n(A)=325,n(B)=175,n(AuB)=470-50=420. Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80. Answer is A #### A QUESTION:A "word" is defined as a sequence of three dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed? options: A)3 B)5 C)6 D)8 E)9 SOLUTION:there are two ways of possibilities.. 1) all three same colour- YYY or BBB- 2 ways 2) two of one colour and one of different colour- 3!/2!-3ways.. now two /one could be Y/B or B/Y.... so 3*2=6.. total 6+2=8 ans D #### D QUESTION:If (x-13)(x-3) < 0, which of the following must be true? options: A)x^2 + 5x + 6 < 0 B)x^2 + 5x + 6 > 0 C)5 - x < 0 D)x - 5 < 0 E)13 - x > 0 SOLUTION:(x-13)(x-3)<0 can be written as (13-x)(x-3)>0 So,to inequality hold true multiple of (13-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<13 Answer Choice E matched which says 13-x>0 or x<13,which must be true (I started to look from E to A for making easy decision first) Correct Answer E #### E QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to: options: A)0.04 B)0.004 C)0.4 D)0.0004 E)None of them SOLUTION:Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is A #### A QUESTION:During a trip on an expressway, Son drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip? options: A)8.5% B)50% C)x/12% D)60/x% E)500/x% SOLUTION:so Son drove (x-5) miles at 60mph and 5 miles at 30mph: (x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance if the entire trip @60mph than time = x/60 so to get percent [(X+5)/60 ]/[x/60] x100 =(x+5)/x *100 =100+500/x so increase of 500/x%[/u]=E #### E QUESTION:A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay? options: A)270 B)360 C)276 D)271 E)272 SOLUTION:12*8 :16*9 = 18*6 8: 12: 9 12/29 * 870 = 360 Answer: B #### B QUESTION:1!+2!+3!+4!+5!+.100! is divided by 24. Find the remainder from this? options: A)4 B)6 C)9 D)10 E)11 SOLUTION:By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24. So the remainder = 1 + 2 + 6 + 0 + 0....... = C #### C QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is? options: A)7 B)4 C)5 D)3 E)1 SOLUTION:Explanation: P(1 + 20/100)n > 2P or (6/5)n > 2 Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years. Answer:B #### B QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d? options: A)2 B)8 C)10 D)11 E)14 SOLUTION:1155 = 3 * 5 * 7 * 11 a = 11 d = 3 a - d = 8 Answer is B #### B QUESTION:When n is divided by 19, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers? options: A)3 B)7 C)10 D)13 E)nineteen SOLUTION:N = 19 q + 6 N = 11 z + 6 Equating 19 Q + 6 = 11z +6 11z=19q 11z/19 = q since q is an integer Z must be divisible by 19. ANSWER:E #### E <<<Examples ends QUESTION:A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430 ? options: A)s. 832 B)s. 830 C)s. 822 D)s. 812 E)s. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2430 = 20 (2430/60) = Rs. 810. Answer: E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5*a1 + 7*b1 = t 5*a2 + 7*b2 = t 5*(a1 - a2) = 7*(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence? options: A)−164 B)0 C)16 D)32 E)64 SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term) sum of 64 terms = 32 ANSWER:D #### D QUESTION:At a circular table for nine will sit seven adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the nine people be arranged around the table. options: A)120 B)240 C)480 D)600 E)720 SOLUTION:Consider the two parents and two children as one unit. Then there are five adults and one family unit. The number of ways 6 can form a line is 6! Around a circular table, there would be 6 rotations so we divide this number by 6. There are 5! ways for 6 to sit around the circular table. Then the two children have two options and the two parents have two options. Then the total number of ways is 5!*2*2= 480 The answer is C. #### C QUESTION:a dealer buys 4 varieties of wheat costing rs. 20,rs.25,rs.30 and rs.35 per kg in the ratio 6:4:3:1 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of wheat? options: A)30.5 B)31.0 C)32.0 D)33.0 E)34.5 SOLUTION:CP = 20*6+25*4+30*3+35*1=345 SP = 1.4*345=483 Total no.of kgs=6+4+3+1=14 SP per kg=483/14 = 34.50 ANSWER:E #### E QUESTION:The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability W that exactly two visitors will buy a pack of candy? options: A)0.343 B)0.147 C)0.189 D)0.063 E)0.027 SOLUTION:3C2 * (3/10)^2 * 7/10 = 3 * 9/100 * 7/10 = 189/1000 = 0.189=W Answer - C #### C QUESTION:How many integers between 5000 and 6000 that have distinct digits and increase from left to right ? options: A)10 B)48 C)60 D)20 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 545_ --> 4 546_ --> 3 547_ --> 2 548_ --> 1 556_ --> 3 557_ --> 2 558_ --> 1 567_ --> 2 568_ --> 1 578_ --> 1 Number of integers =20 D #### D QUESTION:A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-38 E)36-37 SOLUTION:5%(35.5) = 1.775 8%(35.5) = 2.84 total amount could have been 35.5+1.775 and 35.5+2.84 => could have been between 37.275 and 38.34 => approximately between 37 and 38 Answer is B.D #### D QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 128 => x= 8 Answer: A #### A QUESTION:The operation # is defined for all nonzero x and y by x#y = x + x/y. If S>0, then 1#(1#S) = options: A)S B)S+1 C)S/(S+1) D)(S+2)/(S+1) E)(2S+1)/(S+1) SOLUTION:x#y = x + x/y. If S>0, then 1#(1#S) = You can see that a stands for y and 1 stands for x. I like to work with numbers so I did x=1 S=2 and S=y so y=2 1#S= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3 So now you can check by filling in S, which is 2: A. S --> 2 B. S+1 --> 2+1=3 C. S/(S+1)-->2/(2+1)=2/3 D. (S+2)/(S+1)-->(2+2)/(2+1)=4/3 E. (2S+1)/(S+1)-->(2*2+1)/(2+1)=5/3 So E is the answer. #### E QUESTION:Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) options: A)27 B)30 C)33 D)36 E)39 SOLUTION:33/4 ÷ 4 = 33/16 pounds in each container 33/16 pounds * 16 ounces / pound = 33 ounces in each container The answer is C. #### C QUESTION:A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 10 seconds. Find the length of the train and its speed. options: A)10 m/sec B)15 m/sec C)18 m/sec D)19 m/sec E)25 m/sec SOLUTION:If length of train is l and speed of train is s, then l/s = 10 (l+180)/s = 20 (l+180)/l = 20/10 =2 l+180 =2l l= 180 l=180 mtrs s= l/10 = 180/8 = 10 m/sec ANSWER:A #### A QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let the sequence have N terms starting 18*K --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence. The sum of the sequence is ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2). So the average is 153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*). On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**). By *), **) we have K=2, N=14. Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms R which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C. #### C QUESTION:A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers Q are possible? options: A)2 B)4 C)6 D)3 E)Not possible SOLUTION:Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2 Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total of Q= 6 possibilities. C. #### C QUESTION:If BAT = 58 HAT = 52 CAT = 57 then whats RAT = ? options: A)42 B)45 C)34 D)76 E)25 SOLUTION:A 42 #### A QUESTION:A car dealership has 40 cars on the lot, 15% of which are silver. If the dealership receives a new shipment of 80 cars, 30% of which are not silver, what percentage of total number of cars are silver? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:The number of silver cars is 0.15*40 + 0.3*80 = 30 The percentage of cars which are silver is 30/120 = 25% The answer is B. #### B QUESTION:How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? options: A)482 B)725 C)992 D)837 E)923 SOLUTION:20000(11/10)4 - 20000(6/5)2 = 482 Answer:A #### A QUESTION:At present, the ratio between the ages of Akbar and Denial is 4:3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Sol. Let the present ages of Akbar and Danial be 4x years and 3x years respectively. Then, 4x + 6 =26 ⇔ 4x = 20 ⇔ x = 5. ∴ Deepak’s age = 3x =15 years. Answer C #### C QUESTION:A walks at 10 kmph and 5 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A? options: A)100km B)150km C)50km D)120km E)200km SOLUTION:Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 5 hours. x/10 - x/20 = 5 x = 100 km Answer is A #### A QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)*(100%-19%) = 1.07*.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D QUESTION:The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is: options: A)45 B)50 C)51.4 approx. D)54.6 approx. E)54 SOLUTION:Let the required means score be x. Then, 20 * 80 + 25 * 31 + 55 * x = 52 * 100 = 1600 + 775 + 55x = 5200 = 55x = 2825 = x = 565/11 = 51.4. ANSWER:C #### C QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature T in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median T will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer C #### C QUESTION:11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)14 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22] = 1400cm = 14 m. Answer C #### C QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)2528 B)2526 C)2522 D)2722 E)2426 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:How many options are there for a code consisting of 2 even digits followed by 2 odd digits? options: A)4^5 B)5^4 C)5^5 D)4^4 E)10^4 SOLUTION:Even Numbers = 5 digits { 0 , 2 , 4 , 6 , 8 } Odd Numbers = 5 digits { 1 , 3 , 5 , 7 , 9 } EVEN EVEN ODD ODD No of ways is 5*5*5*5 = 5^4 Hence, correct, answer must be (B) 5^4 #### B QUESTION:A and B can do a piece of work in 11 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? options: A)15.5 days B)19.5 days C)17.5 days D)9.2 days E)18.5 days SOLUTION:C = 1/5 – 1/11 = 6/55 => 9.2 days ANSWER:D #### D QUESTION:If |x^2 − 12| = x, which of the following could be the value of x? options: A)-4 B)-3 C)1 D)2 E)3 SOLUTION:|x2−12|=x|x2−12|=x |x2−12||x2−12|cannot be negative; anything that comes out of mod is always positive so |x2−12|>0|x2−12|>0 Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0 Now only Option C=1 or D=2 or E=3 are contenders for right answers. A quick Cursory crude calculation will tell you that E is the right choice |−32−12|=3|−32−12|=3 |9−12|=3|9−12|=3 |−3|=3|−3|=3 3=33=3 ANSWER IS E #### E QUESTION:If ratio of profit of A and B is 4:5 and they together invested Rs.90,000 then money invested by B is options: A)Rs.48,000 B)Rs.45,000 C)Rs.30,000 D)Rs.50,000 E)None of the above SOLUTION:investment by B=(5*90000)/(4+5) =50000 ANSWER:D #### D QUESTION:The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot? options: A)1 B)17 C)88 D)12 E)15 SOLUTION:Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer: B #### B QUESTION:On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done? options: A)2880 B)2778 C)2682 D)8222 E)6282 SOLUTION:Explanation: There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways. Further, in each category (subject), books are to be arranged in different order, we get, Required number of ways: 3! * [2! * 2! * 5!] = 2880 ANSWER: A #### A QUESTION:A = {0, 1, -3, 6, -8, -10} B = {-1, 2, -4, 7, 6, -9} If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0? options: A)1/4 B)1/3 C)5/13 D)5/12 E)1/2 SOLUTION:For the product of 2 numbers to be negative either of them must be positive or negative: P(positive, negative) = 2/6*3/6 = 6/36; P(negative,positive ) = 3/6 * 3/6 = 9/36 P = 6/36 + 9/36 P = 15/36 P = 5/12 Answer: D #### D QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points T is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points T is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] Q=z-x = x+9-x= 9 Ans:D #### D QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 34, what is the minimum possible range in scores of the three test-takers? options: A)a 17 B)b) 34 C)c) 35 D)d) 45 E)e) 80 SOLUTION:It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have: A- 0 and 17 B- 0 and 28 C- 0 and 35 therefore the minimum range is 34, it cant be any lower however you play with the numbers. B #### B QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:9 B)8:7 C)8:1 D)8:2 E)8:8 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8 : 7 Answer:B #### B QUESTION:A research team that must consists of 3 members is to be formed from a pool of 6 scientists. How many different teams are possible? options: A)17 B)10 C)40 D)26 E)20 SOLUTION:Note that the team must consist of 3 members, not at least 3 members. Hence, all you have to do is 6C3 = 20 Answer (E) #### E QUESTION:A 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar? options: A)6%. B)7.5%. C)9.2%. D)10.5%. E)14%. SOLUTION:Denominator: 340+10+3.2+6.8=360 Numerator: 340(1-.80-.06)+3.2 340(0.14)+3.2 47.6+3.2 50.8 Ratio: 50.8/360=0.14 Answer: E #### E QUESTION:A labourer was engaged for 25 days on the condition that for every day, he works, he will be paid Rs. 2 and for every day, he is absent he will be fined 50p. If he receives only Rs. 37•50, find the no. of days he was absent is_____ options: A)3 days B)4 days C)5 days D)6 days E)7 days SOLUTION:if a labour worked for 25 days he should get 50 Rs. but in this he is getting 13 Rs less. if he don't go for work for 1 day he will loose 2.5 Rs then no of days(Absent)=13/2.5=5.2. Means he was absent for 5 days ANSWER:C #### C QUESTION:In 110 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: options: A)20 m B)25 m C)22 m D)9 m E)12 m SOLUTION:Distance covered by B in 9 sec. = 110/45 x 9 m = 22 m. A beats B by 20 metres. Answer: Option C #### C QUESTION:Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is? options: A)2777 B)2888 C)8400 D)2882 E)2781 SOLUTION:Ratio of their shares = 22500 : 35000 = 9:14 Deepak's share = 13800 * 14/23 = Rs. 8400. Answer: C #### C QUESTION:The length of the longest tape in cm which can be used to measure exactly, the length 100cm; 2m25cm; and 7m80cm is: options: A)30 B)5 C)10 D)36 E)25 SOLUTION:The three lengths in cm are 100, 225 &780. HCF of 100, 225 &780 is 5. Hence, the answer is 5 cm. ANSWER:B #### B QUESTION:Certain stocks in January were 10% less than they were in February and 20% greater than they were in March. What was the percentage decrease in the stocks from February to March? options: A)5% B)10% C)20% D)25% E)50% SOLUTION:Let J,F,M be the values of the stock in Jan,Feb and March. Thus, per the question, J = 0.9F = 1.2M ----> M =0.75F Thus the % decrease from F to M = (F-M)/(F) *100 = (F-0.75F)/F * 100 = 0.25*100 = 25 %, D is the correct answer. #### D QUESTION:Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol. What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol? options: A)32 B)21 C)27 D)None of these E)18 SOLUTION:Explanation: Let t be the time after Kajol starts, when she meets Ajay, then \inline t=\frac{300}{(x+y)} This should be less than 2.5 or (x+y)>120 Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72 This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol. Answer: D #### D QUESTION:Two goods trains each 375 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)40 B)45 C)48 D)51 E)36 SOLUTION:Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 375 + 375 = 750 m. Required time = 750 * 6/125 = 36 sec. Answer: Option E #### E QUESTION:A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? options: A)35 hours B)25 hours C)20 hours D)Cannot be determined E)None of these SOLUTION:Suppose the efficiencies of pipes C, B and A are 4K, 2K and K. Since, the tank is filled in 5 hours by the three pipes having combined efficiency equal to 7K, the time required to fill the tank by A alone = 7K×5 /K=35hours Answer A #### A QUESTION:How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet) options: A)37×260^2 B)36×260^2 C)36×270^2 D)10^2×26^3 E)10^3×26^2 SOLUTION:We are given that License plate could be either of the form DDLLL or DDDLL Now, every D could be filled in 10 ways and every L could be filled in 26 ways. or Number of ways for DDLLL = 10 * 10 * 26 * 26 * 26 --(1) Number of ways for DDDLL = 10 *10*10*26*26 --(2) Total ways = (1) + (2) = \(36×260^2\) Answer s B. #### B QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool? options: A)33 1/3% B)46 2/3% C)50% D)62 1/2% E)75% SOLUTION:P = pool S = sauna given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x 50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3% Answer B #### B QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was options: A)960 B)980 C)900 D)970 E)1000 SOLUTION:Explanation: Let original Cost price is x Its Selling price = (105/100) * x = 21x/20 New Cost price = (95/100) * x = 19x/20 New Selling price = (110/100 )* (19x/20 )= 209x/200 [(21x/20) - (209x/200)] = 1 => x = 1000 Answer: E) Rs 1000 #### E QUESTION:Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. options: A)10987 B)11755 C)17576 D)19775 E)21899 SOLUTION:The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways The first two letters can chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 26 =17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter. C #### C QUESTION:210 school students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers? options: A)25 B)40 C)50 D)60 E)75 SOLUTION:We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20. So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40. #### B QUESTION:A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? options: A)480 B)487 C)720 D)729 E)268 SOLUTION:1/x - 1/20 = -1/24 x = 120 120 * 6 = 720 Answer:C #### C QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)12, 9 B)10, 5 C)12, 7 D)11, 6 E)12, 6 SOLUTION:x – y = 5 4x – 6y = 6 x = 12 y = 7 ANSWER:C #### C QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 – 4xy (x- y)2 = 625 – 576 => (x – y) = 7 ANSWER: A #### A QUESTION:If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is options: A)40 B)49 C)80 D)88 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 22 and x2 + y2 = 386. Now, 2xy = (x+y)2 - (x2 + y2) = (22)2 - 386= 484 - 386= 98 xy = 49. Answer B #### B QUESTION:For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score R for the exam? options: A)74 B)76 C)78 D)80 E)82 SOLUTION:A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d Solving above for Mean R= 74. Answer: A. #### A QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24. ANS :C #### C QUESTION:5+3 options: A)8 B)13 C)28 D)6 E)2 SOLUTION:A #### A QUESTION:The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ? options: A)12 B)14 C)15 D)16 E)20 SOLUTION:HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D #### D QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)87 min B)82 min C)86 min D)47 min E)72 min SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:A merchant marks his goods up by 50% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)21% B)25% C)69% D)35% E)19% SOLUTION:Let the price be 100. The price becomes 150 after a 50% markup. Now a discount of 10% on 150. Profit=135-100 35% answer D #### D QUESTION:Y and Z start a business with Rs.3000 and Rs.6000 respectively. How should they share their profits at the end of one year? options: A)4:1 B)1:3 C)1:4 D)1:5 E)1:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by Y and Z = 3000 : 6000 => 1:2 . Answer:E #### E QUESTION:On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled? options: A)80 B)81 C)82 D)83 E)84 SOLUTION:Solution: Mabel handled 90 transactions Anthony handled 10% more transactions than Mabel Anthony = 90 + 90 × 10% = 90 + 90 × 0.10 = 90 + 9 = 99 Cal handled 2/3rds of the transactions than Anthony handled Cal = 2/3 × 99 = 66 Jade handled 15 more transactions than Cal. Jade = 66 + 15 = 81 Jade handled = 81 transactions. Answer: B #### B QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am SOLUTION:In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours. Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am. Answer: D #### D QUESTION:A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much options: A)0.60 loss B)0.70 loss C)0.80 loss D)0.50 loss E)0.40 loss SOLUTION:CP when profit of 25% = 12.8 CP when loss of 20% = 20 Total CP = 32.8 Total SP = 32.00 Total loss = 0.80 ANSWER:C #### C QUESTION:For how many integers n is 1^n+2 = (n+2)^1? options: A)0 B)1 C)2 D)None of these E)3 SOLUTION:If n=0 1^0+2 = (0+2)^1 1^2 = 1 ; 2^1 =2 not ok If n=1 1^1+2 =1 ; (1+2)^1=3^1=3 not OK So, Answer : D #### D QUESTION:Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved? options: A)56% B)64% C)62.2% D)68% E)61% SOLUTION:If initial cost is Rs 100, then Final cost will be 100*0.7*0.6*0.9 = Rs. 37.8 savings = 100-37.8=62.2 so 62.2% ANSWER:C #### C QUESTION:A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes? options: A)100 m B)150 m C)190 m D)200 m E)220 m SOLUTION:Explanation: Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr Distance covered in 6 minutes =1/60X6km=1/10km=100m Distance between the thief and policeman = (200 – 100) m = 100 m. ANSWER IS A #### A QUESTION:14,24,54,34,44,56,53, ? options: A)44 B)55 C)66 D)77 E)88 SOLUTION:14-24...dif -10 54-34..dif -20 44-56..dif-12 53-77...dif-24 ANSWER:D #### D QUESTION:If 45-[28-{37-(15-*)}]= 56, then * is equal to: options: A)-29 B)-19 C)17 D)29 E)39 SOLUTION:45-[28-{37-(15-*)}]= 56 => 45-[28-{37-15+*}]=56 45-[28-37+15-*]=56 => 45[43-37-*]=56 45-[6-*]=56 => 45-6+*=56 39+*=56 => *=56-39 = 17 ANSWER:C #### C QUESTION:Which of the statements can be dispensed with while answering the above question? options: A)A only B)B only C)A or C only D)B or C only E)C or D only SOLUTION:Explanation: Justification: We can find the code for 'home' from the second and third statements. For finding the code for 'they', we need the code for 'go' which cannot be determined from the given data. Clearly, statement A is not necessary. Answer: A #### A QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 6*8.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:If y = ||x – 3| – 2|, for how many values of x is y = 5? options: A)2 B)1 C)3 D)4 E)5 SOLUTION:y = ||x – 3| – 2| can be 4 only and only when X-3= +/-7. so there are 2 values of X Answer : A #### A QUESTION:A man can do a piece of work in 6 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? options: A)7 days B)6 days C)5 days D)4 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/3−1/6)=(6−3)/18=1/6 So son will do whole work in 6 days Answer: B #### B QUESTION:You are filling up your car with gas. Your tank can hold 19 gallons. Your car started with x gallons in it. You paid $20 in gas. What was the cost of gas per gallon? options: A)19/20 B)x/20 C)(19-x)/20 D)x-19)/20 E)19+20/x SOLUTION:Amount of gas you added to your car: 19-x Price per gallon: (19-x)/20 Answer: C #### C QUESTION:2^2*3^3*2^2*3^6 = options: A)3^5*2^5 B)2^9*3^4 C)2^4*3^9 D)5^8 E)6^10 SOLUTION:2^2*3^3*2^2*3^6 = A) 3^5*2^5 B) 2^9*3^4 C) 2^4*3^9 D) 5^8 E) 6^10 If the base is same, powers are added so that follows C) 2^4*3^9. Hence the answer is C #### C QUESTION:Eggs are sold in packages of six or eleven only. If Doris bought 78 eggs exactly, what could be the number of large packs Doris bought? options: A)6. B)2. C)3. D)5. E)4. SOLUTION:No strategy involved. Simple question demanding fast calculation. 11x6 = 66=> 78-66=12 => 12/6 is an integer Ans A. 6. Good luck #### A QUESTION:The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides? options: A)2 B)7 C)5 D)3 E)4 SOLUTION:S = (1 + 1 + 2)/2 = 2 Answer: A #### A QUESTION:There are 9 books on a shelf that consist of 2 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)85 B)91 C)97 D)103 E)110 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 7C4 = 35 The number of combinations with at least one paperback is 126-35 = 91 The answer is B. #### B QUESTION:If the length of an edge of cube M is thrice the length of an edge of cube N, what is the ratio of the volume of cube N to the volume of cube M? options: A)2/13 B)1/27 C)1/5 D)1/9 E)1/8 SOLUTION:The length of cube N = 1; The length of cube M = 3; The ratio of the volume of cube N to the volume of cube M = 1^3/3^3 = 1/27 Answer : B #### B QUESTION:Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X? options: A)25% B)40% C)50% D)60% E)75% SOLUTION:34% is 9%-points above 25% and 6%-points below 40%. Thus the ratio of mixture Y to mixture X is 2:3. The percent of mixture X is 3/5 = 60%. The answer is D. #### D QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)12.6 B)12.0 C)12.1 D)12.3 E)12.2 SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec.Answer: B #### B QUESTION:A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? options: A)A.0.6 B)B.1 C)C.2.1 D)D.3 E)E.2.4 SOLUTION:30% of 6 = 1.8 50% of 6 = 3 shortage is 1.2 so we need to have 1.2/50% to get 50% alcohol content. = 2.4 E #### E QUESTION:The area of a triangle is with base 12m and height 5m? options: A)88 m2 B)30 m2 C)66 m2 D)77 m2 E)31 m2 SOLUTION:1/2 * 12 * 5 = 30 m2 Answer: B #### B QUESTION:A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is? options: A)675 B)680 C)685 D)690 E)695 SOLUTION:Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec. Length of the train = 75 * 9 = 675 m. Answer: Option A #### A QUESTION:James took a 3-hour bike ride. In the second hour he traveled 6 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride? options: A)54.0 B)54.9 C)18.5 D)57.0 E)63.0 SOLUTION:Let the distance travelled in the first hour be x. Thus, 1.2x = 6, x = 5. Now, the distance travelled in the 3rd hour = 6+1/4∗6=7.5 The only option ending with a 0.5 in the decimal place is C. ANSWER:C #### C QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 30¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)66 E)49.5 SOLUTION:Total price of six cans = 6*36.5 = 219 Total price of 4 cans = 4*30 = 120 Total rice of two cans = 219 - 120 = 99 Average price of two cans = 99/2 = 49.5 c Another way to do it is this: Assume that the four leftover cans were of 30c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 2*36.5 + 4*6.5 = 99 Avg cost of the two cans = 99/2 = 49.5c Answer (E) #### E QUESTION:Two trains of equal are running on parallel lines in the same direction at 48 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)60 m B)72 m C)80 m D)82 m E)84 m SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 48 - 36 = 12 km/hr. = 12 * 5/18 = 10/3 m/sec. 2x/36 = 10/3=> x = 60. ANSWER:A #### A QUESTION:A shopkeeper sold an article at $100 with 30% profit. Then find its cost price? options: A)$120 B)$100 C)$91 D)$77 E)$69 SOLUTION:cost price = selling price *100/(100+profit) C.P. = 100*100/130 = $77(approximately) Answer is D #### D QUESTION:Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest W? options: A) 60 B) 61 C) 62 D) 63 E) 64 SOLUTION:60 = 2*2*3*5 factor count =3 61= prime number 62 = 2*31 factor count=2 63=3*3*7 factor count=2 64=2*2*2*2*2*2 factor count=1=W answer is A. #### A QUESTION:In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 93% of the products of M3 III are not defective. What is the percentage of defective in the stockpile? options: A)3% B)5% C)2.5% D)4% E)3.6% SOLUTION:Explanation : Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3. Products from M1 = 40, from M2 = 30 and from M3 = 30. Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.07 x 30 = 2.1 Therefore, total number of defective products = 3.6 Answer : E #### E QUESTION:If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour? options: A)17/140 B)29/180 C)26/143 D)1/5 E)39/121 SOLUTION:50 apprentices can finish the job in 4 hours,thus: 10 apprentices can finish the job in 4*5 = 20 hours; In 1 hour 10 apprentices can finish 1/20 of the job. 30 journeymen can finish the same job in 4,5 hours,thus: 15 journeymen can finish the job in 7*2 = 14 hours; In 1 hour 15 journeymen can finish 1/14 of the job. Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job. Answer: A #### A QUESTION:John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit as the cost price? options: A)Rs.12 B)Rs.8 C)Rs.16 D)Rs.20 E)None of these SOLUTION:Explanation : CP=20×8.5+35×8.75=170+306.25=476.25Profit=40%SP=(100+Profit%)100×CP=(100+40)100×476.25=140 100×476.25=1404×19.05=35×19.05Total quantity = 20 + 35 = 55 KgSP per Kg=35×19.0555=7×19.0511≈7×1911≈13311≈12 Answer : Option A #### A QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 13*0 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 14 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? options: A)13 B)13.5 C)14 D)14.5 E)15 SOLUTION:Ans is E Given d_ab = 2*d_bc let d_ab = d and d_bc = x so d=2x for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time) #### E QUESTION:If k^2 = h^2, which of the following must be true? options: A)k = m B)|k| = |h| C)k = |m| D)k = -|m| E)k = -m SOLUTION:Solution: We are given that k^2 = h^2, and we can start by simplifying the equation by taking the square root of both sides. √k^2 = √h^2 When we take the square root of a variable squared, the result is the absolute value of that variable. Thus: √k^2 = √h^2 is |k| = |h| Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true. Answer: E #### E QUESTION:If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite? options: A)x^2 B)x^2 – y^2 C)y^2 D)(y + x)^2 E)(x – y)^2 SOLUTION:(y^2 − xy)/x=y-x => y^2 − xy = xy -x^2 => x^2 - 2xy + y^2 = 0 => (x-y)^2 = 0 Answer E #### E QUESTION:If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ? options: A)3653 B)3657 C)2977 D)3957 E)2711 SOLUTION:Explanation: Given : Letter : T I E R B A N Code : 7 1 9 3 2 4 5 Thus, the code for RENT is 3957. ANSWER:D #### D QUESTION:If a is a positive integer, which of the following could NOT be the square of a? options: A) 5,008,644 B) 5,004,169 C) 4,999,696 D) 4,995,225 E) 4,990,752 SOLUTION:A number ending with 2 can never be a perfect square. Units digit of a perfect square must be: 1,4,9,6,5 Answer E) #### E QUESTION:If A(k)=(k+1)^-k, and k=0, what is the value of A(A(A(k)))? options: A)0 B)(2/3)^(1/2) C)1 D)(3/2)^(1/2) E)(2/3)^-2 SOLUTION:A(A(A(0)))=A(A(1))=A(1/2)=(1/2+1)^-1/2=(2/3)^(1/2) Thus, the answer is B. #### B QUESTION:In an election between the two candidates ,The candidates who gets 60% of votes polled is winned by 280 votes majority. What is the total number of votes polled? options: A)1200 B)1400 C)1600 D)1500 E)1540 SOLUTION:Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %) 20 % = 60 % - 40 % 20% -----> 280 (20×14 = 280 ) 100% -----> 1400 (100×14 = 1400) Option 'B' #### B QUESTION:After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope? options: A)1/12 B)0 C)12/212 D)11/12 E)11/13 SOLUTION:0 If one letter is in wrong envelope, the letter corresponding to that letter will also be in wrong envelope. ANSWER:B #### B QUESTION:A fruit seller had some oranges. He sells 20% oranges and still has 380 oranges. How many oranges he had originally? options: A)475 B)700 C)220 D)400 E)None of these SOLUTION:Explanation : He sells 20% of oranges and still there are 380 oranges remaining => 80% of oranges = 380 ⇒ (80 × Total Oranges)/100 = 380 ⇒ Total Oranges/100 = 4.75 ⇒ Total Oranges = 4.75 × 100 = 475 Answer : Option A #### A QUESTION:find value for x from below equation? x + 1 = 3 options: A)-5 B)-4 C)4 D)3 E)2 SOLUTION:1. Subtract 1 from both sides: x + 1 - 1 = 3 - 1 2. Simplify both sides: x = 2 E #### E QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(6200*5*3)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:Equal weights of two alloys containing tin, copper and lead in the ratio 6:8:7 and 1:2:4 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy? options: A)11:8:3 B)3:1:8 C)17:28:27 D)9:4: 11 E)9:14: 11 SOLUTION:Let the weight of the two alloys be w each Required ratio = (6w/21+1w/7): (8w/21+2w/7 ): (7w/21+4w/7) = 9w/21 : 14w/21 : 11w/21 = 9:14: 11 ANSWER:E #### E QUESTION:The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers? options: A)87 B)42 C)78 D)76 E)26 SOLUTION:5x 6x 2x 50 25 100 250x + 150x + 200x = 4200 600x = 4200 x = 7 => 6x =42 Answer: B #### B QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 24 times, A has killed: options: A)27 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(24 x 16)/3= 128. Birds killed by A =(5x/24) =(5/24*128)= 27. Answer is A #### A QUESTION:A and B together can do a work in 6 days. If A alone can do it in 10 days. In how many days can B alone do it? options: A)10 B)15 C)77 D)55 E)21 SOLUTION:1/6 – 1/10 = 1/15 => 15 Answer: B #### B QUESTION:50% of a number is 10 less than 3/5th of that number. What is the number? options: A)100 B)50 C)150 D)200 E)75 SOLUTION:Let the number be x Then, 3x/5 - (50% of x) = 10 3x/5-50x/100 = 10 x = 100 Answer is A #### A QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea? options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None SOLUTION:Solution: 1st Method: Let the original price of tea be Rs. x/kg. After reduction the price becomes = x -10% of x = 9x/10 per kg. Now, (22500/(9x/10))-22500/x = 25 Or, 22500[10/9x- 1/x] = 25 Or, 25*9x = 22500; Or, x = (22500/2589) = Rs. 100. Hence, new price = 90 per kg. Thought process Method: Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg. After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg. So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea. Answer: Option C #### C QUESTION:A certain number of men can finish a piece of work in 10 days. However, if there were 10 less men it will take 10 days more for the work to be finished. How many men were there originally? options: A)10 men B)30 men C)40 men D)20 men E)none of these SOLUTION:Let x be the number of men originally Thus, 10x=(10+10)(x-10) 10x=20(x-10) x=2(x-10) x = 20 ANSWER:D #### D QUESTION:How many integers are between 3 and 86/7, inclusive? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:86/7 = 12.xx We are not concerned about the exact value of 86/7 as we just need the integers. Since the values are small, we can write down the integers. The different integers between 3 and 86/7 would be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Total number of integers = 10 Option C If we need to find the number of integers between two numbers n and m, where m > n The number of integers = m - n + 1 In the given question, the number of integers = 12 - 3 + 1 = 10 ANSWER:C #### C QUESTION:The side of a square is increased by 25% then how much % does its area increases? options: A)56.75 % B)56.25 % C)53.85 % D)57.25 % E)56.21 % SOLUTION:a = 100 a2 = 10000 a = 125 a2 = 15625 ---------------- 10000 --------- 5625 100 -------? => 56.25 % Answer:B #### B QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)30% C)32% D)73% E)84% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 ---20 => 20% Answer:A #### A QUESTION:Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? options: A)9 B)10 C)12 D)20 E)8 SOLUTION:Due to stoppages, it covers 9 km less. Time taken to cover 9 km =(9/54x 60)min = 10 min. Answer :B #### B QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3? options: A)3/10 B)3/20 C)2/5 D)1/2 E)1/3 SOLUTION:S={1,2,3,….20} E={3, 6,9,12,15,18} P(E)=6/20 =3/10 Option A #### A QUESTION:A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum N of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ? options: A) 5 B) 7 C) 9 D) 10 E) 14 SOLUTION:Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum N of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D #### D QUESTION:In Town X, 120 percent of the population are employed, and 80 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)33% D)40% E)52% SOLUTION:Total employed people 12%, out of which 80 are employed males, hence 40% are employed females. (employed females)/(total employed people)=40/120=1/3=33% Answer: C. #### C QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? options: A)8/35 B)34/35 C)27/35 D)21/32 E)33/35 SOLUTION:Solution: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)*P(B) = 2/5 * 4/7 = 8/35 ANSWER IS A #### A QUESTION:If A lends Rs.4000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? options: A)112.5 B)122.5 C)132.5 D)114.5 E)180 SOLUTION:(4000*1.5*3)/100 => 180 ANSWER:E #### E QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Solution Start with 11 coins. Sharon takes 3 coins from you: 11 - 3 = 8 coins. Steven takes 4 coins from you: 8 - 4 = 4 coins. So you have 4 at the end. Correct answer : C #### C QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent J of the distribution is less than m +d ? options: A)16% B)32% C)48% D)84% E)92% SOLUTION:D The prompt says that 68% of the population lies between m-d and m+d. Thus, 32% of the population is less than m-d or greater than m+d. Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d. Thus,J= (68+16)% or (100-16)% of the population is less than m+d.D #### D QUESTION:A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water? options: A)22 B)37 C)32 D)27 E)18 SOLUTION:US = 25 DS = 39 M = (39 + 25)/2 = 32 Answer:C #### C QUESTION:If y is an integer, then the least possible value of |23 - 4y| is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We know that 4y is a multiple of 4, so let’s first look at the multiples of 4 closest to 23. We have “20” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 4y = 20, y is 5 and when 4y = 24, y is 5. Let’s start with letting y = 4. |23-4(5)| |23-20| |3| = 3 Next, let’s let y equal 5. |23-4(6)| |23-24| |-1| = 1 We see that the smallest possible value of |23-4y| is 1. Answer A. #### A QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B <<<Examples ends QUESTION:If the price of sugar rises from Rs. 3 per kg to Rs. 5 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by options: A)15% B)20% C)25% D)30% E)40% SOLUTION:Sol. Let the original consumption = 100 kg and new consumption = x kg. So, 100 x 3 = x × 5 = x = 60 kg. ∴ Reduction in consumption = 40%. Answer E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:What is value of (P + Q)/(P - Q) if P/Q = 7 ? options: A)1/3 B)2/3 C)4/3 D)5/3 E)None of these SOLUTION:Explanation: (P + Q)/(P - Q) = (P/Q+1)/(P/Q - 1) = (7 +1)/(7 - 1) = 4/3. Answer: C #### C QUESTION:Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option? options: A)1/2 B)1/6 C)1/12 D)6/10 E)3/10 SOLUTION:as coin has only two faces then probability must be 1/2 ANSWER:A #### A QUESTION:A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price? options: A)$1200 B)$1300 C)$1000 D)$1700 E)$1050 SOLUTION:C $1000 90% 104% -------- 14% ---- 140 100% ---- ? => $1000 #### C QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C QUESTION:In the faculty of Reverse-Engineering, 240 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total? options: A)515. B)545. C)661. D)644. E)666. SOLUTION:Answer is C :661 Solution : Total number of students studying both are 423 + 240 - 134 = 529 (Subtracting the 134 since they were included in the both the other numbers already). So 80% of total is 529, so 100% is approx. 661. #### C QUESTION:Which of the following equations has a root in common with x^2−3x+2=0 ? options: A)x^2-2x+1=0 B)x^2-2x-1=0 C)x^2-x+1=0 D)x^2-3x+3=0 E)x^2-7x=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-2)= 0 so the two roots are 1 and 2. Now put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. A is the answer. #### A QUESTION:Andrew started saving at the beginning of the year and had saved $180 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year? options: A)11% B)25% C)44% D)56% E)100% SOLUTION:Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year. Percentage Change = ( Change in value / Original value ) * 100 Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100 Saving in 2nd year + Saving in 1st year = 540 Saving in 2nd year + 180 = 540 Saving in 2nd year = 540 - 180 = 360 Change in Value = 360 - 180 = 180 Original Value = 180 Percentage Increase = (180 / 180 ) * 100 = 100%..... Answer E...... #### E QUESTION:What is the rate percent when the simple interest on Rs.1600 amount to Rs.200 in 4 Years? options: A)4% B)3.125% C)5% D)6% E)7% SOLUTION:Interest for 1 year = 200/4 = 50 Interest on Rs 1600 p/a = 50 interest rate = 50/1600*100 = 3.125% Answer : B #### B QUESTION:A can do a work in 15 days and B in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is options: A)8/17 B)7/15 C)3/15 D)5/12 E)1/4 SOLUTION:Person ( A ) ( B ) ( A+B ) Time - ( 15 ) ( 20 ) (-) Rate - ( 20 ) ( 15 ) ( 35 ) Work -(300) (300) (300) therefore A+B requires (300/35) days to complete entire work For 1st 5 days they work 35 * 5 = 175 Remaining work is 300 - 175 = 125 Remaining fraction of work is = 125/300 = 5/12 Answer D #### D QUESTION:If w,x,y,z are consecutive positive integers ; then which of the following is always odd? [1] w*x+(y+2)^2*z [2] w^x + z^y [3] 13x^2 options: A)1 B)2 C)3 D)1 and 2 E)2 and 3 SOLUTION:Plug in some numbers w = 1 x = 2 y = 3 z = 4 Check the options - [1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number } [2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number } [3] 13x^2 = 13*4 =52 even [2] B #### B QUESTION:Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? options: A)70 m B)60 m C)80 m D)90 m E)100 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)68 km/hr. B)32 km/hr. C)34 km/hr. D)35 km/hr. E)72 km/hr. SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240 )/12 2x = 40 x = 20. Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr. answer :E #### E QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? options: A)15% B)25% C)35% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(300) / 1000 = 15% The answer is A. #### A QUESTION:If (A+B) = 5, (B+C) = 6 and (C+D) = 3, what is the value of (A+D)? options: A)16. B)8. C)7. D)2. E)-2. SOLUTION:Given A+B = 5 B+C = 6 C+D = 3 (A+B)-(B+C)+(C+D)=(A+D) => 5 - 6+3 = 2. Option D... #### D QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 6 rows or 4 rows or 8 rows, then no tree will be left. Find the least number of trees required options: A)24 B)60 C)28 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(6,4,8) = 24 Answer: A #### A QUESTION:If n is an integer greater than 8, which of the following must be divisible by 3? options: A)1. n (n+1) (n-4) B)2. n (n+2) (n-1) C)3. n (n+3) (n-5) D)4. n (n+4) (n-2) E)5. n (n+5) (n-6) SOLUTION:We need to find out the number which is divisible by three, In every 3 consecutive integers, there must contain 1 multiple of 3. So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three 1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1) 2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1) 3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n) 4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1) 5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2) from the above onlyoption Ais product of consecutive three numbers. C #### C QUESTION:What is the greatest positive integer x such that 7^x is a factor of 343^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:343^10 = (7^3)^10 = 7^30 ANSWER:E #### E QUESTION:A, B and C shared profits in ratio of 3 : 7 : 6. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ? options: A)12 : 49 : 64 B)20 : 49 : 64 C)10 : 19 : 64 D)20 : 29 : 64 E)30 : 29 : 63 SOLUTION:Simply multiply profit sharing ratio with investment ratio to get investment amount ratio. Let X is the total investment ⇒14 x = 3 ⇒ 8 x = 7 ⇒ 7x = 8 ⇒ Final investment ratio = 12 : 49 : 64 A #### A QUESTION:A train 350 m long, running with a speed of 63 km/hr will pass a tree in? options: A)15 sec B)16 sec C)18 sec D)20 sec E)25 sec SOLUTION:Speed = 63 * 5/18 = 35/2 m/sec Time taken = 350 * 2/35 = 20 sec ANSWER: D #### D QUESTION:A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 13, 21, and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box? options: A)7/72 B)1/6 C)7/36 D)5/28 E)21/36 SOLUTION:Probability = No: of desired outcomes / Total No: of outcomes. You are picking two slips out of 8 slips. So Total No: of outcomes = 8C2 = 28 Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there? If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome. (1,2) (2,3) (3,5) (5,8) (8,13) . There are 5 such pairs. If the two numbers which I pick is from any of these 5 pairs, then I get my desired outcome. So No: of desired outcomes = 5 Probability = 5/28 Answer :D #### D QUESTION:Find the greatest number that will divide 48, 210 and 136 leaving 4, 12 and 4 as remainders respectively options: A)19 B)17 C)13 D)22 E)21 SOLUTION:Explanation: Answer will be HCF of (48-4, 210-12, 136-4) HCF of (44, 198, 132) = 22 Option D #### D QUESTION:What is the are of an equilateral triangle of side 4 cm? options: A)2√3 B)3√3 C)5√3 D)4√3 E)8√3 SOLUTION:Area of an equilateral triangle = √3/4 S2 If S = 4, Area of triangle = √3/4 * 4 * 4 = 4√3 cm2; Answer:D #### D QUESTION:In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the fifth row? options: A)10 B)11 C)13 D)14 E)16 SOLUTION:Let x be the number of cans in row 1. The total number of cans is x + (x+3) + ... + (x+27) = 10x + 3(1+2+...+9) = 10x + 3(9)(10)/2 = 10x + 135 Since the total is less than 150, x must equal 1. The number of cans in the 5th row is 1 + 3(4) = 13 The answer is C. #### C QUESTION:The tax on a commodity is diminished by 30% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it? options: A)20% B)18% C)15% D)12% E)14% SOLUTION:100 * 100 = 10000 70 * 115 = 8050 10000------- 1950 100 ------- ? = 20% ANSWER:A #### A QUESTION:An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)267 B)180 C)287 D)177 E)911 SOLUTION:Angle traced by the hour hand in 6 hours =(360/12)*6 Answer: B #### B QUESTION:David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house? options: A)$96,000 B)$94,000 C)$88,000 D)$75,000 E)$40,000 SOLUTION:Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer. #### B QUESTION:12, 24, 16, 32, 24, 48, ? options: A)31 B)32 C)36 D)37 E)40 SOLUTION:E 40 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:Mohit sold an article for Rs. 18000. Had he offered a discount of 25% on the selling price, he would have earned a profit of 8%. What is the cost price of the article? options: A)12500 B)27767 C)16688 D)26678 E)19987 SOLUTION:Let the CP be Rs. x. Had he offered 25% discount, profit = 8% Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 25/100(18000) = Rs. 13500 => 1.08x = 13500 => x = 12500 \Answer: A #### A QUESTION:In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? options: A)48400 B)48000 C)48100 D)48500 E)48600 SOLUTION:Assume that investment of C =x Then, investment of A =2x Investment of B =4x/3 A:B:C =2x:(4x)/3:x =2:4/3:1=6:4:3 B's share =157300×4/(6+4+3) =157300×4/13=12100×4=48400 Answer is A. #### A QUESTION:An elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children? options: A)40: 20 B)42: 21 C)50: 100 D)15: 25 E)It cannot be determined by the information given. SOLUTION:While you can figure out most of this question, there is not enough information to completely tell. the answer is E. #### E QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)76 m B)178 m C)225 m D)187 m E)176 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x)= 750 => x = 225 m. Answer: C #### C QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21 Ans: B #### B QUESTION:The simple form of the ratio 4/5:8/9 is? options: A)5:8 B)4:9 C)5:9 D)5:3 E)9:10 SOLUTION:4/5 : 8/9 = 9:10 Answer: E #### E QUESTION:After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B? options: A)N/15 B)7N/8 C)14N/15 D)N/5 E)4N/5 SOLUTION:1/4 of tested had infection A, thus N/4 had infection A; Of those with infection A, 1/2 also had infection B, thus 1/2*N/4 = N/8 had both infections A and B. Therefore, N - N/8 = 7N/8 did not have both infection A and B. Answer: B. #### B QUESTION:Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)2a2 – ab + 3b2 B)(a – b)(2a – 3b) + 4ab C)(a – b)2 + (a2 + ab + 2b2) D)(a + b)2 + (a2 + 2b2 – 3ab) E)(a + b)(a – b) + (2a2 – ab + 4b2) SOLUTION:The other parts are equal to 34. Answer E #### E QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)3 B)3.3 C)3.5 D)3.6 E)None SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4. Answer: Option D #### D QUESTION:A certain elevator has a safe weight limit of 1950 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 190 pounds and the average weight of the others being 200 pounds? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Lets assume there are 2X people. Half of them have average weight of 190 and other half has 200. Maximum Weight is = 1950 So 190*X + 200*X = 1950 => 390X = 1950 => X is approximately equal to 5. So total people is 2*5 = 10 Answer D. #### D QUESTION:A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Given: positive integer n is a perfect square and a perfect cube --> n is of a form of n=x6 for some positive integer x --> 0<x^6<10^3 --> 0<x^2<10 --> x can be 1, 2 or 3 hence nn can be 1^6, 2^6 or 3^6. Answer: B. #### B QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value D of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] D=z-x = x+9-x= 9 Ans:D #### D QUESTION:Two trains 150 meters and 180 meters long are running in the same direction with speeds of 102 km/hr, 66km/hr. In how much time will the first train cross the second options: A)37 sec B)22 sec C)27 sec D)35 sec E)33 sec SOLUTION:Explanation: Relative speed of the trains = (102 - 66) km/hr = 36 km/hr = (36× 5/18) m/sec = 10 m/sec. Time taken by the trains to cross each other = Time taken to cover (150 + 180) m at 10 m /sec = (330/10) sec = 33 sec. Answer: Option E #### E QUESTION:A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 6% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected. What is the probability that a smartphone bundle that will be rejected by quality control? options: A) 0.25 B) .05^10 C) 1-0.94^10 D) 1-0.05^10 E) 0.95^10 SOLUTION:Find the probability of the opposite event and subtract from 1. The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.94^10. P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.94^10. Answer: C. #### C QUESTION:How many ways can 8 friends be arranged around a circular dinner table? options: A)1280 B)2460 C)5040 D)40320 E)85670 SOLUTION:The number of ways to order 8 people is 8! However, around a circular table, each pattern would be repeated 8 times. So the number of ways to seat 8 friends around a circular table is 7! = 5040 The answer is C. #### C QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)288 B)492 C)877 D)278 E)178 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 20 + 21 = 41 T = 12 D = 41 * 12 = 492 Answer: B #### B QUESTION:The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides. options: A)12, 9 B)18, 3 C)15.16, 6 D)12, 12.37 E)12, 15.16 SOLUTION:CM=3 AREA=PM*CM/2, thus PM=12 By Pythagorean Theorem, we can now find the value of PC. D is the correct option. #### D QUESTION:105,100,...,90,85,80,75 Insert the missing number options: A)95 B)78 C)83 D)84 E)none of the above SOLUTION:Missing number : 95 Answer : A #### A QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? options: A)25 days B)24 C)22 days D)27 days E)21 days SOLUTION:B 24 days B = 1/8 – 1/2 = 1/24 => 24 days #### B QUESTION:If 1535/1038 = a +1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e? options: A)165/2 B)175/2 C)178/3 D)187 by 2 E)197/2 SOLUTION:by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)} =1+(497/1038) now a=1 =1+{1/(1038/497)} =1+{1/(2+42/497)} =1+{1/ (2+1/(497/42)} now b= 2 similarly expand c=11 d= 1 e=34/8 finally a*b *b*c*d*e 1*2*11*1*34/8 187/2 ANSWER:D #### D QUESTION:Find the value of x: x² + 4x + 4. options: A)2 B)4 C)-2 D)-4 E)0 SOLUTION:That quadratic is factored as follows: x² + 4x +4 = (x+2)(x+2). Lesson 17. Now, it is easy to see that the second factor will be 0 when x = -2. The solution is: x = -2 C #### C QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 11 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)64 B)72 C)80 D)90 E)99 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 11 and the total number of coins is 9k = 99. The answer is E. #### E QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/55000 * 100 = 21.6% ANSWER:D #### D QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? options: A)12 B)15 C)16 D)18 E)19 SOLUTION:one day work done by A=1/20 work done by A in 2 days=1/10 work done by A,B,C on 3rd day=1/10+1/10=1/5 1/5th of the work will be completed at the end of 3 days the remaining work =1-1/5=4/5 1/5 of work is completed in 3 days total work wiil be done in 3*5=15 days ANSWER:B #### B QUESTION:A train 120 m long running at 60 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)213 B)298 C)350 D)726 E)267 SOLUTION:D = 60 * 5/18 = 20 = 333 – 120 = 213 Answer: A #### A QUESTION:Subtracting 10% from X is the same as multiplying X by what number? options: A)80% B)90% C)10% D)50% E)60% SOLUTION:Explanation: X - (10/100) X = X * ? ? = 90% ANSWER IS B #### B QUESTION:The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers? options: A)87 B)42 C)78 D)76 E)26 SOLUTION:5x 6x 2x 50 25 100 250x + 150x + 200x = 4200 600x = 4200 x = 7 => 6x =42 Answer: B #### B QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash? options: A)1000 B)3000 C)3500 D)2500 E)2250 SOLUTION:For 20 staffs: 300*100*20 = 60000 for driver and cleaning staff: 300*100*2 =6000 From petty Cash : 1000 Answer is 1000 #### A QUESTION:Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number? options: A)150 B)125 C)140 D)180 E)200 SOLUTION:3x+4x = 420 x=60== 3x=180 ANSWER D #### D QUESTION:If a certain manager had received a 5% raise instead of the 8% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise? options: A)55,000 B)58,806 C)59,290 D)62228.52 E)61,620 SOLUTION:No need of getting involved with decimals ..just work in fractions .. salary(let X) included 5% increase can be written as (1+5/100)X=60500 X=60500/1.05------>57619.05 if there is 8% rise in 57619.05 then the salary now is 8% of 57619.05 8*57619.05/100=4609.52 then toal salary after increment=57619.05+4609.52----->62228.52 Ans D #### D QUESTION:The product of the prime numbers between 0 and 20 is closest to... options: A)10^5 B)10^6 C)10^7 D)10^8 E)10^9 SOLUTION:Write out the primes 1 - 20 2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 Round the numbers off in multiples of 5. Try to alternate rounding up and down 5 x 5 x 5 x 5 x 10 x 10 x 20 x 20 25 x 25 x 10 x 10 x 20 x 20 pull out 10 from each number 10^6 (2.5 x 2.5 x 2 x 2) 10^6 (5 x 4) 10^7 (2) round off the 2. answer is C #### C QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 9:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train? options: A)12:30 B)1:00 C)1:30 D)2:00 E)2:30 SOLUTION:In thirty minutes the first train travels 35 km. The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h. The second train will catch the first train in 35/10 = 3.5 hours, so at 1:00 pm. The answer is B. #### B QUESTION:What percent of 120 are 90? options: A)33 B)66 C)75 D)44 E)31 SOLUTION:(?% /100) * 120 = 90 ? = 75% Answer: C #### C QUESTION:Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:The current of a stream runs at the rate of 3 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)A)7.24 B)B)2 C)C)8.5 D)D)6.67 E)E)3 SOLUTION:S = 3 M = x DS = x + 3 US = x - 3 6/(x + 3) + 6/(x - 3) = 2 x = 7.24 Answer:A #### A QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 11220, how much money did he borrow? options: A)11000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 11220 18x + 45x + 39x = (11220 * 100) 102x = 1122000 => x = 11000. Answer:A #### A QUESTION:A shop keeper marked 30% above the cost price and offered 20% discount then find it's net profit? options: A)2% B)2.5% C)3.7% D)4.6% E)5% SOLUTION:Net profit = 30-20 + (30*(-25)/100) = 2.5% Answer is B #### B QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price? options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3% SOLUTION:Let the price of the article be Rs. 100. 20% of 100 = 20. New price = 100 + 20 = Rs. 120 Required percentage = (120 - 100)/120 * 100 = 20/120 * 100 = 50/3 = 16 2/3%. Answer:A #### A QUESTION:Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ? options: A)0.5% B)1% C)5% D)50% E)500% SOLUTION:x percent can be written as x/100 So, we get: (30/100)(40/100)(50) = (60/100)(x/100)(200) Simplify all fractions to get: (3/10)(2/5)(50) = (3/5)(x/100)(200) Expand: 300/50 = 600x/500 Simplify: 6 = 6x/5 Multiply both sides by 5 to get: 30 = 6x Solve: x = 5 Answer: C #### C QUESTION:The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places options: A)34 B)35 C)56 D)67 E)23.57 SOLUTION:Let the side of the square be a cm. Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm i.e. 4a = 60 A = 15 Diameter of the semicircle = 15 cm Circimference of the semicircle = 1/2(∏)(15) = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places Answer: Option E #### E QUESTION:The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest? options: A)57% B)60% C)58% D)50% E)20% SOLUTION:Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years => C.I - S.I => 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100 => 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5 => 16r/100 + 8r2/(100)2 = 20r/100 => 4r/10 = 8r2/(100)2 => 8[r/100]2 - 4r/100 = 0 => r/100 {8r/100 -4} = 0 => r = 0% of 50% Since r!= 0%, r =50% Answer:D #### D QUESTION:If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is: options: A)Rs. 182 B)Rs. 190 C)Rs. 196 D)Rs. 204 E)Rs. 210 SOLUTION:Explanation: Given ratio =1/2:2/3:3/4=6:8:9 1st part = Rs. 782*6/23=Rs. 204 Answer is D #### D QUESTION:The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)35 kmph D)23 kmph E)14 kmph SOLUTION:S = (10 + 60)/2 = 35 kmph Answer:C #### C QUESTION:How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest? options: A)2 years B)3 years C)1 year D)4 years E)5 years SOLUTION:Explanation: P = Rs.900 SI = Rs.81 T = ? R = 4.5% T= (100×SI)/PR = (100×81)/(900×4.5) = 2 years Answer: Option A #### A QUESTION:There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division? options: A)22 B)35 C)37 D)20 E)75 SOLUTION:D 20 29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30 = 20. #### D QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:On a trip, a cyclist averaged 8 miles per hour for the first 16 miles and 10 miles per hour for the remaining 16 miles. If the cyclist returned immediately via the same route and took a total of 6.8 hours for the round trip, what was the average speed (in miles per hour) for the return trip? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The time to go 32 miles was 16/8+16/10=2+1.6=3.6 hours. The average speed for the return trip was 32 miles/3.2 hours= 10 mph. The answer is B. #### B QUESTION:If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth? options: A)Rs.(b*x) B)Rs.{(b*x)/a} C)Rs.{(a*b)/x} D)None of these E)Cannot be determined SOLUTION:Explanation: Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a). The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a} ANSWER B #### B QUESTION:What percent is 4 gm of 1 kg? options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 % SOLUTION:1 kg = 1000 gm 4/1000 × 100 = 400/1000 =2/5 = 0.4 % B) #### B QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)8% B)7% C)10% D)12% E)4% SOLUTION:Option E Explanation: 65*(90/100)*((100-x)/100) = 56.16 x = 4% #### E QUESTION:John earned 40% more per month than Oscar. If john salary is decreased 10% and Oscar’s salary is increased by 10%, then john would be earning what percent more than Oscar? options: A)10% B)9.09% C)15.54% D)14.54% E)It cannot be determined from the information given. SOLUTION:This Q is all about taking the correct BASE for taking %s.. the very first step requires taking some numbers for each.. ONE should be 100... it is easy to take 60 and 100 here.. but the BASE is 100 here, so the salary can be 100 and 140.. 100 increases 10% =110.. 140 decreases 10%=126.. so the increase is 16.. again the BASE is 110, so answer 16/110 * 100= 14.54% C without calculations, answer cannot be equal to or greater than 16, as 16 is on 110.. so D is the only one left #### D QUESTION:There are 14 songs in that 5 Rock songs, 6 western songs & 3 Hindi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song & 1 western song? options: A)15624 B)16478 C)17953 D)19655 E)28958 SOLUTION:15624 A #### A QUESTION:In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)8 B)9 C)10 D)11 E)12 SOLUTION:The total number of books the students borrowed is 20*2=40. The students who borrowed zero, one, or two books borrowed 8*1+3*2=14 books. The 7 students who borrowed at least three books borrowed 40-14=26 books. If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books. The answer is A. #### A QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded? options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV SOLUTION:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Z Y X W V U T S R Q P O N M L K J I H G F E D C B A So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN. so this way CAMEL becomes OVNZX ANSWER:C #### C QUESTION:What is the remainder when 1014*1047*1050*1053 is divided by 33? options: A)3 B)6 C)30 D)21 E)18 SOLUTION:OA is 'C'. OE: take the remainder from each of 1044/33, 1047/33 and so on.. 1014/33 gives remainder = 24 1047/33 gives remainder = 24 1050/33 gives remainder = 27 1053/33 gives remainder = 30 the net remainder is the product of above individual remainders. i.e = 24*24*27*30 break them into pairs 24*24/33 gives remainder 15 and 27*30/33 gives remainder 18 so 15*18/33 gives remainder 6. B #### B QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students? options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9 SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760 Sum of the marks for the class of 45 students = 45 * 70 = 3150 Sum of the marks for the class of 85 students = 2760 + 3150 = 5910 Average marks of all the students = 5910/85 = 69.5.Answer: D #### D QUESTION:At 6'o clock clock ticks 6 times. The time between first and last ticks was 30sec. How much time it takes at 10'o clock. options: A)60sec B)62sec C)66sec D)64sec E)54sec SOLUTION:At 6'0 clock, clock ticks 6 times. So, there must be 5 intervals between clock ticks. Time Between first and last ticks = 30sec So, 1 interval = 30/5 = 6sec So 6'o clock 5 *6=30sec 7'o clock 6 *6=36sec . . 9'o clock 8 *6=48sec 10'o clock 9 *6=54sec So, 54sec at 10'o clock. ANSWER:E #### E QUESTION:What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11, 60 and 61? options: A)6.5 B)12.5 C)28 D)30.5 E)40 SOLUTION:Some of pyhtagron triplets we need to keep it in mind. Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61). So now we know the triangle is an right angle triangle. The circle circumscribes the triangle. The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5 Ans. D #### D QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age 4 years back was: options: A)12 years. B)14 years. C)17 years. D)20 years. E)19 years. SOLUTION:Let the son's present age be x years. Then, (48 - x) = x 2x = 48. x = 24 Son's age 4 years back (24- 4) = 20 years. ANSWER :D #### D QUESTION:For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2? options: A)5 B)3 C)2 D)1 E)0 SOLUTION:4”2= 4 - 4=0 Answer: E #### E QUESTION:A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose? options: A)120 B)335 C)784 D)217 E)210 SOLUTION:Let x be the number he chose, then 2*x*138=102 2x=240 x=120 correct answer A #### A QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used? options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7 SOLUTION:Rate of machine R =1/50 Rate of machine S =1/20 since same no of machines used for R and S to do the same work in 5 hrs So collective rate needed to finish the work in 5 hrs= 1/5 Let the no of machine be x So, x/50 +x/20 =1/5 (2x+5x)/100=1/5 7x=20 x=20/7 So no of machine R is 20/7 Answer E #### E QUESTION:A retailer buys 140 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)105 B)155 C)125 D)185 E)285 SOLUTION:let the market price of each pen be $1 then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60 profit %=((102.60*100)/36) %=285% Answer E #### E QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth? options: A)80 B)28 C)90 D)26 E)11 SOLUTION:Explanation: SP of 1m of cloth = 8925/85 = Rs. 105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 105 - Rs. 25 = Rs. 80. Answer: A #### A QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:If 4x = 8^y, which of the following expresses x in terms of y? options: A)2^(y-2) B)2^(y-1) C)2^(3y-2) D)2^(2y-3) E)2^y SOLUTION:By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: C #### C QUESTION:If 6 (A's capital) = 8 (B's capital) = 8 (C's capital). Then the ratio of their capitals is? options: A)4:15:16 B)4:15:68 C)4:3:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 8 C A:B:C = 1/6:1/8:1/8 = 4:3:3 Answer: C #### C QUESTION:In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 200 more than the correct answer. Find the number. options: A)384 B)76 C)26 D)28 E)11 SOLUTION:Explanation: Let the number be x. 5*x/6 = 5*x/16 + 200 25*x/48 = 200 x = 384 ANSWER: A #### A QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students Q in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? options: A)18.1 B)21.1 C)36.5 D)42.2 E)84.4 SOLUTION:Let x and z be the smallest and largest of the original set, respectively. z - x = 84.4 The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4. Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1 The answer is B. #### B QUESTION:A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred. options: A)Rs. 5750 B)Rs. 6000 C)Rs. 5500 D)Rs. 5000 E)Rs. 7000 SOLUTION:The price varies as the square of the weight, P = K x W2 12250 = K x 352 K = 10 Thus, P = 10W2 When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively. Their values should be : 10g piece: 10 x 102 = Rs. 1000; 25g piece: 10 x 252 = Rs. 6250. Total value of stone now, = 1000 + 6250 = Rs. 7250 Loss incurred = 12250 - 7250 = Rs. 5000 ANSWER:D #### D QUESTION:In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg? options: A)16 : 30 B)30 : 14 C)16 : 31 D)31 : 15 E)15 : 31 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (31.50 - 23.75) / (23.75 - 20) = 31/15 ANSWER:D #### D QUESTION:The average successfull Search time for sequential search on n items is options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1 SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison. Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons. Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons. so we can write total search time will be: (1+2+3+........+n) average search time will be (1+2+3+........+n)/n NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2 ANSWER: C #### C QUESTION:At a party, there were seven times as many females as males and twice times as many adults as children. Which of the following could NOT be the number of people at the party? options: A)384 B)258 C)215 D)120 E)72 SOLUTION:Five times as many females as males --> F = 7M. Three times as many adults as children --> (F + M) = 2C. The number of people at the party = F + M + C = 2C + C = 3C. The number of people at the party must be a multiple of 3. The only answer choice which is NOT a multiple of 3 is C. Answer: C. #### C QUESTION:Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him? options: A)2000 B)3000 C)4000 D)1000 E)5000 SOLUTION:Let the money he took for shopping be m. Money he spent = 30 % of m = 30/100 × m = 3/10 m Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10 But money left with him = $ 2100 Therefore 7m/10 = $ 2100 m = $ 2100× 10/7 m = $ 21000/7 m = $ 3000 Therefore, the money he took for shopping is $ 3000. Answer:B #### B QUESTION:A boat can move upstream at 30 kmph and downstream at 15 kmph, then the speed of the current is? options: A)5 B)7.5 C)32.5 D)9.2 E)5.8 SOLUTION:US = 30 DS = 15 M = (30 - 15)/2 = 7.5 Answer: B #### B QUESTION:10^(600) ÷ 10^(580) = ? options: A)10^10 B)10^20 C)10^22 D)10^23 E)10^24 SOLUTION:10^(600) ÷ 10^(580) = 10^ (600-580) = 10^20 Answer : B #### B QUESTION:A person travels first 100km at 40km/hr and the next 100km at 60km/hr. The average speed for the first 200km of the tour is? options: A)36km/hr B)50km/hr C)48km/hr D)60km/hr E)55km/hr SOLUTION:Total time taken = 100/40 + 100/60 = 25/6 hrs Average speed = 200*6/25 = 48km/hr Answer is C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? options: A)250 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Answer: A #### A QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:In 1 hour, a boat goes 5 km along the stream and 9 km against the stream. The speed of the boat in still water (in km/hr) is : options: A)3 km/hr. B)2 km/hr. C)7 km/hr. D)8 km/hr. E)5 km/hr. SOLUTION:Speed in still water = 1/2(9 + 5) km/hr = 7 km/hr. ANSWER :C #### C QUESTION:A sum amounts to Rs.8820 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? options: A)s.4000 B)s.5000 C)s.4500 D)s.4800 E)s.8000 SOLUTION:CI=8820,R=5,N=2 CI=P[1+R/100]^2 =P[1+5/100]^2 8820=P[21/20]^2 8820[20/21]^2 8000 ANSWER:E #### E QUESTION:A student is ranked 13th from right and 8th from left.how many are there? options: A)18 B)19 C)20 D)21 E)22 SOLUTION:13th from right means = x + 12 8th from left means = 7 + x Total = 12+7+1 = 20 ANSWER:C #### C QUESTION:The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what is the speed of the car? options: A)30km/h B)40km/h C)50km/h D)60km/h E)80km/h SOLUTION:The main idea used in this kind of problems is that the distance equals speed multiplied by time S=V⋅t Car x + 5 (V (km/hr)) 4 t (hr) 4(x +5) S (km) Truck X V (km/hr) 4 t (hr) 4x S (km) 4(x+5)+4x=380 4x+4x=380−20 8x=360 x=3608 x=45 Therefore the truck's speed is 45 km/hr, and the car's speed is 45+5=50 km/hr correct answer is C)50km/hr #### C QUESTION:A = {0, 1, -3, 6, -8, -10} B = {-1, 2, -4, 7, 6, -9} If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0? options: A)1/4 B)1/3 C)5/13 D)5/12 E)1/2 SOLUTION:For the product of 2 numbers to be negative either of them must be positive or negative: P(positive, negative) = 2/6*3/6 = 6/36; P(negative,positive ) = 3/6 * 3/6 = 9/36 P = 6/36 + 9/36 P = 15/36 P = 5/12 Answer: D #### D QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)820 SOLUTION:The word ‘ORANGE’ contains 6 different letters. Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time =6P6 = 6! = 6*5*4*3*2*1 = 720 ANSWER:B #### B QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle? I. 4 II. 12 III. 24 options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only SOLUTION:Answer = A. I, II, and III With dimensions of only 2 sides given (for a triangle), this becomes an open ended question Any area is possible out of the three #### A QUESTION:The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit? options: A)Rs. 2000 B)Rs. 2200 C)Rs. 2400 D)Data inadequate E)Cannot be determined SOLUTION:Explanation : Let the C.P. of the article be Rs. x Given that % profit earned by selling article at Rs. 1920 = % loss incurred by selling article at Rs. 1280 (1920−x/x)∗100 = (x−1280/x)∗100 => 1920 - x = x - 1280 => 2x = 3200 => x = 1600 S.P. for 25% profit = Rs. 1600 + 25% of Rs. 1600 = Rs. 1600*(125/100) = Rs. 2000 Answer : A #### A QUESTION:If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 5. II. x is an integer multiple of 3 III. x is an integer multiple of 6 options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6. Let us take example n, n+1, n+2 as 3 three consecutive positive integers. In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12 Hence in a product of 3 consecutive integers, the product is always divisible by 3. Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also. Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even Answer E #### E QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 6? options: A)1/4 B)5/36 C)2/11 D)3/13 E)1/5 SOLUTION:n(S) = 6*6 = 36 E = {(1,5),(2,4),(3,3),(4,2),(5,1)} Probability = 5/36 Answer is B #### B QUESTION:In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes? options: A)32 B)16 C)64 D)80 E)16 or 48 SOLUTION:Let total number be x No in the interior = (x/8)^2 No outside = 16 So : x - (x/8)^2=16 x^2-64x+16*64=0 (x-32)^2=0 x=32 A #### A QUESTION:What is the average of xx,2x2x,and 66? options: A)x+2 B)x+2x C)x+2x+2 D)2x+2 E)x+2x-2 SOLUTION:By the definition of an average, we get: x+2x+63=3x+63x+2x+63=3x+63 =3(x+2)3=x+2.=3(x+2)3=x+2. Hence, the answer is x+2x+2 or Option C #### C QUESTION:A certain galaxy is known to comprise approximately 5 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun? options: A)800 B)1,250 C)8,000 D)12,000 E)10,000 SOLUTION:Total no. of stars on galaxy = 5 * 10^11 Of every 50 million stars, 1 is larger than sun. 1 million = 10^6 therofore, 50 million = 50 * 10^6 total no. of stars larger than sun = 5 * 10^11 / 50 * 10^6 =50 * 10^3 /5 = 10000 therefore answer is E #### E <<<Examples ends QUESTION:Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number? options: A)150 B)125 C)140 D)180 E)200 SOLUTION:3x+4x = 420 x=60== 3x=180 ANSWER D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? options: A)10% B)5% C)12% D)6% E)4% SOLUTION:In such a case there is always a loss Loss% = (20/10)^2 = 4% Answer is E #### E QUESTION:The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is options: A)51:53 B)52:53 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (102% of x) / (106% of x) =102/106 =51/53 = 51:53. Answer: A #### A QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)7 D)82 E)43 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:A trader bought a car at 30% discount on its original price. He sold it at a 80% increase on the price he bought it. What percent of profit did he make on the original price? options: A)18% B)26% C)12% D)32% E)15% SOLUTION:Original price = 100 CP = 70 S = 70*(180/100) = 126 100 - 126= 26% Answer: B #### B QUESTION:If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 25% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? options: A)50% B)75% C)120% D)133 1/3% E)150% SOLUTION:The price on June 1st = 12 (assume); The price on May 1st = 2/3*12 = 8; The price on July 1st = 8*1.25 = 10. The average price of the bond on May 1st and July 1st = (8+10)/2 = 9. The price of the bond on June 1st (12) is 4/3 times (134%) the average price of the bond on May 1st and July 1st. Answer: D. #### D QUESTION:Two wheels are connected via a conveyor belt. The larger wheel has a 48cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r? options: A)90r B)75r C)48r D)24r E)(64π)/3 SOLUTION:Interesting to note that the larger wheel has a diameter of 48 (8*6) while the smaller one has a diameter of 32 (8*4)... If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 48pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.5 = 15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.5 = 900 revolutions per hour. If r = 10, then the answer choice must be b. A. 90r #### A QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3*1*10+3*10*10 = 330 ANSWER:A #### A QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)22.7 kmph B)12.7 kmph C)27.6 kmph D)12.5 kmph E)22.1 kmph SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph.Answer: D #### D QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is? options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25 SOLUTION:The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50. Number of favourable cases are 34. Required probability = 34/50 = 17/25. Answer: E #### E QUESTION:Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? options: A)675.5 B)635.5 C)635.28 D)635.98 E)635.03 SOLUTION:4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 Answer:B #### B QUESTION:Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers? options: A)21, 12 B)9, 0 C)15, 6 D)10, 1 E)14, 5 SOLUTION:the larger number: x the smaller number: y twice the larger: 2x three more than five times the smaller: 5y + 3 relationship between ("is"): 2x = 5y + 3 four times the larger: 4x three times the smaller: 3y relationship between ("sum of"): 4x + 3y = 71 Now I have two equations in two variables: 2x = 5y + 3 4x + 3y = 71 I will solve, say, the first equation for x: x = (5/2)y + (3/2) Then I'll plug the right-hand side of this into the second equation in place of the "x": 4[ (5/2)y + (3/2) ] + 3y = 71 10y + 6 + 3y = 71 13y + 6 = 71 13y = 65 y = 65/13 = 5 Now that I have the value for y, I can solve for x: x = (5/2)y + (3/2) x = (5/2)(5) + (3/2) x = (25/2) + (3/2) x = 28/2 = 14 Answer: E #### E QUESTION:If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n? options: A)10 B)12 C)15 D)18 E)20 SOLUTION:There are 10 numbers divisible by 2 There are 5 numbers divisible by 4 There are 2 numbers divisible by 8 There is 1 number divisible by 16. Hence the total number of 2’s in 20! are 10+5+2+1=18 ANSWER:D #### D QUESTION:Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky's salary more than Ashu's? options: A)96% B)51.1% C)90% D)52.1% E)None of these SOLUTION:Solution: Let Ashu's salary = 100; Ashu's salary after rise = 125. Then Vicky's salary = 175. Vicky's salary after rise of 40% = 245. [As 10% of Vicky's salary is 17.5 then 40% = 17.5*4 = 70] . Difference between Vicky's salary and Ashu's salary = 245-125 = 120; . % more Vicky's salary than Ashu's = 120*100/125 = 96%. Answer: Option A #### A QUESTION:A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay? options: A)Rs.270 B)Rs.185 C)Rs.215 D)Rs.380 E)Rs.315 SOLUTION:12*8 :16*9 = 18*6 8: 12: 9 9/29 * 870 = 270 ANSWER:A #### A QUESTION:Which of the following is closest to 1/6+1/66+1/666 options: A)1/4.5 B)1/7 C)1/5.67 D)1/9 E)1/8 SOLUTION:1/6+1/66+1/666=0.16+0.015+0.0015=0.1765=1/5.665 Answer C #### C QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be: options: A)5:2 B)7:3 C)9:2 D)13:4 E)3:4 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 ANSWER:B #### B QUESTION:There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)320 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence 3x + 5x = 600 Solve for x 8x = 600 x = 75 Number of boys 3x = 3 × 75 = 225 Number of girls 5x = 5 × 75 = 375 C #### C QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)56 B)50 C)72 D)27 E)25 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B #### B QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base * Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? options: A)1178 B)144 C)66 D)8 E)55 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways. Hence the total ways are 24 * 6 = 144. Answer: B #### B QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:How many numbers from 29 to 79 are exactly divisible by 11? options: A)4 B)6 C)8 D)5 E)7 SOLUTION:Numbers=(79/11)-(29/11) =7-2 =5 numbers Option D is answer #### D QUESTION:In a test containing 16 questions , contestants get a base core of 20 points for taking the test. 5 points for each correctly answered question and 2 points for each unanswered question.An incorrectly answeredquestion is worth 0 points.Of the following scores which one is not attainable options: A)96 B)97 C)94 D)95 E)93 SOLUTION:1. 15 corrected and 1 uncorrected 20+5*15+0=95 2.15 corrected and 1attempted 20+5*15+2=97 3. 14corrected+2attempted 20+14*5+2*2=94 so 96 is not possible ANSWER:A #### A QUESTION:The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:6C1*5C2 = 6*10 = 60 The answer is C. #### C QUESTION:A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters) options: A)92 B)90 C)82 D)78 E)75 SOLUTION:I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5. O=12.5*6 = 75=E #### E QUESTION:Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture? options: A)1 : 9 B)1 by 5 C)1 : 7 D)1 : 3 E)1 : 1 SOLUTION:Selling price of the mixture = 70 and profit = 20% Cost price of the mixture = 70×100120=70×5670×100120=70×56 By applying alligation rule: So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5 Answer:B #### B QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1 SOLUTION:Explanation: Let the cost of the brand be Rs. X per kg. C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x) S.P of 5 kg = Rs. (5 * 177) = Rs. 885 [885 - (400 + 3x)]/(400 + 3x) * 100 = 18 24250 - 150x = 3600 + 27x 177x = 20650 => x = 116 2/3 So, cost of the other brand = Rs. 116.66. Answer: D #### D QUESTION:If a - b = 3 and a^2 + b^2 = 31, find the value of ab. options: A)12 B)15 C)10 D)11 E)13 SOLUTION:2ab = (a^2 + b^2) - (a - b)^2 = 31 - 9 = 22 ab = 11. Answer is D. #### D QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)2 months B)7 months C)8 months D)10 months E)12 months SOLUTION:Explanation: 7 * 8 : 9 * x = 8:9 => x= 7 months ANSWER:B #### B QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage? options: A)33 B)50 C)99 D)87 E)71 SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 150 (30 * 5) Profit percentage = (150 - 100)/100 * 100 = 50% Answer: B #### B QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)10 m B)16 m C)245 m D)19 m E)235 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: E #### E QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+99)=? options: A)7000 B)7250 C)7500 D)7750 E)6750 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 99=1+(n-1)2 => n=50 Use value of n in (1) then, Sn = (50/2)(1+99) = 2500 Ans:- 3(Sn) = 7500 Answer : C #### C QUESTION:The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 4. If the project took 90 hours, how many more hours did the hardest working person work than the person who worked the least? options: A)18 hours B)22 hours C)25 hours D)26 hours E)20 hours SOLUTION:Let the persons be A, B, C. Hours worked: A = 2*90/9 = 20 hours B = 3*90/9 = 30 hours C = 4*90/9 = 40 hours C is the hardest worker and A worked for the least number of hours. So the difference is 40-20 = 20 hours. Answer : E #### E QUESTION:There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is: options: A)9 B)13 C)15 D)12 E)19 SOLUTION:Explanation: abc/bcd=385/1001=>a/d=5/13 So d = 13 Option B #### B QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)6 SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours Answer: option E #### E QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer is C. #### C QUESTION:In what time will a train 140 m long cross an electric pole, it its speed be 144 km/hr? options: A)3.5 sec B)4.25 sec C)5 sec D)12.5 sec E)6 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 140/40 = 3.5 sec. ANSWER:A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform? options: A)338 B)240 C)287 D)400 E)191 SOLUTION:Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m. Answer: D #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent? options: A)28% B)25% C)11.11% D)28% E)55% SOLUTION:900 --- 100 100 --- ? => 11.11% Answer: C #### C QUESTION:n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4? options: A)3 B)2 C)1 D)0 E)None of these SOLUTION:Let n=4q+3. 2n=8q+6=4(2q+1)+2 Thus, when 2n is divided by 4, the remainder is 2. Correct Option: B #### B QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 45 years, was replaced by a new person. Find the age of the new person? options: A)12 B)15 C)18 D)21 E)25 SOLUTION:Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 45 + Q => Q = 15 ANSWER:B #### B QUESTION:The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: options: A)10º B)75º C)90º D)130º E)180º SOLUTION:Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º. Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º. Required angle = (130 - 120)º = 10º. Answer A #### A QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is? options: A)40m2 B)45m2 C)49m2 D)51m2 E)55m2 SOLUTION:39/360 * 22/7 * 12 * 12 = 49m2 Answer:C #### C QUESTION:A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class? options: A)45 B)40 C)35 D)30 E)50 SOLUTION:Explanation: Let the total number of students = x The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks. But total increase in the marks = 1/2×x=x/2 Hence we can write as x/2=20 ⇒x=20 x 2=40 Answer: Option B #### B QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)7 1/2 years B)20 years C)15 years D)38 years E)30 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years ANSWER:B #### B QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions? options: A)2112 m B)2704 m C)2278 m D)2288 m E)2378 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions. = 1500 * 2 * 22/7 * 22.4 = 211200 cm = 2112 m Answer: A #### A QUESTION:In a college, 95 percent of students Passed in math, 97 percent of students Passed in English, 99 percent Passed in French and 92 percent Passed in German. Can you find out the percentage of students who Passed in all 4 subjects ? options: A)92% B)90% C)96% D)83% E)89% SOLUTION:D 83% of student Passed in all four subjects. #### D QUESTION:If a^2+b^2=177and ab=54 then find the value of a+b/a-b? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:(a+b)^2=a^2+b^2+2ab=117+2*24=225 a+b=15 (a-b)^2=a^2+b^2-2ab=117-2*54 a-b=3 a+b/a-b=15/3=5 Answer is C. #### C QUESTION:In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth? options: A)39 B)24 C)28 D)26 E)30 SOLUTION:x x+4 x+8 x+12 x+16 x+20 x+24 x+28 x+32 x+36 10x+180=340 10x=160 x=16 3rd question = x+8 = 16+8 = 24 Answer B #### B QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1). options: A)320 B)350 C)340 D)360 E)400 SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there? 99+(912-9-90*2)/3=340 Answer : C #### C QUESTION:P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. options: A)5 B)8 C)9 D)10 E)11 SOLUTION:Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3×7/36 = 7/12 Remaining work = 1 – 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/12) = 5 Option A #### A QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 6*8.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/12 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 2*x Hence, a1+a2+..+a20+n = 22x So, the fraction asked = 2x/22x = 1/12 B #### B QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now? options: A)14years B)15years C)16years D)17years E)18years SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years ANSWER:A #### A QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse? options: A)27 B)98 C)27 D)80 E)71 SOLUTION:CP = SP + 1CP = SP - g 620 + x = 860 - 2x 3x = 240 => x = 80 Answer:D #### D QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)4 B)6 C)2 D)3 E)8 SOLUTION:9261 = 8000(21/20)N (21/20)3 = (21/20)N => N = 3 ANSWER D #### D QUESTION:we have 7 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg one of 15 kg one of 20 kg by using only five weight how many weight u can weight options: A)19 B)18 C)24 D)21 E)32 SOLUTION:select 5 weight out of 7, 7C5=21 ANSWER:D #### D QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats? options: A)12 B)302 C)1 D)250 E)286 SOLUTION:Total number of hats = 13 Possible number of formations = 13C3 = 286 Correct answer is E #### E QUESTION:A single letter is selected at random from the word 'SIMS'. The probability that it is a vowel is..?? options: A)1/4 B)3/11 C)4/11 D)3/7 E)1/2 SOLUTION:total vowels = 1, total number of letters = 4 so probability = 1/4 ANSWER:A #### A QUESTION:Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively options: A)19 B)17 C)13 D)9 E)18 SOLUTION:Explanation: Answer will be HCF of (28-10, 128-2, 147-3) HCF of (18, 126, 144) = 18 Option E #### E QUESTION:The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? options: A)4538 B)2778 C)2608 D)4530 E)2001 SOLUTION:Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs. 4530 Answer:D #### D QUESTION:A chair is bought for Rs.200/- and sold at Rs.310/- find gain or loss percentage options: A)15% loss B)20% gain C)25% gain D)30% gain E)55% gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (310- 200)/200= 55% gain E #### E QUESTION:A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. options: A)6/63 B)2/63 C)125/126 D)1/126 E)1/63 SOLUTION:Required probability = 1 - 1/126 = 125/126 ANSWER:C #### C QUESTION:The sector of a circle has radius of 20 cm and central angle 135o. Find its perimeter? options: A)91.5 B)87.1 C)91.7 D)91.3 E)91.1 SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 20) + 2(20) = 47.1 + 40 = 87.1 cm Answer:B #### B QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:If mn > 0, which of the following must be negative? options: A)mn B)mn^2 C)m/-n D)m/n E)m+n SOLUTION:Given mn> 0 So both will be the positive integers. If both are positive, then A,B,D,E also positive. Answer :C #### C QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 10 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 50 will be in team A 50 will be in team B The larger diff is 70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10. Answer choice C #### C QUESTION:Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested? options: A)Rs.20,000 B)Rs.20,028 C)Rs.20,298 D)Rs.20,029 E)Rs.20,291 SOLUTION:Let the second amount be Rs. x. Then, (12000 * 10 * 1)/100 + (x * 20 * 1)/100 = [(12000 + x) * 14 * 1] / 100 120000 + 20x = 16800 + 14x x = 8000 Total investment = 12000 + 8000 =Rs.20,000. Answer:A #### A QUESTION:The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Perimeter = 2(W+L) = 5W 3W = 2L W = 2L/3 WL = 54 2L^2/3 = 54 L^2 = 81 L = 9 cm The answer is D. #### D QUESTION:A manufacturer of a certain type of screw rejects any screw whose length is less than 2.44 + 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable? options: A)|k + 0.03| > 2.5 B)|k — 0.03| <= 2.5 C)|k — 2.5| > 0.03 D)|k — 2.5| >= 0.06 E)|k — 2.5| <= 0.03 SOLUTION:So, let's go through this step by step: rejects any screw whose length is less than 2.44 + 0.03 centimeters or greater than 2.5 + 0.03 centimeters. In other words, any screw that is less than: 2.44 + 0.03 =2.47 or greater than 2.50 + 0.03 =2.53 will be rejected. If k represents the length of a screw In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So: 2.47 ≤ K ≤ 2.53 You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths. Let's look at (E): |k — 2.5| <= 0.03 For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53 For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47 2.47 ≤ k ≤ 2.53 (E) #### E QUESTION:In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum? options: A)1 1/4 B)1 1/6 C)1 1/0 D)1 1/5 E)1 5/1 SOLUTION:Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10% Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.Answer: A #### A QUESTION:The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth? options: A)Rs. 600 B)Rs. 500 C)Rs. 400 D)Rs. 300 E)None of these SOLUTION:Explanation : T = 2 years R = 10% TD = (BG ×100)/TR = (24 × 100)/(2×10) = 12 × 10 = Rs. 120 TD = (PW × TR)/100 ⇒ 120 = (PW × 2 × 10)/100 ⇒ 1200 = PW × 2 PW =1200/2 = Rs. 600 Answer : Option A #### A QUESTION:The age of man is three times the sum of the ages of his two sons.Five years hence,his age will be double of the sum of the ages of his sons.The father's present age is : options: A)50 years B)46 years C)20 years D)45 years E)30 years SOLUTION:Let the sum of present ages of the two sons be x years. then father's present age =3x years. (3x+5)=2(x+10) 3x+5=2x+20 x=15. Hence, father's present age =45 years. Answer is D #### D QUESTION:If x^2=3x+2, then x^3 = ? options: A)3x+2 B)6x+2 C)11x+6 D)8x-3 E)5x+4 SOLUTION:x^2 = 3x+2 x^3 = x*x^2 = x*(3x+2) = 3x^2 + 2x = 3(3x+2)+2x = 11x+6 The answer is C. #### C QUESTION:One night a certain hotel rented 1/2 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned? options: A)25% B)30% C)35% D)40% E)50% SOLUTION:The rooms which were not rented is 1/2 The AC rooms which were not rented is (1/3)*(3/5) = 1/5 The percentage of unrented rooms which were AC rooms is (1/5) / (1/2) = 2/5 = 40% The answer is D. #### D QUESTION:Speed of boat in water is 12km/hr. and the speed of the stream is 3km/hr. Find the time taken by the boat to go upstream a distance of 45km. options: A)3 B)4 C)5 hrs. D)6 E)2 SOLUTION:US =speed of the boat - speed of the stream 12-3 =9km/hr. Time taken to cover 45km =45/9 = 5hrs. Answer : C #### C QUESTION:Average of first five multiples of 2 is options: A)9 B)6 C)13 D)15 E)16 SOLUTION:Explanation: Average=2(1+2+3+4+5)5=6 Answer: Option B #### B QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group? options: A)87 B)67 C)23 D)75 E)25 SOLUTION:Let the initial number of members in the group be n. Initial total weight of all the members in the group = n(48) From the data, 48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23 Therefore there were 23 members in the group initially. Answer: C #### C QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option? options: A)1/2 B)1/6 C)1/12 D)6/10 E)3/10 SOLUTION:as coin has only two faces then probability must be 1/2 ANSWER:A #### A QUESTION:You roll two six sided dices together. Can you calculate the probability that the first dice gives the number 2 while the second dice gives the number 5? options: A)2/23 B)1/33 C)1/36 D)3/54 E)6/35 SOLUTION:C 1/36 The number of possibilities for the first as well as the second dice are 6 and 6 respectively. Therefore the total possibilities or outcome are 6 * 6 = 36. Out of 36 outcomes, we need only one case i.e. the first gives 2 and the second gives 5. Therefore, the probability will be 1 on 36 or 1/36. #### C QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900 Vehicles inspected within 3 hours = 60*3/9 = 19 P = 19/900 Ans:D #### D QUESTION:JERRY has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If JERRY needs to pay exactly $128, what is the least number of bills he will need to use? options: A)16 B)35 C)46 D)577 E)576 SOLUTION:128 is the total sum of money. as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils 128-120 = 8 so now we need to get 8 from either 5 dollar bills or 1 dollar bills 8 - 5 (use only 1 5 dollar bill) = 3 so we can get 3 from using 3 $1 bills. Hence 16 ( 12+1+3 ) ANSWER IS A #### A QUESTION:A total of 22 men and 30 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women? options: A) 31 B) 31.5 C) 32.8 D) 32.5 E) 33 SOLUTION:Let Aw = average age of women Average = (Number of men X average age of men + Number of women X average age of women)/total number of people 35 * 52 = 22 * 38 + 30 * Aw =>1820 = 836 + 30 Aw => 30 Aw = 984 =>Aw = 32.8 Answer C #### C QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)11 B)18 C)99 D)77 E)51 SOLUTION:A:B = 2:3 B:C = 2:5 A:B:C = 4:6:15 6/25 * 75 = 18 Answer: B #### B QUESTION:The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A? options: A)81 B)65 C)75 D)89 E)90 SOLUTION:A + B + C = 3 *70 = 210 A + B + C + D = 4 * 70 = 280 ---- (i) So, D = 70& E = 70 + 3 = 73 B + C + D +E =68 * 4 = 272 --- (ii) From Eq. (i) & (ii) A-E = 280 –272 = 8 A = E +8 = 73 + 8 = 81 Answer : A #### A QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent? options: A)70% B)45% C)48% D)30% E)40% SOLUTION:Explanation: 840 ---- 380 100 ---- ? => 45% Answer: B #### B QUESTION:A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join? options: A)4 months B)5 months C)6 months D)7 months E)8 months SOLUTION:Explanation: Assume that C was there in the business for x months A:B:C =40000×12:60000×10:120000 × x =40×12:60×10:120x =40:5×10:10 x =8:10:2x =4:5:x C's share =375000 x/ 9+x=375000 x/9+x ⇒375000 x/9+x=150000 ⇒375x9+x=150 ⇒15x=6(9+x) ⇒5x=18+2x ⇒3x=18 ⇒x=6 It means C was there in the business for 6 months. Given that B joined the business after 2 months. Hence C joined 4 months after B joined. Answer: Option A #### A QUESTION:In how many different ways can the letters of the word 'CAREER' be arranged? options: A)10 ways B)20 ways C)180 ways D)60 ways E)40 ways SOLUTION:Totally there are 6 letters on the word CAREER. it contains 1C,1A,2R,2E. The no of ways is 6!/2!2!=180 ways. ANSWER:C #### C QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:What is the different between the place value and face value of 6 in the numeral 5468? options: A)45 B)54 C)60 D)36 E)44 SOLUTION:place value of 6 = 6 * 10 = 60 face value of 6 = 6 60 - 6 = 54 Answer is B #### B QUESTION:The average age of the district level hockey team of eleven is 35 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ? options: A)43 yrs. B)44 yrs. C)45 yrs. D)47 yrs. E)46 yrs. SOLUTION:Explanation: Total age of players in team = 35 x 11 = 385 When coach is included, total members = 12, Avg age increases by one becomes 23 Total age when coach is included = 36x12 = 432 Age of coach = 432-385 = 47 yrs. Answer:D #### D QUESTION:The average of 50 numbers id 20. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is : options: A)22.75 B)33.25 C)22.25 D)11.75 E)18.75 SOLUTION:Explanation: Total of 50 numbers = (50×20)=1000 Total of 48 numbers =(1000-(45+55)]=900 Required average = 900/48=18.75 Answer:E #### E QUESTION:If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is? options: A)A)15 B)B)10 C)C)14 D)D)12 E)E)11 SOLUTION:2 * 22/7 * 14 * x = 880 => x = 10 ANSWER:B #### B QUESTION:A man saves 10% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 5%, he is only able to save Rs. 400 per month. What is his monthly salary? options: A)Rs.6500 B)Rs.7500 C)Rs.7200 D)Rs.7273 E)Rs.6300 SOLUTION:Income = Rs. 100 Expenditure = Rs. 90 Savings = Rs. 10 Present Expenditure 90+90*(5/100) = Rs.94.5 Present Savings = 100 – 94.5 =Rs. 5.50 If savings is Rs. 5.50, salary = Rs. 100 If savings is Rs.400, salary = 100/5.5*400 = 7273 Answer : D #### D QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:If the cost price is 96% of the selling price, then what is the profit percent? options: A)4.17% B)5% C)6.12% D)3.25% E)5.75% SOLUTION:Let S.P. = $100 C.P. = $96 Profit = $4 Profit% = 4/96 * 100 = 25/6 = 4.17% Answer is A #### A QUESTION:Find compound interest on $ 8000 at 15% per annum for 2 years 4 months, compounded annually. options: A)3109 B)3209 C)3108 D)3107 E)3100 SOLUTION:Time = 2 years 4 months = 2(4/12) years = 2(1/3) years. Amount = $ [8000 X (1+­(15/100))2 X (1+((1/3)*15)/100)] =$ [8000 * (23/20) * (23/20) * (21/20)] = $ 11109. . :. C.I. = Rs. (11109 - 8000) = $ 3109. Answer A. #### A QUESTION:When positive integer F is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when F is divided by B? options: A) 13 B) 14 C) 15 D) 16 E) 17 SOLUTION:the remainder will be obtained from the decimal part when F is divided by B i.e. 0.35 0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this PS: for B-14 F=174 and B=40 #### B QUESTION:There are two inlets and one outlet to a cistern. One of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full? options: A)2 hours B)2.5 hours C)3 hours D)3.5 hours E)8 hours SOLUTION:The combined inflow rate of the two inlets is 1/4 + 1/8 = 3/8 cistern/hour. Thus, working together, it takes 8/3 hours (time is reciprocal of rate) to fill the cistern. From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) =2*3/8 = 3/4 th of the cistern . Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour. Letting x to be the rate of the outlet, we would have: 3/8 - x = 1/4 --> x = 1/8 cistern/hour, which means that it takes 8 hours the outlet working alone to empty the cistern. Answer: E. #### E QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)Rs.500 B)Rs.1000 C)Rs. 3630 D)Rs.2500 E)Rs.6000 SOLUTION:Explanation: 6300:4200:10500 3:2:5 3/10 * 12100 =Rs. 3630 ANSWER:C #### C QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? options: A)5/20 B)9/25 C)8/20 D)9/20 E)6/20 SOLUTION:Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20} answer 9/20 Answer D #### D QUESTION:Find the greatest number which leaves the same remainder when it divides 25, 57 and 105. options: A)18 B)8 C)12 D)16 E)None of these SOLUTION:105 - 57 = 48 57 - 25 = 32 105 - 25 = 80 The H.C.F of 32, 48 and 80 is 16. ANSWER:D #### D QUESTION:Find the number such that when 15 is subtracted from 7 times the number,the result is 10 more than twice the number? options: A)4 B)3 C)5 D)2 E)6 SOLUTION:Let the number be x. 7x-15=2x+10 7x-2x=15+10 5x=25 x=5 answer is option C #### C QUESTION:Three friends X, Y, Z rented a auto for Rs.520. A used it for 6 hours, B used it for 9 hours and C used it for 11 hours. What is the hire charges paid by Y: options: A)Rs 140 B)Rs 160 C)Rs 180 D)Rs 200 E)None SOLUTION:X : Y : Z = 7 : 8 : 11. Hire charges paid by Y = Rs(520×9/26) = Rs.180. Answer C #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 140 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)49 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 140 / 20 = 7 sandwiches in one part For bologna we have 7 parts so: 7 * 7 = 49 Answer is E #### E QUESTION:An inspector rejects 0.06% of the meters as defective. How many will he examine to reject 2? options: A)A)1500 B)B)2000 C)C)2500 D)D)3000 E)E)3333 SOLUTION:Let the number of meters to be examined be x Then, 0.06% of x = 2 (6/100)*((1/100)*x = 2 x = 3333 Answer is E #### E QUESTION:The third proportional to 2 and 6 is? options: A)18 B)17 C)14 D)15 E)13 SOLUTION:(6*6)/2 = 18 Answer:A #### A QUESTION:A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $45,000 commission, how many machines did she sell? options: A) 140 B) 103 C) 105 D) 115 E) 120 SOLUTION:First 100 machines = 3% commission = 0.03*100*10000 = 30000 Commission from sale of next machines = 46000 - 30000 = 16000 So 40 more machines.. Total = 140 machines IMO A.. #### A QUESTION:(0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is: options: A)0.8 B)0.4 C)0.96 D)0.69 E)0.76 SOLUTION:Given expression = (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2) = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2) = (a - b) = (0.5 - 0.1) = 0.4 Answer is B #### B QUESTION:In boring a well 50 m deep, the cost is Rs.4/– for the first meter. The cost of each successive meter increases by Rs.2/–. What is the cost of boring the entire well? options: A)1650 B)2650 C)3650 D)4650 E)2850 SOLUTION:For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2 So Sum=(n/2)[2a+(n-1)d]= Total cost of boring =(50/2)[2*4+(50-1)*2]=25(8+98) = 2650 ANSWER:B #### B QUESTION:The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is options: A)62 kg B)60 kg C)64 kg D)72 kg E)None of these SOLUTION:Explanation : Let the weight of student be x kg. Given, Difference in average weight = 8 kg => (96-x)/4 = 8 => x = 64 Answer : C #### C QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:John professes to sell his goods at the cost price but he made use of 800 grams instead of a kg, what is the gain percent? options: A)12 1/3% B)12 1/4% C)12 2/3% D)12 2/1% E)12 1/2% SOLUTION:800 --- 100 100 --- ? => 12 1/2% Answer:E #### E QUESTION:On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have four times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences? options: A)6 B)7 C)8 D)10 E)12 SOLUTION:If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does: (w + 4) = 4(p - 4) If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded: p + 5 = w - 5 Solving gives p = 10 and w = 20. Answer: D. #### D QUESTION:X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 54 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is : options: A)34 B)43.2 C)40 D)38 E)29 SOLUTION:Solution: Average speed = 2XY / X+Y = 2*54*36 / 54+36 = 43.2 Answer : B #### B QUESTION:The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5/18 = 30 m/s Hence time taken to cover 330 m = 330/30 = 11 seconds. Answer: A #### A QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students? options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9 SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760 Sum of the marks for the class of 45 students = 45 * 70 = 3150 Sum of the marks for the class of 85 students = 2760 + 3150 = 5910 Average marks of all the students = 5910/85 = 69.5.Answer: D #### D QUESTION:On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done? options: A)2880 B)2778 C)2682 D)8222 E)6282 SOLUTION:Explanation: There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways. Further, in each category (subject), books are to be arranged in different order, we get, Required number of ways: 3! * [2! * 2! * 5!] = 2880 ANSWER: A #### A QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)78% D)48% E)11% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/10 B)1/8 C)1/6 D)1/5 E)1/4 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 5*3*2=30. P(dispensing one of each color)=30/120=1/4. The answer is E. #### E QUESTION:The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class. options: A)47.55 kg B)48 kg C)48.55 kg D)49.25 kg E)59.25 kg SOLUTION:16*50.25+8*45.15/24=48.55 ANSWER:C #### C QUESTION:The division of a whole number N by 14 gives a quotient of 18 and a remainder of 2. Find N. options: A)797 B)254 C)597 D)997 E)297 SOLUTION:According to the division process of whole numbers, N can be written, using multiplication, as follows N = quotient *divisor + remainder = 18* 14 + 2 = 254 correc answer B #### B QUESTION:A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum? options: A)7000 B)7029 C)7290 D)7010 E)7102 SOLUTION:Let the sum be Rs. x. (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840 => 12x/100 = 840 => x = 7000. Answer:A #### A QUESTION:What is the remainder when 4^381 is divided by 5 ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:I also agree that the remainder is '4' (using the last digit of the powers of 7). Could we have the official answer please?E #### E <<<Examples ends QUESTION:What is the units digit of (52^5)(37^3)(71^9)? options: A)3 B)4 C)6 D)7 E)8 SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2. The units digit of 37^3 is the units digit of 7^3 which is 3. The units digit of 71^9 is the units digit of 1^9 which is 1. The units digit of 2*3*1 is 6. The answer is C. #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The length of a rectangular plot is 10 meters more than its width. If the cost of fencing the plot at $15.50 per meter is $744, what is the length of the plot in meters? options: A)11 B)13 C)15 D)17 E)19 SOLUTION:perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20 cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 744 62L = 1054 L = 17 meters The answer is D. #### D QUESTION:A toy RC car goes 3 feet per second. A boy wants to add an updated part to his RC that will allow the RC car to travel at 6 feet per second. How far will the upgraded car travel in 1 minute? Round to the nearest hundredth. options: A)200 feet B)250 feet C)300 feet D)360 feet E)400 feet SOLUTION:6 feet per sec x 60= 360 feet Answer D #### D QUESTION:What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x options: A)2450 B)2560 C)3200 D)3400 E)3158 SOLUTION:12 12 × 3 + 2 = 38 38 × 3 + 2 = 116 116 × 3 + 2 = 350 350 × 3 + 2 = 1052 1052 × 3 + 2 = 3158 E #### E QUESTION:The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what is the width of the field? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:Let L be the length and W be the width. L = (7/5)W Perimeter: 2L + 2W = 240, 2(7/5)W + 2W = 240 Solve the above equation to find: W = 50 m and L = 70 m. correct answer A)50 #### A QUESTION:Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144? options: A) 0 B) 25 C) 49 D) 81 E) 100 SOLUTION:144 =12 *12 (1!)^3=1 2!=2, therefore (2!)^3=2*2*2=8 3!=6, therefore (3!)^3=6*6*6=216 4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144 thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0 now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144 now remainder when 225 is divided by 144 is 81. hence answer should be D #### D QUESTION:Set R has a mean of 9 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){18, 20} B){8, 10} C){28, 38} D){6, 10} E){5, 10} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 9,the values (8,10) are closer than others. Hence Answer : B #### B QUESTION:A man buys s cycle for $100 and sells it at a loss of 30%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 70% of the $100 = 70/100 * 100 = $70 Answer is C #### C QUESTION:Q. How many 9-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6, 6, 7? options: A)180 B)140 C)210 D)270 E)300 SOLUTION:the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2 i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _ case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6 when the units digit is 2 i.e 1 _ _ _ _ _ 2 number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60 when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30 case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6) number of ways this can be done would be 5! / (2!) for 2 =60 and 5! / 2! for 6 ... = 60 adding all of these ... gives the answer 140 ... the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat B #### B QUESTION:Set A = {1, 2, 3, 4, 5, 6, q} Which of the following possible values for q would cause Set A to have the smallest standard deviation? options: A) 1 B) 2.5 C) 3 D) 3.5 E) 7 SOLUTION:I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice. Answer D. #### D QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 21% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? options: A)40% B)45% C)55% D)60% E)63.5% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 63.5%. E #### E QUESTION:If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72? options: A)24 B)36 C)12 D)18 E)16 SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. 72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12 C #### C QUESTION:Six lights begin to flash together at 12:00 noon and flash respectively at intervals of 3, 4, 5, 6, 7, and 8 seconds. Not including the flash at 12:00 noon, how many more times will all six lights flash together before 1:00 pm (i.e. one hour later)? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:The least common multiple is 2*2*2*3*5*7=840. 3600 seconds / 840 = 4 + remainder. The answer is A. #### A QUESTION:Two trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ? options: A)10.7 Seconds B)10.8 Seconds C)10.9 Seconds D)11.8 Seconds E)None of these SOLUTION:Explanation: Relative Speed = 60+40 = 100 Kmph = 100*(5/18) = 250/9 m/sec Distance to be covered = 140 + 160 = 300 metres Time = Distance/Speed Time=300∗9/250=54/5=10.8 seconds Option B #### B QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)20 SOLUTION:In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3. 5! = 120 has 1 trailing zeros. 10! will have 2 trailing zeros. 15! will have 3 trailing zeros. 20! will have 5 trailing zeros. Answer: E. #### E QUESTION:Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number? options: A)6 B)9 C)11 D)12 E)15 SOLUTION:Explanation: 3x/5 – x/5 = 6 => x =15 1 + 5 = 6 A) #### A QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-4)(x+9)(2X+5) = 0? options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2 SOLUTION:x = -2.5 Prob =1/12 Answer - A #### A QUESTION:Simple interest on a certain sum at a certain annual rate of interest is 1/3 of the sum. If the numbers representing Time is three times the Rate percent , then the Rate is: options: A)1 1/3 %. B)2 1/3 %. C)3 1/3 %. D)4 1/3 %. E)5 1/3 %. SOLUTION:Explanation : Let sum = x. Then, S.I. = x/3 Let N =3R [x * 3R * R / 100] = x/3? R^2 = 100/9 R = 10/3 = 3 1/3%. Hence, Rate = 3 1/3 %. Answer : C #### C QUESTION:Set A: {1, 3, 4, 6, 9, 12, 16} If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 4? options: A)3/14 B)2/7 C)9/14 D)5/7 E)1/35 SOLUTION:using probability you can solve: 3/7*2/6*1/5=1/35. Ans E #### E QUESTION:A certain street contains 100 buildings.They are numbered from 1 to 100. How many 9s are used in numbering these buildings? options: A)21 B)20 C)19 D)18 E)9 SOLUTION:9,19,29,39,49,59,69,79,89,90,91,92,93,94,95,96,97,98,99 so number of 9's=20 ANSWER:B #### B QUESTION:Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 2 screws and 4 nails? options: A)a. 4 B)b. 5/2 C)c. 2 D)d. 3/2 E)e. 5/4 SOLUTION:let the weight of nail be n and that of screw be s.. so s+w=1/2 * (6s+1n)... or 1n = 4s.. lets see the weight of 3 s and 3n= 3s+3*4s=15s.. and weight of 2s and 4n= 2s+4*2s=10s.. ratio= 15s/10s=15/10=3/2 D #### D QUESTION:On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4*[sqrt(t-9)] for t>9, where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur? options: A)17 B)21.25 C)12.25 D)14.05 E)18 SOLUTION:radius=7mm. So dia= 14mm. putting D=14 in equation we can easily calculate t=21.25 ANSWER:B #### B QUESTION:A train 500 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? options: A)298 m B)279 m C)500 m D)289 m E)800 m SOLUTION:Speed = 78 * 5/18 = 65/3 m/sec. Time = 1 min = 60 sec. Let the length of the train be x meters. Then, (500 + x)/60 = 65/3 x = 800 m. Answer: E #### E QUESTION:The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is: options: A)89.25 km/hr. B)77 km/hr. C)90.25 km/hr. D)94.25 km/hr. E)96.25 km/hr. SOLUTION:Let the speed of two bullet trains be 7x and 8x km/hr. Then, 8x = (440/5) = 88 x = (88/8) = 11 Hence, speed of first bullet train = (7 x 11) km/hr = 77 km/hr. B #### B QUESTION:A data set with a mean of 60 has a standard deviation of 1.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)53 B)56 C)58 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=60-1.5=58.5 to{mean}+{deviation}=60+1.5=61.5. The smallest number within this range from the options is 58. Answer: C. Hope this helps. #### C QUESTION:Mark drove for 1/2 of the trip, and Justin drove for 1/4 of the trip. Gina and Kaitlyn divided the rest of the driving evenly between them. If the entire trip was 128 miles, how many miles did Kaitlyn drive? options: A)26 miles B)16 miles C)20 miles D)18 miles E)17 miles SOLUTION:1/2 x 128 = 64 miles Mark drove 1/4 x 128 = 32 miles Justin drove 64 + 32 = 96 miles driven 128 - 96 = 32 miles left 32 ÷ 2 = 16 miles driven by Kaitlyn correct answer B #### B QUESTION:The greatest common factor of positive integers m and n is 9. What is the greatest common factor of (2m^2, 2n^2)? options: A)9 B)81 C)162 D)324 E)405 SOLUTION:m = 9j and n = 9k, where the greatest common factor of j and k is 1. 2m^2 = 2*9*9*j^2 and 2n^2 = 2*9*9*k^2 The greatest common factor of 2m^2 and 2n^2 is 2*9*9 = 162 The answer is C. #### C QUESTION:A three digit number divisible by 7 becomes divisible by 3 when 7 is added to it. The largest such number is : options: A)891 B)896 C)882 D)867 E)864 SOLUTION:Out of all the 5 options, only 896 is NOT divisible by 3. All others are divisible So Answer = B(No further calculation required) Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3 7 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3 Applying the above rule,It means that the number which we are going to add should be non-divisible by 3 So comes the answer = 896 Answer : B #### B QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)87 min B)82 min C)86 min D)47 min E)72 min SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:A, Band C are three contestants in a kmrace. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ?. options: A)540 m B)178 m C)936 m D)234 m E)713 m SOLUTION:While A covers 1000 m, B covers (1000 - 40) m = 960 m and C covers (1000 - 64) m or 936 m. When B covers 960 m, C covers 936 m Option C #### C QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:Of the science books in a certain supply room, 40 are on botany, 45 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same area science? options: A)186 B)225 C)294 D)302 E)314 SOLUTION:The worst case scenario is to remove all the books on botany, zoology, and geology. Also we can remove 79 books each from physics and chemistry. The total is 40 + 45 + 50 + 79 + 79 = 293. The next book removed must either be physics or chemistry, ensuring 80 books in that subject. The answer is C. #### C QUESTION:A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? options: A)Rs. 105 and Rs. 6 B)Rs. 216 and Rs. 12 C)Rs. 210 and Rs. 12 D)Rs. 210 and Rs. 6 E)None SOLUTION:Explanatory Answers Let half of the full basic fare be Rs. X. Therefore, full basic fare is Rs. 2X. Let the reservation charge be Rs. Y per ticket. Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge) 2X + Y = 216 --- (1) The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y. Hence, 3X + 2Y = 327 --- (2) Solving (1) and (2) we get, X = 105 and Y = 6 Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6 Answer D #### D QUESTION:A man lent money of Rs. 2500 on simple interest for rate on interest being same as number of years. If he got Rs. 900 as interest amount at the end of the period then what is the rate of interest? options: A)6% B)4% C)5% D)3% E)2% SOLUTION:Explanation : SI = pnr SI = (2500*3r*3r)=900 r2 = 25 r = 5% Answer : C #### C QUESTION:Susan, Tim, Matt and Kim need to be seated in 4 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ? options: A)360 B)12 C)80 D)240 E)60 SOLUTION:Total # of arrangement of 4 people is 4!. In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?). So, # of arrangements to satisfy the given condition is 4!/2=12. Answer: B. #### B QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was? options: A)16 years B)14 years C)18 years D)19 years E)15 years SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38 => x = 19 Son's age 5 years back = (19 - 5) = 14 years. Answer: B #### B QUESTION:It takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate. If 5 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 1:00 PM, at what time will the machine be complete? options: A)4:30 B)4:45 C)5:00 D)5:15 E)5:30 SOLUTION:3 workers build 1/15 of a machine in one hour. 1 worker builds 1/45 of a machine in one hour. In the first 2 hours, 5 workers build 5*(1/45)*2=10/45 of a machine. From 1:00 to 2:00, 6 workers build another 6/45. The total is 16/45. From 2:00 to 3:00, 7 workers build another 7/45. The total is 23/45. From 3:00 to 4:00, 8 workers build another 8/45. The total is 31/45. From 4:00 to 5:00, 9 workers build another 9/45. The total is 40/45. To build another 5/45, 10 workers need (5/10)*60 minutes which is 30 minutes. The machine is complete at 5:30. The answer is E. #### E QUESTION:The distance light travels in one year is approximately 5,890,000,000,000 miles. The distance light travels in 100 years is options: A)A) 587 × 108 miles B)B) 587 × 1010 miles C)C) 587 × 10-10 miles D)D) 589 × 1012 miles E)E) 587 × 10-12 miles SOLUTION:The distance of the light travels in 100 years is: 5,890,000,000,000 × 100 miles. = 589,000,000,000,000 miles. = 589 × 1012 miles. The answer is (D) #### D QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:let no. of right ques be x, then no. of wrong ques will be= 26 - x now, according to ques 8x - (26-x)5 = 0, hence x=10...no. of right ques is 10 ANSWER:B #### B QUESTION:How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? options: A)482 B)226 C)276 D)266 E)181 SOLUTION:Explanation: 20000(11/10)4 - 20000(6/5)2 = 482 Answer: A #### A QUESTION:Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number? options: A)37 B)85 C)48 D)43 E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 48 6x = 48 => third number is 48. Answer: Option C #### C QUESTION:Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255 options: A)18 B)19 C)27 D)29 E)31 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong. C #### C QUESTION:A no. when divided by 35leaves a remainder 20, what is the remainder if the same no.be divided by 15? options: A)2 B)4 C)7 D)8 E)9 SOLUTION:Explanation: 35 + 25 = 60/15 = 4 (Remainder) B #### B QUESTION:A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back? options: A)$4,040 B)$4,120 C)$1,960 D)$4,920 E)$1,400 SOLUTION:In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost. So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost. Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $5,000-$880=$4,120. Answer: B. #### B QUESTION:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster? options: A)30 B)44 C)42 D)46 E)50 SOLUTION:Total # of students 20+28+18-(9+7+10)+4=44. Answer: B. #### B QUESTION:A train 280 m long, running with a speed of 63 km/hr will pass a tree in? options: A)18 sec B)16 sec C)19 sec D)11 sec E)12 sec SOLUTION:: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec Answer: B #### B QUESTION:A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? options: A)388 B)299 C)266 D)400 E)2871 SOLUTION:2*12 : 3*12 : 4*24 1: 3: 4 1/8 * 3200 = 400.Answer: D #### D QUESTION:A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? options: A)1 kmph. B)2 kmph. C)3 kmph. D)4 kmph. E)5 kmph. SOLUTION:DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A #### A QUESTION:Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.? options: A)28 B)60 C)32 D)36 E)44 SOLUTION:the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13. using the elimination method look for a number that is both divisible by 7 and 13, of all the options only 60 is divisible by 4 and 20. [ 60/4=15 and 60/20=3] answer :B #### B QUESTION:A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:In one hour, the crow eats 1/24 of the nuts. (1/4) / (1/24) = 6 hours The answer is A. #### A QUESTION:9, 16, 18, 25, 36,49 options: A)9 B)16 C)18 D)25 E)36 SOLUTION:Each of the numbers except 18, is perfect square. Answer: Option C #### C QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B QUESTION:A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle? options: A)Rs.1148 B)Rs.1160 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 82% of Rs.1400 = Rs.(82/100×1400) Rs.1148. Answer A #### A QUESTION:If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost? options: A)24 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 60 : x 250 * x = (100 * 60) x = (100 * 60) / 250 x = 24 ANSWER: A #### A QUESTION:A sum of Rs. 12500 amounts to Rs. 16500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)4% B)5% C)6% D)8% E)14% SOLUTION:S.I. = (16500 - 12500) = Rs. 4000/- Rate = (100 * 4000) / (12500 * 4) = 8% ANSWER:D #### D QUESTION:The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? options: A)8 : 9 B)21 : 22 C)17 : 18 D)12 : 20 E)Cannot be determined SOLUTION:Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x). (120/100 x 7x) and (110/100 x 8x) 42x/5 and 44x/5 The required ratio = (42x/5 : 44x/5)= 21 : 22. ANSWER B #### B QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle? options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 85% of Rs.1200 = Rs.(85/100×1200) Rs.1020. Answer B #### B QUESTION:Two pipes can fill a tank in 10 hours & 12 hours respectively. While 3rd pipe empties the full tank n 20 hours. If all the three pipes operate simultaneously,in how much time will the tank be filled? options: A)6 hrs 43 min B)2 hrs 25 min C)7 hrs 30 min D)6 hrs 32 min E)7 hrs 10 min SOLUTION:tank filled in 1 hr = 1/10 + 1/12 - 1/20 = 8/60 = 2/15 part so full tank is filled in 15/2 hrs = 7 hr 30 min.. ANSWER:C #### C QUESTION:A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit , what is their total profit? options: A)28000 B)30000 C)32000 D)34000 E)None of these SOLUTION:Explanation : Suppose B's investment = x. Then A's investment= 3x Suppose Bs period of investment = y, then A's period of investment = 2y A : B = 3x * 2y : xy = 6 : 1 Total profit * 1/7 = 4000 => Total profit = 4000*7 = 28000. Answer : Option A #### A QUESTION:Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 asquotient and the 15 as remainder? options: A)1245 B)1567 C)1678 D)1335 E)1635 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Large number = 270+1365 = 1635 E #### E QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is options: A)35 B)37 C)38 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 8) years. (x+8+10)=2(x—10) hence x=38. Present age of B = 38 years Answer: Option C #### C QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 24*5= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 24*5 + 2y =124 then y=2 24*4 + 2y = 124 then y=14 24*3 +2y = 124 then y= 26 24*2 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer:A #### A QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(6200*5*3)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have? options: A)576 B)800 C)726 D)484 E)500 SOLUTION:(4/15) * A = (2/5) * B A / B = 3 / 2 Therefore A's share is = (1210 * (3/5)) = 726 Ans - C #### C QUESTION:If x is positive integer,y is negative integer, and 5x+2y=4, which of the following could be the value of x ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Use answer options to solve this problem - Put x = 2 So, 5x+2y=4 Or, 5(2)+2y=4 Or, 10+2y=4 Or, 2y=4-10;2y=-6 Or, y=-3(y is negative integer) Answer will be (C) #### C QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)355 SOLUTION:Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14) = 322. ANSWER:C #### C QUESTION:At what rate percent of simple interest will a sum of money double itself in 11 years? options: A)9.09 % B)4.54 % C)8 .2 % D)4.94 % E)5.54 % SOLUTION:Let sum = x. Then, S.I. = x. Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 11) = 100/11 = 9.09 % ANSWER:A #### A QUESTION:With 630 ml mixture of milk & water in the ratio 7:2. How much water mustbe added to make the ratio 7:3? options: A)60 ml B)80 ml C)70 ml D)90 ml E)92 ml SOLUTION:concentration of water in mixture1 =2/9 (since the ratio of milk and water = 7:2) ...(1) concentration of water in pure water= 1 ...(2) Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3 => concentration of water in mixture2 =3/10 By rule of alligation, concentration of water in mixture1 (2/9) concentration of water in pure water (1) Mean concentration (3/10) 1−3/10=7/10 =1:19 => Quantity of water =630×1/9=70 ml C #### C QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C QUESTION:In how many different number of ways 9 men and 2 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)170 C)C)190 D)D)210 E)E)1663200 SOLUTION:11p7 = 11 x 10 x 9 x 8 x 7 × 6 × 5 = 1663200 Option 'E' #### E QUESTION:The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? options: A)1267 B)1201 C)1200 D)1209 E)1216 SOLUTION:P --- 10 ---- 600 P --- 5 ----- 300 3P --- 5 ----- 900 ------ => 1200 Answer: C #### C QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000 SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager. Average company salary * Number of employees = Total company salary >>> $80,000 * 10 = $800,000 Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000) >>> $800,000 - $300,000 - $240,000 = $260,000. The correct answer is C. #### C QUESTION:If 6 (A's capital) = 8 (B's capital) = 16 (C's capital). Then the ratio of their capitals is? options: A)8:15:16 B)8:15:68 C)8:6:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 16 C A:B:C = 1/6:1/8:1/16 = 8:6:3 Answer: C #### C QUESTION:From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? options: A)a) 1/21 B)b) 35/2 C)c) 4/21 D)d) 2/7 E)e) 3/7 SOLUTION:Total number of ways to choose 5 out of 9 = 9C5 = 144. Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520. P = favorable/total = 2520/144 = 35/2. Answer: B. #### B QUESTION:A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy options: A)s. 600 B)s. 800 C)s.500 D)s.900 E)s. 1300 SOLUTION:Let the cost of one toy = X. Then, cost of 18 toys = 18X. Gain = 3X. SP of 18 toys = Rs. 27300. Gain = SP – CP 3X = 27300 – 18X 21X = 27300 X = Rs. 1300. ANSWER : OPTION E #### E QUESTION:The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? options: A)4 years B)8 years C)6 years D)5 years E)1 years SOLUTION:Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 => x = 4. Age of youngest child = x = 4 years. Answer: A #### A QUESTION:The product of three consecutive numbers is 336. Then the sum of the smallest two numbers is ? options: A)13 B)15 C)20 D)38 E)56 SOLUTION:Product of three numbers = 336 336 = 6*7*8. So, the three numbers are 6, 7 and 8. And Sum of smallest of these two = 6+7 = 13. ANSWER : OPTION A #### A QUESTION:A committee of three people is to be chosen from 6 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee? options: A)16 B)24 C)26 D)30 E)160 SOLUTION:One of the approaches: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 6 to send only onerepresentativesto the committee: 6C3=20. But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8. Total # of ways: 6C3*2^3=160. Answer: E. #### E QUESTION:Arun and Varun appeared at an examination. Arun secured 9 marks more than Varun and his marks was 56% of the sum of their marks. What are the marks obtained by them options: A)42, 33 B)42, 36 C)44, 33 D)44, 36 E)44, 37 SOLUTION:Explanation : Let the marks secured by them be x and (x + 9) Then sum of their marks = x + (x + 9) = 2x + 9 Given that (x + 9) was 56% of the sum of their marks =>(x+9)=56/100(2x+9)=>(x+9)=14/25(2x+9) => 25x + 225 = 28x + 126 => 3x = 99 => x = 33 Then (x + 9) = 33 + 9 = 42 Hence their marks are 42 and 33 Answer : A #### A QUESTION:If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q options: A)1 B)3 C)5 D)7 E)9 SOLUTION:3/7 = 0.428571... (a repeating pattern one digit long) B #### B QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum Q of even integers from 102 to 200 inclusive? options: A)5100 B)7550 C)10100 D)15500 E)20100 SOLUTION:My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then: Q=2550+(100*50)=7550.B #### B QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C? options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480 SOLUTION:Explanation : Amount of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400 Answer : Option D #### D QUESTION:If n is a natural number, then(6n^2+6n) is always divisible by? options: A)6 only B)6 and 12 C)12 only D)by 18 only E)None of these SOLUTION:(6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Correct Option: B #### B QUESTION:To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ? options: A)52.5 B)62.5 C)72.5 D)82.5 E)81.5 SOLUTION:Explanation: Let the capacity of 1 bucket = x. Then, capacity of tank = 25x. New capacity of bucket = 2/5 x. Required no of buckets = 25x / (2x /5) = 62.5 ANSWER IS B #### B QUESTION:How many integers between 500 and 1000 are there such that their unit digit is even? options: A)250 B)150 C)500 D)100 E)200 SOLUTION:500 numbers between - 500 and 1000 Out of which half would be even, half odd. Number of even unit digit number = 250. correct option is A #### A QUESTION:A and B go around a circular track of length 900m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point? options: A)120 sec B)165 sec C)186 sec D)180 sec E)168 sec SOLUTION:Time taken to meet for the first time at the starting point = LCM { length of the track / speed of A , length of the track / speed of B} = LCM { 900/ (36 * 5/18) , 900/ (54 * 5 /18) } = LCM (90, 60) =180 sec. Answer:D #### D QUESTION:Rs.12320 were divided among W, X & Y in such a way that W had Rs.640 more than X and Y had Rs 480 more than X . How much was X’s share? options: A)Rs.4590 B)Rs.4610 C)Rs.4620 D)Rs.4630 E)Rs.4640 SOLUTION:Let X gets Rs x. Then We can say W gets Rs (x + 640 ) and Y gets Rs ( x + 560) . x + 640 + x + x + 1120 = 12320 3x = 10560 x = 3520 . C’s share = Rs ( 3520+1120 ) = Rs.4640 E #### E QUESTION:there is four light.all light glow in blue,white,yellow and red. all glow together and take different color.every time each light change its color in given four of the color.but at same time no two light have same color then tell how many design will form? options: A)20 B)24 C)18 D)16 E)22 SOLUTION:it is so simple,it is just permutation of 4 item. 4P4=4!=24 answer B #### B QUESTION:A car covers a distance of 424 km in 6 ½ hours. Find its speed? options: A)65.9 kmph B)75.2 kmph C)65.2 kmph D)66.2 kmph E)55.2 kmph SOLUTION:424/(13/2) = 424*2/13 =65.2 kmph ANSWER:C #### C QUESTION:Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4, find P (E|F) and P(F|E)? options: A)1/4 B)1/7 C)3/7 D)4/9 E)5/11 SOLUTION:Here, E and F are events P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1 P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4. A) #### A QUESTION:On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1? options: A) 8 B) 12 C) 24 D) 32 E) 36 SOLUTION:Jan 1 = C Feb 1 = C - 3 March 1 = C - 6 April 1 = C - 9 May 1 = C - 12 June 1 = C - 15 July 1 = C - 18 Aug 1 = C - 21 Sept 1 = C - 24 Difference between stock on September 1 than were in stock on January 1 will be - C - ( C - 24 )= 24 Hence answer will be (C) #### C QUESTION:Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)50 B)88 C)77 D)55 E)23 SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 46 - 36 = 10 km/hr. = 10 * 5/18 = 25/9 m/sec. 2x/36 = 25/9 => x = 50. Answer: A #### A QUESTION:In X game of billiards, X can give Y 20 points in 45 and he can give Z 30 points in 45. How many points can Y give Z in X game of 100? options: A)30 B)20 C)25 D)40 E)50 SOLUTION:X scores 45 while Y score 40 and Z scores 30. The number of points that Z scores when Y scores 100 = (100 * 30)/25 = 60. In X game of 100 points, Y gives (100 - 60) = 40 points to C. D #### D QUESTION:7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ? options: A)502 B)503 C)504 D)505 E)506 SOLUTION:7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3. Now,we see 3,7,11,15....2015 are in AP tn=a+(n-1)d 2015=3+(n-1)4 2015=3+4n-4 4n=2016 n=504 ANSWER:C #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts and we should calculate how many sandwiches holds 1 part: 120 / 20 = 6 sandwiches in one part For bologna we have 7 parts so: 5* 6 = 30 Answer is B #### B QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A #### A QUESTION:A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems? options: A)676 B)833 C)1023 D)839 E)1035 SOLUTION:Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted. Hence, the required number of ways = 45 - 1. = 210 - 1 = 1024 - 1 = 1023 Answer:C #### C QUESTION:Naomi was ordering yarn from a discount web site. If she ordered more than $50 worth of yarn labeled “discountable”, she could take an extra 10% from the price of that yarn. Only some of the yarn she ordered was eligible for the discount. Here is what Naomi ordered: 2 skeins at $2.50 per skein (not discountable) 8 skeins at $8.40 per skein (discountable) 7 skeins at $5.99 per skein (discountable) Tax is 5% and shipping is 8%. How much did Naomi pay for her yarn? options: A)$116.64 B)$216.64 C)$316.64 D)$416.64 E)$516.64 SOLUTION:8 x $8.40 = $67.20 (All money is rounded to hundredths at each step.) 7 x $5.99 = $41.93 $67.20 + $41.93 = $109.13 discountable $109.13 x .10 = $10.91 (rounded) $109.13 - $10.91 = $98.22 for discounted yarn 2 x $2.50 = $5.00 for un-discounted $98.22 + $5.00 = $103.22 cost of yarn $103.22 x 1.13 = $116.64 with tax and shipping (5% + 8% = 13%) correct answer A #### A QUESTION:In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group? options: A)12 B)3 C)5 D)8 E)10 SOLUTION:Let the number of buffaloes be x and the number of ducks be y. Then 4x+2y=2(x+y)+24 =>x=12 ANSWER A 12 #### A QUESTION:In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way? options: A)3 sec B)4 sec C)8 sec D)6 sec E)7 sec SOLUTION:T = 52/24 * 18/5 = 8 sec ANSWER:C #### C QUESTION:Combine terms: 15a + 26b -4b – 16a. options: A)4a + 22b B)-28a + 30b C)-a + 22b D)28a + 30b E)5a + 30b SOLUTION:Solution: 15a + 26b -4b – 16a. = 15a – 16a + 26b – 4b. = -a + 22b. Answer: (C) #### C QUESTION:The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year? options: A)12300 B)12350 C)12000 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 120/100 = 12000 C #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 8 sec, then the speed of each train is? options: A)54 B)77 C)36 D)88 E)21 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/8 => x = 15 Speed of each train = 15 m/sec. = 15 * 18/5 =- 54 km/hr.Answer: A #### A QUESTION:Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)22 B)30 C)48 D)99 E)12 SOLUTION:Relative speed = 90 + 30 = 120 km/hr. 120 * 5/18 = 100/3 m/sec. Distance covered = 500 + 500 = 1000 m. Required time = 1000 * 3/100 = 30 sec. Answer: B #### B QUESTION:A coin is tossed 6 times. What is the probability of getting exactly 5 heads? options: A)3/8 B)3/16 C)5/16 D)3/32 E)7/64 SOLUTION:The number of possible outcomes is 2^6 = 64 There are 6 ways to get exactly 5 heads. P(exactly 5 heads) = 6/64 = 3/32 The answer is D. #### D QUESTION:A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings? options: A)12 B)13 C)46 D)37 E)26 SOLUTION:16x + 85 = 17(x + 3) x = 34 + 3 = 37 Answer: D #### D QUESTION:The product Z of two prime numbers is between 10 and 30 . If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24, then what is Z? options: A)21 B)15 C)14 D)10 E)6 SOLUTION:The smallest possible product is 21 which is 3*7. All other products are too big. The answer is A. #### A QUESTION:From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 40 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009? options: A)80 B)126 C)95 D)100 E)108 SOLUTION:Assume a value at the beginning of 2007. As this is a % question, assume P=100. At the end of 2007 it becmae = 1.2*100=120 At the end of 2008 it decreased by 25% = 120*.75 = 90 At the end of 2009 it increased by 40% = 90*1.2 = 126 Thus ratio = 126/100 = 1.26 (in % terms = 126%). Thus B is the correct answer. #### B QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14×30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×14) Ratio of the capacity of a man and woman =1/(15×14) : 1/(14×30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ? options: A)7.2 kg. B)10.8 kg. C)12.4 kg. D)18.0 kg E)None SOLUTION:Answer ∵Weight of 13 m long rod = 23.4 kg ∴ Weight of 1 m long rod = 23.4 / 13 kg ∴ Weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg Option: B #### B QUESTION:Mother,her daughter and her grand child weighs 160 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter? options: A)46 B)47 C)48 D)49 E)40 SOLUTION:mother + daughter + child = 160kg daughter + child = 60kg mother = 160 - 60 = 100kg child = 1/5th of mother = (1/5)*100 = 20kg So now daughter = 120 -(mother + child) = 160 - (100+20) = 40kg ANSWER:E #### E QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now? options: A)14years B)15years C)16years D)17years E)18years SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years ANSWER:A #### A QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? options: A)13680 B)13885 C)14005 D)14280 E)14680 SOLUTION:dana borrows 6000 and returns 2% per month. so returns 120 per month. and 1440 per year. so dana owes 6000-1440=4560 per year. after 3 years she will owe 13680. Ans (A) #### A QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exact 8 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)6 B)7 C)8 D)4 E)2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 4No. of days when B works = 4 → 4x + 4y = 1 When B starts: No. of days when A works = 5No. of days when B works = 3 → 5x + 3y = 1 Solving the above two equations for xy x = 1/8 y = 1/8 → Total work done by AB in a day = 1/8 + 1/8 = 1/4 → No. of days to complete the work when both work together = 4 Answer: D #### D QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is: options: A)233 B)37 C)25 D)27 E)11 SOLUTION:Explanation: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x Gain = (5x - 4x) = Rs. x Gain % = (x * 100)/ 4x = 25%. Answer: C #### C QUESTION:The present ratio of students to teachers at a certain school is 35 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:We are given that the ratio of students to teacher is 35 to 1. We can rewrite this using variable multipliers. students : teachers = 35x : x We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation: Students/Teachers  25/1 = (35x + 50)/(x + 5) If we cross multiply we have: 25(x + 5) = 35x + 50 25x + 125 = 35x + 50 7.5 = x x~8 Since x is the present number of teachers, currently there are 8 teachers. Answer B. #### B QUESTION:If (x + 1) times (2x + 1) is an odd integer, then x must be options: A)an odd integer B)an even integer C)a prime number D)a composite number E)a negative integer SOLUTION:(x + 1) times (2x + 1) means (x + 1) * (2x + 1).. (x + 1)*(2x + 1)= 2x^2+3x+1... for 2x^2+3x+1 to be odd, 3x+1 should be odd.. hence 3x should be even, which further leads to x as even.. so x is even integer.. ANSWER:B #### B QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)40 E)55 SOLUTION:Total = 75 books. 65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned. Now, there are 66 books, thus 76-68=7 books are NOT returned. {loaned out}*0.30=7 --> {loaned out}=30. Answer: B. #### B QUESTION:What is the sum of the first 24 natural numbers (starting from 1)? options: A)250 B)300 C)350 D)400 E)450 SOLUTION:The sum of n natural numbers = n*(n+1) / 2 = 24*25/2 = 300 The answer is B. #### B QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? options: A)20% B)40% C)50% D)60% E)70% SOLUTION:70 + 55 + 35 = 160% The number is 60% above 100% because 60% of the counties were counted twice. The answer is D. #### D QUESTION:31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 14 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates? options: A)A)11 B)B)18 C)C)25 D)D)29 E)D)36 SOLUTION:lets solve by creating equation.. W = 31.. Total = 50.. Not W = 50 -31= 19.. Now let people who were neither be x, so out of 19 who won Nobel = x+3.. so x+x+3=19 or x=8.. so who won Nobel but not Wolf = x+3 = 11.. But people who won BOTH W and N = 13.. so total who won N = 11+14 = 25.. C #### C QUESTION:In what time will a train 125 m long cross an electric pole, it its speed be 130 km/hr? options: A)3.5 B)2.7 C)2.9 D)2.3 E)2.1 SOLUTION:Speed = 130 * 5/18 = 36 m/sec Time taken = 125/36 = 3.5 sec. Answer: A #### A QUESTION:A man on tour travels first 160 km at 64 km/he and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is? options: A)71.11 km/hr B)66.11 km/hr C)78.11 km/hr D)81.11 km/hr E)54.11 km/hr SOLUTION:A 71.11 km/hr Total time taken = (160/64 + 160/8) = 9/2 hrs. Average speed = 320 * 2/9 = 71.11 km/hr. #### A QUESTION:In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is: options: A)12 km/hr B)11 km/hr C)10 km/hr D)8 km/hr E)15 km/hr SOLUTION:EXPLANATION Let speed of the boat in still water = a and speed of the stream = b Then a + b = 14 a - b = 8 Adding these two equations, we get 2a = 22 => a = 11 ie, speed of boat in still water = 11 km/hr ANSWER IS B #### B QUESTION:1401 x 1401 = ? options: A)1962800 B)1962801 C)1960000 D)1951611 E)1951613 SOLUTION:1401 x 1401 = (1401)2 = (1400+1)2 = (1400)2 + (1)2 + (2 x 1400 x 1) = 1960000 + 1 + 2800 = 1960001+ 2800 = 1962801. B) #### B <<<Examples ends QUESTION:A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained? options: A)9:1 B)4:7 C)7:1 D)2:5 E)5:6 SOLUTION:Explanation: Milk = 3/5 * 20 = 12 liters, water = 8 liters If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 liters Remaining water = 8 - 4 = 4 liters 10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters. The ratio of milk and water in the new mixture = 16:4 = 4:1 If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters. Amount of water removed = 2 liters. Remaining milk = (16 - 8) = 8 liters. Remaining water = (4 -2) = 2 liters. The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1. ANSWER IS A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A certain quantity is measured on two different scales, the T-scale and the S-scale, that are related linearly. Measurements on the T-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the T-scale corresponds to a measurement of 100 on the S-scale? options: A) 20 B) 36 C) 48 D) 60 E) 84 SOLUTION:First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is. From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that T increases, S increases by 5. We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, T will go up by 8 jumps of 3. 24 + 8(3) = 24 + 24 = 48=C #### C QUESTION:Two numbers have a H.C.F of 9 and a product of two numbers is 1800. Find the L.C.M of the two numbers? options: A)200 B)150 C)160 D)170 E)180 SOLUTION:L.C.M of two numbers is given by (Product of the two numbers) / (H.C.F of the two numbers) = 1800/9 = 200. ANSWER:A #### A QUESTION:Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 5 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes? options: A) 5.5% B) 3.6% C) 4.4% D) 5.2% E) 6.0% SOLUTION:Let amount spent by Jill = 100 Clothing=50, Food=20, others=30 Tax on clothing= 2.5 Tax on others=3 Percentage= 5.5/100=5.5% Answer: A #### A QUESTION:There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)410 B)490 C)493 D)455 E)445 SOLUTION:Answer: A. #### A QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour? options: A)E982 B)27 C)12 D)14.6 E)28 SOLUTION:Explanation: T = 11/45 * 60 = 14.6 Answer: Option D #### D QUESTION:A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car? options: A)22 B)28 C)120 D)287 E)278 SOLUTION:Let speed of the car = x kmphThen speed of the train = (100+50)100x=150100x=32x kmphTime taken by the car to travel from A to B=75x hoursTime taken by the train to travel from A to B=75(32x)+12.560 hoursSince Both start from A at the same time and reach point B at the same time75x=75(32x)+12.56025x=12.560x=25×6012.5=2×60=120 Answer : C #### C QUESTION:The price of stock decreased by 5% last year and rose by 10% this year. What is the net percentage change in the price of the stock? options: A)0.2% B)0.8% C)1.2% D)1.6% E)4.5% SOLUTION:(100% - 5%) * (100% + 10%) = 0.95 * 1.10 =1.045 = 104.5%. The net percentage change in the price of the stock is (+) 4.5% The answer is E #### E QUESTION:A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red? options: A)2/13 B)3/17 C)5/26 D)5/21 E)7/15 SOLUTION:P(Both are red), =6C213C2=6C213C2 =5/26 C #### C QUESTION:Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year? options: A)10% B)16% C)70% D)80% E)20% SOLUTION:Let the rate of interest during the second year be R%. Given, 4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544 R = 10% Answer:A #### A QUESTION:The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)8:9 B)B)3:5 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 6x and 8x years respectively. Then, 8x - 6x = 4 => x =2 Required ratio = (6x + 4) : (7x + 4) 16 : 18 = 8:9 ANSWER:A #### A QUESTION:If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq. m. If the length is creased by 1 m and breadth is decreased by 1m, then the area is decreased by 5 sq. m. The perimeter of the floor is: options: A)27 B)35 C)40 D)49 E)38 SOLUTION:Let length = x meters and breadth = y meters. Then, (x + 1) (y + 1) - xy = 21 x + y = 20 ………………1 And, xy - [(x + 1) (y - 1)] = 5 x - y = 6 ………………..2 Solving (i) and (ii), we get : x = 13 and y = 7 So, length = 13 m and breadth = 7 m. Perimeter = [2 (13 + 7)] m = 40 m. answer : C #### C QUESTION:A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)40 E)55 SOLUTION:Total = 75 books. 65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned. Now, there are 66 books, thus 76-68=7 books are NOT returned. {loaned out}*0.30=7 --> {loaned out}=30. Answer: B. #### B QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B QUESTION:If x^2 + 1/x^2 = 3,what is the value of x^4 + 1/x^4 ? options: A)7 B)12 C)14 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 3 andSQUAREboth sides: (x² + 1/x²)²= 9 So, (x² + 1/x²)(x² + 1/x²) = 9 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 9 Simplify: x⁴ + 1/x⁴ = 7 Answer: A #### A QUESTION:20 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. options: A)190 B)200 C)210 D)220 E)230 SOLUTION:1st person will shake hand with 19 people 2nd person will shake hand with 18 people 3rd person will shake hand with 17 people ...... total no. of handshakes = 19+18+17+...+3+2+1 = 19*(19+1)/2 = 190 or, if there are n persons then no. of shakehands = nC2 = 20C2 = 190 ANSWER:A #### A QUESTION:In a consumer survey, 88% of those surveyed liked at least one of three products: 1, 2, and 3. 55% of those asked liked product 1, 40% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:55 + 40 + 20 = 115 This number includes some people counted twice and some people counted three times. 115 - 88 = 27, and this number represents people counted twice or three times. 7% of the people are counted two extra times. The percentage of people counted one extra time is 27 - 7(2) = 13. The percentage of people who liked more than one product is 7% + 13% = 20%. The answer is B. #### B QUESTION:How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4? options: A)288 B)173144 C)144 D)297 E)2181 SOLUTION:Explanation: If a number has to be divisible by 4, the last two digit of that number should be divisible by 4. So _ _ _ x y. Here xy should be a multiple of 4. There are two cases: Case 1: xy can be 04, 20 or 40 In this case the remaining 3 places can be filled in 4×3×2 = 24. So total 24×3 = 72 ways. Case 2: xy can be 12, 24, 32, 52. In this case, left most place cannot be 0. So left most place can be filled in 3 ways. Number of ways are 3×3×2 = 18. Total ways = 18×4 = 72. Total ways = 144 Answer:C #### C QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-3 < x < 7 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -3 < x < 7 - true because x can be between -3 < x < 7 E. none of the above. Answer: D #### D QUESTION:Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the work ? options: A)10 hours B)12 hours C)16 hours D)18 hours E)None of these SOLUTION:ExplanaƟon: Work done by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12 Work done by B in 1 hour = (7/12)�(1/2) = 1/12 => B alone can complete the work in 12 hour Answer: B #### B QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B? options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these SOLUTION:Explanation : Assume that investment of C = x Then, investment of A =2x A receive 48000 Then C will receive = 48000/2 = 24000 And B receive = 180000 - (24000+48000) = 108000 Ratio of investment between A and B = 48000 : 108000 = 4 : 9 Answer : Option A #### A QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even now subtract X + (X+2) - (X+4) doing this leaves us with X -2 what even number can we substitute in X to yield an answer choice B works 2 (plug in 4 for X) #### B QUESTION:If the cost price is 99% of selling price then what is the profit percentage. options: A)1 B)1.11 C)1.01 D)1.1 E)1.21 SOLUTION:selling price=Rs100 : then cost price=Rs 99:profit =Rs 1. Profit={(1/99)*100}%=1.01% Answer is C. #### C QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)11 B)18 C)99 D)77 E)51 SOLUTION:A:B = 2:3 B:C = 2:5 A:B:C = 4:6:15 6/25 * 75 = 18 Answer: B #### B QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.8 sec C)5 sec D)2.2 sec E)4.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 200/40 = 5 sec. Answer:C #### C QUESTION:A rectangular garden is to be twice as long as it is wide. If 150 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:ALTERNATE APPROACH Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations. Given Perimeter is 150 So, 2 ( L + B ) = 150 Or, L + B = 75 Now use the answer options ( Given Length ; Breath will be half the length) (A) 40 L = 40 ; B = 20 L + b = 60 (B) 50 L = 50 ; B = 25 L + b = 75 (C) 60 L = 60; B = 30 L + b = 90 (D) 70 L = 70; B = 35 L + b = 105 (E) 80 L = 80; B = 40 L + b = 120 Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (B) #### B QUESTION:One packet of flower seeds was enough to just fill the area of the smaller garden in #3. How many packets of seed are needed for the larger garden? Round each answer to the nearest square foot before continuing. options: A)1 seed packet B)2 seed packets C)3 seed packets D)4 seed packets E)5 seed packets SOLUTION:3.14 x 32 = 28.26 sq. ft. area of small garden 28 sq. ft. rounded 3.14 x 62 = 113.04 sq. ft. area of large garden 113 sq. ft. rounded 113 ÷ 28 = 4.04 or 4 seed packets (rounded) correct answer D #### D QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)50 SOLUTION:Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec t=500*3/50=30sec ANSWER:B #### B QUESTION:As x increases from 151 to 152, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x options: A)II only B)II,III only C)I,II only D)I only E)III only SOLUTION:On Increasing the value of x from 151 to 152 I) x−1/x will increase as 1/x will be very small and x will increase by 1 unit II) 17−1/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x) III) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x) Answer: C #### C QUESTION:Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system? options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3 SOLUTION:26^2+26^3 = 26^2(1+26)=27*26^2 The answer is C. #### C QUESTION:Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is: options: A)Rs. 4800 B)Rs. 5000 C)Rs. 5400 D)Rs. 5600 E)Rs. 6600 SOLUTION:let investment is x... den remaining investment is (9800-x) x*9/75= (9800-x)*10/80 x=4800 9800-x=5000 ANSWER:B #### B QUESTION:A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr. What is the speed of the boat? options: A)2.5 kmph B)3.5 kmph C)4.5 kmph D)1.5 kmph E)9.5 kmph SOLUTION:speed upstream = 10/3 speed of boat down stream = 10/6 speed of boat = 1/2(10/3 + 10 /6 ) = 2.5 kmph ANSWER:A #### A QUESTION:In some quantity of alcohol, 50% of pure alcohol and 30% of is water. If 20liters of pure alcohol is added, then the strength of alcohol solution becomes 20%. The original quantity was? options: A)1.42liters B)2.5liters C)3liters D)5.6liters E)7liters SOLUTION:Let the original quantity be x liters alcohol solution in x liters = 30/100 *x = 3x/10 kg (3x/10)/(x+20) = 20/100 3x = x/5 + 4 14x = 20 x = 1.42liters Answer is A #### A QUESTION:How many figures are required to number the pages the pages of a book containing 365 pages? options: A)987 B)977 C)967 D)897 E)997 SOLUTION:1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 365 = 266 * 3 = 798 ----------- 987 ANSWER:A #### A QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)21% C)21.33% D)22.109% E)23% SOLUTION:Lets say the indicated weight is x for $10 but the trader actually get 1.1x for $10 now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1 so profit % = (12.1-10)/ 10 = 0.21 = 21% ANSWER:B #### B QUESTION:The first three terms of a proportion are 3, 9 and 12. The fourth term is? options: A)22 B)28 C)27 D)36 E)88 SOLUTION:(9*12)/3 = 36 Answer:D #### D QUESTION:The sum of the squares of three number is 138,while the sum of their products taken two at a time is 131. their sum is : options: A)20 B)30 C)40 D)None of these E)Cannot be determined SOLUTION:Solution Let the numbers be a,b and c then, a 2 + b 2+ c 2 = 138 and (ab + b c + ac) = 131. (a + b+ c)2 = a 2 + b 2 + c 2 + 2(ab + b c + ca) = 138 + 2 * 131 = 400 . ⇒ (a + b + c) = 400/20= 20 Answer A #### A QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)5 B)6 C)9 D)7 E)3 SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 Answer: D #### D QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these SOLUTION:Solution Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr. Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B QUESTION:For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| = options: A)ab-4+b B)2b-ab-4 C)ab+4 D)ab-2b+5 E)4-ab SOLUTION:Given: |ab| = ab and |a| = -a Question: |b-3| + |ab-b| = ? **** Looking at |ab| = ab tells us that a and b are either both positive or negative **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: a and b are both negative values Let a=-1 and b=-1 |b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5 Test a) ab-4 = (-1)(-1)-4 = -5 Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7 Test c) ab+4 = 1 + 4 = 5 Answer: C #### C QUESTION:A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 m B)200 m C)240 m D)320 m E)450 m SOLUTION:Sol. Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x metres. Then, x + 300 / 50 = 15 ⇔ x + 300 = 750 ⇔ x = 450 m. Answer E #### E QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet? options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m SOLUTION:D = 50 * 1 ½ = 75 km RS = 75 – 50 = 25 T = 75/25 = 3 h 3.30 + 3 h = 6.30 p.m. Answer: C #### C QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40 SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35 P(at least one graduate) = 1- 1/35 = 34/35 The answer is D. #### D QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale? options: A)(P-7)*6 B)(P-7)*5 C)(P-7)*2 D)(P-7)*3 E)(P-7)*4 SOLUTION:M/84 =(P-7)/21 M = (P-7)*84/21 =(P-7)*4 E #### E QUESTION:15 + sqrt(- 6 + 8×5÷4) =? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:According to order of operations, inner brackets first where 8x5÷4 is first calculated since it has a multiplication and a division. 8x5÷4 = 40÷4 = 10 Hence 15 + sqrt(- 6 + 8×5÷4) = 15+ sqrt(- 6 + 10) = 15 + sqrt(4) = 15 + 16 = 31 correct answer A)31 #### A QUESTION:Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 13 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip? options: A)48 B)42.5 C)44 D)50 E)52.5 SOLUTION:Total Time taken by jerry = (8/40)*60 Minutes + 13 Minutes + (20/60)*60 Minutes = 35 Minutes Average Speed = Total Distance / Total Time = (8+20) miles / (35/60)Hours = 28*60 / 35 = 48 Miles per hour Answer: option A #### A QUESTION:A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent? options: A)33 1/8 % B)33 7/3 % C)50 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 24. If he buys 6 a rupee, his CP = 4 He selling at 4 a rupee, his SP = 6 Profit = SP - CP = 6 - 4 = 2 Profit Percent = 2/4 * 100 = 50 % Answer: C #### C QUESTION:One of the longest sides of the triangle is 20 m,the other side is 10 m.Area of the triangle is 80m^2.What is the another side of the triangle? options: A)2sqrt(61) B)2sqrt(62) C)2sqrt(63) D)2sqrt(64) E)2sqrt(65) SOLUTION:base of triangle is 20 and area is 80 therefore height=2*80/20=8. now one side of triangle is of 10. so we can get the point were the base is divided by applying Pythagoras therm so division pt =sqrt(10^2-8^2)=sqrt(36)=6 threfore other half is 14. now second side=sqrt(14^2+8^2)=sqrt(260)=2sqrt(65) ANSWER:E #### E QUESTION:The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 360 metres, what is its area? options: A)1320 sq.metres B)4260 sq.metres C)6870 sq.metres D)7875 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 360 ⇒ x = 15 Area = 7 × 15 × 5 × 15 = 7875 sq.m. Answer D #### D QUESTION:The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg. What is the correct weight? options: A)58kgs B)58.85kgs C)58.9kgs D)59kgs E)59.85kgs SOLUTION:Actual total weight is (20X 58.4 - 56 + 66) = 1178 Kgs Actual average weight is 1178/20 = 58.9kgs C #### C QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10 SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others C #### C QUESTION:A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit W on this shipment? options: A)a) $100 B)b) $115 C)c) $125 D)d) $130 E)e) $135 SOLUTION:I recommend one should use fractions to solve this one rather than converting it into decimals Sol: 1500 heads -> $600 1 head -> $600/1500 1 head -> $(2/5) 25% more of (2/5) -> 125/100 * 2/5 = $(1/2) He sold 2/3*1500 = 1000 heads for $(1/2) per head Total revenue by selling 1000 heads = 1000 * 1/2 = $500 Heads left: 500 Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20) Total revenue by selling 500 heads = 9/20 * 500 = 225 Total revenue after selling 1500 cabbage heads - 225+500 = $725 Money spent on the purchase: $600 Profit W= 725-600 = $125 Ans:C #### C QUESTION:Which of the following must be divisible by 4, given that y is a positive integer? options: A)(y−1)*y*(y+3) B)y^2*(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3) SOLUTION:option A) (y−1)*y*(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A QUESTION:If 60 percent of the members of a certain organization are women and 6/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization. options: A)II B)III C)I, II D)I E)II, III SOLUTION:6/10 (60%) of the members are women and 6/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 6/10*80 = 48 women; 80 - 48= 32 men; 6/8*32 = 24 married men; 32 - 24 = 8 unmarried men. So, option I,II is true. Answer: C #### C QUESTION:Three clocks were set to true time and starts to run together, makes a beep sound at intervals of 8,10 and 12 minutes respectively. In 2 days, how many times do they will make the sound together ? options: A)12 B)15 C)25 D)30 E)35 SOLUTION:Explanation : The clocks make sound at intervals of 8, 10 and 12 minutes respectively. The LCM of 8,10 and 12 is 120. So, the clocks will make sound together after every 120 minutes. i.e., after every 2 hours. In 2 days(48 hours), they will make the sound together (48/2) = 24 times. At the end of 2nd day, they will make one more beep together. Therefore, totally (24+1) 25 times beep sound is made together. Hence the answer is 25 times. Answer : C #### C QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer) options: A)Rs. 8167 B)Rs. 4261 C)Rs. 4269 D)Rs. 4266 E)Rs. 4262 SOLUTION:Explanation: CI = 14800{ [ 1 + 13.5/100]2 - 1 } = 14800 { [1 + 27/200]2 - 1 = 14800 { 2 + 27/200}{27/200} = (74)[2 + 27/200](27) = 1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266 Answer:D #### D QUESTION:A person was fined for exceeding the speed limit by 10 km/hr.Another person was also fined for exceeding the same speed limit by twice the same.If the second person was traveling at a speed of 35 km/hr,find the speed limit. options: A)487 B)15 C)76 D)29 E)12 SOLUTION:If x is speed limit, Speed of first person = x + 10 Speed of 2nd person = x + 20 But speed of 2nd person = 35 kmph x + 20 = 35 x = 15 kmph. so speed limit is 15 kmph option D Answer: B #### B QUESTION:A firm has 5 senior partners and 7 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.) options: A)145 B)155 C)165 D)175 E)185 SOLUTION:The number of ways to form a group of 3 is 12C3 = 220 The number of groups with no senior partner is 7C3 = 35 The number of groups with at least one senior partner is 220-35 = 185 The answer is E. #### E QUESTION:The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? options: A)51.25 B)52.5 C)53.75 D)55.0 E)55.5 SOLUTION:Rate of flow of water in second hour = 18 gallons per hour Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons Answer B #### B QUESTION:A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ? options: A)5 sec B)6 sec C)7 sec D)10 sec E)None SOLUTION:Solution Speed of train relative to man =(60+6) km/hr= 66km/hr =(66x5/18) m/sec =(55/3) m/sec ∴ Time taken to pass the man = (110x3/55)sec = 6sec Answer B #### B QUESTION:The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)33 B)88 C)66 D)12 E)99 SOLUTION:Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 60/5 = 12 seconds. Answer: D #### D QUESTION:A rectangular tiled patio is composed of 48 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 48 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout? options: A)5 B)6 C)10 D)13 E)28 SOLUTION:Suppose there are c columns and there are r rows Original Situation So, Number of tiles = c*r = 48 Also. Reach column has r tiles and each row has c tiles New Situation Number of tiles in each column is r-2 and number of tiles in each row is c+4 So, number of rows = r-2 and number of columns is c+4 So, Number of tiles = (r-2)*(c+4) = 48 Comparing both of them we get c*r = (r-2)*(c+4) => 4r -2c = 8 c = 2r - 4 Putting it in c*r=48 (2r-4)*r = 48 2r^2 - 4r - 48=0 r cannot be negative so r = 6 and c = 8 So, Answer will be B #### B QUESTION:A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 3 percent and 6 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate? options: A) 3/8 B) 21/25 C) 1/2 D) 3/5 E) 3/4 SOLUTION:x * 3/100 * 1 + (20000 - x) * 8/100 * 1 = 1440 3x - 8x = 144000 - 160000 => -5x = -16000 => x = 32000 So 16800/20000 = 21/25 Answer - B #### B QUESTION:The sum of two numbers is 18. Their difference is 4. What are the numbers? options: A)8,6 B)9,9 C)11,7 D)15,3 E)13,9 SOLUTION:Let two numbers be x and y. Equation (i): x + y = 18 Equation (ii): x - y = 4 Solve system of equations: 2x=22 x=11 y=7 Answer C is correct. #### C QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 36. options: A)5 B)4 C)12 D)32 E)35 SOLUTION:First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7. Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc and n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above) Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form n = 5a + 1 and n = 7b + 3 Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10. Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4) Now this question is exactly like the question above. So when you divide n by 36, remainder will be -4 i.e. n will be 4 less than a multiple of 36. So you must add 5 to n to make it a multiple of 36 A #### A QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2? options: A)5 B)3 C)2 D)1 E)0 SOLUTION:4”2= 4 - 4=0 Answer: E #### E QUESTION:Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)? options: A) 22 hours B) 30 hours C) 44 hours D) 60 hours E) It cannot be determined from the information above. SOLUTION:Say the rates of machines A, B and C are a, b, and c, respectively. Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4; Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11. Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours. Answer: C. #### C QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:In a certain code language, '3a, 2b, 7c' means 'Truth is Eternal'; '7c, 9a, 8b, 3a' means 'Enmity is not Eternal' and '9a, 4d, 2b, 8b' means 'Truth does not perish'. Which of the following means 'enmity' in that language ? options: A)3 B)9 C)8 D)6 E)2 SOLUTION:Explanation: Justification: In the second and third statements, the common code is '9a' and the common word is 'not'. So, '9a' means 'not'. In the first and second statements, the common codes are '7c' and '3a' and the common words are 'is' and 'Eternal'. So, in the second statement, '8b' means 'enmity'. Answer: C) 8b #### C QUESTION:20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours X will it take 12 beavers that work at the same pace, to build the same dam? options: A)2. B)4. C)X=5. D)X=6. E)8. SOLUTION:C. 5 hrs If there were 10 beavers it qould have taken double X = 6hrs.. so closest to that option is 5. #### C QUESTION:Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 41 pages per hour. If Tom starts reading a novel at 3:20, and Jan begins reading an identical copy of the same book at 4:26, at what time will they be reading the same page? options: A)6:26 B)6:56 C)7:26 D)7:56 E)8:26 SOLUTION:Since Tom reads an average of 1 page every 2 minutes, Tom will read 33 pages in the first 66 minutes. Jan can catch Tom at a rate of 11 pages per hour, so it will take 3 hours to catch Tom. The answer is C. #### C QUESTION:In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together? options: A)A)360 B)B)480 C)C)720 D)D)5040 E)of these SOLUTION:The word 'SINGING' has 7 different letters. When the vowels II are always together, they can be supposed to form one letter. Then, we have to arrange the letters SNGNG (II). Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways. The vowels (II) can be arranged among themselves in 1! = 1 way. Required number of ways = (720 x 1) = 720. ANSWER:C #### C QUESTION:A train 120 m long running at 60 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)213 B)298 C)350 D)726 E)267 SOLUTION:D = 60 * 5/18 = 20 = 333 – 120 = 213 Answer: A #### A QUESTION:If a is an odd integer and b is an even integer which of the following must be an integer : options: A)a/b B)ab C)2a+b D)2(a+b) E)option B C and D SOLUTION:a= odd = e.g 3 b=even = e.g 6 A. odd/even for example 3/6 = 0.5 no even no odd B. odd * even = 3 * 6 = 18 even C. 2*odd + even = even + even even D. 2(even + odd) = 2(odd) even Hence E it is. #### E QUESTION:Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80? options: A)18% B)21% C)20% D)19% E)None of these SOLUTION:CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621 SP = Rs. 496.80, Discount = 621 - 496.80 = 124.20 Discount % = 124.2/621 * 100 = 20% ANSWER:C #### C QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: options: A)5% B)8% C)10% D)12% E)6% SOLUTION:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =(80/1600x 100)% = 5%. Answer is A. #### A QUESTION:The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 150 sq. cm, what is the width of the rectangle? options: A)10 cm B)12 cm C)14 cm D)16 cm E)18 cm SOLUTION:2L+2W = 5W L = 3W/2 W*L = 150 3W^2/2 = 150 W^2 = 100 W = 10 The answer is A. #### A QUESTION:The divisor is 12, the quotient is 4 and the remainder is 1. What is the dividend? options: A)48 B)49 C)96 D)97 E)72 SOLUTION:D = d * Q + R D = 12 * 4 + 1 D = 48 + 1 D = 49 Answer: B #### B QUESTION:There are 8 balls in a bucket, 4 balls are blue and 4 balls are red. If two ball chosen randomly , how many chances there are at least one blue ball will present? options: A)21 B)25 C)16 D)22 E)20 SOLUTION:Two ball will be chosen. At least 1 blue ball Total ways = 8C2 = 28 Total without any blue ball = 4C2 = 6 Hence ways in which at least one blue will be present = 28 - 6 = 22 Correct option: D #### D QUESTION:How much water must be added to 64 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)16 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 64 litres of milk = (1⁄4 × 64) litres = 16 litres. Answer A #### A QUESTION:A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit? options: A)Rs. 64 B)Rs. 69 C)Rs.72 D)Rs.75 E)Rs.90 SOLUTION:C.P. = Rs. (100/122.5)x392 = Rs. (1000/1225)x392 = Rs. 320 Profit = Rs. (392 - 320) = Rs. 72. Answer:C #### C QUESTION:A shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal? options: A)18% B)20% C)17% D)18% E)None of these SOLUTION:Explanation: Let the CP of the article = Rs.100. Then labeled price = Rs.130. SP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117. Gain = Rs.117 – Rs.100 = Rs.17 Therefore, gain/profit percent = 17%. Answer: Option C #### C QUESTION:Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? options: A)3 B)9 C)5 D)6 E)7 SOLUTION:Suppose Anoop joined after 3 months. Then, 20000 * 12 = 80000 * (12 – x) => x = 9. ANSWER:B #### B QUESTION:A small college reduced its faculty by approximately 15 percent to 195 professors. What was the original number of faculty members? options: A)182 B)208 C)224 D)229 E)302 SOLUTION:If x is the original number of faculty members, then after 15% reduction in faculty members number is .85x but we are given .85x = 195 x = 229 So the original number of faculty members is 229 Correct Answer - D #### D QUESTION:In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? options: A)508 B)500 C)800 D)570 E)503 SOLUTION:We can select one boy from 20 boys in 20 ways. We select one girl from 25 girls in 25 ways We select a boy and girl in 20 * 25 ways i.e., = 500 ways. Answer:B #### B QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second? options: A)1234 B)1567 C)1349 D)1456 E)1356 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:Let the number of buffaloes be x and the number of ducks be y. Then 4x+2y=2(x+y)+24 =>x=12 ANSWER D 12 #### D QUESTION:In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the fifth row? options: A)10 B)11 C)13 D)14 E)16 SOLUTION:Let x be the number of cans in row 1. The total number of cans is x + (x+3) + ... + (x+27) = 10x + 3(1+2+...+9) = 10x + 3(9)(10)/2 = 10x + 135 Since the total is less than 150, x must equal 1. The number of cans in the 5th row is 1 + 3(4) = 13 The answer is C. #### C QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:m:n = 5: 8 , n: p = 6 : 7 , m:n:p = ? options: A)30 : 48 : 54 B)30 : 48 : 56 C)30 : 48 : 50 D)30 : 48 : 52 E)30 : 48 : 58 SOLUTION:m:n = 5: 8 n: p = 6 : 7 m:n:p =30 : 48 : 56 Answer : B #### B QUESTION:The sum of three consecutive numbers is 87. The greatest among these three numbers is : options: A)22 B)24 C)26 D)30 E)44 SOLUTION:Sol. Let the numbers be x, x + 1 and x + 2. Then, x + (x + 1) + (x + 2) = 87 ⇔ 3x = 84 ⇔ x = 28. Greatest number = (x + 2) = 30. Answer D #### D QUESTION:If 9^y = 3^12, what is y? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:A grocery store bought some apples at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples? options: A)1:7 B)1:5 C)1:4 D)1:2 E)2:5 SOLUTION:To avoid fractions, assume there were 45 apples. So the store bought them for 45/5 = 9 dollars. To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these. 45 split in the ratio 1:4 gives 9 and 36. 9 apples split into 3 apples each will give $3. 36 apples split into 6 apples each will give $6. They add up to $9 so we have hit the right answer. Answer (C) #### C QUESTION:Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is: options: A)228gallons B)267gallons C)120gallons D)767gallons E)167gallons SOLUTION:Explanation: Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying] Volume of {\color{Black} \frac{1}{40}} part = 3 gallons Volume of whole = (3 x 40) gallons = 120 gallons. Answer: C #### C QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:Which of the following is equal to the value of 2^7 + 2^7 + 3^7 + 3^7 + 3^7 ? options: A)2^8 + 3^8 B)2^6 + 3^8 C)2^8 + 3^6 D)2^9 + 3^9 E)2^5 + 3^5 SOLUTION:2^7 + 2^7 + 3^7 + 3^7 + 3^7 = 2 (2^7) + 3 (3^7) = 2^1 (2^7) + 3^1 (3^7) = 2^(1+7) + 3^(1+7) = 2^8 + 3^8 Ans: A #### A QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300 B)320 C)350 D)345 E)568 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 39 = 50/3 3(x + 300) = 1950 è x = 350 Answer: Option C #### C QUESTION:If a is a number such that –2 ≤ a ≤ 2, which of the following has the largest possible absolute value? options: A)3a – 1 B)x^2 + 1 C)3 – x D)x – 3 E)x^2 – x SOLUTION:Ans is A .. leads to the max value of 7 for a = -2 #### A QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:A man can do a piece of work in 6 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? options: A)7 days B)6 days C)5 days D)4 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/3−1/6)=(6−3)/18=1/6 So son will do whole work in 6 days Answer: B #### B QUESTION:A salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 210 items for $150 each, what will her monthly salary be? options: A)$1,500 B)$1,800 C)$2,100 D)$2,500 E)$2,800 SOLUTION:Ans : 1000+ 7.5 % * 150 * (210-50) = $ 2800 ANSWER:E #### E QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)13.9 sec B)12.1 sec C)17.9 sec D)61.9 sec E)47.98 sec SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec. Answer:B #### B QUESTION:A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? options: A)A)452000 B)B)200000 C)C)800000 D)D)500000 E)E)652000 SOLUTION:3 children got = 3*15% = 45% wife got = 30% orphan house = 5% total = 45+30+5 = 80% remaining = 100-80 = 20% 20% = 40000 100% = 40000*100/20 = $200000 Answer is B #### B QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit. options: A)Rs. 1900 B)Rs. 2660 C)Rs. 2800 D)Rs. 2840 E)Rs. 3000 SOLUTION:Explanation: For managing, A received = 5% of Rs. 7400 = Rs. 370. Balance = Rs. (7400 - 370) = Rs. 7030. Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3) = 39000 : 42000 : 30000 = 13 : 14 : 10 B's share = Rs.(7030 X 14/37)=Rs. 2660. ANSWER IS B #### B QUESTION:Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil. options: A)12 B)10 C)15 D)19 E)20 SOLUTION:Let the cost of a pen ands a pencil be Rs. X and Rs. Y respectively. Then, 2x + 3y = 86 ….(i) and 4x + y =112. Solving (i) and (ii), we get: x = 25 and y = 12. Cost of a pen =Rs. 25 and the cost of a pencil =Rs. 12. Answer is A. #### A QUESTION:In how many ways can the letters of word INTELLIGENT be arranged such that all the vowels as well as all the Consonants always appear together? options: A)9! B)5!*4! C)5!*5! D)5!*4!*2! E)4!*7!*2! SOLUTION:Since all the vowels and consonants have to be together there can only be there are 4! way to order the vowels and 7! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2. So 4!7!2! (E) #### E QUESTION:If -1 < x < 0, which of the following must be true? I. x^8 < x^3 II. x^4 < 1 – x III. x^3 < x^2 options: A)III only B)II only C)I only D)I,II,III only E)II,III only SOLUTION:Answer : D #### D QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction? options: A)5hours B)40hours C)8hours D)20hours E)30hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 40 =20 hours Answer is D #### D QUESTION:A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work ? options: A)5 days B)6 days C)7 days D)8 days E)9 days SOLUTION:Explanation: Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them, So, A's 1 day work = 1/10 B's 1 day work = 1/15 (A+B)'s 1 day work = (1/10+1/15)=(3+2/30)=1/6 So together they can complete work in 6 days. Option B #### B QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)None of these SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =((100 x 3000)/(12500 x 4))% = 6% Answer :D #### D QUESTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ? options: A) None B) Two C) Four D) Five E) Seven SOLUTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain? R=2,4,6,8,10,12... S=4,16,36,64... Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets. Solution: Five Answer: D #### D QUESTION:9, 12, 11, 14, 13, ?, 15 options: A)16 B)12 C)14 D)17 E)20 SOLUTION:A 16 Alternatively, 3 is added and one is subtracted. #### A QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers. options: A)28 B)30 C)32 D)34 E)36 SOLUTION:Given: Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6) Average = Sum of Quantities/Number of Quantities = [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27 Simplifying we get, x = 24 Therefore, Largest number = (x + 6) = (24 + 6) = 30 Smallest number = 24 ANSWER IS B #### B QUESTION:10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 2 women and 10 children take to complete the work? options: A)4 B)5 C)7 D)8 E)10 SOLUTION:1 women's 1 day work = 1/70 1 child's 1 day work = 1/140 (2 women + 10 children)'s 1 day work = (2/70 + 10/140) = 1/10 2 women and 10 children will complete the work in 10 days. E #### E QUESTION:How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt? options: A)16.67 B)30 C)50 D)60.33 E)150 SOLUTION:let x=ounces of 60% salt solution to be added .2*50+.6x=.5(50+x) x=150 Answer E #### E QUESTION:A jogger jogs at 1/6 of his usual speed. how much % he has to increase speed to reach normal pace of walking options: A)100 B)200 C)300 D)400 E)500 SOLUTION:suppose usual speed is x, then current speed is x/6. to gain normal speed, he has to gain 5x/6 % increase = 100*(5x/6)/(x/6) = 500% ANSWER:E #### E QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6? options: A)300 B)992 C)772 D)552 E)280 SOLUTION:1/3:1/3:1/6 = 2:2:1 1/5*1400 = 280 560-280 = 280 Answer: E #### E QUESTION:If a^2+b^2=177and ab=54 then find the value of a+b/a-b? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:(a+b)^2=a^2+b^2+2ab=117+2*24=225 a+b=15 (a-b)^2=a^2+b^2-2ab=117-2*54 a-b=3 a+b/a-b=15/3=5 Answer is C. #### C QUESTION:A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected? options: A)1/3 B)2/5 C)2/7 D)3/7 E)3/8 SOLUTION:Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected) = = 2/5 B #### B QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? options: A)3 B)5 C)4 D)2 E)6 SOLUTION:A rate = 1/8 B rate = 1/24 (A+B) rate = (1/8)+(1/24) = 1/6 A & B finish the work in 6days correct option is E #### E QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)295 C)322 D)345 E)354 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A <<<Examples ends QUESTION:An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 1/2M + 15, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold? options: A)a. A - 10 B)b. B - 15 C)c. C – 22.5 D)d. D – 30 E)e. E – 67.5 SOLUTION:A --- 10/2 + 15 = 20 --- CORRECT B --- 15/2 + 15 = not an integer --- wrong C --- 22.5(1/2) + 15 = not an integer --- wrong D --- 30/2+15 =30 --- wrong This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method. A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different pencils.20!/((4!)^5) Answer - C #### C QUESTION:A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ? options: A)160 B)180 C)200 D)220 E)None SOLUTION:Answer Let the number be N. Then, (N/5) + 4 = (N/4) - 4 ⇒ (N/4) - (N/5) = 8 ⇒ (5N - 4N)/20 = 8 ∴ N = 160 Option: A #### A QUESTION:9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day? options: A)18 B)9 C)10 D)8 E)11 SOLUTION:We have, M1D1H1 = M2D2H2 So, 9*12*4= 6*D2*8 D2 = 9*12*4/6*8 = 9 ANSWER:B #### B QUESTION:If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s? options: A)8 B)2 C)− 2 D)− 3 E)− 5 SOLUTION:Given: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x - 5)(x + 3) = (x + r)( x + s) Rewrite as: (x + -5)(x + 3) = (x + r)( x + s) So, it's possible that r = -5 and s = 3 Here, r - s = (-5) - 3 = -8 Try REVERSING the factorization: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x + 3)(x - 5) = (x + r)( x + s) Rewrite as: (x + 3)(x + -5) = (x + r)( x + s) So, it's possible that r = 3 and s = -5 Here, r - s = 3 - (-5) = 8 Answer: A #### A QUESTION:How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ? options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters SOLUTION:Let x ltr water to be added 2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x))) 2=5%*(13+x)-------->x=27 Ans B #### B QUESTION:Mary travels the first 9 hours of her journey at 40 mph speed and the remaining 6 hours at 30 mph speed. What is the average speed of Mary's travel in mph? options: A)32 mph B)34 mph C)36 mph D)35 mph E)31 mph SOLUTION:Explanation : Average speed=Total Distance/Time. Total distance travelled by mary = Distance covered in the first 9 hours + Distance covered in the next 6 hours. Distance covered in the first 9 hours = 9×40=360 miles Distance covered in the next 6 hours= 6×30=180 miles Therefore, total distance travelled = 360+180=540 miles. The total time taken = 9+6=15hours. Hence, the average speed =540/15= 36 mph. Answer : C #### C QUESTION:A can do a piece of work in 13 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in? options: A)15 10/11 days B)10 10/11 days C)12 10/11 days D)19 10/11 days E)13 10/11 days SOLUTION:B (x – 5)/13 + x/20 = 1 x = 10 10/11 days #### B QUESTION:A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days,then B alone could do it in : options: A)15 days B)20 days C)25 days D)30 days E)None of these SOLUTION:Solution (A +B)’s 1 day’s work =1/50; C's 1 day's work = 1/50 (A+B+C)’s 1 day’s work = (1/10+1/50)=6/50=3/25…..(i) Also,A’s 1 day’s work =(B +C)’s 1 day’s work ……(ii) From (i) and (ii),we get : 2 × (A’s 1 day’s work) =3/25 ⇒ A’s 1 day’s work = 3/50 ∴ B’s 1 day’s work = (1/10-3/50)=2/50=1/50 So, B alone could do the work in 25 days. Answer C #### C QUESTION:Janet has to pay back her bank loan over 10 months following the below sequence. $50, $55, $65, $80, $85, $95, $110, $115, $125, ? How much will she pay back on the tenth month? options: A)$155 B)$140 C)$135 D)$125 E)$130 SOLUTION:The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 10th Month is $140 Ans B #### B QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have? options: A)5 B)12 C)19 D)36 E)50 SOLUTION:A+P+G= 39*3 A=3G P=2.5G 3G+2.5G+G= 39*3 G=39*3/6.5= 18 A= 6*3=54 Difference = 36 'D' is the answer #### D QUESTION:The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Perimeter = 2(W+L) = 5W 3W = 2L W = 2L/3 WL = 54 2L^2/3 = 54 L^2 = 81 L = 9 cm The answer is D. #### D QUESTION:Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? options: A)28 B)10 C)28 D)27 E)13 SOLUTION:4/12 + x/15 = 1 x = 10 Answer:B #### B QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:The average age 10 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)20 B)99 C)77 D)26 E)12 SOLUTION:10 * 2 = 20 years Answer: A #### A QUESTION:Two cars are driving toward each other. The first car is traveling at a speed of 100 km/h, which is 20% slower than the second car's speed. If the distance between the cars is 1125 km, how many hours will it take until the two cars meet? options: A)4 B)4.5 C)4.8 D)5 E)5.5 SOLUTION:The speed of the first car is 100 km/h. The speed of the second car is 100 / 0.8 = 125 km/h. The two cars complete a total of 225 km each hour. The time it takes the cars to meet is 1125 / 225 = 5 hours. The answer is D. #### D QUESTION:A store reduced the price of all items in the store by 12% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? options: A)80.0 B)79.2 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 12% price becomes = 0.88 *100 = $ 88 after the final reduction of 10% price becomes = 0.9* 88 = $ 79.2 price of all items on second day is 79.2% of price on first day correct answer option B #### B QUESTION:If December 3rd, 1999 is a Friday, what day is January 7th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000. 35/7 has a remainder of 0. Jan. 7th is: Friday + 0 days = Friday The answer is C. #### C QUESTION:If |z|/w = 5,which of the following must be true? options: A)z = -5w B)z = 5w C)z^2 = 25w^2 D)z^2 = 25w^3 E)z^3 = 125w^3 SOLUTION:|z|/w = 5. |z| = 5w. Then z = 5w or -5w and so z^2 = 25w^2. The answer is C. #### C QUESTION:In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 13 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:The class borrowed a total of 40*2 = 80 books. The 27 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 13*2 = 38. To maximize the number of books borrowed by 1 student, let's assume that 12 students borrowed 3 books and 1 student borrowed the rest. 80 - 38 - 3*12 = 6 The maximum number of books borrowed by any student is 6. The answer is D. #### D QUESTION:If each side of a square is increased by 20%, find the percentage change in its area? options: A)40% B)42% C)46% D)44% E)38% SOLUTION:let each side of the square be a , then area = a x a New side = 120a / 100 = 6a / 5 New area =(6a x 6a) / (5 x 5) = (36a²/25) increased area== (36a²/25) - a² Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44% answer :D #### D QUESTION:Which of the following lines has x-intercept and y-intercept that are integers T? options: A)y=3x+1 B)y=√x+1 C)y=-2/x D)y=x^2-1 E)xy=1 SOLUTION:Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers T and the correct answer is D. #### D QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B QUESTION:John Purchased 1365 large bottles at $1.89 per bottle and 720 small bottles at $1.42 per bottle. What was the approximate average price paid per bottle? options: A)$1.63 B)$1.64 C)$1.68 D)$1.73 E)$1.76 SOLUTION:(1365*1.89+720*1.42)/(1365+720) =~1.73 Option (D) #### D QUESTION:By selling an article at Rs.600, a profit of 30% is made. Find its cost price? options: A)400 B)267 C)287 D)480 E)811 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+50)] = 600 * [100/150] = Rs.400 Answer: A #### A QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green? options: A)23/35 B)23/38 C)23/18 D)53/18 E)23/22 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂ = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7 = 46/70 = 23/35 Answer:A #### A QUESTION:A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age 10 years back was: options: A)10 years. B)14 years. C)17 years. D)16 years. E)12 years. SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22 Son's age 10 years back (22 - 10) = 12 years. ANSWER :E #### E QUESTION:How many integers between 323,700 and 458,600 have tens digit 1 and units digit 3? options: A)10,300 B)10,030 C)1,353 D)1,352 E)1,349 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ... The difference between 323,700 and 458,600 is 458,600-323,700=134,900 - one number per each hundred gives 134,900/100=1,349 numbers. Answer: E. #### E QUESTION:The population of a city increases by 6% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years? options: A)9% B)9.27% C)27% D)15.76% E)None of these SOLUTION:Actual increase in population=5% Let, earlier population=100 then the population after 3 years =100(1+5/100)^3=115.7625 ∴Required percentage=15.7625% ANSWER:D #### D QUESTION:What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81? options: A)1020600 B)1020593 C)56693 D)28343 E)18900 SOLUTION:14 = 2 * 7 25 = 5 * 5 36 = 2 * 2 * 3 * 3 81 = 3 * 3 * 3 * 3 So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C. #### C QUESTION:A die is tossed. Find the probability of getting a multiple of 2 ? options: A)1/5 B)2/3 C)1/6 D)1/3 E)1/2 SOLUTION:S = {1,2,3,4,5,6} E= event of getting a multiple of 2 = {2,4,6} P(E) = 3/6 = 1/2 Answer is E #### E QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was options: A)960 B)980 C)900 D)970 E)1000 SOLUTION:Explanation: Let original Cost price is x Its Selling price = (105/100) * x = 21x/20 New Cost price = (95/100) * x = 19x/20 New Selling price = (110/100 )* (19x/20 )= 209x/200 [(21x/20) - (209x/200)] = 1 => x = 1000 Answer: E) Rs 1000 #### E QUESTION:If 2x = 3y = 20, then 12xy = ? options: A) 1,200 B) 800 C) 120 D) 40 E) 20 SOLUTION:2x = 20;x=10 3y = 20;y=20/3 Multiply: 12xy=12*10*20/3=800. Answer: B. #### B QUESTION:A train covers a distance in 50 min ,if it runs at a speed of 48kmph on an average.The speed at which the train must run to reduce the time of journey to 40min will be. options: A)60kmph B)63kmph C)57kmph D)70kmph E)61kmph SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=S*T=48*5/6=40km time=40/60hr=2/3hr New speed = 40* 3/2 kmph= 60kmph Answer is A. #### A QUESTION:Which of the following is not divisible by 6? options: A)10032 B)21192 C)47816 D)91232 E)72031 SOLUTION:Divisibility rule of 6: Number must be divisible by both 2 and 3 Option A: 10032, Divisible by 2. Hence divisible by 6 Option B: 21192, Divisible by 2 & 3. Hence divisible by 6 Option C: 47816, Divisible by 2. Hence divisible by 6 Option D: 91232, Divisible by 2. Hence divisible by 6 Option E: 72031, Not divisible by 2 or 3. Hence 72031 is not divisible by 6 #### E QUESTION:Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt? options: A)1/216 B)5/216 C)7/216 D)1/36 E)5/36 SOLUTION:The total number of ways the dice can land is 6*6*6=216. Bob must get a score of 18=6+6+6. There is only 1 way to do this. P(Bob wins)=1/216 The answer is A. #### A QUESTION:The difference between the ages of two persons is 10 years.Fifteen years ago ,the elder one was twice as old as the younger one.The present age of the elder person is : options: A)25 years B)35 years C)45 years D)55 years E)75 years SOLUTION:Solution Let their ages be x year and (x + 10) years respectively. Then,(x + 10) - 15 = 2 (x - 15) ⇔ x-5 = 2x-30 ⇔ x =25. ∴ Present age of the elder person =(x + 10) =35 years. Answer B #### B QUESTION:All of the citizens of a country have a four-character or five-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes? options: A)37(36^4) B)36^9 C)35(36^5) D)37(36^5) E)35(36^9) SOLUTION:The number of possible 4-digit codes is 36^4. The number of possible 5-digit codes is 36^5. The total sum is 36^4 + 36^5 = 36^4(1+36) = 37(36^4) The answer is A. #### A QUESTION:Joshua is fifth from the bottom in a queue of 100 boys. What is the position of Joshua from the top of the queue? options: A)51 B)52 C)53 D)54 E)55 SOLUTION:Solution: 51 Explanation: The position of boys higher than Joshua in the queue is 100 - 50 = 50. Therefore, the position of Joshua from the top is 50 + 1 = 51. Answer A #### A QUESTION:The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 15 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1? options: A)28% B)40% C)68% D)70% E)72% SOLUTION:Let initial price be 1000 Price in day 1 after 10% discount = 900 Price in day 2 after 15% discount = 765 Price in day 3 after 20% discount = 612 So, Price in day 3 as percentage of the sale price on day 1 will be = 612/900*100 => 68% Answer will definitely be (C) #### C QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit? options: A)2777 B)2999 C)2799 D)2781 E)10500 SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 24500 * 3/7 = Rs. 10500.Answer: E #### E QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is? options: A)11 B)72 C)36 D)99 E)27 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240)/12 => x = 20 Speed of each train = 20 m/sec. = 20 * 18/5 =72 km/hr. Answer: B #### B QUESTION:If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in? options: A)7 days B)3 days C)9 days D)8 days E)2 days SOLUTION:C 9 days C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C QUESTION:Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood? options: A)a) 90 B)b) 100 C)c) 110 D)d) 130 E)e) 140 SOLUTION:C. 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3rd piece (sorted in increasing length) length = 140 (median) for sum of first 2 wood length to become max, last two should be least. let 4th, 5th wood also have length 140 each. total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220/2 = 110 Answer C #### C QUESTION:A thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 15km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ? options: A)A)1km B)B)300m C)C)650m D)D)750m E)E)800m SOLUTION:Relative speed of the policeman = 20-15 = 5 km/hr time taken by policeman to cover 100m = (100/1000)*(1/5) = 1/50 hr In 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m Answer is B #### B QUESTION:A fill pipe can fill 1/3 of cistern in 20 minutes in how many minutes, it can fill 3/4 of the cistern? options: A)15 min B)45 min C)25 min D)40 min E)50 min SOLUTION:1/3 of the cistern can fill in 20 min 3/4 of the cistern can fill in = 20*3*3/4 = 45min Answer is B #### B QUESTION:John deposited $10,000 to open a new savings account that earned 2 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened? options: A)$10,100.25 B)$10,101.50 C)$10,200.75 D)$10,201.00 E)$10,400.35 SOLUTION:2 percent annual interest compounded quarterly --> 0.5% in 3 moths. For the first 3 moths interest was 0.5% of $10,000, so $50; For the next 3 moths interest was 0.5% of $10,000,plus0.25 earned on previous interest of $100, so $50+$0.25=$50.25; Total interest for 6 months was $50+$50.25=$100.25, hence balance after 6 months was $10,000+ $100.25=$10,100.25. Answer: A. #### A QUESTION:The measure of the side of a square is quadrupled. If x represents the perimeter of the original square, what is the value of the new perimeter? options: A)3x B)4x C)9x D)12x E)27x SOLUTION:Original perimeter = x Hence original side = x/4 New side = 4x/4 New perimeter = 4*4x/4 = 4x Correct Option: B #### B QUESTION:A certain galaxy is known to comprise approximately 5 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun? options: A)800 B)1,250 C)8,000 D)12,000 E)10,000 SOLUTION:Total no. of stars on galaxy = 5 * 10^11 Of every 50 million stars, 1 is larger than sun. 1 million = 10^6 therofore, 50 million = 50 * 10^6 total no. of stars larger than sun = 5 * 10^11 / 50 * 10^6 =50 * 10^3 /5 = 10000 therefore answer is E #### E QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)20 B)15 C)25 D)18 E)12 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 6 = 26 => x = 5 Deepak's age = 3x = 15 years. ANSWER B #### B QUESTION:What is the sum of the different positive prime factors of 380? options: A)5 B)10 C)15 D)17 E)26 SOLUTION:Prime factorization of 380 =38 * 10 =2*19 * 10 =2*19 * 2*5 =2^2 * 5 * 19 Sum of the different positive prime factors of 380 = 2+5+19 =26 Answer E #### E QUESTION:In how many no. between 10 and 50 exactly Two of the digits is 5? options: A)47 B)65 C)1 D)35 E)65 SOLUTION:It's simple can be solved by elimination of answer choices. Option B and D are too large, not possible. Even AE are large to have correct choice. Ans : C #### C QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40 Answer:A #### A QUESTION:Which of these lines in the xy-plane does not contain any point with two negative coordinates? options: A)y = 4x B)y = x + 6 C)y = x^2 - 5 D)y = x^3 + 3x E)y = 2x^4 SOLUTION:2x^4 is 0 when x is 0 and positive for all other values of x. The answer is E. #### E QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)95 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)56 km/hr SOLUTION:Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr. ANSWER: A #### A QUESTION:In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 1 ounces of corn syrup, how many ounces of water does it contain? options: A)15 B)30 C)45 D)60 E)90 SOLUTION:Standard: Fl: Corn S: Water = 1:12:30 Sport: Fl: Corn S: Water = 3:12:180 This simplifies to 1:4:60 If the large bottle has a capacity of x ounces, then 4x / 65 = 1. So, x =65 / 4 ounces. Water = (60 / 65) * (65 / 4) = 15 ounces. Ans A #### A QUESTION:A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent? options: A)8 B)10 C)15 D)17 E)19 SOLUTION:30 * 25 = 750 425 ----------- 325 25 + 7.50 = 32.5 325/32.5 = 10 B #### B QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 9 people all together .how many people can sit in a bus? options: A)52 B)49 C)95 D)90 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 27*3=81 People can seat in Last Seat = 9 Total People can seat= 81+9=90 ANSWER:D #### D QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 2050*5=10250 10250-10000=250 Answer E #### E QUESTION:Find the ratio between whole surfaces of a sphere and a hemisphere? options: A)4:3 B)3:4 C)3:2 D)5:2 E)4:6 SOLUTION:4 Ï€r2 : 3 Ï€r2 => 4:3 ANSWER A #### A QUESTION:Simple interest on a certain sum at a certain annual rate of interest is 1/3 of the sum. If the numbers representing Time is three times the Rate percent , then the Rate is: options: A)1 1/3 %. B)2 1/3 %. C)3 1/3 %. D)4 1/3 %. E)5 1/3 %. SOLUTION:Explanation : Let sum = x. Then, S.I. = x/3 Let N =3R [x * 3R * R / 100] = x/3? R^2 = 100/9 R = 10/3 = 3 1/3%. Hence, Rate = 3 1/3 %. Answer : C #### C QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:65 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? options: A)64 B)128 C)151 D)216 E)256 SOLUTION:65 small cube will make a large cube with 4 cubes in each line i.e. Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line. Total number of small cubes in new cube = 6^3 = 216 Extra cube required = 216 - 65 = 151 Hence, C is the answer. #### C QUESTION:A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/10 B)1/8 C)1/6 D)1/5 E)1/4 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 5*3*2=30. P(dispensing one of each color)=30/120=1/4. The answer is E. #### E QUESTION:Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)3 hours B)6 hours C)4 hours D)8 hours E)10 hours SOLUTION:Number of pages typed by Ronald in one hour = 32/6 = 16/3 Number of pages typed by Elan in one hour = 40/5 = 8 Number of pages typed by both in one hour = ((16/3) + 8) = 40/3 Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours. ANSWER:D #### D QUESTION:Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ??? options: A)a,b B)a,c C)b,c D)a,d E)b,d SOLUTION:a. 3i+2j and c. 2i-3j are orthogonal pair. as the dot product of two vectors is zero;so they are orthogonal. ANSWER:B #### B QUESTION:Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. options: A)z=3x B)x=3z C)y=2x D)x=2y E)y=3x SOLUTION:Rovert Travelled for x,y and for z min. Total Time : x + y + z Which is equal to : 3y Equating both sides we get x+y+z = 3y => x+z =2y ........ Eqn 1 Looking out at options D Says x =2y Using it in Eqn 1 2y + z = 2y => Z = 0 mins, Which I guess is not possible. The Ans isD #### D QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1123 B)1234 C)1452 D)1356 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:Karthikeyan arranged a party to celebrate his birth day.20 of his close friends were invited. One friend left before the cake was cut due to an urgent phone call.The big cake was drawing the attention of the party visitors. This cake is to be divided among friends and of course Karthikeyan will get his share. A man eats 3 pieces, a woman eats two pieces and a child eats half a piece of cake. Including Karthikeyan count the number of men,women and children in the party. There are 20 pieces of cake in all. options: A)6 women, 2 men and 12 children B)7 women, 1 men and 12 children C)5 women, 1 men and 14 children D)4 women, 2 men and 14 children E)None of these SOLUTION:Let the number of men be m, number of women be w and number of children be c Total number of pieces = Pieces ate by men + Pieces ate by women + Pieces ate by children There are 20 total pieces. Also a man eats 3 pieces, a woman eats 2 and children half. Therefore above equation becomes. 20 = 3m + 2w + 1/2c In the above equation, you have to substitute the values given in options to find which one satisfies the equation. Option c with m = 1, c = 14 and w = 5 perfectly satisfies the equation as follows 20 = 3(1) + 2(5) + (1/2)(14) 20 = 20 i,e our equation is satisfied perfectly by option c ANSWER:C #### C QUESTION:A,B,C invested the capitals in a business. If A invested Rs. 20,000 more than B and C invested Rs.10,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000 options: A)5500, 2500, 6000 B)5200, 2800, 6000 C)4250, 2250, 7500 D)5250, 1750, 7000 E)5300, 2700, 6000 SOLUTION:A==30,000 B==10,000 C==40,000 so, ration are3:1:4 profit 14000 so,, 14000/8==1750 so,, A==5250, B==1750,, C==7000 ANSWER:D #### D QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ? options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9 SOLUTION:Here is how I did it. Probably there may be better way to do it. First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90. That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment. So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17) Number of integers, whose digits add to 1: 1 and 10 = 2 Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4 Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6 Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8 Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10 Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8 Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6 Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4 Number of integers, whose digits add to 16: 79, 88 = 2 So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers Probability B= 50/90 = 5/9 Correct answer E #### E QUESTION:If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? options: A)10,573 B)11,908 C)12,322 D)13,924 E)14,537 SOLUTION:The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9. The answer is D. #### D QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers? options: A)28 B)56 C)76 D)84 E)85 SOLUTION:Explanation: Let the numbers be 3x and 4x LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x) Given that LCM of 3x and 4x is 48 => 12x = 48 => x = 48/12 = 4 Sum of the numbers = 3x + 4x = 7x = 7 x 4 = 28 Answer: Option A #### A QUESTION:An aeroplane covers a certain distance at a speed of 100 kmph in 2 hours. To cover the same distance in 1 hours, it must travel at a speed of? options: A)100km/hr B)150km/hr C)200km/hr D)250km/hr E)300km/hr SOLUTION:Distance = 100*2 = 200 km Required speed = 200 *1 = 200km/hr Answer is C #### C QUESTION:If 15% of 40 is greater than 25% of a number by 2, the number is options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Explanation: 15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16 Option B #### B QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y? options: A)96 B)75 C)50 D)25 E)12 SOLUTION:Guys, one more simple funda. 5/2= 2.5 now .5 x2 =1 is the remainder 25/4 = 6.25 now .25x4=1 is the remainder 32/5=6.4 now.4x5 = 2 is the remainder given x/y = 6.12 and remainder is 6 So .12 X y = 6 hence y= 50 Ans C #### C QUESTION:There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5 of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students. options: A)200 B)210 C)220 D)230 E)240 SOLUTION:210 ANSWER:B #### B QUESTION:Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely? options: A)15 sec B)19 sec C)12 sec D)10 sec E)11 sec SOLUTION:Explanation: D = 250 m + 250 m = 500 m RS = 80 + 40 = 120 * 5/18 = 100/3 T = 500 * 3/100 = 15 sec Answer: Option A #### A QUESTION:A password for a computer uses three digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero? options: A)1/32 B)1/16 C)1/8 D)2/5 E)1/2 SOLUTION:To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 = 1,000 possible combinations. Prime numbers constitute 2, 3 In addition to zero, this is 3 total possibility for each digit. So the number of satisfactory variants is 3× 3 × 3 . So the probability is 1/2 × 1/2 × 1/2 = 1/8. The right answer is choice (C). #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)68 km/hr. B)32 km/hr. C)34 km/hr. D)35 km/hr. E)72 km/hr. SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240 )/12 2x = 40 x = 20. Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr. answer :E #### E QUESTION:Compute all real solutions to 16x + 4x+1 - 96 = 0 options: A)3/2 B)3/3 C)2/4 D)4/4 E)4/5 SOLUTION:If we substitute y = 4x, we have y2 +4y-96 = 0, so y = -4 or y = 8. The first does not map to a real solution, while the second maps to x =3/2 correct answer A #### A QUESTION:1.14 expressed as a per cent of 1.9 is: options: A)6% B)10% C)60% D)90% E)None SOLUTION:Solution: Required percentage = (1.14*100)/1.9 = 60%. Answer: Option C #### C QUESTION:Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride? options: A)14 mph B)20 mph C)70/3 mph D)80/3 mph E)30 mph SOLUTION:Average speed for first two hours, S1 = 30 mph Distance travelled in these two hours, D1 = 60 miles Average speed for the entire 5 hour ride, S = 30 mph Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles. Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90 Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30 Hence, the correct answer is E #### E QUESTION:A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)80 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B #### B QUESTION:What distance will be covered by a bus moving at 126 kmph in 10 seconds? options: A)287 B)600 C)350 D)276 E)207 SOLUTION:126 kmph = 126 * 5/18 = 35 mps D = Speed * time = 35 * 10 = 350 m. Answer:C #### C QUESTION:One out of every 600 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment? options: A)60,000 B)5,000 C)10,000 D)50,000 E)52,000 SOLUTION:20 broken glasses indicates that 10*10= 100 defected bulbs are present. 100 defected bulbs indicates that 100*600= 60,000 light bulbs are present. A is the answer #### A QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students? options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9 SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760 Sum of the marks for the class of 45 students = 45 * 70 = 3150 Sum of the marks for the class of 85 students = 2760 + 3150 = 5910 Average marks of all the students = 5910/85 = 69.5.Answer: D #### D QUESTION:In the new budget, the price of rice rose by 20%. By how much percent must a common man reduce his consumption so that his expenditure on it does not increase? options: A)16.66% B)17% C)15.8% D)12% E)None of these SOLUTION:Explanation : Solution: reduction in consumption = [r/(100+r) * 100]% = (20/120 * 100) = 16.66% Answer : A #### A QUESTION:Find the area, diameter = 12m. options: A)113.00 square meter B)113.04 square meter C)113.08 square meter D)113.24 square meter E)113.43 square meter SOLUTION:Diameter = 12 meter. Radius = diameter/2. = 12/2. = 6 meter. Area of a circle = πr2. Here, pi (π) = 3.14 meter, radius (r) = 6. Area of a circle = 3.14 × 6 × 6.. = 3.14 × 36. = 113.04 square meter or 113.04 m2. ANSWER : B #### B QUESTION:A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased? options: A)7 B)6 C)5 D)2 pineapples E)3 SOLUTION:Explanation: The equation for this problem can be made as: 5x + 7y =38 Where x is the number of watermelons and y is the number of pineapples. Now test for 2, 3 and 4: For y = 2 5x + 14 =38 x is not an integer For y = 3 5x = 17 X not an integer For y =4 X = 2 So 4 pineapples and 2 watermelons can be bought by 38 Rs. ANSWER:D #### D QUESTION:Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.? options: A)28 B)60 C)32 D)36 E)44 SOLUTION:the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13. using the elimination method look for a number that is both divisible by 7 and 13, of all the options only 60 is divisible by 4 and 20. [ 60/4=15 and 60/20=3] answer :B #### B QUESTION:If 60 percent of the members of a certain organization are women and 6/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization. options: A)II B)III C)I, II D)I E)II, III SOLUTION:6/10 (60%) of the members are women and 6/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 6/10*80 = 48 women; 80 - 48= 32 men; 6/8*32 = 24 married men; 32 - 24 = 8 unmarried men. So, option I,II is true. Answer: C #### C QUESTION:Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 18 hours. If all the three pipes are opened together, then the tank will be filled in? options: A)3 9/97 hrs B)4 2/4 hrs C)3 9/17 hrs D)3 9/27 hrs E)3 9/19 hrs SOLUTION:Net part filled in 1 hour = 1/9 + 1/6 - 1/18 = 4/18 The tank will be full in 18/4 hrs, i.e., 4 2/4 hrs. Answer:B #### B QUESTION:If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due? options: A)8 months B)11 months C)10 months D)9 months E)12 months SOLUTION:Explanation : F = Rs. 498 TD = Rs. 18 PW = F - TD = 498 - 18 = Rs. 480 R = 5% TD = (PW × TR)/100 ⇒ 18 = (480 × T × 5)/100 ⇒ 18 = 24 × T ⇒ T = 18/24 = 3/4 years = (12×3)/4 months = 9 months Answer : Option D #### D QUESTION:In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are finance majors? options: A)3 B)5 C)8 D)11 E)17 SOLUTION:pqrs = 1365 = 3* 5 *7 * 13 Since 1< p < q < r < s, the number of students who are finance majors is q = 5. The answer is B. #### B QUESTION:A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 35% impurities to the product. Find the net profit percentage of the dealer? options: A)44% B)40% C)68.75% D)56.25% E)36% SOLUTION:The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight. It means that he is selling $4 worth of product for $5. The dealer then further added 35% impurities to the product. It means that he is selling $5 worth of product for $6.75. So his profit is $6.75-$4 = $2 and his profit percent is (2.75/4)*100 = 68.75% Answer:- C #### C QUESTION:The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P? options: A)0.54 B)0.77 C)0.82 D)0.97 E)1.62 SOLUTION:This is a fairly straightforward question that can be solved quickly by just applying the options We are provided with Mean, m= 0 and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2*PD or m - 2*PD So, if these elements lie within 2 and 3 PDs of mean, m=0 we can find which one of these values of PD satisfies each value within Q Only PD = 0.77 does Answer : B #### B QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long? options: A)76 sec B)89 sec C)87 sec D)15 sec E)16 sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 650)/10 = 89 sec. Answer:B #### B QUESTION:The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 80%? I will see what is the quickest way to solve it then I will provide the explanation options: A)6 B)7 C)9 D)10 E)11 SOLUTION:The following approach might be the easiest one and less error prone. We need on-time departure rate to be higher than 8/10, so it should be at least 9/11, which means that 9 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 9-3=6 subsequent flights need to depart on-time. Answer: A #### A QUESTION:If x and y are perfect squares, then which five of the following is not necessarily a perfect square? options: A)x^2 B)xy C)4x D)x+y E)x^5 SOLUTION:If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square. Answer: A. #### A QUESTION:In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is: options: A)12 km/hr B)11 km/hr C)10 km/hr D)8 km/hr E)15 km/hr SOLUTION:EXPLANATION Let speed of the boat in still water = a and speed of the stream = b Then a + b = 14 a - b = 8 Adding these two equations, we get 2a = 22 => a = 11 ie, speed of boat in still water = 11 km/hr ANSWER IS B #### B QUESTION:On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled? options: A)80 B)81 C)82 D)83 E)84 SOLUTION:Solution: Mabel handled 90 transactions Anthony handled 10% more transactions than Mabel Anthony = 90 + 90 × 10% = 90 + 90 × 0.10 = 90 + 9 = 99 Cal handled 2/3rds of the transactions than Anthony handled Cal = 2/3 × 99 = 66 Jade handled 15 more transactions than Cal. Jade = 66 + 15 = 81 Jade handled = 81 transactions. Answer: B #### B QUESTION:Marts income is 50 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income options: A)124% B)b) 120 % C)c) 96 % D)d) 90 % E)e) 64 % SOLUTION:M = (150/100)T T = (60/100)J => M = (90/100)J Answer D. #### D QUESTION:In a clock (Conventional clock with numbers 1 to 12 in order)is cut into 3 pieces such that the sum of each piece in AP with a common difference of 1. What is the count of numbers in each piece? and what are the numbers? options: A)25 B)26 C)27 D)28 E)29 SOLUTION:Sum of the 12 numbers=1+2+3+......+12=12*13/2=78 So we have to divide it into 3 slots such that the sum is 78 and sum of each slot is in AP, thus the 3 slots are 25,26,27. So the numbers can be: 3+4+5+6+7=25 8+9+10=27 11+12+1+2=26 ANSWER:B #### B QUESTION:40, 45, 50, 55, 60, 75, 75, 90, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 21.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 55, 60, 75, 75, 90, 100, 100} is 69. 1 standard deviation below the mean is 69 - 21.2 = 47.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate? options: A)576 B)425 C)215 D)321 E)None of these SOLUTION:Explanation : In a circle, 5 boys can be arranged in 4! ways Given that the boys and the girls alternate. Hence there are 4 places for girls which can be arranged in 4! ways Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A QUESTION:If x:y=9:4 then (7x-3y) : (7x+3y)=? options: A)51:76 B)6:13 C)51:75 D)51:76 E)None of these SOLUTION:Explanation: x/y = 9/4 (Given) (7x − 3y)/(7x + 3y) 7(x/y) − 3/7(x/y)+3 ( on dividing Nr and Dr by y) (7(9/4) − 3)/(7(9/4) + 3) (63/4 − 3/1)/(63/4 + 3/1) [(63 − 12)/4]/[(63 + 12)/4] = 51/75 (7x-3y) : (7x+3y) = 51:75 Answer: Option C #### C QUESTION:How many positive integers r less than 30 have no common prime factor with 30? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:r=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5. This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers. Answer: D. #### D QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in: options: A)14 hrs B)15 hrs C)10 hrs D)8 hrs E)9 hrs SOLUTION:work done by leak in 1 hr = (1/2-3/7)=1/4 =>14 hrs ANSWER A #### A QUESTION:A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected? options: A)1/3 B)2/5 C)2/7 D)3/7 E)3/8 SOLUTION:Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected) = = 2/5 B #### B QUESTION:A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 130 pounds? options: A)8 B)14 C)12 D)9 E)none of the above SOLUTION:Ans is B: 39 pounds --> 6 days 130 pounds --> x days x = 130*6/39 = 20 the animal has already consumed food in 6 days so the the number of days for it's total consumption be 130 pounds is 20-6 = 14 #### B QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3? options: A)3/10 B)3/20 C)2/5 D)1/2 E)1/3 SOLUTION:S={1,2,3,….20} E={3, 6,9,12,15,18} P(E)=6/20 =3/10 Option A #### A QUESTION:Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $3 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans? options: A)9% B)56.6% C)11% D)12% E)15% SOLUTION:You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So 3(15) = 45 - Fox 2(18) = 36 - Pony The total discount discount is $3 and you are asked to find the percent discount of pony jeans, so 45(18 - X)/100 + 36(X)/100 = 3 or 45*18 -45*x + 36*x =3*100 or 9x = -3*100 +45*18 x= 510/9 = 56.6% B #### B QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 5400 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)30000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 5400 ( 18 × 300 = 5400) 100% -------> 30000 votes (100 × 300 = 30000) C #### C QUESTION:A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income? options: A)Rs.900 B)Rs.800 C)Rs.500 D)Rs.1000 E)Rs.1200 SOLUTION:X * 4/5 * 80/100 = 576 X = 14400/16 X = 900 ANSWER:A #### A QUESTION:X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13750 ? options: A)3200 B)4000 C)3250 D)3825 E)3985 SOLUTION:Ratio of investment, as investments is for different time. Investment x Number of units of time. Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8. X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16. Ratio of investments => X : Y : Z = 18 : 21 : 16. Investment Ratio = Profit sharing Ratio. Z = 13750 × 16/55 = Rs.4000. Share of Z in the profit is Rs.4000. Option B #### B QUESTION:If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF options: A)13 - 11 - 9 - 7 - 8 B)13 - 11 - 9 - 7 - 6 C)13 - 11 - 9 - 7 - 7 D)13 - 11 - 9 - 7 - 3 E)13 - 11 - 9 - 7 - 1 SOLUTION:MLIGF = 13 - 11 - 9 - 7 - 8 Note: this is a dummy question. Dont answer these questions Answer:A #### A QUESTION:In the formula V = 1/(4r)^2, if r is halved, then V is multiplied by options: A)64 B)8 C)4 D)64 E)1/64 SOLUTION:Say r=2 => V1 = 1/64 when r=1; V2 = 1/16 V2 = 4*V1. Answer=C=4 #### C QUESTION:Find the product of place value and face value of 5 in 65231 options: A)28000 B)25000 C)27000 D)26000 E)28000 SOLUTION:Place value of 5 in 65231 = 5 x 1000 = 5000 Face value = 5 required product = 5000 x 5 = 25000 Answer :B #### B QUESTION:A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 85, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? options: A)74 B)75 C)76 D)77 E)78 SOLUTION:ratio is 4:6:5 , numbers are 4x, 6x, 5x total scores of each class is (65*4x + 6x * 85 + 77*5x) = 260x+510x+385x = 1155x total number of students = 15x average = 1155x/15x = 77 D is the answer #### D QUESTION:In a certain game, a player begins with a bag containing tiles numbered 3 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd? options: A)5/18 B)13/36 C)3/8 D)5/8 E)23/36 SOLUTION:player begins with containing tiles 1 to 10 and have equal probability of selecting means Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there. Next , player draws one title , if number is even player stops or otherwise title is odd without replacement player draws second title. If second title is even , player stops or title is odd without replacement player draws third title. in third title , without replacement of first and second title, player draws and stops it. the sum of tilte probability is odd. here two conditions are possible. 1st condition is 1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1. Here are we are not selecting 1st condition as even stops because sum of tile is odd. Here 5 odd numbers are there we can select 1out of 5 odd numbers. without replacement of fist we select second tilte is even. is 5/10*5c1/9c1. here we are selecting one number out of remaining 9 numbers. so probability is 5/18. we are selecting 1 even number out of 5. 2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title. Then probability is 5/10*4/9*3/8=1/12. Finally sum of probability of two conditions is 5/18+1/12 =5/18. so option A is correct. #### A QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? options: A)336 B)425 C)275 D)235 E)689 SOLUTION:B 425 (68 ÷ 16) × 100 #### B QUESTION:x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 9 will be equal to: options: A)3 B)6 C)1/9 D)1/3 E)9 SOLUTION:Explanation : Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9. .'. x = 9/y^2 => x =9 /9^2 = 1/9 Answer : C #### C QUESTION:If a(a - 8) = 9 and b(b -8) = 9, where a ≠ b, then a + b = options: A)−48 B)−2 C)8 D)9 E)48 SOLUTION:i.e. if a = -1 then b = 9 or if a =9 then b = -1 But in each case a+b = -1+9= 8 Answer: option C #### C QUESTION:In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class? options: A)1/2 B)1/3 C)2/3 D)1/4 E)3/4 SOLUTION:(1/2)G=(1/3)(B+G) 3G=2B+2G G=2B B/G=1/2. The answer is A. #### A QUESTION:3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? options: A)45% B)48% C)57% D)59% E)61% SOLUTION:Total number of votes polled = (5136 + 7636 + 11628) = 24400 So, Required percentage = 11628/24400 * 100 = 48% B #### B QUESTION:If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12. options: A)6 B)1 C)3 D)8 E)7 SOLUTION:Every prime number greater than 3 can be written 6N+1 or 6N-1. If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3 If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3 When divided by 12, it must leave a remainder of 3. The answer is C. #### C <<<Examples ends QUESTION:What distance will be covered by a bus moving at 36 kmph in 30 seconds? options: A)287 B)600 C)289 D)300 E)207 SOLUTION:36 kmph = 36 * 5/18 = 10 mps D = Speed * time = 10 * 30 = 300 m. Answer:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer: A #### A QUESTION:JOHN and ANDREW can finish the work 9 days if they work together. They worked together for 6 days and then ANDREW left. JOHN finished the remaining work in another 6 days. In how many days JOHN alone can finish the work? options: A)30 days B)60 days C)18 days D)80 days E)90 days SOLUTION:Amount of work done by JOHN and ANDREW in 1 day = 1/9 Amount of work done by JOHN and ANDREW in 6 days = 6 × (1/9) = 2/3 Remaining work – 1 – 2/3 = 1/3 JOHN completes 1/3 work in 6 days Amount of work JOHN can do in 1 day = (1/3)/6 = 1/18 => JOHN can complete the work in 18 days Answer : C #### C QUESTION:A tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 9.33% D) 10.67% E) 11.7% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 700 gallons (7% of initial solution of 10,000 gallons) then sodium chloride is 700/7,500*100=~9.33% of the remaining solution of 7,500 gallons. Answer: C. #### C QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+79)=? options: A)4500 B)4250 C)4350 D)4800 E)4150 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 79=1+(n-1)2 => n=40 Use value of n in (1) then, Sn = (40/2)(1+79) = 1600 Ans:- 3(Sn) = 4800 Answer : D #### D QUESTION:How many odd 4-digit positive integers W that are multiples of 5 can be formed without using the digit 3? options: A)648 B)729 C)900 D)1296 E)3240 SOLUTION:I choose A. Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded) Possible n° of 2nd digit: 9 (3 is excluded) Possible n° of 3rd digit: 9 (3 is excluded) Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0) So, W=8*9*9*1=648 (A) #### A QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? options: A)25% B)33 1/3% C)50% D)66 2/3% E)75% SOLUTION:General formula for percent increase or decrease, (percent change): percent=Change/Original∗100 So, the time between maintenance checks increased by 25−20/20∗100=25 Answer: A. #### A QUESTION:Three numbers are in the ratio 1:2:3 and their H.C.F is 62. The numbers are: options: A)62, 124, 186 B)60, 124, 186 C)10, 20, 30 D)62, 24, 186 E)12, 24, 186 SOLUTION:Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 62. The numbers are 62, 124, 186. ANSWER:A #### A QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)19% B)11% C)18% D)218% E)14% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer:C #### C QUESTION:One day a car rental agency rented 3/4 of its cars, including 4/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players? options: A)23/40 B)17/30 C)12/25 D)7/15 E)3/10 SOLUTION:The cars with CD players which were not rented is (1/5)(3/5) = 3/25 of all the cars. The cars which were not rented is 1/4 of all the cars. The percent of non-rented cars which had CD players is (3/25) / (1/4) = 12/25 The answer is C. #### C QUESTION:All the faces of cubes are painted with red colour.It is then cut into 64 equal small cubes.Find How many small cubes are there whose three faces are coloured ? options: A)4 B)8 C)16 D)24 E)2 SOLUTION:There are 64 small cubes,Hence one side side of the big cube is 3√64=4 cm Number of small cubes having three faces coloured = No. of corners = 8 Answer: B #### B QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items? options: A)15% B)12.16% C)13.4% D)20.2% E)None of these SOLUTION:Explanation : Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively. And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively. Overall loss percentage of the 1st two items = 14.33% =>(0.21p+0.11q)/(p+q)=0.1433 =>p/q=1/2. Overall loss percentage of the 2nd and 3rd item =10.4% =>(0.11q+0.1r)/(q+r)=0.104. =>q/r=2/3. Therefore, the overall loss percentage is : =>(0.21p+0.11q+0.1r)x100/(p+q+r). =>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3). =>0.1216×100. =>12.16%. Answer : B #### B QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50 SOLUTION:Others equal 5650. Answer D #### D QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is: options: A)51:52 B)52:53 C)51:53 D)52:55 E)53:54 SOLUTION:Explanation: Let C.P. of the article be Rs. x. Then, required ratio = 104% of x / 106% of x = 104/106 = 52/53 = 52:53 ANSWER IS B #### B QUESTION:A large box contains 21 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? options: A)250 B)350 C)450 D)550 E)525 SOLUTION:The number of chocolate bars is equal to 21 * 25 = 525 correct answer E #### E QUESTION:The product of all the prime numbers less than 30 is closest to which of the following powers of 10? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^9 SOLUTION:Quickly approximate 2, 3, 5, 7, 11, 13, 17, 19 ,23, 29 = 1*10^7 *2.3*2.9*10^9 =6.67*10^9 E #### E QUESTION:There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes? options: A)18 B)21 C)35 D)42 E)56 SOLUTION:Note that each handshake includes two people. The total number of handshakes is 14*3/2 = 21 The answer is B. #### B QUESTION:Yesterday's closing prices of 2,640 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday? options: A) 484 B) 726 C) 1,100 D) 1,320 E) 1,440 SOLUTION:Lets consider the below - The number of stocks that closed at a higher price = H The number of stocks that closed at a lower price = L We understand from first statement -> H+L = 2640 ----(1) We understand from second statement -> H = (120/100)L => H = 1.2L ----(2) Solve eq (1)(2) to get H = 1440. E is my answer. #### E QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)375 SOLUTION:Explanation: Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. ANSWER IS C #### C QUESTION:One type of liquid contains 10% of water and the second type of liquid contains 15% of water. A glass is filled with 5 parts of 1st liquid and 2 parts of 2nd liquid. The percentage of water in the new mixture in the glass is? options: A)5.6% B)11.4% C)15.6% D)21.3% E)18.9% SOLUTION:Required percentage = (10% of 5 + 15% of 2)/5+2 *100 = 0.8/7 * 100 = 11.4% Answer is B #### B QUESTION:A store reduced the price of all items in the store by 12% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? options: A)80.0 B)79.2 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 12% price becomes = 0.88 *100 = $ 88 after the final reduction of 10% price becomes = 0.9* 88 = $ 79.2 price of all items on second day is 79.2% of price on first day correct answer option B #### B QUESTION:Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible? options: A)10 B)25 C)126 D)252 E)630 SOLUTION:With 10 players, the process of figuring out how many groups of 5 can be formed is pretty straight-forward.... 10C5 = 10!/(5!5!) = 256 possible groups of 5 Once forming that first group of 5, the remaining 5 players would all be placed on the second team by default. The 'twist' is that the two teams of 5 can "show up" in either order: For example, if we call the two teams of 5 players: A,B,C,D,E and F,G,H,I,J ABCDE vs. FGHIJ is the SAME match-up as.... FGHIJ vs. ABCDE So we are NOT allowed to count that matchup twice. This means we have to divide the 256 by 2. Final Answer:C #### C QUESTION:What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected? options: A)76 ways B)66 ways C)30 ways D)56 ways E)43 ways SOLUTION:The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5 = 30 ways. Answer: C #### C QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6 SOLUTION:Explanation: 40*(48/100) = 19.2 --- 64 ? --- 12 => Rs.3.6 Answer: D #### D QUESTION:In an examination, 34% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both? options: A)975 B)1150 C)1175 D)1243 E)1525 SOLUTION:Failed in 1st subject = 34*2500/100 = 850 Failed in 2nd subject = 42*2500/100 = 1050 Failed in both = 15*2500/100 = 375 Failed in 1st subject only = 850-375 = 475 Failed in 2nd subject only = 1050-375 = 675 Passed in either subject but not in both = 675+475 = 1150 Answer is B #### B QUESTION:In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent W of her bushes have only yellow roses? options: A)20 B)30 C)50 D)70 E)80 SOLUTION:let, the number of bushes with only yellow flowers be x so, number of bushes with only yellow flowers will be 1.5x if total number of bushes of flowers= T then total number of bushes with yellow flowers= 0.8T we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers so, W=0.8T+x=T x=0.2T so, 1.5x=0.3T 30% flowers are yellow flowers OA B #### B QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? options: A)336 B)425 C)275 D)235 E)689 SOLUTION:B 425 (68 ÷ 16) × 100 #### B QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? options: A)4% B)8% C)4.2% D)4.8% E)5% SOLUTION:Let's say there is a TOTAL of100students at this college. 60 percent of the total number of students are freshmen. # of freshmen = 60% of 100 =60 40 percent of the fresh-men are enrolled in the school of liberal arts... Number of liberal arts freshmen = 40% of 60 =24 ...and, of these, 20 percent are psychology majors... Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8 What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? 4.8/100= 4.8% Answer:D #### D QUESTION:How many words can be formed by using all letters of the word ‘DESK’ ? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The word contains 4 different letters. The number of permutations is 4! = 24 The answer is C. #### C QUESTION:What is the smallest possible common multiple of three integers, all larger than 53? options: A)27. B)54. C)846. D)19,656. E)21,924. SOLUTION:The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54. Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer B. #### B QUESTION:If A : B = 4 : 9 and B : C = 5 : 9 then A : B : C is : options: A)20 : 35 : 63 B)35 : 36 : 63 C)30 : 35 : 65 D)20 :45: 81 E)None of these SOLUTION:Expl : A : B = 4 : 9 B : C = 5 :9 = 5*9/5 : 9 *9/5 = 9 : 81/5 A : B : C = 4 : 9 : 81/5 = 20 : 45 : 81 Answer: D #### D QUESTION:If 3 women can color 180 m long cloth in 2 days, then 5 women can color 300 m long cloth in? options: A)2 days B)3 days C)5 days D)1 day E)4 days SOLUTION:The length of cloth painted by one woman in one day = 180/ 3× 2 = 30 m No. of days required to paint 300 m cloth by 5 women = 300/ 5 × 30 = 2 days Answer : A #### A QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 30*16=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: options: A)4 B)6 C)5 D)7 E)9 SOLUTION:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4 Answer: Option A #### A QUESTION:A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water? options: A)22 B)37 C)32 D)27 E)18 SOLUTION:US = 25 DS = 39 M = (39 + 25)/2 = 32 Answer:C #### C QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)22 B)71 C)54 D)77 E)99 SOLUTION:S = 240/16 * 18/5 = 54 kmph Answer: C #### C QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 7 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank? options: A)0.07 B)0.049 C)0.7 D)0.49 E)4.9 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi*49*10 = pi*h*100*100 (h is distance that the oil level dropped) h = 490/10,000 = 49/1000 = 0.049 ft The answer is B. #### B QUESTION:The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January? options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500 SOLUTION:Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8600 = 34400 ----(2) (2)-(1) i.e. May - Jan = 2400 Salary of May is Rs.6500 Salary of January = Rs.4100 Answer:A #### A QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 20 years = (20 + 20) years =40 years. Answer : C #### C QUESTION:A password for a computer uses three digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero? options: A)1/32 B)1/16 C)1/8 D)2/5 E)1/2 SOLUTION:To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 = 1,000 possible combinations. Prime numbers constitute 2, 3 In addition to zero, this is 3 total possibility for each digit. So the number of satisfactory variants is 3× 3 × 3 . So the probability is 1/2 × 1/2 × 1/2 = 1/8. The right answer is choice (C). #### C QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5 B)6 C)7 D)1 E)2 SOLUTION:160 = (180*4*R)/100 R = 5% Answer: A #### A QUESTION:A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)30 B)60 C)75 D)90 E)105 SOLUTION:Answer : A Let number of notes of each denomination be x. Then, x + 5x + 10x = 160 16x = 160 x = 10. Hence, total number of notes = 3x = 30. #### A QUESTION:Sheena has a pet frog and it is growing fast and eating more flies each day. When she first brought it home on Monday it ate 3 flies, Tuesday it ate 6, Wednesday it ate 9, and Friday it ate 15. How many flies did her frog eat on Thursday? options: A)12 B)14 C)10 D)11 E)13 SOLUTION:A) 12. The frog started eating 3 more flies each day. 3 +3 =6 6+3=9 9+3=12 12+3=15 #### A QUESTION:A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:The cost of 3 kg of sugar is $30. What will the cost of 8 kg of sugar be? options: A)20 B)40 C)80 D)160 E)180 SOLUTION:3 kg costs $30 1 kg costs $10 8 kg costs $80 The answer is C. #### C QUESTION:If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$60.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10 Total spent 50.50 + 10.10 = $60.60 correct answer B #### B QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)8 B)15 C)16 D)18 E)None SOLUTION:Solution Capacity of the tank = (12×13.5) litres = 162 litres. Capacity of each bucket = 9 litres. Number of buckets needed = (162/9) ‹=› 18. Answer D #### D QUESTION:If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost? options: A)24 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 60 : x 250 * x = (100 * 60) x = (100 * 60) / 250 x = 24 ANSWER: A #### A QUESTION:If (A+B) = 5, (B+C) = 6 and (C+D) = 3, what is the value of (A+D)? options: A)16. B)8. C)7. D)2. E)-2. SOLUTION:Given A+B = 5 B+C = 6 C+D = 3 (A+B)-(B+C)+(C+D)=(A+D) => 5 - 6+3 = 2. Option D... #### D QUESTION:The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is? options: A)6 kmph B)7 kmph C)9 kmph D)4 kmph E)2 kmph SOLUTION:S = 1 M = x DS = x + 1 US = x - 1 35/(x + 1) + 35/(x - 1) = 12 x = 6 Answer: A #### A QUESTION:I. q-14, q, q, q, q+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of q or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A QUESTION:Of the employees in a company, 50 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female? options: A)60% B)62.5% C)63.25% D)63.5% E)65% SOLUTION:Let E be total no. of employees and F be total no of female employees. Question asked what is F/E X 100%? No. of female employees with Masters = 0.5 x E (From the question) No. of female employees without masters = 0.2 x F (From the question) Therefore No. of female employees with masters = F - 0.2 F = 0.8 F The 2 expressions equal each other therefore 0.8F = 0.5E; F/E = 0.5/0.8 = 62.5% Ans: B #### B QUESTION:A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train. options: A)15 kmph B)36 kmph C)21 kmph D)17 kmph E)19 kmph SOLUTION:Let the speed of the goods train be x kmph. Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours 10x = 4 x 90 or x =36. So, speed of goods train = 36kmph. Ans: B #### B QUESTION:A train 120 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)443 m B)354 m C)450 m D)380 m E)250 m SOLUTION:D 350 D = 72 * 5/18 = 25 = 500 – 120 = 380 #### D QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)None of these SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111.. Answer : Option C #### C QUESTION:Acording to a military code, SYSTEM is SYSMET and NEARER is AENRER. What is the code for FRACTION ? options: A)CARFTINO B)CARFTION C)ARFCNOIT D)CARFNOIT E)SUIIQQWE SOLUTION:Explanation: The letter is the first half and the letter half of the word are separately reversed to obtain the code. Answer: D #### D QUESTION:Reena took a loan of 1500 with simple interest for as many years as the rate of interest. If she paid 735 as interest at the end of the loan period, what was the rate of interest? options: A)3.6 B)7 C)18 D)Cannot be determined E)None SOLUTION:Explanation: Let rate = R% and time = R years. Then, (1500 x R x R)/100 = 735 15R² = 735 R² = 49 R = 7. Answer: Option B #### B QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1⁄7 hours B)6 2⁄7 hours C)8 2⁄7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 × 2 = 16 km Distance covered in next two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 – 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. ∴ Time taken = 4⁄12 = 1⁄3 hour. Total time= 6 + 1⁄3 = 6 1⁄3 hour Answer E #### E QUESTION:A, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each. options: A)360000;180000;270000 B)270000;180000;360000 C)180000;360000;270000 D)270000;360000;270000 E)None of them SOLUTION:Let the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then, (3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5 1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5 108x /(72x+6480000)=3/4  432x = 216x + 19440000 =216x = 19440000 =x=90000 Hence, A’s initial investment = 3x = Rs. 2,70,000; B's initial investment = 2x = Rs. 1,80,000; C's initial investment = 4x = Rs. 3,60,000. Answer is B. #### B QUESTION:If a man buys 10 lollipops for $90 and sold them for $6 dollars determine his loss. options: A)50 B)60 C)70 D)20 E)90 SOLUTION:Cost of 10 lollipops = $80 Sold each lollipop for $6 So he sold 10 lollipops for $(10 × 6) = $60 Loss = $(80 – 60) = $20 answer :D Therefore, loss = $ 20. #### D QUESTION:In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/6 of the absentee ballets were thrown out and 3/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)4,000 D)8,000 E)9,000 SOLUTION:5/6 * 2/5 (total absentee votes) = 1/3 (total votes)=1/3*12000=4000 Answer is C #### C QUESTION:A shopkeeper sold an article for 240 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’? options: A)25% B)50% C)23% D)28% E)None of these SOLUTION:Cost price = 240×100/120= 200 S.P. at no discount = 240×100/80 = 300 ∴ % profit = 100×100/200 = 50 % Answer B #### B QUESTION:The successive discounts 20% and 15% are equal to a single discount of? options: A)43% B)72% C)32% D)44% E)29% SOLUTION:C 32% Let the CP of an article be Rs. 100 Given that successive discounts are 20% and 15%. SP = 85% of 80% of 100 = (85/100)(80/100)(100) => SP = Rs. 68 Clearly, single discount is 32%. #### C QUESTION:A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle? options: A)Rs.1148 B)Rs.1160 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 82% of Rs.1400 = Rs.(82/100×1400) Rs.1148. Answer A #### A QUESTION:If the average (arithmetic mean) of a and b is 45 and the average of b and c is 85, what is the value of c − a? options: A)25 B)80 C)90 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=170 --2 subtracting 1 from 2 we have c-a=80; ANSWER:B #### B QUESTION:Scott's average (arithmetic mean) golf score on his first four rounds was 58.What score does he need on his fifth round to drop his average score by 2 points? options: A)48 B)72 C)78 D)88 E)312 SOLUTION:Average score for first 4 rounds = 58 Average score after 5 rounds = 56 Score Scott needs on his 5th round to drop average score by 2 points = 58 - (2*5) = 48 Answer A #### A QUESTION:A jogger jogs at 1/6 of his usual speed. how much % he has to increase speed to reach normal pace of walking options: A)100 B)200 C)300 D)400 E)500 SOLUTION:suppose usual speed is x, then current speed is x/6. to gain normal speed, he has to gain 5x/6 % increase = 100*(5x/6)/(x/6) = 500% ANSWER:E #### E QUESTION:There are 9 books on a shelf that consist of 2 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)85 B)91 C)97 D)103 E)110 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 7C4 = 35 The number of combinations with at least one paperback is 126-35 = 91 The answer is B. #### B QUESTION:A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)227 B)400 C)230 D)288 E)271 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 42 = 50/3 3(x + 300) = 2100 è x = 400m. Answer: B #### B QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 45 years, was replaced by a new person. Find the age of the new person? options: A)12 B)15 C)18 D)21 E)25 SOLUTION:Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 45 + Q => Q = 15 ANSWER:B #### B QUESTION:A train running at the speed of 30 km/hr crosses a pole in 6 sec. What is the length of the train? options: A)20 m B)70 m C)50 m D)Cannot be determined E)None of these SOLUTION:Speed = 30 * 5/18 = 25/3 m/sec Length of the train = speed * time = 25/3 * 6 = 50 m ANSWER:C #### C QUESTION:Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10? options: A)2140 B)2520 C)2980 D)3260 E)3680 SOLUTION:The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5. The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520 The answer is B. #### B QUESTION:A man can row with a speed of 10 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is? options: A)10 kmph B)5 kmph C)40 kmph D)22 kmph E)25 kmph SOLUTION:M = 10 S = 30 DS = 10 + 30 = 40 ANSWER:C #### C QUESTION:A 6 litre sol is 40% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? options: A)A.0.6 B)B.1.2 C)C.2.1 D)D.3 E)E.5.4 SOLUTION:40% of 6 = 2.4 50% of 6 = 3 shortage is 0.6 so we need to have 0.6/50% to get 50% alcohol content. = 1.2 B #### B QUESTION:40 is subtracted from 60% of a number, the result is 50. Find the number? options: A)150 B)140 C)130 D)120 E)110 SOLUTION:(60/100) * X – 40 = 50 6X = 900 X = 150 ANSWER:A #### A QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)420 E)663 SOLUTION:1h ----- 3 ? ------ 60 12 h RS = 16 + 19 = 35 T = 12 D = 35 * 12 =420 Answer: D #### D QUESTION:The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 60 with him, what was the average amount with the group before his joining the group? options: A)s. 25.6 B)s. 25 C)s. 16.6 D)s. 26 E)s. 25.6 SOLUTION:Total members in the group = 7 Average amount = Rs. 30 Total amount with them = 7 * 30 = Rs. 210 One number has Rs. 60. So, the amount with remaining 6 people = 210 - 60 = Rs. 150 The average amount with them = 150/6 = Rs. 25 ANSWER:B #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.27 C)Rs.51.79 D)Rs.51.8 E)Rs.51.93 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs.51.25. Answer: A #### A QUESTION:John Purchased 1365 large bottles at $1.89 per bottle and 720 small bottles at $1.42 per bottle. What was the approximate average price paid per bottle? options: A)$1.63 B)$1.64 C)$1.68 D)$1.73 E)$1.76 SOLUTION:(1365*1.89+720*1.42)/(1365+720) =~1.73 Option (D) #### D QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000*(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:A batsman makes a score of 100 runs in the 17th inning and thus increases his averages by 5. What is his average after 17th inning? options: A)39 B)35 C)20 D)40.5 E)41.5 SOLUTION:let the average after 16th inning =x then total run after 16th inning=16x then total run after 17th inning=16x+100 then average run after 17th inning=(16x+100)/17 (16x+100)/17=x+5 = > 16x+100 = 17x+85 => x =15 x=15; average after 17th inning =15+5=20 ANSWER:C #### C QUESTION:Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is options: A)4 : 5 B)1 : 2 C)6 : 7 D)5 : 6 E)None SOLUTION:Solution Let us name the brothers as A and B. = (A'S speed) : (B's speed) =√b : √a = √25 : √36 = 5 : 6 Answer D #### D QUESTION:What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58 ? options: A)1288 B)2797 C)3944 D)1299 E)1082 SOLUTION:Let the side of the square plot be 'a' ft. Given area of the plot (a x a) = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 x 58 = Rs. 3944. Answer: C #### C QUESTION:If a is a number such that –2 ≤ a ≤ 2, which of the following has the largest possible absolute value? options: A)3a – 1 B)x^2 + 1 C)3 – x D)x – 3 E)x^2 – x SOLUTION:Ans is A .. leads to the max value of 7 for a = -2 #### A QUESTION:Which of the statements can be dispensed with while answering the above question? options: A)A only B)B only C)A or C only D)B or C only E)C or D only SOLUTION:Explanation: Justification: We can find the code for 'home' from the second and third statements. For finding the code for 'they', we need the code for 'go' which cannot be determined from the given data. Clearly, statement A is not necessary. Answer: A #### A QUESTION:There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is options: A) 0.005 B) 0.002 C) 0.001 D) 0.0003 E) 0.0002 SOLUTION:It is very easy if x is the diameter, then the magnified length is 1000x. ince 1000x=0.3 then x=0.3/1000=0.0003. The answer is D #### D QUESTION:A carpenter makes 4 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:I believe it is C because if 1C makes 3 beds in 1 day then: 1C's rate = 3/1 So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day. Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed. Time = Amount / Rate Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 4.7 So, in order for the carpenters to be able to finish they need 5 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day. C #### C QUESTION:A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere interest rate is increased by 8%, it would amount to bow mucb ? options: A)Rs 990 B)Rs 995 C)Rs 997 D)Rs 992 E)Rs 999 SOLUTION:S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _ . R = ((100 x 120)/(800*3) ) % = 5%. New rate = (5 + 3)% = 8%. New S.l. = Rs. (800*8*3)/100 = Rs. 192. :. New amount = Rs.(800+192) = Rs. 992 Answer is D. #### D QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 9 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)22 litres E)18 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+9)=4/5 20x=4(3x+9) 8x=36 x=4.5 Quantity of alcohol = (4 x 4.5) litres = 18 litres. Answer is E #### E QUESTION:What should come in place of the question mark (?) in the following equation? 5978 + 6134 + 7014 = ? options: A)19226 B)16226 C)19216 D)19126 E)None of these SOLUTION:? = 5978 + 6134 + 7014 = 19126 Answer D #### D QUESTION:A meal cost $ 32.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-39 E)36-37 SOLUTION:10%(32.5) = 3.25 15%(32.5) =4.875 total amount could have been 32.5+3.25 and 32.5+4.875 => could have been between 35.75 and 37.375 => approximately between 36 and 37 Answer is E. #### E QUESTION:At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? options: A)15 B)18 C)11 D)12 E)19 SOLUTION:D 12 If there are n people, the first person will shake hand with n-1 persons, the second with n-2, the third with n-3, and the (n-1)th person with n-(n-1)=1 person means the last person. Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1 Which can be equated using n(n-1)/2=66 Hence, n=12 #### D QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)228 B)240 C)188 D)266 E)281 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:John has taken four (4) tests that have an average of 81. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade? options: A)87 B)90 C)92 D)94 E)99 SOLUTION:87-81=6*4=24 points 2*87=174 174+24=198 points to be scored in the 2 tests. Avg of 2 tests = 198/2=99 Answer: E Traditional Method: Total scored till now 81*4=324 Total score to avg 87 in 6 tests = 87*6=522 Total to be scored on 2 tests = 522-324=198 Avg on 2 tests = 198/2 = 99 Answer E #### E QUESTION:Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt? options: A)25/33 B)31/44 C)41/55 D)53/66 E)65/77 SOLUTION:Total possible ways to choose 4 students out of 12 = 12C4 = 495 The number of ways to choose 4 students with no green shirts = 9C4 = 126 P(no green shirts) = 126/495 = 14/55 P(at least 1 green shirt) = 1 - 14/55 = 41/55 The answer is C. #### C QUESTION:The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 guards will be available to patrol the fairgrounds on the following Saturday night? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:For any given day, only the guards patrolling on the previous day won't be available. So, 3 guards who patrolled on Friday won't be available. We are thus left with 4 guards. To choose 3 out of 4, we will have 4C3 = 4 different groups. The answer is B. #### B QUESTION:The sale price sarees listed for Rs.200 after successive discount is 20% and 5% is? options: A)187 B)169 C)152 D)178 E)175 SOLUTION:200*(80/100)*(95/100) = 152 Answer:C #### C QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers? options: A)28 B)56 C)76 D)84 E)85 SOLUTION:Explanation: Let the numbers be 3x and 4x LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x) Given that LCM of 3x and 4x is 48 => 12x = 48 => x = 48/12 = 4 Sum of the numbers = 3x + 4x = 7x = 7 x 4 = 28 Answer: Option A #### A QUESTION:In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had? options: A)10.7% B)20% C)25% D)33 1/3 E)58 1/3 SOLUTION:No of bank customers in 1985 = 60 x .45 = 27 No of bank customers in 1987 = 144 x .25 = 36 increase in % = 100 X 9/27 = 100/3 or 33 1/3 D is the correct answer #### D QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)40% D)62% E)80% SOLUTION:We need multipliers. multiplier for a 10% increases = 1 + 0.10 = 1.1 multiplier for a 20% decreases = 1 – 0.20 = 0.8 multiplier for a 50% increases = 1 + 0.50 = 1.5 Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3 (0.8)*(1.5) = (0.4)*(3) = 1.2 Now, multiply this by 1.1 1.2*1.1 = 1.32 Thus, the three percent changes combined produce a 32% increase. Answer = (B). #### B QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120? options: A)1000 B)289 C)209 D)280 E)892 SOLUTION:1120 = P [1 + (5*12/5)/100] P= 1000 Answer: A #### A QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ? options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points SOLUTION:A: B = 80 : 75, A : C = 80 : 65. B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5 Therfore ,In a game of 60, B can give C 8 points. Answer is E. #### E QUESTION:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts? options: A)6 B)14 C)19 D)20 E)81 SOLUTION:< 6 hours sleep>= 6 hours sleepTOTAL Tired75-- Not Tired-0.7*X? TOTAL80X100 Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5; TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14; Interns who areNot Tired S= 5 + 14 = 19. Answer: C. #### C QUESTION:A chair is bought for Rs.200/- and sold at Rs.310/- find gain or loss percentage options: A)15% loss B)20% gain C)25% gain D)30% gain E)55% gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (310- 200)/200= 55% gain E #### E QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.18000? options: A)6620 B)2888 C)2776 D)2997 E)5958 SOLUTION:A = 18000(11/10)^3 = 23958 = 18000 ---------- 5958 Answer: E #### E QUESTION:The ratio of cats to dogs to birds to fish is 3:4:5:6. There are no other types of animals in the pet store. which of the following cannot be the total number of animals in the store? options: A)36 B)54 C)72 D)90 E)101 SOLUTION:The parts add up to 3 + 4 + 5 + 6 = 18, so we know that any possible number of total answers must be a multiple of 18. All five answer choices are multiples of 18: (A) 36 = 18*2 (B) 54 = 18*3 (C) 72 = 18*4 (D) 90 = 18*5 (E) 101 = not a multiple of 18 ans is E #### E QUESTION:Select the one which is different from other Four alternatives. options: A)988 B)1140 C)1064 D)1197 E)1352 SOLUTION:E (A) 988 ÷ 19 = 52 (B) 1352 ÷ 19 = 71.15 (C) 1064 ÷ 19 = 56 (D) 1197 ÷ 19 = 63 (E) 1140 ÷ 19 = 60 #### E QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 450. Find the total worth of the stock? options: A)20029 B)22500 C)20289 D)20027 E)20026 SOLUTION:Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 450 => x = 22500 Answer: B #### B QUESTION:From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn options: A)4/13 B)1/52 C)1/4 D)1/5 E)None of above SOLUTION:Explanation: Total number of cases = 52 Total face cards = 16 [favourable cases] So probability = 16/52 = 4/13 Answer: A #### A QUESTION:A die is thrown three times. Events X and Y are defined as below: X : 4 on the third throw Y : 6 on the first and 5 on the second throw What is the probability of X given that Y has already occurred. options: A)1/6 B)1/7 C)1/8 D)1/11 E)1/13 SOLUTION:The sample space has 216 outcomes. Now X = (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4) (3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4) (5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4) Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)} and X n Y = {(6,5,4)}. Now P(Y) = 6/216 and P (X n Y) = 1/216 Then P(X|Y) = (1/216)/(6/216) = 1/6. A #### A QUESTION:A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? options: A)59020 B)59299 C)59020 D)59300 E)59008 SOLUTION:Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500. Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000. Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P) Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally. Income of A = Twice the income of B (2500 + 18000 + P) = 2(P) P = 20500 Total profit = 2P + 18000 = 2*20500 + 18000 = 59000 Answer: D #### D QUESTION:A data set with a mean of 40 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)18 B)36 C)59 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=40-3.5=36.5 to{mean}+{deviation}=40+3.5=43.5. The smallest number within this range from the options is 36. Answer: B. Hope this helps. #### B QUESTION:The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town? options: A)3. B)7. C)10. D)16. E)15. SOLUTION:Time taken by the birds to meet = 20/(4 + 1) = 4 mins Distance traveled by the bird traveling from West-Town = 4 *4= 16 Answer: D #### D QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points? options: A)25 B)29 C)48 D)26 E)54 SOLUTION:A 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. #### A QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? options: A)4.5 B)5 C)5.6 D)5.7 E)6.5 SOLUTION:if $x$ is the number, x/6 * 12 = 9 => 2x = 9 => x = 4.5 A #### A QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum. options: A)800 B)700 C)600 D)500 E)None of them SOLUTION:Let the sum be Rs. x Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40 = (7x/20)-(3x/10)=40 x = (40 * 20) = 800. Hence, the sum is Rs. 800. Answer is A. #### A QUESTION:Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers k did Carl drive each way? options: A) 350 B) 345 C) 320 D) 280 E) 240 SOLUTION:Let us backsolve here. The answer option has to be divisible by 7 to give us 1/2. Let us try k=280 km. Time taken will be 3.5 hours and 4 hours. Hence D is the answer. #### D QUESTION:The area of the largest circle that can be drawn inside a square of side 98 Cm in length is: options: A)8600 B)3646 C)7546 D)7636 E)1606 SOLUTION:Radius of required circle = 49 Cm its area = 22/7 × 49 × 49 154 × 49 = 7546 Cm(power)2 Answer is C. #### C QUESTION:For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? options: A)18.1 B)21.1 C)36.5 D)42.2 E)84.4 SOLUTION:Let x and z be the smallest and largest of the original set, respectively. z - x = 84.4 The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4. Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1 The answer is B. #### B QUESTION:If P (A) = 0.18, P (B) = 0.5 and P (B|A) = 0.2, find P(A n B)? options: A)0.28 B)0.36 C)0.45 D)0.56 E)0.7 SOLUTION:P(B|A) = P(A n B)/P(A) P(A n B) = P(B|A) × P(A) P(A n B) = 0.2 × 0.18 P(A n B) = 0.36 B) #### B QUESTION:If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element? options: A)27 grams B)28 grams C)29 grams D)42 grams E)32 grams SOLUTION:Let original mass be 100 The final mass of that element will be 7 So whatever option we have it will be divisible by 7 Check for the options the one that doesn't produce non terminating decimal is our answer A. 27 grams 27/7 = 3.857... B. 25 grams 25/7 = 3.571... C. 29 grams 29/7 = 4.142....... D. 42 grams 42/7 = 6 E. 32 grams 32/7 = 4.571.... Hence our answer will be (D) #### D QUESTION:A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially? options: A)25 B)21 C)20 D)10 E)15 SOLUTION:Suppose the can initially contains 7x and 5x litres mixtures A and B respectively Quantity of A in mix. left =[7x –7/12 * 9 ] =[7x –21/4] Quantity of B in mix. left =[5x –5/12 *9 ] = [ 5x - 15/4 ] Therefore [ 7x-21/4 ] =7/9 or 28x-21 = 7/9 [5x-15/4]+9 20x+21 252x -189 =140x+147 or 112x =336 , x = 3. Quantity of A in the can initially =7*3 =21 ANSWER:B #### B <<<Examples ends QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A tap can fill a tank in 2 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely? options: A)1 hr 40 min B)4 hr C)3 hr D)1 hr 20 min E)2 hr 50 min SOLUTION:Explanation: 1 tap can fill the tank in 2 hours. Therefore 1 tap can fill half tank in 1 hours. 3 taps can fill the tank in 2/3 hour. Therefore 3 taps can fill half tank in 2/6 hour =20 minutes. Total time taken=1 hour 20 minutes Answer: Option D #### D QUESTION:A man can row his boat with the stream at 25 km/h and against the stream in 13 km/h. The man's rate is? options: A)1 kmph B)2 kmph C)6 kmph D)8 kmph E)3 kmph SOLUTION:DS = 25 US = 13 S = ? S = (25 - 13)/2 = 6 kmph Answer:C #### C QUESTION:Which of the following is greatest? options: A)1/2 B)1/4 C)1/3 D)1/6 E)1/7 SOLUTION:simply we know that 1/2 is greater than all others. So, Answer : A #### A QUESTION:If B and C are digits and 8BC is a 3-digit number that is divisible by 5, which of the following is a possible product of B and C? options: A)1 B)2 C)5 D)7 E)14 SOLUTION:Try with the options - A. If BC = 1 , both B and C must be 1 B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3 C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3 D. If BC = 6 , then we can have the following possibilities i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3 ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3 E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 5 Thus answer is (D) #### D QUESTION:There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. options: A)300 B)T=400 C)T=500 D)600 E)None of these SOLUTION:{Managers} = {Female Managers} + {Male Managers}; We are told that the total number of managers in the company is 2/5 of all the employees , thus {Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively. Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200; Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500. Answer: C. #### C QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 10%? options: A)20% B)29% C)10% D)35% E)90% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 90 2/3 SP1 = 90 SP1 = 135 100 --- 35 => 35% Answer: D #### D QUESTION:A division of a company consists of six men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/11 D)5/12 E)7/15 SOLUTION:Total number of ways to select 2 members = 11C2 = 55 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/55 = 2/11 The answer is C. #### C QUESTION:Weights of two friends Ram and Shyam are in the ratio 2:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased? options: A)17% B)10% C)21% D)16% E)None SOLUTION:Solution: given ratio of Ram and Shayam's weight = 2:5 Hence, (x-15)/(15-10) = 2/5 Or, x = 17%. Answer: Option A #### A QUESTION:The diameter of a garden roller is 1.4 m and it is 3 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22⁄7) options: A)60 m2 B)64 m2 C)68 m2 D)66 m2 E)None of these SOLUTION:Required area covered in 5 revolutions = 5 × 2Ï€rh = 5 × 2 × 22⁄7 × 0.7 × 3 = 66 m2 Answer D #### D QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 4 candidates are there to fill the 4 positions? options: A)420 B)770 C)840 D)165 E)315 SOLUTION:1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer None of the 4 chosen people can be in more than one departments. We can choose any of the 7 candidates for the math dep., which gives as 7 selections. We can choose 3 of the 10 candidates for the computer dep., which gives us 3 selections and 7 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /3!*7!= 120 We are multiplying our individual selections: 7*120 = 840 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans C #### C QUESTION:In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes? options: A)32 B)16 C)64 D)80 E)16 or 48 SOLUTION:Let total number be x No in the interior = (x/8)^2 No outside = 16 So : x - (x/8)^2=16 x^2-64x+16*64=0 (x-32)^2=0 x=32 A #### A QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 1/5 Km B)2 1/5 Km C)4 Km D)4 1/5 Km E)3 3/5 Km SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km A #### A QUESTION:4, 6, 12, 14, 28, 30, ? options: A)32 B)64 C)62 D)60 E)52 SOLUTION:The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60 Answer : D. #### D QUESTION:If the price of 23 toys is 230, then what will the price of 18 toys ? options: A)144 B)361 C)180 D)287 E)112 SOLUTION:One toy price = 230/23 = 10 18 toy price = 18 * 10 = 180 Answer : C #### C QUESTION:There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division? options: A)22 B)35 C)37 D)20 E)75 SOLUTION:D 20 29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30 = 20. #### D QUESTION:From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x) options: A)10 B)14 C)15 D)16 E)30 SOLUTION:Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations E #### E QUESTION:In a bowl, the number of marbles gets doubled after every minute. If the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled. options: A)1 hour and 59 minutes B)2 hour and 59 minutes C)4 hour and 59 minutes D)4 hour and 59 minutes E)5 hour and 59 minutes SOLUTION:Solution: The correct way to solve this question is go backwards. If the number of marble gets doubled every minute and after two hours, it is filled completely, one minute ago it would be half. So, it will take 1 hour and 59 minutes for it to be filled half. Answer A #### A QUESTION:If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 740 will be: options: A)Rs. 300 B)Rs. 200 C)Rs. 240 D)Rs. 350 E)None of these SOLUTION:Z share = Z, Y = 1.2Z X = 1.25×1.2Z, X+Y+Z =740 (1.25× 1.2+1.2+1)Z=74 3.7Z=740, Z=200 Answer: . B. #### B QUESTION:A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting? options: A)12 B)22 1/2 C)37 1/2 D)88 E)80 SOLUTION:(16/2) ( 2+3) * 2 = 80=E #### E QUESTION:What is the sum of all the multiples of 10 between 0 and 75? options: A)500 B)620 C)450 D)340 E)280 SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280. Final Answer: E #### E QUESTION:A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit? options: A)37 B)299 C)72 D).32 E)01 SOLUTION:Explanation: Let cost price of lemons be x. Selling price of lemons becomes CP - loss. =>SP=x-(20/100)x =>40=x(80/100) =>50 So 45 lemons cost Rs 50 Cost of 1 lemon = 50/45 Rs Cost of 24 lemons = (50/45)*24 =80/3 Rs Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32 ANSWER:D #### D QUESTION:21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement. options: A)7/41 B)3/41 C)9/42 D)4/51 E)5/13 SOLUTION:The probability that first toy shows the even number, =1021=1021 Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left. Hence, probability that second toy shows the even number, =920=920 Required probability, =(1021)×(920)=(1021)×(920) =9/42 C #### C QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)198 E)200 SOLUTION:185 Answer is B #### B QUESTION:1 quarter Kg of potatoes cost 60 paise. Calculate the cost of 200 grams options: A)48 paise B)77 paise C)96 paise D)66 paise E)55 paise SOLUTION:Explanation: Let 200 gm potato cost X paise According to question, Cost of 1/4 Kg potato = 60 Paise => Cost of 250 gm potato = 60 Paise => 1 Kg = 1000 gm => 1/4 Kg = 1000/4 gm = 250 gm By direct proportion, more quantity, more cost 200 grams : 250 grams = X : 60 => 200*60 = 250 X => 12000 = 250 X => X = 48 => Thus, the cost of 200 grams is 48 paise. ANSWER: A #### A QUESTION:If 0.75: x :: 5:12, then x is equal to: options: A)1.12 B)1.16 C)1.8 D)1.3 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *12) X=9/5 = 1.80 Answer: C #### C QUESTION:If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x? options: A)-1 B)2 C)1 D)-2 E)0 SOLUTION:If we solve the question, we get x=-2. Option: D #### D QUESTION:What is the 10th term in this sequence? 3,5,8,15,25,40,67,104,171 options: A)273 B)278 C)279 D)377 E)277 SOLUTION:3+5 =8 +0 =8 8+5 =13+2 =15 15+8 =23+2 =25 25+15=40+0 =40 40+25=65+2 =67 67+35=102+2 =104 104+67=171+0=171 171+104=275+2=277 so 9th term is 277 ANSWER:E #### E QUESTION:In a school the number of girls is 30% the number of boys. Find the number of boys as a percentage of girls? options: A)112% B)12% C)333% D)150% E)16% SOLUTION:It is given that in a school the number of girls is 30% the number of boys. If boys=10 girls=3 We are asked for the number of boys as a percentage of girls b/g=10/3=10 1/3=3.333=333% Answer is C #### C QUESTION:Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 55% nuts, what percent of the combined mixture is dried fruit? options: A)8.5% B)11.7% C)14.2% D)17.6% E)20.5% SOLUTION:55% is 25%-points above 30% and 5%-points below 60%. So the ratio of Sue's mix to Jane's mix is 1:5. 1/6*70% = 11.7% The answer is B. #### B QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? options: A)1/2 B)1/2 C)8/15 D)9/20 E)9/24 SOLUTION:Explanation : Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9/20 Answer : D #### D QUESTION:Find the missing in the series: 70, 54, 45, 41,___ options: A)22 B)287 C)2679 D)2767 E)2771 SOLUTION:Answer:B #### B QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 * (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 650 = 13 Answer: E #### E QUESTION:Car Z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour? options: A)320 B)384 C)400 D)408.3 E)440 SOLUTION:The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed. The stem tells us that at 45 miles/hour, the car will run 48 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 38.4 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 38.4 miles/gallon * 10 gallons = 384 miles. Answer B. #### B QUESTION:The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle? options: A)8m. B)6m. C)4m. D)2m. E)5m. SOLUTION:Explanation: Let the sides of the rectangle be l and b respectively. From the given data, (√l2 + b2) = (1 + 108 1/3 %)lb => l2 + b2 = (1 + 325/3 * 1/100)lb = (1 + 13/12)lb = 25/12 lb => (l2 + b2)/lb = 25/12 12(l2 + b2) = 25lb Adding 24lb on both sides 12l2 + 12b2 + 24lb = 49lb 12(l2 + b2 + 2lb) = 49lb but 2(l + b) = 28 => l + b = 14 12(l + b)2 = 49lb => 12(14)2 = 49lb => lb = 48 Since l + b = 14, l = 8 and b = 6 l - b = 8 - 6 = 2m. Answer: Option D #### D QUESTION:Which one of the following is not a prime number? options: A)31 B)61 C)71 D)91 E)101 SOLUTION:91 is divisible by 7. So, it is not a prime number. answer :D #### D QUESTION:Evaluate 28% of 550 + 45% of 280 options: A)232 B)242 C)252 D)262 E)280 SOLUTION:Explanation: = (28/100) * 550 + (45/100) * 280 = 154 + 126 = 280 Answer: Option E #### E QUESTION:Of 55 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? options: A)49 B)55 C)59 D)71 E)92 SOLUTION:Total = 55 Thrower = 37 Rest = 55 - 37 = 18 Left Handed = 18/3 = 6 Right handed = 12 If all Thrower are right handed then total right handed is 37 + 12 = 49 so A. 49 is the right answer #### A QUESTION:On a certain farm the ratio of horses to cows is 3:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 5:3. After the transaction, how many more horses than cows would the farm own? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:Originally, there were 3k horses and k cows. 3(3k-15) = 5(k+15) 9k-5k = 75+45 4k = 120 k = 30 The difference between horses and cows is (3k-15)-(k+15) = 2k-30 = 30 The answer is B. #### B QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3600 C)Rs. 3900 D)Rs. 4000 E)Rs. 4100 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C #### C QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:Find the odd man out. 18, 7, 12, 24, 48, 34, 46 options: A)16 B)46 C)24 D)11 E)7 SOLUTION:Explanation : 7 is the only odd number in the given series Answer : Option E #### E QUESTION:2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost? options: A)26 B)56 C)110 D)28 E)54 SOLUTION:Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D #### D QUESTION:Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:Let x be the number of guests. Number of muffins prepared = 5x + 2 Number of muffins eaten + Number of muffins remaining = Number of muffins prepared 6(x - 1) + 4 = 5x + 2 6x - 4 = 5x + 2 x = 6 Answer: D #### D QUESTION:A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 140 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)19 sec B)38 sec C)36 sec D)16 sec E)11 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 240 + 140 = 360 m. Time taken = 380/10 = 38 sec. Answer: B #### B QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)48 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E QUESTION:A 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar? options: A)6%. B)7.5%. C)9.2%. D)10.5%. E)14%. SOLUTION:Denominator: 340+10+3.2+6.8=360 Numerator: 340(1-.80-.06)+3.2 340(0.14)+3.2 47.6+3.2 50.8 Ratio: 50.8/360=0.14 Answer: E #### E QUESTION:Two trains leave the same train station at 6:00 am and 6:45 am and they travel at 100 kph and 125 kph respectively. How many kilometers from the train station will the two trains be together? options: A)300 B)325 C)350 D)375 E)400 SOLUTION:At 6:45, the first train is 75 km ahead. The second train gains 25 km each hour. The time it takes the second train to catch the first train is 75 / 25 = 3 hours. In this time, the second train travels 3*125=375 km. The answer is D. #### D QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 27 cm * 16 cm. What is the perimeter of the square? options: A)140 B)240 C)340 D)144 E)122 SOLUTION:Area of the square = s * s = 3(27 * 16) => s = 9 * 4 = 36 cm Perimeter of the square = 4 * 36 = 144 cm. Answer: D #### D QUESTION:A train is 360 meter long is running at a speed of 75 km/hour. In what time will it pass a bridge of 140 meter length? options: A)87 B)69 C)40 D)72 E)24 SOLUTION:Speed = 75 Km/hr = 75*(5/18) m/sec = 125/6 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 * (6/125) = 24 seconds Answer: E #### E QUESTION:The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km? options: A)300 B)400 C)250 D)350 E)450 SOLUTION:50 kmph consumption is 1 lt/hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance. 1 lt costs $30 so 8 lt costs $240 extra expenses for 1 hr - $20 8 hrs - $160 total expense - $240 + $160= $400 Answer : B #### B QUESTION:A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid? options: A)$2.25 B)$3.25 C)$2.00 D)$3.50 E)$3.00 SOLUTION:Explanation: 3 1 2 $3.00 $2.50 $4.00 $9.00 + $2.50 + $8.00 = $19.50/6 = $3.25 B #### B QUESTION:5800 * 99 options: A)574580 B)574200 C)584250 D)576460 E)None of these SOLUTION:Explanation: 5800 * (100 - 1) = 580000 - 5800 = 574200 Option B #### B QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Solution Start with 11 coins. Sharon takes 3 coins from you: 11 - 3 = 8 coins. Steven takes 4 coins from you: 8 - 4 = 4 coins. So you have 4 at the end. Correct answer : C #### C QUESTION:Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:Three years ago, the average age of M and N was 18 years. With P joining them, the average age becomes 22 years, How old is P now? options: A)24 years B)27 years C)28 years D)30 years E)40 years SOLUTION:Explanation : Present age of (M + N) = (18 x 2 + 3 x 2) years = 42 years. Present age of (M + N + P) = (22 x 3) years = 66 years. P's age = (66 - 42) years = 24 years. Answer : A #### A QUESTION:In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ? options: A)45 B)48 C)52 D)58 E)None SOLUTION:Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48 Correct Option: B #### B QUESTION:The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 3: 00 p.m., at what time were there 32 million bacteria in the dish? options: A)6: 00 p.m. B)9: 00 p.m. C)6: 00 a.m. D)8: 00 a.m. E)10: 00 a.m. SOLUTION:Given: The number of bacteria in a petri dish increased by 50 percent every 2 hours There were 108 million bacteria in the dish at 2: 00 p.m Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours. Required: At what time were there 32 million bacteria in the dish? Assume that there were n intervals of 2 hours between 32 million and 108 million. 32 * (1.5)^n = 108 (3/2)^n = 108/32 = 27/8 = (3/2)^3 Hence n = 3 intervals. Each interval was of 2 hours. Therefore, the number of hours = 6 Subtracting 6 hours from 3 PM, we get 9 AM as the answer. Option B #### B QUESTION:A can complete a project in 20 days and B can complete the same project in 20 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed? options: A)18 days B)27 days C)26.67 days D)16 days E)15 days SOLUTION:Let X = the number of days taken to complete the project. The amount of work done by A is (x-10) * (1/20). The amount of work done by B is (x) * (1/30). (1/20)*(x-10) + (1/20)*(x) = 1 (x/20) + (x/20) - (10/20) = 1 x/10 = 3/2 x = 15 Therefore, the answer is E: 15. #### E QUESTION:At what time between 5.30 and 6 will the hands of a clock be at right angles? options: A)43 7/12 min. past 5. B)43 7/13 min. past 5. C)42 7/11 min. past 5. D)42 7/18 min. past 5. E)43 7/11 min. past 5. SOLUTION:At 5 o'clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces. 55 min. spaces are gained in 60 min. 40 min. spaces are gained in 60/55 x 40 min = 43 7/11 min. Required time = 43 7/11 min. past 5. Answer: E #### E QUESTION:Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds? options: A)186 B)130 C)180 D)181 E)120 SOLUTION:LCM of 9, 12, 15 and 18 is 180 LCM=180 ANSWER:C #### C QUESTION:It takes Jim three hours to wash the gym and it takes Julia two hours to wash the gym. Working together, how many minutes will it take them to wash the gym? options: A)70 B)72 C)74 D)76 E)78 SOLUTION:Jim can wash (1/3) of the gym per hour. Julia can wash (1/2) gym per hour. Together they can wash 1/3+1/2=5/6 of the gym per hour. 1 gym / (5/6) of the gym per hour = 6/5 hours = 72 minutes. The answer is B. #### B QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)2 C)3 D)4 E)6 SOLUTION:The distance between the nest and the ditch is 200 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 200 = 6000. D = ST 6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km) D) #### D QUESTION:Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)Rs.7000 B)Rs.8000 C)Rs.8500 D)Rs.8600 E)Rs.8700 SOLUTION:The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000. B) #### B QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence. options: A)19 B)20 C)21 D)22 E)23 SOLUTION:in case of cycle no of handshakes = no of persons hence ans = 20 ANSWER:B #### B QUESTION:A goods train runs at the speed of 72 kmph and crosses a 250m long platform in 26seconds. what is the length of the goods train? options: A)230 m B)240 m C)260 m D)270 m E)250 m SOLUTION:Speed =(72 *5/18)m/sec= 20 m/sec. then (x+250)/26=20 x+250 =520 x=520-250 then x=270 Answer: D #### D QUESTION:Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries? options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140 SOLUTION:Probability of basket = 3/5 Probability of no basket = 2/5 Required probability=3* 3/5*2/5*2/5 =36/125 A is the answer . #### A QUESTION:A is twice as good a workman as B and together they complete a work in 12 days. In how many days A alone can do the work? options: A)32 B)33 C)34 D)35 E)36 SOLUTION:A’s one day’s work : B’s one day’s work= 2:1 (A+B)’s one day’s work= 1/12 B’s one day’s work= 1/12 *1/3 = 1/36 B alone can do the work in 36 days ANSWER:E #### E QUESTION:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be options: A)45 min B)60 min C)55 min D)70 min E)80 min SOLUTION:Time = 50/60 hr = 5/6hr Speed = 48mph distance = S*T = 48 * 5/6 = 40km time = 40/60hr = 2/3hr New speed = 40* 3/2 kmph = 60kmph Answer : B. #### B QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie? options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9 SOLUTION:There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9 Answer: E #### E QUESTION:Share Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John? options: A)900 B)1000 C)1254 D)1795 E)1400 SOLUTION:Amount received by sanjay. 4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount So, the Amount received by sanjay is 1400. E #### E QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 210 sq. feet, how many feet of fencing will be required? options: A)34 B)41 C)68 D)88 E)None SOLUTION:EXPLANATION We have: l = 20 ft and lb = 210 sq. ft. So, b = 10.5 ft. Length of fencing = (l + 2b) = (20 + 21) ft = 41 ft. Answer B #### B QUESTION:Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+30 3x + 6 = x + 30 2x = 24 \inline \therefore x = 12 \inline \therefore Middle number = x + 2 = 12+2 = 14 C #### C QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4 Total factors = (4+1)*(4+1) = 6*4 = 24 Answer C. #### C QUESTION:Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm. options: A)456 B)234 C)285 D)342 E)213 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2 Answer: Option C #### C QUESTION:If the two hands in a clock are 11 minutes divisions apart,then the angle between them is options: A)66° B)18° C)24° D)60° E)None of these SOLUTION:In a clock, each minute makes 6° ∴ 11 minutes will make 6 × 11 = 66° Answer A #### A QUESTION:When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z? options: A)3/4 B)1[1/5] C)1[2/5] D)1[3/4] E)2 SOLUTION:Rate*Time=Work Let Painter W's rate be W and Painter X's rate be X R*T = Work W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2 X * z = 1 => X = 1/z When they both work together then their rates get added up Combined Rate = (W+X) R*T = Work (W+X) * 3/4 = 1 => W+X = 4/3 => 1/2 + 1/z = 4/3 => 1/z = (8-3)/6 = 5/6 => z = 6/5 = 1[1/5] Answer B #### B QUESTION:According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)100 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer C, 50 cans #### C QUESTION:If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ? options: A)3653 B)3657 C)2977 D)3957 E)2711 SOLUTION:Explanation: Given : Letter : T I E R B A N Code : 7 1 9 3 2 4 5 Thus, the code for RENT is 3957. ANSWER:D #### D QUESTION:A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is: options: A)6 hours B)10 hours C)15 hours D)30 hours E)35 hours SOLUTION:suppose first pipe filled the tank in x hour so second in x-5 and third in x-9 1/x+1/(x-5)=1/(x-9) by solving it we get x=15 ANSWER:C #### C QUESTION:A seven-digit phone number is divisible by 5. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code? options: A)05. B)06. C)03. D)04. E)02. SOLUTION:Given that 7 digit number is divisible by 5 we know any number will not be divisible by 5 if the sum of all digits of the number is not the multiple of5. Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 5... hence answer is A #### A QUESTION:Thompson had the following scores in an exam (out of 100): Social Studies: 60 Science: 89 Art: 62 Music: 69 Spanish:84 Biology: 89 What are his average marks ? options: A)61.5 B)72.5 C)71.5 D)85.5 E)75.5 SOLUTION:Explanation: Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75. Answer: E) 75.5 #### E QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 3 days at a time. If A starts they finish the task in exactly 9 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)8 B)6 C)4 D)5 E)9/2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 6No. of days when B works = 3 → 6x + 3y = 1 When B starts: No. of days when A works = 4 No. of days when A works = 5 → 5x + 4y = 1 Solving the above two equations for xy x = 1/9 y = 1/9 → Total work done by AB in a day = 1/9 + 1/9 = 2/9 → No. of days to complete the work when both work together = 9/2; Answer: E #### E QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:2*6=12.Answer is B. #### B QUESTION:The prices of tea and coffee per kg were the same in june. In August the price of coffee shot up by 20% and that of tea dropped by 20%. if in August , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ? options: A)45 B)50 C)40 D)35 E)30 SOLUTION:Let the price of tea and coffee be x per kg in June. Price of tea in August = 1.2x Price of coffee in August = 0.8x . In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50 1.2x(1/2) + 0.8x(1/2) = 50 => x =50 B #### B QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)6 months B)8 months C)10 months D)7 months E)12 months SOLUTION:Explanation: 7 * 8 : 9 * x = 8:9 => x= 7 ANSWER IS D #### D QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)288 B)200 C)279 D)992 E)208 SOLUTION:(800*3*3)/100 = 72 920 + 72 = 992 Answer: D #### D QUESTION:Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest? options: A)12 to 1 B)6 to 1 C)5 to 1 D)20 to 7 E)1 to 5 SOLUTION:The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job; The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 3*7=21 The ratio thus is 60 to 21, or 20 to 7. Answer: D. #### D QUESTION:How many three letter words are formed using the letters of the word TIME? options: A)28 B)21 C)26 D)24 E)29 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24. Answer: D #### D QUESTION:Mixture A is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture A, how many kilograms of mixture A must be added to make a 70% material B in the new mixture? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Old mix has 20% oil. You add 2 kgs of 100% oil. You get new mix with 30% oil (70% material B). w1/w2 = (100 - 30)/(30 - 20) = 70/10 = 7/1 For every 7 parts of mix A, you have added 1 part of oil. Since you have added 2 kgs oil, mix A must be 7*2 = 14 kgs. You already had 8 kgs of mix A, so extra mix A added must be 14 - 8 = 6 kgs. Answer (A) #### A QUESTION:A book is bought for $60 and sold for $75. What is the profit in percentage? options: A)12 B)15 C)20 D)25 E)30 SOLUTION:75/60 = 1.25 The answer is D. #### D QUESTION:The distance between A&B is 450km. A person is traveling from A to B at 70km/hr started at 9AM and another person is traveling from B to A at 80km/hr and started at same time. Then at what time they meet together.? options: A)A)12PM B)B)4PM C)C)1PM D)D)3PM E)E)5PM SOLUTION:Let x hours be they will meet together distance covered by 1st person+distance covered by 2nd person = 450km 70x+80x = 450 x= 3 hr They will meet = 9AM +3hr = 12PM Answer is A #### A QUESTION:A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 95, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? options: A)74 B)75 C)76 D)77 E)81 SOLUTION:ratio is 4:6:5 , numbers are 4x, 6x, 5x total scores of each class is (65*4x + 6x * 95 + 77*5x) = 260x+570x+385x = 1215x total number of students = 15x average = 1215x/15x = 81 E is the answer #### E QUESTION:If $500 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years? options: A)500 (1.056)(3) B)500 (3+1.056) C)500 (1+3(0.056)) D)500 (1.056)^3 E)500 (1+(0.056)^3) SOLUTION:the formula is CI=P(1+r/100)^t in this case i think D is the ans #### D QUESTION:20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours X will it take 12 beavers that work at the same pace, to build the same dam? options: A)2. B)4. C)X=5. D)X=6. E)8. SOLUTION:C. 5 hrs If there were 10 beavers it qould have taken double X = 6hrs.. so closest to that option is 5. #### C QUESTION:A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $45,000 commission, how many machines did she sell? options: A) 140 B) 103 C) 105 D) 115 E) 120 SOLUTION:First 100 machines = 3% commission = 0.03*100*10000 = 30000 Commission from sale of next machines = 46000 - 30000 = 16000 So 40 more machines.. Total = 140 machines IMO A.. #### A QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B QUESTION:The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? options: A)165 B)161 C)162 D)163 E)164 SOLUTION:To minimize one quantity maximize other. 164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165. Answer: A. #### A QUESTION:ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region? options: A)1:1 B)2:1 C)3:1 D)5:3 E)8:3 SOLUTION:Let's join the midpoints as shown in the figure then we'll get four small squares... AODX be 1 and similarly all squares..and we can split the unit 1 into half and half as per the mid points... Then shaded will be 1+1/2+1/2+1/2 = 5/2 and unshaded is 1/2+1/2+1/2 = 3/2.. shaded : unshaded is 5:3.. ANS option D. #### D QUESTION:In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary options: A)42,000 B)43,000 C)44,000 D)45,000 E)46,000 SOLUTION:as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned) Rest amounts are in the form of greater than or lesser than , Hence C $45000 answer is D #### D QUESTION:30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years? options: A)15% B)20% C)80% D)70% E)90% SOLUTION:Explanation : Let number of men = 100. Then, 80 men are less than or equal to 50 years old i.e 20 men are greater than 50 years of age. Now, the number of men above 50 years who play football = 20% of 20 = 4. 20% of all men play football i.e total no. of men who play football = 20, out of which 4 men are above 50 years old. So, 20 - 4 = 16 men are less than or equal to 50 years old. Therefore, percentage of football players less than or equal to 50 years = (16/20) x 100 = 80% . Answer : C #### C QUESTION:One student to pass the subject as probability 1/4. another man to get driving licence and student passed subject probability 1/6. find the probability man get driving licence. options: A)1/3 B)2/3 C)4/3 D)5/3 E)1/4 SOLUTION:Let the probability of the man get driving licence is x. so, 1/4 * x = 1/6 x = 2/3. ANSWER:B #### B QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 4 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank? options: A)1.6 B)1 C)0.4 D)0.16 E)0.016 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi*16*10 = pi*h*100*100 (h is distance that the oil level dropped) h = 160/10,000 = 16/1000 = 0.016 ft The answer is E. #### E QUESTION:The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? options: A)240 B)270 C)295 D)360 E)300 SOLUTION:Explanation: Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Smaller number = 270. ANSWER IS B #### B QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:A certain bacteria colony doubles in size every day for 25 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit? options: A)6.33 B)7.5 C)10 D)15 E)24 SOLUTION:If there is one bacteria colony, then it will reach the limit of its habitat in 25 days. If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 24 times. Answer: E. Similar questions to practice: Hope it helps. #### E QUESTION:For some integer m, m^2 - 5 is divisible by all of the following EXCEPT options: A)38 B)41 C)30 D)31 E)29 SOLUTION:Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: C #### C QUESTION:You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg. And each emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What should you collect to get the maximum wealth? options: A)20 rubies and 15 emeralds B)40 rubies C)28 rubies and 9 emeralds D)None of these E)Cannot be determined SOLUTION:Explanation : The limits our wealth is the capacity of bag which is 12 Kg. So we should make each unit of weight to worth the max. Rubee: 0.3 Kg worth 4 Crore, so 1 Kg of Rubee is worth 4/(0.3) = 40/3 = 13.33 Crore. Emerald: 0.4 Kg worth 5 crore so 1 Kg of Emerald is worth 5/(0.4) = 50/4 = 12.5 Crore. As value per kilogram is more for Rubee we should pick max rubees for max wealth. Here we can accomadate the whole 12Kg with 40 rubees which is worth 160 Crore. Answer : B #### B QUESTION:5, 11, 17, 25, 33, 43, ? options: A)49 B)51 C)52 D)53 E)54 SOLUTION:The sequence is +6, +6, +8, +8, +10, .... Answer : D. #### D QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)12:17 C)17:12 D)21:32 E)15:19 SOLUTION:Here capital is not the same. Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =(20000×6+15000×6) Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio =(30000×4+50000×4) Suresh : Kiran =(20000×6+15000×6) :(30000×4+50000×4) =(20×6+15×6):(30×4+50×4) =(20×3+15×3):(30×2:50×2) =105:160 =21:32 Answer is D. #### D QUESTION:S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the tenth digit of p, counting right to left from the units digit? options: A)1 B)2 C)4 D)6 E)9 SOLUTION:C Sum of unit digits of first 30 terms = 60 Sum of tens digits of first 30 terms = 58 Sum of thousands digits of first 30 terms = 56 and so on.. p1 = 0 p2 = (6+58) = 4 p3 = (6+56) = 2 p4 = (6+54) = 0 p5 = (6+52) = 8 p6 = (5+50) = 5 p7 = (5+48) = 3 p8 = (5+46) = 1 p9 = (5+44) = 9 p10= (4+42) = 6 ANSWER : D #### D QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)81 km/hr B)88 km/hr C)62 km/hr D)46 km/hr E)56 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y - 4.5)(10/36) ---(1) x/8.5 = (y - 5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y - 4.5)/ (y - 5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5 × 5.4 0.1y = 8.5 × 5.4 - 8.4 × 4.5 => .1y = 45.9 - 37.8 = 8.1 => y = 81 km/hr ANSWER:A #### A QUESTION:Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 81 hours respectively. The ratio of their speeds is? options: A)4:9 B)9:4 C)4:5 D)4:1 E)4:2 SOLUTION:Let us name the trains A and B. Then, (A's speed) : (B's speed) = √b : √a = √81 : √16 = 9:4 Answer:B #### B QUESTION:x =3 4 5 y= 27 36 9 then what is the relation between x and y options: A)1*X)^2 B)1*X)^3 C)1*X)^4 D)1*X)^5 E)1*X)^6 SOLUTION:Y=(1*X)^2 9=(1*3)^2 9=9 ANSWER:A #### A QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce options: A)100 B)65 C)25 D)11 E)18 SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. So if machine X produces 100 widgets, then machine Y produces 120 widgets. Ratio of 120/100 = 6/5. This is their speed of work (Y:X). i.e. speed of their work (X:Y) = 5/6 Now, time is inversely proportional to speed. Hence the ratio of the time spent (X:Y)= 6/5 Let us assume that they spend 6x and 5x hours. Given that 6x-5x = 10 So, x = 10. Hence 6x = 6*10 = 60 hours. Hence X takes 120 hours to produce 1080 widgets. So, in 1 hour, it can produce (1 * 1080)/60 = 18 Hence option (E). #### E QUESTION:Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 3 specific shirts with 2 specific pants? options: A)66 B)51 C)36 D)70 E)56 SOLUTION:Total no of combinations available is= 8 shirts X 9 pants = 72 Eliminate the 3shirts X 2 pants combo = 6 which gives.......>> 72-6=66 ANSWER: A #### A QUESTION:Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers k did Carl drive each way? options: A) 350 B) 345 C) 320 D) 280 E) 240 SOLUTION:Let us backsolve here. The answer option has to be divisible by 7 to give us 1/2. Let us try k=280 km. Time taken will be 3.5 hours and 4 hours. Hence D is the answer. #### D QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:If it were a line/column combination/permutation problem, the solution would be : 5! = 120. However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24. ANS:C #### C QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 1500. What is their H.C.F.? options: A)5 B)15 C)25 D)35 E)45 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 1500 x = 25 The numbers are (3 x 25), (4 x 25) and (5 x 25). The H.C.F. is 25. The answer is C. #### C QUESTION:The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence? options: A)−164 B)0 C)16 D)32 E)64 SOLUTION:sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term) sum of 64 terms = 32 ANSWER:D #### D QUESTION:12 buckets of water fill a tank when the capacity of each bucket is 49 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 7 litres? options: A)39 B)84 C)80 D)82 E)86 SOLUTION:Capacity of the tank = (12 × 49) litre Number of buckets required of capacity of each bucket is 17 litre = 12×49/7=12×7=84 Answer is B #### B QUESTION:Today is Monday.After 61 days,it will be options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)None of these SOLUTION:Solution Each day of the week is repeated after 7 days So,after 63 days,it will be Monday. ∴ After 61 days,it will be Saturday. Answer B #### B QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true? I. b-a = 2 II. abc is an even integer. III. (a + b + c)/3 is an integer. options: A) I only B) II only C) I and II only D) II and III only E) I, II, and III SOLUTION:Since a, b, and c are consecutive positive integers and a < b < c, thenb= a + 1, from which it follows that b - a = 1. So, I is false. Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true. Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well. Answer: D. #### D QUESTION:The ratio of two quantities is 2 to 3. If each of the quantities is increased by 4, what is the ratio of these two new quantities? options: A)5/5 B)It cannot be determined from the information given. C)11/5 D)12/5 E)13/5 SOLUTION:let the actual ratio be 2k/3k, increase numerator and denominator by 4=> 2k+4/3k+4 Until the value of k is unknown we can not determine the actual ratio. OR let the actual be 3/4. After increasing 4 => 7/8 let the actual be 6/8. After increasing 4 => 10/12 Therefore without actual quantities we cannot determine the actual ratio. Answer : B #### B <<<Examples ends QUESTION:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 20 terms of the sequence? options: A)201/100 B)99/100 C)100/101 D)1/10000 E)20/21 SOLUTION:Easy task and accomplish X1=1-1/2 x2=1/2-1/3 x3=1/3-1/4 ..... x20=1/20-1/21 sum=X1+X2+X3+....X20=1-1/2+1/2-1/3+.......1/20-1/21=1-1/21=20/21 E is the answer #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there? options: A)22896 B)25423 C)26980 D)24698 E)24360 SOLUTION:Code consists of 3 digits and no digit is repeated. First digit of the code can have 30 possibilities Second digit can have 29 possibilities Third digit can have 28 possibilities Total number of possible codes = 30*29*28 = 24360 Answer: E #### E QUESTION:W is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in W? I. 9 II. 15 III. 27 options: A)I only B)II only C)I and II only D)I and III only E)I, II, and III SOLUTION:Ans: C W->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3 means x must contain 3^2 and 5^2 so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25 but 27 is not a divisor because it can't divide 9*25 fully. so Ans : C #### C QUESTION:From a number of mangoes, a man sells half the number of existing mangoes plus 1 to the first customer, then sells 1/3rd of the remaining number of mangoes plus 1 to the second customer, then 1/4th of the remaining number of mangoes plus 1 to the third customer and 1/5th of the remaining number of mangoes plus 1 to the fourth customer. He then finds that he does not have any mangoes left. How many mangoes did he have originally? options: A)12 B)14 C)15 D)13 E)16 SOLUTION:Let the No. of mangoes that the man had originally = X No. of mangoes sold balance 1st customer = (X/2) + 1 (X - 2)/2 2nd customer = (X - 2)/6 + 1 (X - 5)/3 3rd customer = (X - 5)/12 + 1 (X - 9)/4 4th customer = (X - 9)/20 + 1 0 (X - 9)/20 + 1= (X - 9)/4 => X = 14 ANSWER:B #### B QUESTION:John purchased a house for Rs.45000 and a site for Rs.25000 respectively, if he sold the house for Rs.55000 and the site for Rs.16000, then find the resultant percentage of gain? options: A)1.39% B)1.40% C)1.41% D)1.42% E)1.43% SOLUTION:Sol. Total CP = 70000 & total SP = 71000 ⇒ gain = SP/CP = 71000/70000 = 1.0142 = 1.42%. Answer D #### D QUESTION:A train ,135 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)270 m B)245 m C)235 m D)220 m E)240 m SOLUTION:Explanation: Assume the length of the bridge = x meter Total distance covered = 135+x meter total time taken = 30s speed = Total distance covered /total time taken = (135+x)/30 m/s => 45 × (10/36) = (135+x)/30 => 45 × 10 × 30 /36 = 135+x => 45 × 10 × 10 / 12 = 135+x => 15 × 10 × 10 / 4 = 135+x => 15 × 25 = 135+x = 375 => x = 375-135 =240 Answer: Option E #### E QUESTION:how many square are there between 2001....2300 I don't remember the exact series. options: A)1 B)4 C)2 D)3 E)5 SOLUTION:series was from 2001 to 2300 45^2=2025 46^2=2116 47^2=2209 48^2=2304 (so exclude 48) so ans is 3 (45,46 and 47) ANSWER:D #### D QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is: options: A)1:3 B)2:4 C)9:3 D)7:8 E)3:4 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y= 8 1/x + 4/y = 1/15 ....(i) And, 200/x + 400/y = 25/3 1/x + 2/y = 1/24 ....(ii) Solving (i) and (ii), we get: x = 60 and y = 80. Ratio of speeds = 60 : 80 = 3 : 4. answer :E #### E QUESTION:If x^2+(1/x^2)=7, x^4+(1/x^4)=? options: A)10 B)11 C)12 D)14 E)47 SOLUTION:-> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47. Thus, the answer is E. #### E QUESTION:There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Let the number of men be m and so the number of women = 15-m Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start. Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days). Let the total work be 360 units (LCM of 180 and 120). 1 man does 360/120 = 3 units per day 1 woman does 360/180 = 2 units per day Based on above facts, Total work by men + women in these 17 days = 360 units m*9*3 + (15-m)*6*2 = 360, 27m + 180 -12m = 360, Solving m=12. Num of men = 12 and number of women = 15-12 = 3 ANSWER:C #### C QUESTION:A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English? options: A)55 B)66 C)77 D)44 E)None of these SOLUTION:Given student scores 55% marks in english in 8 papers of 100 marks each. so,his total marks are (55*800)/100 =>440 15% of his 440 marks is 440*(15/100)=>66 so,he scored 66 marks in english. ANSWER:B #### B QUESTION:Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)18 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 2 = 26 => x = 6 So Deepak age is = 3(6) = 18 Option B #### B QUESTION:A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? options: A)63 B)336 C)567 D)3024 E)5040 SOLUTION:All the cordinates are integer hence, possible AT values are {-1,0}, {-1,1} ....{-1,7}: 8 ways .... {7,-1}, {7,0} ......{7,6}: 8 ways 9*8 ways = 72 for AC values can be {1,2}, {1,3} .... {1,7} : 6ways ...... {7,1}, {7,2} ..... {7,6} : 6 ways 7*6 = 42 Total = 72 * 42 = 3024 hence D #### D QUESTION:Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:The average (arithmetic mean) of the integers from 100 to 400, inclusive, is how much greater than the average of the integers from 50 to 250, inclusive? options: A) 100 B) 175 C) 200 D) 125 E) 300 SOLUTION:For an AP the mean or average of series is average of first and last term. So, average of numbers between 100 to 400, inclusive = (100+400)/2 = 250 average of numbers between 50 to 250, inclusive = (50+250)/2 = 150 difference = 250 - 150 = 100 Answer is A #### A QUESTION:10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)2 B)1 C)7 D)6 E)4 SOLUTION:1 women's 1 day work = 1/70 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/10 + 10/140) = (1/14 + 1/14) = 1/7 5 women and 10 children will complete the work in 7 days. Answer:C #### C QUESTION:A man sells two articles for Rs.3600 each and he gains 40% on the first and loses 40% on the next. Find his total gain or loss? options: A)16% loss B)400 C)4000 D)324 E)8% LOSS SOLUTION:(40*40)/100 = 16%loss ANSWER:A #### A QUESTION:In a survey of parents, exactly 7/8 of the mothers and 3/4 of the fathers held full-time jobs. If 60 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs? options: A)25.5% B)21.5% C)17.5% D)13.5% E)9.5% SOLUTION:Fathers without full-time jobs are 1/4*2/5 = 2/20 of all the parents surveyed. Mothers without full-time jobs are 1/8*3/5 = 3/40 of all the parents surveyed. The percent of parents without full-time jobs is 2/20 + 3/40 = 7/40 = 17.5% The answer is C. #### C QUESTION:If x=-2, which of the following is(are) true? I. x^2=-|x| II |x|=-x III x/-3 = -2/3 options: A)II only B)I only C)III only D)I,II only E)II, III only SOLUTION:I. x^2=-|x| -2^2 = - |-2| Not true II |x|=-x |-2| =-( -2 ) true III x/-3 = -2/3 Not true Answer : A #### A QUESTION:5% of (25% of $1600) is? options: A)$20 B)$30 C)$45 D)$15 E)$60 SOLUTION:5% of (25% of $1600) = 5/100 (25/100 * 1600) = $20 Answer is A #### A QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d? options: A)2 B)8 C)10 D)11 E)14 SOLUTION:1155 = 3 * 5 * 7 * 11 a = 11 d = 3 a - d = 8 Answer is B #### B QUESTION:The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum? options: A)8 B)2 C)9 D)4 E)6 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96 15000[(1 + R/100)2 - 1 - 2R/100] = 96 15000[(100 + R)2 - 10000 - 200R]/10000 = 96 R2 = (96 * 2)/3 = 64 => R = 8 Rate = 8% Answer: Option A #### A QUESTION:If a^x = b^y, then options: A)log a/b= x/y B)log a/ log b = x/y C)log a/ log b = y/x D)log b/a = x/y E)log b/a = y/x SOLUTION:a^x = b^y => log a^x = log b^y => x log a = y log b => log a/ log b = y/x ANSWER:C #### C QUESTION:A Baker decides to make a cake of 5 layers, one of strawberry, chocolate, butterscoch, vanila and pista. Baker decides not to put the layers of butterscoch and vanila next to each other as they both are white in colour. How many different type of such cakes can he make? options: A)5! - (4!×2!) B)4! - (6!×2!) C)3! - (2!×4!) D)4! - (4!×2!) E)5! × (4!×3!) SOLUTION:We can find the answer by substracting the number of arrangements in which V and B comes together from the total number of arrangements of 5 layers. Arrangements in which V and B comes next to each other: We can consider V and B as a single object having 2! Variations(VB and BV). VB, S, C, P can be arranged in 4! Ways. In total there are 4!×2! Ways of arranging 5 layers with B and V layers coming next to each other. Required answer = A. 5! - (4!×2!) #### A QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)1/4 C)3/8 D)7/8 E)None of these SOLUTION:Explanation: Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E) = n(E) / n(S) =7/8. ANSWER IS D #### D QUESTION:The G.C.D. of 1.08, 0.36 and 0.9 is: options: A)0.03 B)0.9 C)G.C.D.=0.18 D)0.2 E)0.21 SOLUTION:Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. Answer: Option C #### C QUESTION:A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:A wildlife preserve is being planned for 6,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population? options: A) 340 B) 330 C) 670 D) 310 E) 300 SOLUTION:Number of rhinos = 6000 Watering area = 10,000 acres Number of rhino to increase by 10 percent ,then number of rhino = 6600 Grazing area for a rhino = 100 Total grazing area for 6600 rhinos= 6600 * 100 = 6,60,000 Total area required for the wildlife preserve = 6,60,000 + 10,000 = 6,70,000 = 670 * 1000 Answer C #### C QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)20 B)10 C)15 D)5 E)7 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days Answer: A #### A QUESTION:When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8? options: A)3 B)4 C)5 D)6 E)2 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 24) 3n = 3(6) =18, which leaves a remainder of 2 when divided by 8. Answer E #### E QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age? options: A)22 B)15 C)77 D)21 E)182 SOLUTION:Present age is 4x and 3x, => 4x + 6 = 34 => x = 7 So Deepak age is = 3(7) = 21 Answer: D #### D QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)18 sec B)70 sec C)21 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 120 + 280 = 400 m. The time required = d/s = 400/20 = 20 sec. Answer: D #### D QUESTION:1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus? options: A)98 B)99 C)97 D)96 E)95 SOLUTION:Let x be the no of initial passenger no of passengr left in 1st stop (2x/3)+30 no of passenger in the 2nd stop 3/4((2x/3)+30) + 12 which is equal to 84 (passngr on last stop) so final eqn....3/4((2x/3)+30) + 12 = 84 Ans x = 99 ANSWER:B #### B QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum z of all the even integers between 99 and 301? options: A)10,100 B)20,200 C)22,650 D)40,200 E)45,150 SOLUTION:I would solve it in a different way. First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101 Average = (301+99)/2 = 400/2 = 200 Sum z= Average*total count = 200*101 = 20,200 Answer is B #### B QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%? options: A)20% B)30% C)32% D)73% E)84% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 ---20 => 20% Answer:A #### A QUESTION:A man's age is 125% of what it was 10 years ago, but 83 X 1/3% of what it will be after 10years. What is his present age? options: A)20 B)60 C)50 D)70 E)80 SOLUTION:C 50 Let the age before 10 years =x Then, 125x/100=x+10 ⇒125x=100x+1000 ⇒x=1000/25=40 Present age =x+10=40+10=50 #### C QUESTION:The average age of a group of 10 students was 24. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group? options: A)22 years B)36 years C)32 years D)44 years E)None of these SOLUTION:The total age of 10 students with average 24 = 240 The total age of 12 students with average 26 = 312 The total age of 2 new students = 72 Their average =36 Correct Option B #### B QUESTION:In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is: options: A)24 B)26 C)42 D)46 E)48 SOLUTION:Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2. Sum of digits = x + (x + 2) = 2x + 2. (11x + 2)(2x + 2) = 144 22x2 + 26x - 140 = 0 11x2 + 13x - 70 = 0 (x - 2)(11x + 35) = 0 x = 2. Hence, required number = 11x + 2 = 24. Answer:A #### A QUESTION:x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days? options: A)x2/y2 units B)y3/x2 units C)x3/y2 units D)y2/x2 units E)None SOLUTION:Explanation: Let amount of work completed by y men working y hours per in y days = w units More men, more work(direct proportion) More hours, more work(direct proportion) More days, more work(direct proportion) Hence we can write as (men)x:y (hours)x:y (days)x:y }::x:w ⇒x^3w=y^3x ⇒w=y^3x/x^3 =y^3/x^2 Answer: Option B #### B QUESTION:A girl has 10 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts? options: A)A)100 B)B)102 C)C)108 D)D)110 E)E)120 SOLUTION:The girl can select one jeans in 10 ways. The girl can select one shirt in 12 ways. The number of ways in which he can select one jeans and one shirt is 10 * 12 = 120 ways. E #### E QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:Adidas company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks? options: A) 16 B) 64 C) 256 D) 576 E) 4096 SOLUTION:MAGOOSHOFFICIAL SOLUTION: Adidas company has four empty trucks that will head out in the morning, all four to the same destination. Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices. N = 4*4*4*4 = 16*16 = 256 Answer = (C) #### C QUESTION:At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time? options: A)1/3 B)1/4 C)3/8 D)2/9 E)5/18 SOLUTION:Males who did not arrive on time are 1/4*2/3 = 1/6 of the attendees. Females who did not arrive on time are 1/6*1/3 = 1/18 of the attendees. The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9 The answer is D. #### D QUESTION:If the price of gold increases by 40%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? options: A)331/8% B)26.67% C)28.5% D)332/3% E)131/3% SOLUTION:100 140 ------ 140-------40 100-------? => 28.5% Answer:C #### C QUESTION:Bob bikes to school every day at a steady rate of e miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home? options: A)(x + y) / t B)2(e + t) / ey C)2eyt / (e + y) D)2(e + y + t) / ey E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for e 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:Zeynep (the lady of the rings) has 10 identical gold, 10 identical silver and 10 identical bronze rings. (total of 30) She always wears exactly 3 rings on each of her 10 fingers in a particular sequence: first gold, then silver and last bronze. In how many different orders can she wear her 30 rings? options: A)(10!)^3 / 2^10 B)(10!)^3 / 3^10 C)30! / 2^10 D)30! / 3^10 E)30! / 6^10 SOLUTION:By convention, the answer choice letters are typically listed as capital letters, not lower case. Also, professional math notation is always preferable to plain text shortcuts. 30! / 6^10 ANSWER:E #### E QUESTION:One-third of 1200 is what percent of 236 ? options: A)169.49 B)30 C)120.32 D)125.32 E)15.152 SOLUTION:Answer Let one-third of 1200 is N% of 236. ∵ 1200/3 = (N x 236)/100 ∴ N = (400 x 100) / 236= 169.49 Correct Option: A #### A QUESTION:If 6 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? options: A)3:2 B)2:2 C)3:4 D)1:2 E)6:1 SOLUTION:B 2:2 6M + 2B = 4(1M + 1B) 6M + 2B = 4M + 4B 2M = 2B The required ratio of work done by a man and a boy = 2:2 #### B QUESTION:Six cards numbered from 1 to 6 are placed in a cardboard box . First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 5 ? options: A)1/2 B)1/4 C)1/5 D)1/6 E)1/3 SOLUTION:(6,4) (4,6) (5,5) – only 3 possible scenarios for sum to be 10. One from this 5 has already happened. From this three cases, only in one we have 5. So, the probability is 1 chances out of 3 that the one that occurred had 5: P=1/3. Answer: E. #### E QUESTION:While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%) options: A)4.09 B)4.0 C)4.04 D)4.02 E)4.01 SOLUTION:Explanation: Given Error = 2% while measuring the side of a square. If the correct value of the side of square is 100, the measured value: => 100 + 2% *100 = 100+2=102 The area of square with edge 100 = side*side => 100*100 => 10000 The area of square with side 102 = 102*102= 10404 Error in area calculation = 10404-1000 = 404 % error= (404/10000)*100 = 4.04% ANSWER: C #### C QUESTION:If n is a positive integer, what is the remainder when (6^(4n+3))(6^n) is divided by 10? options: A)7 B)2 C)4 D)6 E)8 SOLUTION:This one took me bout 3 1/2 min. Just testin numbers and what not. First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p. 1-7 stands for ^1 thru 6 1: 7*1=7 2: 7*7=9 3: 7*9=3 4: 7*3=1 5: 7*1=7 6: 7*7=9 7: 7*9=3 Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems. so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8 Now from here if id double check just to make sure. 7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit). Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern) so again 3*6=18/10 ---> R =7. A or J in this problem. #### A QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)15.125% D)27.78% E)none SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land. What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options. The correct answer is (D). #### D QUESTION:Two coins are tossed, find the probability that two Tails are obtained options: A)1/3 B)1/4 C)1/5 D)1/7 E)2/3 SOLUTION:The sample space S is given by. S = {(H,T),(H,H),(T,H),(T,T)} Let E be the event "two heads are obtained". E = {(T,T)} P(E) = n(E) / n(S) = 1/4 B #### B QUESTION:If x^2 + y^2 = 13 and xy = 3, then (x − y)^2 = options: A)7 B)11 C)14 D)17 E)20 SOLUTION:but you cannot take xy+ 3 to mean xy=-3.. only if xy+3=0, it will mean xy=-3.. rest your solution is perfect and you will get your correct answer as 13-2*3=7.. Answer A #### A QUESTION:Sum of Rs.4000 is given out in 2 pieces, one at 8% S.I. and the other at 10% S.I. If the annual interest is Rs 352, the sum is given at 8% is options: A)2000 B)2200 C)2300 D)2400 E)None of these SOLUTION:Explanation : i) Given the total sum = Rs. 4000 If the sum given at 8% be Rs.a ie) P = a , n=1, R = 8% (aX18/100) = (8a/100) If the addition given at 10% be Rs. 4000 – a P = 4000-a , n=1, R = 10% (4000 – aX1X10)/(100) = (40000-10a)/100 Given Annual interest is Rs. 352 (8a/100) + (40000-10a)/100 = 352 8a – 10a = 35200 – 40000 -2a = -4800 X = (4800/2)= Rs.2400/- Answer : D #### D QUESTION:What is the greatest positive integer x such that 5^x is a factor of 125^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:125^10 = (5^3)^10 = 5^30 ANSWER:E #### E QUESTION:What distance will be covered by a bus moving at 72 kmph in 30 seconds? options: A)287 B)600 C)289 D)276 E)207 SOLUTION:72 kmph = 72 * 5/18 = 20 mps D = Speed * time = 20 * 30 = 600 m. Answer:B #### B QUESTION:In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive? options: A)None B)One C)Two D)Three E)Four SOLUTION:Non - Negative ( zero to positive infinity ) Solution to the question : -4,-3,-2,-1,0 , 1,2,3 Hence ans is 3 ..option D #### D QUESTION:The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red options: A)4% B)4.65% C)6.125% D)7.24% E)7.45% SOLUTION:Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125% C #### C QUESTION:A train 150 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)22 B)50 C)99 D)288 E)59 SOLUTION:Speed of the train relative to man = (150/10) m/sec = (15) m/sec. [(15) * (18/5)] km/hr = 54 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 54 ==> x = 59 km/hr.Answer: E #### E QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm? options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM. It travels at 500 kmph. Hence, the plane flying north would have covered 1000 kms from the city at 2 PM. The plane flying east would have traveled for 1.5 hours at 2 PM. It travels at 400 kmph. Hence, the plane flying east would have covered 1.5*400 = 600 kms from the city at 2 PM. The two planes are flying at right angles to each other. The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes. Hence, distance = 1000square + 200 square = 1166 km The nearest 100 km distance between the two planes = 1200 kms. Answer D #### D QUESTION:A sum was put at simple interest at a certain rate for 6 years Had it been put at 4% higher rate, it would have fetched 144 more. Find the sum. options: A)500 B)600 C)700 D)800 E)900 SOLUTION:Difference in S.I. = P×T/100(R1−R2) ⇒ 144 = P×6x4/100(∵ R1 - R2 = 2) ⇒ P = 144×100/6×4=600 Answer B #### B QUESTION:Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)25 C)27 D)29 E)31 SOLUTION:Solution: We know that the average value is 24 therefore (a+b+c)/3 = 24 so a+b+c = 72 and b = a + 11 therefore a + (a + 11) + c = 72 The least value of c is when c = b so take c = a + 11 hence, a + (a + 11) + (a + 11) = 72 i.e., a = 50/3 a non integer therefore c is not equal to b so take c = b+1 therefore c = a+12 a + (a + 11) + (a + 12) = 72 i.e., a= 49/3 again a non integer therefore c is not equal to b+1 next take c= b+2 therefore c = a+13 a + (a + 11) + (a + 13) = 72 i.e., a=48/3 = 16 hence, a = 16, b = 27, and c = 29 Answer: D #### D QUESTION:Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)6 : 8 : 9 D)4 : 6 : 8 E)None of these SOLUTION:Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). (140/100 * 5x), (150/100 * 7x) and (175/100* 8x) 7x, 21x/2 and 14x The required ratio = 7x : 21x/2 : 14x 14x : 21x : 28x 2 : 3 : 4 Answer = A #### A QUESTION:what is the smallest integer that is multiple of 7, 12 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 7, 12 and 20 which is 420 #### E QUESTION:An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount? options: A)3728 B)3726 C)3720 D)3722 E)3721 SOLUTION:A = P(1 + TR/100) => 3600 = 3000[1 + (4 * R)/100] => R = 5% Now R = 6% => A = 3000[1 + (4 * 6)/100] = Rs. 3720. Answer: C #### C QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process? options: A)4.15 B)4.21 C)4.52 D)4.81 E)4.93 SOLUTION:X is the initial quantity of salt in the water. After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination. So we have: X1=1/3 X X2=1/3 X1 X3=1/3 X2 By multiplying both ends of the equations we get: X1*X2*X3 = (1/3)^3 X*X1*X2 Simplification leaves us with: X3 = (1/3)^3 X X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3) In this case, given X was: X=5 g So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81 Answer: D #### D QUESTION:A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14 years B)18 years C)20 years D)22 years E)16 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 24) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :B #### B QUESTION:A set of numbers has the property that for any number t in the set,t+3 is in the set. If -1 is in the set, which of the following must also be in the set? I. 2 II. 5 III. 7 options: A)II only B)I only C)I,II only D)II,III only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+3 must be there. if -1 is the starting element the sequence is as follows. S ={-1,2,5,8,11....} if -1 is not the starting element the sequence is as follows S = {...-4,-1,2,5,8,11...} By observing the above two sequences we can say that 2,5 must be there in set S. Answer : C #### C QUESTION:Find the value of (1-(1/3))(1-(1/4))(1-(1/5))….(1-(1/100)). options: A)1/50 B)3/50 C)4/50 D)6/50 E)9/50 SOLUTION:Answer is A. #### A QUESTION:What is 2/5 of 5/9 of 1/2? options: A)1/4 B)1/9 C)9/16 D)5/8 E)16/9 SOLUTION:2/5 * 5/9 * 1/2= 1/9 Answer: B #### B QUESTION:Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100) options: A)1/19 B)1/20 C)1/23 D)2/17 E)1/17 SOLUTION:(2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100) 5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20 B) #### B QUESTION:I purchased a superb bike and like my bike my number plate is also superb. The number plate is a five digit number plate and its water image is 78633 more than the number plate. Also all digits are unique. Whats is my number plate number ? options: A)10935 B)10968 C)23984 D)13725 E)11332 SOLUTION:B 10968 Water image is 89601 #### B QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 46 years, was replaced by a new person. Find the age of the new person? options: A)18 B)56 C)16 D)17 E)14 SOLUTION:Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 46 + Q => Q = 16 Answer:C #### C QUESTION:Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride? options: A)28 B)30 C)32 D)34 E)36 SOLUTION:The cost of Annie's ride was 2.5+5+(0.25*14) = $11 Let x be the distance of Mike's ride. The cost of Mike's ride is 2.5+(0.25*x) = 11 0.25*x = 8.5 x = 34 miles The answer is D. #### D QUESTION:In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ? options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these SOLUTION:solution: Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)] =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4. ∴ Required average =8.4/2 = 4.2 Answer B #### B QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ? options: A)20 years B)21 years C)22 years D)34 years E)24 years SOLUTION:The average age of the 5 members is 20 years => The sum of the ages of the 5 members is 20*5 = 100 years Once the new member joins, the average age becomes 24 years. Let the age of the new member be x. Then (110+x)/6 = 24 => x = 34 years Answer D #### D QUESTION:Mohit sold an article for Rs. 18000. Had he offered a discount of 25% on the selling price, he would have earned a profit of 8%. What is the cost price of the article? options: A)12500 B)27767 C)16688 D)26678 E)19987 SOLUTION:Let the CP be Rs. x. Had he offered 25% discount, profit = 8% Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 25/100(18000) = Rs. 13500 => 1.08x = 13500 => x = 12500 \Answer: A #### A QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:In how many different number of ways a Committee of 4person of can be selected from 4boys and 4girls such that at least 1 girl is included in the committe options: A)70 B)69 C)67 D)68 E)65 SOLUTION:1G 3B 2G 2B 3G 1B 4G =(4C1*4C3)+(4C2*4C2)+(4C3*4C1)+4C4 = (4*4)+(6*6)+(4*4)+1 = 16+36+16+1=69 Total 4M 4W 8C4=70 4C4=1 At least one girl = total - with out girl At least one girl =70-1=69 B) #### B QUESTION:The side of a cube is 8 m, Find the voiume? options: A)515 B)509 C)502 D)508 E)512 SOLUTION:Cube Volume = a(power)3 a(power)3 = 8(power)3 = 512 m(power)3. Answer is E. #### E QUESTION:10 people can write 55 book in 12 days working 8 hour a day.then in how many day 198 can be written by 48 people? options: A)9 B)13 C)21 D)24 E)23 SOLUTION:work per day epr hour per person= 55/(12*8*10) // eq-1 people=48; let suppose day=p; per day work for 8 hours acc. to condition work per day epr hour per person= 198/(p*8*48) // eq-2 eq-1==eq-2; p= 9 ANSWER:A #### A QUESTION:It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn options: A)16 B)45 C)36 D)20 E)90 SOLUTION:1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min.. only A and B are left.. if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins.. ans 20 D #### D QUESTION:A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent? options: A)35 B)45 C)25 D)15 E)55 SOLUTION:A : B : C =10×7:12×5:15×3 =2×7:12×1:3×3 =14:12:9 Amount that C should pay =175×9/35=5×9=45 Answer is B. #### B QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)34 SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER:A #### A QUESTION:In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg? options: A)5/6 B)3/9 C)5/0 D)5/3 E)5/9 SOLUTION:Explanation: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6 Answer: Option A #### A QUESTION:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output? options: A)17% B)24% C)30% D)32% E)79% SOLUTION:take it as original output =100. to meet demand increase by 10%, then output=110. to meet holiday demand , new output increase by 10% then output equals 121 To restore new holidy demand output to original 100. final -initial/final*100 =21/121*100=8/33*100=17% approxiamately. option A is correct. #### A QUESTION:Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey? options: A)432 miles B)651 miles C)387 miles D)954 miles E)556 miles SOLUTION:The number of miles to drive to finish his journey is given by 1200 - 768 = 432 miles correct answer A #### A QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:A ship sails out to a mark at the rate of 19 kmph. and sails back at the rate of 13 kmph. The average rate of sailing is ? options: A)15 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None SOLUTION:Answer Average = ( 2uv / u +v ) km/hr = ( 2 x 19 x 13 ) / (19 +13 ) km/hr. = 15 km/hr. Correct Option: A #### A QUESTION:If the average (arithmetic mean) of x + 2, x + 3, and x + 4 is 0, then x = options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:(x+2 + x+3 + x+4)/3 = 0 =>3x + 9 = 0 =>x = -3 Answer B #### B QUESTION:Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number. options: A)42 B)48 C)72 D)67 E)54 SOLUTION:Sol: Let the third number be x. Then second number = 3x. First number=3x/2. Therefore x+3x+(3x/2)=(44*3) or x=24 So largest number= 2nd number=3x=72 ANSWER :C #### C QUESTION:John Purchased 1365 large bottles at $1.89 per bottle and 720 small bottles at $1.42 per bottle. What was the approximate average price paid per bottle? options: A)$1.63 B)$1.64 C)$1.68 D)$1.73 E)$1.76 SOLUTION:(1365*1.89+720*1.42)/(1365+720) =~1.73 Option (D) #### D QUESTION:Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is: options: A)Rs. 4800 B)Rs. 5000 C)Rs. 5400 D)Rs. 5600 E)Rs. 6600 SOLUTION:let investment is x... den remaining investment is (9800-x) x*9/75= (9800-x)*10/80 x=4800 9800-x=5000 ANSWER:B #### B QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:What approximate value should come in place of the question mark (?). 36.0001 ÷ 5.9998 × √? = 108.0005 options: A)325 B)316 C)256 D)16 E)18 SOLUTION:Using approximation, we get 36⁄6 × √? = 108 or, √? = 108⁄6 or, √? = 18 or, ? = 324 ≈ 325 Answer E #### E QUESTION:A circular logo is enlarged to fit the lid of a jar. The new diameter is 40 per cent larger than the original. By what percentage has the area of the logo increased? options: A)50 B)96 C)100 D)125 E)250 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 5.6 , so radius is 2.8 New area = 7.84π Increase in area is 3.84π % increase in area = 3.84/4*100 So, % increase is 96% Answer will be (B) #### B QUESTION:Rs.12320 were divided among W, X & Y in such a way that W had Rs.640 more than X and Y had Rs 480 more than X . How much was X’s share? options: A)Rs.4590 B)Rs.4610 C)Rs.4620 D)Rs.4630 E)Rs.4640 SOLUTION:Let X gets Rs x. Then We can say W gets Rs (x + 640 ) and Y gets Rs ( x + 560) . x + 640 + x + x + 1120 = 12320 3x = 10560 x = 3520 . C’s share = Rs ( 3520+1120 ) = Rs.4640 E #### E QUESTION:The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 10 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house? options: A)20 km B)30 km C)40 km D)50 km E)60 km SOLUTION:Number of stops in an hour: 60/5 = 12 Distance between stops: 60/12 = 5 km Distance between Yahya's house and Pinedale Mall: 5 x 10 = 50 km IMO, correct answer is "D." #### D QUESTION:Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered? options: A)17603 B)17608 C)17628 D)17600 E)176023 SOLUTION:Price at which the TV set is bought = Rs. 12,500 Discount offered = 20% Marked Price = 12500 * 100/80 = Rs. 15625 The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000 The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600 Answer: D #### D QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required? options: A)34 B)40 C)68 D)88 E)26 SOLUTION:We have: l = 20 ft and lb = 60 sq. ft. So, b = 3 ft. Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft. ANSWER:E #### E QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)8 C)9 D)11 E)15 SOLUTION:220 + 43 = 263/17 = 8 (Remainder) B #### B QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B? options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these SOLUTION:Explanation : Assume that investment of C = x Then, investment of A =2x A receive 48000 Then C will receive = 48000/2 = 24000 And B receive = 180000 - (24000+48000) = 108000 Ratio of investment between A and B = 48000 : 108000 = 4 : 9 Answer : Option A #### A QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced? options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None SOLUTION:Explanation : Time = 80*4 / 60 = 5 hours 33 mins Answer – B #### B QUESTION:Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose? options: A)5 B)8 C)11 D)15 E)17 SOLUTION:Explanation : Let a, b, c be the Englishmen and d, e, f be the Frenchmen. Let a be the Englishman who knows French. 'a' calls 'b & c' and now knows the secret of both of them. So now 'a' knows 'abc' secrets. 'd' calls 'e & f' and now knows the secret of both of them. So now 'd' knows 'def' secrets. 'a' now calls 'd', and exchange all secrets in French, so now 'a' and 'd' know all the 6 secrets. Now 'a' calls 'b & c' again, and 'd' calls 'e & f' again and tell all the secrets. So, totally 9 calls. Answer : B #### B QUESTION:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time? options: A)70 min B)94 min C)110 min D)112 min E)120 min SOLUTION:First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) And now we have 4 robots So Total = (1) + (2) = 70 minutes Answer - A #### A QUESTION:In certain code 'TWICE' is written as '34$5δ' and 'WEARS' is written as '4δ29%'. How is 'SEAT' written in that code? options: A)22 B)23 C)697 D)66P E)82 SOLUTION:Answer: Option B #### B QUESTION:1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10 what is....? options: A)7 B)8 C)9 D)6 E)10 SOLUTION:Equation 28 + 8 + 92 = 10 can be derived from twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10 Similarly for equation, 1 + 9 + 8 One (o) + nine (n) + eight (e) => one (1) correct answer is E)10 #### E QUESTION:If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before? options: A)A)3/22% B)B)10% C)1/9 % D)1/11 % E)% SOLUTION:100 – 12 = 88 88------12 100------? => 11 3/22% ANSWER:A #### A QUESTION:A circle graph shows how the budget of a certain company was spent: 60 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation? options: A)18° B)36° C)54° D)72° E)90° SOLUTION:The percent of the budget for transportation is 100 - (60+9+5+4+2)= 20% 100% of the circle is 360 degrees. Then (20%/100%)*360 = 72 degrees The answer is D. #### D QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean a. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than a+d? options: A) 16% B) 32% C) 48% D) 84% E) 92% SOLUTION:16% ________________________________________________ a+d 34% ________________________________________________ a 34% ________________________________________________ a-d 16% since 68% lies one standard deviation from mean a, => 50% of 68% lies on either side as it is symmetric about a. thus 16% lie below a-d and 16% lie above a+d now below a+d = 16+34+34 = 84% hence D #### D QUESTION:Convert the 8/36 m/s into kilometers per hour? options: A)0.8 kmph B)9.9 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:8/36 m/s = 8/36 * 18/5 = 8/10 = 0.8 kmph. Answer: A #### A QUESTION:The average of 35 students in a class is 18 years. The average age of 25 students is 20. What is the average age of remaining 10 students? options: A)17 years B)16 years C)15 years D)14 years E)13 years SOLUTION:Sum of the ages of 14 students = (18 * 35) - (20 * 25) = 630 - 500 = 130 Required average = (130/10) = 13 years. Answer:E #### E QUESTION:A meal cost $ 32.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-39 E)36-37 SOLUTION:10%(32.5) = 3.25 15%(32.5) =4.875 total amount could have been 32.5+3.25 and 32.5+4.875 => could have been between 35.75 and 37.375 => approximately between 36 and 37 Answer is E. #### E QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)17 kmph B)45 kmph C)86 kmph D)197 kmph E)15 kmph SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer:B #### B QUESTION:The cost price of an article is 70% of the marked price. Calculate the gain percent after allowing a discount of 10%. options: A)13.6% B)28.6% C)35.6% D)42.3% E)none SOLUTION:Sol. Let marked price = Rs. 100. Then, C.P. = Rs. 70. S.P = Rs. 90. ∴ Gain % = [20/70 * 100]% = 28.6%. Answer B #### B QUESTION:o mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by 33×13%33×13%, and finished the work 1 day earlier than it was planned. A) What is the area of the grass field? B) How many days did it take to mow the whole field? C) How many days were scheduled initially for this job? options: A)387 B)39 C)37 D)20 E)28 SOLUTION:Hint: See problem 20 and solve by yourself. Answer: A) 120 hectares; B) 7 days; C) 8 days. Answer:D #### D QUESTION:How many multiples of 6 are less than 5000, and also multiples of 8? options: A)104 B)208 C)625 D)832 E)833 SOLUTION:LCM of 6 & 8 = 24 Tried dividing 5000 by 24 Got quotient 208.33'So B is answer #### B QUESTION:I. q-14, q, q, q, q+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of q or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A <<<Examples ends QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)22 B)73 C)99 D)42 E)11 SOLUTION:Explanation: Just go in reverse order. Check the options with th subtracting 18 from each option for getting reverse number. 42 – 18 = 24 (which is in reverse). So answer is 42. Answer D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? options: A)315min B)325min C)335min D)345min E)None of these SOLUTION:Explanation: Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = (19+16)=(518) So both punctures will make the type flat in (185)mins=335mins Answer: C #### C QUESTION:Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other? options: A)1:2 B)2:1 C)1:3 D)3:1 E)1:4 SOLUTION:root (b):root(a) 2:1 ANSWER:B #### B QUESTION:A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective? options: A)316/439 B)316/438 C)316/435 D)316/299 E)316/199 SOLUTION:Let A be the event of getting two oranges and B be the event of getting two non-defective fruits. and be the event of getting two non-defective oranges Answer: C) 316/435 #### C QUESTION:If circles x and y have the same area and circle x has a circumference of 14π, half of the radius of circle y is: options: A)16 B)8 C)4 D)3.5 E)1 SOLUTION:x be radius of circle x y be radius of circle y given: pi*x^2 = pi*y^2 also, 2*pi*x = 14*pi x =7 thus y =7 y/2 = 3.5 Ans: D #### D QUESTION:In a group of pigs and hens, the number of legs are 22 more than twice the number of heads. The number of pigs is options: A)5 B)7 C)10 D)12 E)11 SOLUTION:Explanation: Let the number of pigs be x and the number of hens be y. Then, 4x + 2y = 2 (x + y) + 22 4x + 2y = 2x + 2y + 22 2x = 22 x = 11 Answer: E #### E QUESTION:It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish? options: A)20 B)22 C)24 D)26 E)28 SOLUTION:The bacteria doubles each day, so after 29 days, the dish was half full. After 28 days, the dish was one quarter full. After 27 days, the dish was one eighth full. After 26 days, the dish was one sixteenth full. After 25 days, the dish was 1/32 full. After 24 days, the dish was 1/64 full. The answer is C. #### C QUESTION:A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target? options: A)175/256 B)451/365 C)312/456 D)156/754 E)164/784 SOLUTION:The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes. So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes. The event of not hitting the target even once is the complement of the event of hitting the target at least once. The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾ Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256 The probability that he will hit the target at least in one of the four shots=1-81/256 =175/256 Ans:A #### A QUESTION:After working for 6 days, David was joined by Moore. Together they completed the remaining job in 3 days. How many days will it take both of them to complete the entire job, given that it would have taken David 12 days to complete the job alone? options: A)7 B)4 C)6 D)2 E)7 SOLUTION:Explanation: David and Moore complete half work in 3 days => they can complete whole work in 6 days Answer: Option C #### C QUESTION:In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what q percent of all the people in Smithtown are left-handed women? options: A) 50% B) 40% C) 25% D) 20% E) 10% SOLUTION:looking at the ratio we can take total number of people q=20.. ans 5/20 or 25% C #### C QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (750 ~ 1020)/1020 = 26% Loss A #### A QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1). options: A)320 B)350 C)340 D)360 E)400 SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there? 99+(912-9-90*2)/3=340 Answer : C #### C QUESTION:The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is? options: A)2:6 B)2:3 C)4:5 D)2:1 E)2:4 SOLUTION:Let the ratio be k : 1. Then, k * 16.3 + 1 * 15.4 = (k + 1) * 15.8 = (16.3 - 15.8)k = (15.8 - 15.4) = k = 0.4/0.5 = 4/5 Required ratio = 4/5 : 1 = 4:5. Answer:C #### C QUESTION:In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y = options: A)6 B)7 C)5 D)8 E)3 SOLUTION:Line k passes through the origin and has slope 1/7 means that its equation is y=1/7*x. Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6. Answer: A #### A QUESTION:What distance will be covered by a bus moving at 126 kmph in 10 seconds? options: A)287 B)600 C)350 D)276 E)207 SOLUTION:126 kmph = 126 * 5/18 = 35 mps D = Speed * time = 35 * 10 = 350 m. Answer:C #### C QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)18 B)24 C)42 D)81 E)28 SOLUTION:Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 * 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. ANSWER:B #### B QUESTION:If x and y are different integers and x^2 = xy, which of the following must be true ? I. y = 0 II. x = 0 III. x = y options: A)I only B)II only C)III only D)I and III only E)II, and III SOLUTION:Answer choice A is correct. The question gives you x^2=xy you can simplify that as x^2-xy=0 x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer. Answer E #### E QUESTION:In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:Let x be the number of cars and let y be the number of cars parked illegally. 4%*x = 20%*y y/x = 1/5 = 20% The answer is A. #### A QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots? options: A)4/M B)4M C)900M D)M/900 E)M/4 SOLUTION:The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours. The answer is E. #### E QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 3 : 3? options: A)16 B)48 C)277 D)92 E)11 SOLUTION:Let the distances between city A to B and B to C be 3x km and 3x km respectively. Total time taken to cover from A to C = (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph. Answer:B #### B QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 70% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ? options: A)1/7 m B)1/3 m C)1/4 m D)1/5 m E)1/6 m SOLUTION:After the final transaction: Angela received $(m-n) for t hours; Linda received $(m+n) for 1.5t hours; We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/7. Answer: A. #### A QUESTION:In 16 minutes, the minute hand gains over the hour hand by options: A)16° B)80° C)88° D)96° E)None of these SOLUTION:In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minute, the minute hand gains 330° over the hour hand. ∴ In 16 minutes, the minute hand gains over the hour hand by 330°⁄60 × 16° = 88° Answer C #### C QUESTION:In Bangalore there is a well known Science Institute. During a visit I asked two of the men to tell me their ages. One replied, 'One of our ages subtracted from the other's equal 30.' Then the other man spoke . 'Our ages multiplied together equal 1624.' What were their ages? options: A)60 and 23 B)66 and 25 C)29 and 56 D)71 and 43 E)58 and 28 SOLUTION:E Their ages were respectively 58 and 28 #### E QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A QUESTION:Find the odd man out.10, 25, 45, 50, 66, 70, 80 options: A)45 B)50 C)66 D)70 E)80 SOLUTION:Each of the numbers except 66 is multiple of 5. ANSWER :C #### C QUESTION:The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought? options: A)42. B)38. C)33. D)22. E)20. SOLUTION:Let X pizzas of 2 slices and Y pizzas of 4 slices. 2X + 4Y. Lets check options wise. A. 42 => 2(15) + 4(3) B. 38 => 2(15) + 4(2) C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out. D. 22 => 2(10) + 4(3) E. 20 => 2(6) + 4(2) Answer: correct option is C #### C QUESTION:The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is: options: A)1439 B)1440 C)1459 D)1449 E)1549 SOLUTION:LCM = 1440 1440 - 1 = 1439 ANSWER:A #### A QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit. options: A)Rs. 1900 B)Rs. 2660 C)Rs. 2800 D)Rs. 2840 E)Rs. 3000 SOLUTION:Explanation: For managing, A received = 5% of Rs. 7400 = Rs. 370. Balance = Rs. (7400 - 370) = Rs. 7030. Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3) = 39000 : 42000 : 30000 = 13 : 14 : 10 B's share = Rs.(7030 X 14/37)=Rs. 2660. ANSWER IS B #### B QUESTION:The average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:The average of 24, 35, and 58 is 39. The average of 19, 51 and x is 33. Then 19 + 51 + x = 99. x = 29. The answer is D. #### D QUESTION:The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is: options: A)60 kg B)59 kg C)62 kg D)63 kg E)61 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (75 x 3) = 225 …. (i) A + B = (88 x 2) = 176 …. (ii) B + C = (72 x 2) = 144 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 288 …. (iv) Subtracting (i) from (iv), we get : B = 63. B’s weight = 63 kg. Answer D #### D QUESTION:A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze? options: A)154 cm2 B)113 m2 C)123 m2 D)115 m2 E)None of these SOLUTION:Area of the shaded portion = 1⁄4 × π × (12)2 = 113 m2 Answer B #### B QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order? options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2 SOLUTION:RT = W Given: R = 1/3 + 1/3 = 2/3 T = ? W = 1 T = 1 / (2/3) = 3/2 = 1 1/2 Answer: E #### E QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these SOLUTION:Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.150 15x + 5x = Rs.150 X = 150/20 = 7.50 :. Cost of 1 pen = 5x = 5 x 7.50 = 37.50 :. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450 Answer: Option D #### D QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his original salary? options: A)25% B)50% C)75% D)85% E)95% SOLUTION:Salary he get after reduced 20% = 100-20% = 80% So,percentage should be added to get back his salary = (20/80)*100 = 25% ANSWER:A #### A QUESTION:The wages earned by Robin is 40% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? options: A)14% B)23% C)30% D)50% E)100% SOLUTION:Let wage of Erica = 10 Wage of Robin = 1.4*10 = 14 Wage of Charles = 1.6 *10 = 16 Percentage by which wage earned by Charles is more than that earned by Robin = (16-14)/14 * 100% = 2/14 * 100% =14% Answer A #### A QUESTION:If a × b = 2a - 3b + ab, then 4 × 5 + 5 × 4 is equal to : options: A)31 B)32 C)43 D)45 E)26 SOLUTION:Explanation: 4 × 5 + 5 × 4 = (2 × 4 - 3 × 5 + 4 × 5) + ( 2 × 5 - 3 × 4 + 5 × 4) = (8 -15 + 20 + 10 - 12 +20) = 31. Answer: A #### A QUESTION:A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially? options: A)25 B)21 C)20 D)10 E)15 SOLUTION:Suppose the can initially contains 7x and 5x litres mixtures A and B respectively Quantity of A in mix. left =[7x –7/12 * 9 ] =[7x –21/4] Quantity of B in mix. left =[5x –5/12 *9 ] = [ 5x - 15/4 ] Therefore [ 7x-21/4 ] =7/9 or 28x-21 = 7/9 [5x-15/4]+9 20x+21 252x -189 =140x+147 or 112x =336 , x = 3. Quantity of A in the can initially =7*3 =21 ANSWER:B #### B QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall? options: A)120 B)350 C)1470 D)2,520 E)5,040 SOLUTION:Number of ways to choose 2 colors among 7 - 7c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 7c2 * 2* 7c4 = 1470 C #### C QUESTION:What percent of 60 is 90? options: A)133 1⁄3 B)150 C)60 D)33 1⁄3 E)25 SOLUTION:% of 60 is 90? = 90/60 = 3/2 = 150% Thus B is the correct answer. #### B QUESTION:Mary's income is 70 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income? options: A) 124% B) 102% C) 96% D) 80% E) 64% SOLUTION:Juan's income = 100 (assume); Tim's income = 60 (40 percent less than Juan's income); Mary's income = 102 (70 percent more than Tim's income). Thus, Mary's income (102) is 102% of Juan's income (100). Answer: B. #### B QUESTION:Find the product of the local value and absolute value of 8 in 564823 options: A)1600 B)6400 C)16000 D)12000 E)18000 SOLUTION:Explanation: Place value = Local value Face value = Absolute value The place value of 8 in 564823 is 8 x 100 = 800 The face value of 8 in 564823 is nothing but 8. => 800*8=6400 Answer: Option B #### B QUESTION:In the quadrilateral PQRS d=10 cm, h1=4.6 cm and h2=2.3 cm. Find the area options: A)21 B)22 C)23 D)34.5 E)25 SOLUTION:area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona) so 1/2*10*(4.6+2.3)=34.5 ANSWER:D #### D QUESTION:The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? options: A)3 B)7 C)8 D)5 E)1 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer:C #### C QUESTION:If two letters are chosen at random (without replacement) from the word COMPUTER, what is the probability that none of the letters are vowels? options: A)2/7 B)3/7 C)3/14 D)5/14 E)11/28 SOLUTION:The number of ways to choose two letters is 8C2 = 28 The number of ways to choose two consonants is 5C2 = 10. P(no vowels) = 10/28 = 5/14 The answer is D. #### D QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33*100 = 180% of 3.33. Answer: E. #### E QUESTION:There are 450 birds at a small zoo. The number of birds is 5 times the number of all the other animals combined. How many more birds are there than non bird animals at the zoo? options: A)400 B)360 C)270 D)180 E)90 SOLUTION:Total birds = 450 = 5 * Other Animals (X) or X = 90. So, Difference in Birds and X = 450-90 = 360. Answer is B. #### B QUESTION:The average of 50 numbers id 20. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is : options: A)22.75 B)33.25 C)22.25 D)11.75 E)18.75 SOLUTION:Explanation: Total of 50 numbers = (50×20)=1000 Total of 48 numbers =(1000-(45+55)]=900 Required average = 900/48=18.75 Answer:E #### E QUESTION:A toy train started on a 12-feet loop trail at a rate of 4 feet per minute. One minute afterwards, a toy scooter from the same starting point on the loop trail at 6 feet per minute. What is the shortest time that the scooter would take on the trail in order to catch up with the train? options: A)4 minutes B)3 minutes C)2 minutes D)1 minutes E)0.8 minutes SOLUTION:we don't need to assume here the direction.we need to find which will take less time so there are 2 cases 1)both moving in same direction...then time would be 2 minutes 2)both moving in opp direction then time would be 0.8 minutes as we need the shortest time it would be the second case Answer:E #### E QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:If 80% of 90 is greater than 70% of a number by 30, what is the number? options: A)70 B)60 C)10 D)75 E)85 SOLUTION:Explanation: 80/100 * 90 - 70/100 * x = 30 72 - 70/100 * x = 30 72 - 30 = 70/100 *x 42 = 70/100 * x 42 * 100 / 70 = x 60 = x Answer: Option B #### B QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A. options: A)256 B)388 C)379 D)277 E)122 SOLUTION:Explanation: (3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 672 = 256 Answer: A #### A QUESTION:A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 130 pounds? options: A)8 B)14 C)12 D)9 E)none of the above SOLUTION:Ans is B: 39 pounds --> 6 days 130 pounds --> x days x = 130*6/39 = 20 the animal has already consumed food in 6 days so the the number of days for it's total consumption be 130 pounds is 20-6 = 14 #### B QUESTION:A school has received 30% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 60% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$250 C)$100 D)$350 E)$875 SOLUTION:Let us suppose there are 100 people. 60% of them donated $30000 ( 500 * 60 ) $30000 is 30% of total amount. So total amount = 30000 * 100/60 Remaining amount is 70% of total amount. 70% of total amount = 30000 * (100/60) * (70/100) = 35000 This amount has to be divided by 40 ( remaining people are 40 ) So per head amount is 35000/40 = $875; ANSWER:E #### E QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10200 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv) Subtracting (ii) from (iv), we get, P = 4050. P's monthly income = Rs.4050. Answer: A #### A QUESTION:Joshua is fifth from the bottom in a queue of 100 boys. What is the position of Joshua from the top of the queue? options: A)51 B)52 C)53 D)54 E)55 SOLUTION:Solution: 51 Explanation: The position of boys higher than Joshua in the queue is 100 - 50 = 50. Therefore, the position of Joshua from the top is 50 + 1 = 51. Answer A #### A QUESTION:The population of a town is 10000. It increases annually at the rate of 25% p.a. What will be its population after 2 years? options: A)14000 B)14400 C)14500 D)15625 E)14700 SOLUTION:Formula : 10000 × 125/100 × 125/100 = 15625 Answer : D #### D QUESTION:What is the total surface area in square meters of a rectangular solid whose length is 8 meters, width is 7 meters, and depth is 4 meters? options: A)132 m2 B)145 m2 C)165 m2 D)152 m2 E)120 m2 SOLUTION:Surface Area of a cuboid = 2(lb+bh+lh) = 2(8*7+7*4+8*4)=2(56+28+32)=2*116=132 m2 Answer : A #### A QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 14 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)17 E)72 SOLUTION:Explanation: As there is meal for 70 adults and 14 have their meal, the meal left can be catered to 56 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 56 adults = 72 children Hence, the meal can be catered to 72 children. ANSWER: E #### E QUESTION:The speed of a boat in still water in 65 km/hr and the rate of current is 15 km/hr. The distance travelled downstream in 25 minutes is: options: A)55.55 km B)44.44 km C)33.33 km D)22.22 km E)11.11 km SOLUTION:Explanation: Speed downstream = (65 + 15) = 80 kmph Time = 25 minutes = 25/60 hour = 5/12 hour Distance travelled = Time × speed = (2/5)×80 = 33.33 km Answer: Option C #### C QUESTION:Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is? options: A)109 B)106 C)104 D)108 E)101 SOLUTION:Let the present ages of the father and son be 2x and x years respectively. Then, (2x - 18) = 3(x - 18) => x = 36 Required sum = (2x + x) = 108 years.Answer: D #### D QUESTION:In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate? options: A)576 B)425 C)215 D)321 E)None of these SOLUTION:Explanation : In a circle, 5 boys can be arranged in 4! ways Given that the boys and the girls alternate. Hence there are 4 places for girls which can be arranged in 4! ways Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A #### A QUESTION:A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting? options: A)200 B)250 C)350 D)800 E)830 SOLUTION:science books sold = 2x × 0.2 = 0.4x science books unsold = 2x – 0.4x = 1.6x art books sold = 5x × 0.2 = x art books unsold = 5x – x = 4x total books unsold = 1.6x + 4x = 5.6x 5.6x = 2240 x = 400 2x science = 800 D #### D QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)2% C)1% D)6% E)7% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\ Rate = (100 * 3000) / (12500 * 4) = 6% Answer: D #### D QUESTION:At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ? options: A)Rs.7.50 per kg B)Rs.8.20 per kg C)Rs.8.85 per kg D)Rs.9 per kg. E)None SOLUTION:Explanation: Total C.P of 200 kg of sugar = Rs.(80×6.75+120×8)=Rs.1500 C.P of 1 kg = Rs.[1500/200]=Rs.7.50 Gain required = 20% S.P of 1 kg = (120% of Rs.7.50) = Rs.[120/100×7.50]=Rs.9 per kg. Correct Option : D #### D QUESTION:There are 30 doors marked with numbers 1 to 30. There are 30 individuals marked 1 to 30. An operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, and 30. If every individual in the group gets one turn, then how many doors are open at the end? options: A)0 B)1 C)2 D)4 E)5 SOLUTION:If a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors. The doors which are open at the end are: 1, 4, 9, 16, 25 for a total of 5 doors. The answer is E. #### E QUESTION:A hall 36m long and 15m broad is to be paved with stones, each measuring 8dm by 5 dm. The number of stones required is: options: A)180 B)1800 C)18 D)18000 E)1350 SOLUTION:Area of the hall= 3600*1500 Area of each stone= (80*50) Therefore, number of stones= (3600*1500/ 80*50)= 1350 ANSWER:E #### E QUESTION:In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight ? options: A)3 hours B)2.4 hours C)1.4 hours D)1 hour E)None of these SOLUTION:Explanation: Let the duration of the flight be x hours. Then 600x−600x+12=200600x−12002x+1=200x(2x+1)=32x2+x−3=0=>(2x+3)(x−1)=0 Neglecting the negative value for x we get x = 1 Answer: D #### D QUESTION:Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:Two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? options: A)10 B)11.3 C)13 D)14 E)15 SOLUTION:Speed of the first train = 120/9 = 13.3 m/sec. Speed of the second train = 120/15 = 8 m/sec. Relative speed = 13.3 + 8 = 21.3 m/sec. Required time = (120 + 120)/21.3 = 11.3 sec. Answer: Option B #### B QUESTION:At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time? options: A)1/3 B)1/4 C)3/8 D)2/9 E)5/18 SOLUTION:Males who did not arrive on time are 1/4*2/3 = 1/6 of the attendees. Females who did not arrive on time are 1/6*1/3 = 1/18 of the attendees. The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9 The answer is D. #### D QUESTION:A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items? options: A)15% B)12.16% C)13.4% D)20.2% E)None of these SOLUTION:Explanation : Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively. And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively. Overall loss percentage of the 1st two items = 14.33% =>(0.21p+0.11q)/(p+q)=0.1433 =>p/q=1/2. Overall loss percentage of the 2nd and 3rd item =10.4% =>(0.11q+0.1r)/(q+r)=0.104. =>q/r=2/3. Therefore, the overall loss percentage is : =>(0.21p+0.11q+0.1r)x100/(p+q+r). =>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3). =>0.1216×100. =>12.16%. Answer : B #### B QUESTION:What is the sum of all the prime numbers greater than 30 but less than 50? options: A)126 B)199 C)198 D)188 E)122 SOLUTION:Required sum = (31 + 37 + 41 + 43 + 47) = 199 Note: 1 is not a prime number Answer B #### B QUESTION:If 100 microns = 1 decimeter, and 10,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? options: A)100 B)10 C)0.01 D)0.0001 E)0.0001 SOLUTION:Given that 100 microns = 1 decimeter =10,000 angstroms So, 1 micron = 10,000/100 =100 Answer : A #### A QUESTION:What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300? options: A) 100 B) 150 C) 140 D) 200 E) 250 SOLUTION:{100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200. Answer: D. #### D QUESTION:Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen options: A)44/221 B)55/221 C)76/221 D)45/221 E)63/221 SOLUTION:WE HAVE N(S)=52C2=(52*51)/(2*1)=1326. LET A=EVENT OF GETTING BOTH BLACK CARDS B=EVENT OF GETTING BOTH QUEENS AB=EVENT OF GETTING QUEEN OF BLACK CARDS N(A)=26C2=(26*25)/(2*1)=325, N(B)=4C2=(4*3)/(2*1)=6 AND N(AB)=2C2=1 P(A)=N(A)/N(S)=325/1326; P(B)=N(B)/N(S)=6/1326 AND P(AB)=N(AB)/N(S)=1/1326 P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221 Option: B #### B QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:If one-third of one-fourth of a number is 15, then three-tenth of that number is options: A)35 B)15 C)60 D)54 E)57 SOLUTION:Let the number be x. then 1/3 of ¼ of x=15 X=15x12=180 The required number=(3/10)*180=54 ANSWER D 54 #### D QUESTION:The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? options: A)2197 B)1267 C)1750 D)2267 E)1262 SOLUTION:Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000] = (4000 * 11/10 * 11/10 - 4000) = Rs. 840. Sum = (420 * 100)/(3 * 8) = Rs. 1750 Answer:C #### C QUESTION:In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons? options: A)A)160 B)B)17 C)C)19 D)D)21 E)E)20 SOLUTION:5p3 =5 x4= 20 Option 'E' #### E QUESTION:The price of rice falls by 10%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously? options: A)5 kg B)15 kg C)25 kg D)30 kg E)None SOLUTION:Solution: Let Rs. 100 be spend on rice initially for 20 kg. As the price falls by 10%, new price for 20 kg rice, = (100 -10% of 100) = 90 New price of rice = 90/20 = Rs. 4,5 per kg. Rice can bought now at = 100/4,5 = 22,22 kg. Answer: Option E #### E QUESTION:What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$788 B)$812 C)$864 D)$878 E)$912 SOLUTION:After one year: 1.2 * $500 After two years: (1.2)^2 * $500 After three years: (1.2)^3 * $500 = $864 The answer is C. #### C QUESTION:Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756 options: A)16 B)33 C)105 D)424 E)2124 SOLUTION:2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16. 3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34 4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105 5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424 6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125 3th term should 34 instead of 33. B #### B QUESTION:P, Q and R can do a work in 6 , 9 and 12 days respectively. They completed the work and got Rs.195. What is the share of P? options: A)80 B)70 C)85 D)90 E)95 SOLUTION:The ratio of their working rates = 1/6 : 1/9 : 1/12 = 6 : 4 : 3. Since, they work together, the share of P = 6/13 * 195 = Rs.90 Answer: D #### D QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially? options: A)16 B)24 C)32 D)28 E)54 SOLUTION:after 7 girls left remaining 7 girls now boys 14 are twice as many as remaining girls. initially boys=14 and girls=14. ANSWER:D #### D QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600: options: A)200 B)250 C)300 D)350 E)400 SOLUTION:X = Rs.5000/- Y = Rs.15000/- X share 1 part & Y share 3 parts Total 4 parts -----> Rs.1600/- ----> 1 part -------> Rs.400/- X share = 1 part -----> Rs.400/- E #### E QUESTION:Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? options: A)4 B)8 C)12 D)14 E)16 SOLUTION:The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. Answer: D. #### D QUESTION:A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:13 C)23:12 D)11:9 E)11:10 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only. A : B 8000*18 : (8000*8) + (4000*10) 144000 : 104000 A:B = 18:13 ANSWER:B #### B QUESTION:If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is: options: A)80% B)90% C)33% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12. Gain % = 3/9 * 100 = 33% Answer:C #### C QUESTION:If the President and Vice President must sit next to each other in a row with 2 other members of the Board, how many different seating arrangements are possible? options: A)10 B)16 C)18 D)12 E)18 SOLUTION:We need to take President and VP as one unit. Therefore we have 3 people to arrange=3! ways Also, we both President and VP can be arranged in 2 ! ways. Reqd no of ways=3!*2!=12 ways Answer D #### D QUESTION:he average of 15 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)14 D)19 E)8 SOLUTION:Average of 15 numbers = 0. Sum of 15 numbers (0 x 15) = 0. It is quite possible that 14 of these numbers may be positive and if their sum is a the 15th number is (-a). Answer: Option C #### C QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)355 SOLUTION:Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14) = 322. ANSWER:C #### C QUESTION:x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 9 will be equal to: options: A)3 B)6 C)1/9 D)1/3 E)9 SOLUTION:Explanation : Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9. .'. x = 9/y^2 => x =9 /9^2 = 1/9 Answer : C #### C QUESTION:A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability Q that both will be juniors? options: A)1/10 B)1/5 C)2/9 D)2/5 E)1/2 SOLUTION:I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors. 2 seniors = P(Senior) * P(Senior) = 2/9 1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9 Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability Q that it is two juniors is 1- (7/9) = 2/9.C #### C QUESTION:The volume of the sphere QQ is (dfrac{37}{64}%)less than the volume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP? options: A)56% B)68% C)75% D)85% E)95% SOLUTION:Let the volume of sphere PP be 64 parts. Therefore volume of sphere QQ =64−3764%=64−3764% of 6464 =64−37=27=64−37=27 parts. The volume of RR =27−1927×27=27−1927×27 =27−19=8=27−19=8 parts. Volume ratio: =P:Q:R=64:27:8=P:Q:R=64:27:8 Radius ratio: =P:Q:R=4:3:2=P:Q:R=4:3:2 The surface area will be 16:9:516:9:5 Surface area of RR is less than the surface area of sphere PP 16k−4k=12k16k−4k=12k Now, =12k16k×100=12k16k×100 =75%=75% Thus surface area of sphere RR is less than the surface area of sphere P by 75% C #### C QUESTION:Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 0.5. What value is exactly 2 standard deviations less than the mean? options: A) 10.5 B) 11 C) 11.5 D) 12 E) 12.5 SOLUTION:The value which is exactly two SD below the mean is: mean-2*SD=13.5-2*0.5=12.5. Answer: E. #### E QUESTION:A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? options: A)5/6 km/hr B)25 km/hr C)79.2 km/hr D)15 km/hr E)38 km/hr SOLUTION:Explanation: Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr Answer:C #### C QUESTION:Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1245 B)1345 C)1455 D)1577 E)1671 SOLUTION:Let the smaller number be x. Then larger number = (x + 1395). x + 1395 = 6x + 15 5x = 1380 x = 276 Large number = 276+1395 = 1671 E #### E QUESTION:By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article? options: A)72.0 B)75.0 C)70.00 D)68.00 E)None of these SOLUTION:Let the cost price of the article be x. Then,2(84 –x) = 96 – x l68 – 2x= 96 – x \ x = 72 Answer A #### A QUESTION:A man can row his boat with the stream at 19 km/h and against the stream in 11 km/h. The man's rate is? options: A)4 kmph B)2 kmph C)7 kmph D)8 kmph E)3 kmph SOLUTION:DS = 19 US = 11 S = ? S = (19 - 11)/2 = 4 kmph Answer:A #### A QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit? options: A)s.2323 B)s.2380 C)s.2329 D)s.2660 E)s.2312 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 7790 * 14/41 = Rs.2660. Answer: D #### D QUESTION:The radius of a semi circle is 6.3 cm then its perimeter is? options: A)35.4 cm B)32.4 cm C)32 cm D)30 cm E)35 cm SOLUTION:Explanation: 36/7 r = 6.3 = 32.4 ANSWER IS B #### B QUESTION:If it takes a machine 1⁄3 minute to produce one item, how many items will it produce in 2 hours? options: A)1⁄3 B)4⁄3 C)80 D)120 E)360 SOLUTION:1 item takes 1/3 min so it takes 120 min to produce x x/3=120 the x=360 Answer:E #### E QUESTION:If 0 < a < b and k = (2a + 8b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 10 D)k > 10 E)k > 11 SOLUTION:Here's another approach: k = (2a + 8b)/b = 2a/b + 8b/b = 2(a/b) + 8 Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2. So, we get k = (some number less than 2) + 8 From here, we can see that k must be less than 10 Answer: C #### C QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:How many even multiples of 55 are there between 549 and 1101? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:550 = 10*55 1100 = 20*55 The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was options: A)Rs 1.56 B)Rs 2.40 C)RS 3.00 D)Rs 3.80 E)Rs 4.20 SOLUTION:first 1/5 mile costs = 1.00 remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14, hence 14*0.20=2.80 total fare = 2.80 + 1.00 =3.80 ANSWER:D #### D QUESTION:If 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days? options: A)127 B)237 C)360 D)450 E)281 SOLUTION:Explanation: Let the required no of hectares be x. Then Men --- Hectares---Days 10---------80---------24 36---------x---------30 More men, More hectares (Direct proportion) More days, More hectares (Direct proportion) x=36/10*30/24*80 x= 360 Answer: C #### C QUESTION:A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ? options: A)11:10:15 B)20:17:23 C)19:19:18 D)5:4:9 E)None of these SOLUTION:Explanation: A:B:CA:B:C =(25 lakhs××1)+(35 lakhs××2) :(35 lakhs××2+25 lakhs××1) :(30 lakhs××3) = 95 lakhs : 95 lakhs : 90 lakhs =19:19:18=19:19:18. ANSWER IS C #### C QUESTION:Which of the following CANNOT be the median of the 3 positive integers a, b, and c? options: A)a B)c C)a+c D)(a+c)/2 E)(a+c)/3 SOLUTION:The median of a set with odd number of terms is justa middle term, so it's a, b or c. Eliminate A and B right away. Now, the median can also be (a+c)/2 and (a+c)/3 (for example: {1, 2, 3} and {1, 2, 5}). But since a, b, and c are positive integers then it no way can be a+c . Why? Because a middle term (the median) cannot possibly be greater than two terms (a and c) in a set with 3 terms. Answer: C. #### C QUESTION:A merchant who marked his goods up by 50% subsequently offered a discount of 20% on the marked price. What is the percentage profit that the merchant made after offering the discount? options: A)30% B)125% C)25% D)20% E)16.66% SOLUTION:Explanatory Answer The easiest way to solve these kinds of problems is to assume a value for the merchant's cost price. To make calculations easy, it is best to assume the cost price to be $100. The merchant marks his goods up by 50%. Therefore, his marked price (quoted price) = cost price + mark up. Marked price = $100 + 50% of $100 = 100 + 50 = $150. The merchant offers a discount of 20% on his marked price. Discount offered = 20% of 150 = $30. Therefore, he finally sold his goods for $150 - $30 = $ 120. We assumed his cost to be $100 and he sold it finally for $120. Therefore, his profit = $20 on his cost of $ 100. Hence, his % profit = profit/cost price * 100 = 20/100 * 100 = 20%. Choice D #### D QUESTION:Two brothers took the GMAT exam, the higher score is M and the lower one is N. If the difference between the two scores is equal to their average, what is the value of N/M ? options: A)3 B)2 C)1/2 D)1/3 E)There isn't enough data to answer the question. SOLUTION:M - N = (M + N)/2 Solving for N/M = 1/3 D #### D QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5% B)7% C)3% D)9% E)1% SOLUTION:160 = (180*4*R)/100 R = 5% Answer:A #### A QUESTION:A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:What should come in place of the question mark (?) in the following equation? 5978 + 6134 + 7014 = ? options: A)19226 B)16226 C)19216 D)19126 E)None of these SOLUTION:? = 5978 + 6134 + 7014 = 19126 Answer D #### D QUESTION:For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| = options: A)ab-4+b B)2b-ab-4 C)ab+4 D)ab-2b+5 E)4-ab SOLUTION:Given: |ab| = ab and |a| = -a Question: |b-3| + |ab-b| = ? **** Looking at |ab| = ab tells us that a and b are either both positive or negative **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: a and b are both negative values Let a=-1 and b=-1 |b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5 Test a) ab-4 = (-1)(-1)-4 = -5 Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7 Test c) ab+4 = 1 + 4 = 5 Answer: C #### C QUESTION:In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000 SOLUTION:total vote = N vote cast by independent voters = 0.4 N vote cast by registered voters = 0.6 N vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N Answer choice E #### E QUESTION:Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 6 and the product of the given number and the sum of its digits is equal to 136. options: A)82 B)93 C)39 D)28 E)17 SOLUTION:Using the elimination method the option that fits this description is 17 7-1 = 3 (unit's digit that exceeds its ten's digit by 3) 17*8 = 136 (the product of the given number and the sum of its digits is equal to 175) answer :E #### E QUESTION:Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? options: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm SOLUTION:Total distance, which should be covered by both cars is 190+35=225 miles. Let t be the time so the equation will be 46t+54t=225 thus, t=2.25 hours Answer: D #### D QUESTION:Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ? options: A)6000 B)5400 C)6200 D)7200 E)8200 SOLUTION:Investment Ratio = Profit Sharing Ratio. Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6. Giri share = 13200 × 6 / 11 = Rs.7200 Hari share = 13200 × 5 / 11 = Rs.6000 Option A #### A QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table? options: A)6925 B)6887 C)6728 D)6725 E)2871 SOLUTION:: CP = SP * (100/(100 + profit%)) = 8587(100/124) = Rs. 6925. Answer: A #### A QUESTION:Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is S? options: A)50+A/200 B)50+3S/100 C)50+S/40 D)100+S/50 E)100+3S/100 SOLUTION:50+S/40=C #### C QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour ⇒ x/7+x/5=1 ⇒5x+7x=35 ⇒12x=35 ⇒x=2.9 km Answer: Option C #### C QUESTION:The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and three-fourths of the females in the class? options: A)218 B)226 C)234 D)242 E)250 SOLUTION:1/2*2/5 + 3/4*3/5 = 4/20 + 9/20 = 13/20 The number of degrees is 13/20 * 360 = 234 degrees The answer is C. #### C QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A? options: A)12 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:After t hours the distances D1 traveled by car A is given by D1 = 40 t Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by D2 = 60 (t-1) When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives 40 t = 60 (t-1) Solve the above equation for t to find t = 3 hours Car B passes car A at 9 + 3 = 12 pm Answer A #### A <<<Examples ends QUESTION:If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $81, how much does one shirt cost? options: A)$10 B)$12 C)$13.20 D)$21 E)$16.80 SOLUTION:3J + 2S = 69 2J + 3S = 81 ---------------- 5J + 5S = 150 ----(divide by 5)---> J + S = 30 3J + 2S = J + 2(J + S) = J + 60 = 69 ---> J = 9 3*9 + 2S = 69 27 + 2S = 69 2S = 42 S = 21 Answer: D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C QUESTION:In a certain country, 60 percent of the population likes basketball, and 34 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf? options: A)20% B)33% C)40% D)57% E)67% SOLUTION:Correct Answer: (D). Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 34 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 34/60 = 57%, or choice D. #### D QUESTION:If w is a positive integer and 10^w – 74 in decimal notation has digits whose sum is 440, what is the value of w? options: A)40 B)44 C)45 D)46 E)50 SOLUTION:Answer E = 50 We have (10^w)-74, where the sum of the digits is 440. 100-74 = 26, so we already have 2+6 = 8 from the 440. Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926. So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction. So we have 48 + 2 as an w = 50 #### E QUESTION:After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day? options: A)$1.25 million B)$80,000 C)$750,000 D)$27,000 E)$10,000 SOLUTION:Let sales in previous month = X 1.25 X=2,000,000 5/4 X= 2,000,000 ..........> X=2,400,000 sales per day= 2,400,000/30= less than 80,000 Answer:B #### B QUESTION:From the given equation find the value of x: x² − 3x + 2 options: A)3 B)2 C)5 D)6 E)7 SOLUTION:(x − 1)(x − 2) x = 1 or 2. C #### C QUESTION:In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden. What is the length of the garden? options: A)22 B)24 C)26 D)28 E)30 SOLUTION:Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length Also, 3 meter is left from all sides of the boundary of the garden. Hence, length of the garden = (11 × 2) + 3 + 3 = 28 meter Answer is D. #### D QUESTION:Two roads XY and YZ of 15 metres and 20 metres length respectively are perpendicular to each other. What is the distance between X & Z by the shortest route? options: A)35 metres B)30 metres C)24 metres D)25 metres E)None of these SOLUTION:XYZ is a right-angled triangle XZ =√15(2)+20(2)=√=625=25m Answer D #### D QUESTION:The average of two numbers is P. If one number is Q, then the other number is options: A)2Q B)2P C)P - Q D)2P-Q E)None of these SOLUTION:Explanation : Let the other number be x, According to the question, => ( x + Q ) / 2 = P. => x + Q = 2P. => x = 2P - Q. Hence, the required number is 2P - Q. Answer : D #### D QUESTION:The value of (4.7×13.26 + 4.7×9.43+4.7×77.31) is options: A)0.47 B)47 C)470 D)4700 E)None SOLUTION:Solution Given expression = 4.7×(13.26+9.43+77.31) = 4.7 ×100 = 470. Answer C #### C QUESTION:What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for two years? options: A)29893 B)27773 C)29989 D)28800 E)23400 SOLUTION:Simple interest = (18000 * 2 * 15)/100 = Rs. 5400 Amount = P + I = 18000 + 5400 = Rs. 23400 Answer: E #### E QUESTION:"A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap? options: A)90 seconds B)54.44 seconds C)110 seconds D)63 seconds E)77 seconds SOLUTION:A is faster than B. Every second he increases distance between A and B. They will meet for the first time again when he increases distance between them by one full circle. (Say the lap is of 100m. He keeps increasing distance between them. When he is 90 m ahead of him, it is the same as 10 m behind him because they are moving in a circle. Finally when he is 100 m ahead of him, he is exactly 1 lap ahead and hence both are at the same point). A takes 70 secs for one full lap. So he covers 4.5 laps in exactly 70*4.5 = 315 seconds. In 315 secs, B completes 3.5 laps. So for each lap, he takes 315/3.5 = 90 secs Answer (A) #### A QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:First, reach to the point of getting the equation W: x + y = 18 It should take about 20 seconds. Then Substitute the answer choices into the equation. I don't know what the answer choices in this case are. But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds). Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.) The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds). Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D QUESTION:Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 75 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains? options: A)93% B)97% C)100% D)107% E)99% SOLUTION:Say Arthur's fortune was $100. Then: A = 20*1.5*1.1 = 33 B = 20*1.5*1.1 = 33 C = 20*1.5*0.4 = 12 D = 20*0.6*1.75 = 21 E = 0 Total 33 + 33 + 12 + 21 = 99. Answer: E. #### E QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)77 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-79)*(50-80)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:If it takes a machine 1⁄3 minute to produce one item, how many items will it produce in 2 hours? options: A)1⁄3 B)4⁄3 C)80 D)120 E)360 SOLUTION:1 item takes 1/3 min so it takes 120 min to produce x x/3=120 the x=360 Answer:E #### E QUESTION:Calculate the HCF of 64, 318, 250 options: A)6 B)5 C)4 D)3 E)2 SOLUTION:Explanation: Lets solve this question by factorization method. 64=2 x 2 x 2 x 2 x 2 x 2, 318=2 × 3 × 53, 250=2 × 5 × 5 × 5 So HCF will be minimum term present in all three, i.e. 2×32=18 Answer: Option E #### E QUESTION:How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits? options: A) 48 B) 52 C) 66 D) 68 E) 84 SOLUTION:Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero: 0 1 1 1 2 2 2 3 3 2 5 5 Number of possibilities = 3*4*4 = 48. Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52. Answer: B #### B QUESTION:Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 3.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn? options: A)1/3 B)1/30 C)1/42 D)2 E)30 SOLUTION:Pete covered 3.5*60=210 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/210=1/42. Answer: C. #### C QUESTION:The area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:L * W = 750 : area , L is the length and W is the width. 2 L + 2 W = 110 : perimeter L = 55 - w : solve for L (55 - W) * W = 750 : substitute in the area equation W = 25 and L = 30 correct answer E #### E QUESTION:5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.180 only. Men’s wages are? options: A)6Rs B)2Rs C)4Rs D)9Rs E)12Rs SOLUTION:5M = xW = 8B 5M + xW + 8B ----- 180 Rs. 5M + 5M + 5M ----- 180 Rs. 15M ------ 180 Rs. => 1M = 12Rs. Answer: E #### E QUESTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day? options: A)27 B)34 C)50 D)61 E)78 SOLUTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. Machine starts manufacturing Red and ended on Black. This means that either machine has manufactured 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78 Only 78 is given in the options. So answer = 78 ANSWER:E #### E QUESTION:When positive integer x is divided by positive integer y, the remainder is 12. If x/y = 75.12, what is the value of y? options: A)84 B)98 C)51 D)65 E)100 SOLUTION:When positive integer x is divided by positive integer y, the remainder is 12 --> x=qy+12; x/y=75.12 --> x=75y+0.12y (so q above equals to 75); 0.12y=12 --> y=100. Answer: E. #### E QUESTION:The average age of a class of 23 students is 22 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? options: A)40 B)41 C)46 D)42 E)49 SOLUTION:Total age of all students =23×22 Total age of all students + Age of the teacher =24×23 Age of the teacher =24×23−23×22=23(24−22)=23×2=46 Answer is C. #### C QUESTION:Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 13 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip? options: A)48 B)42.5 C)44 D)50 E)52.5 SOLUTION:Total Time taken by jerry = (8/40)*60 Minutes + 13 Minutes + (20/60)*60 Minutes = 35 Minutes Average Speed = Total Distance / Total Time = (8+20) miles / (35/60)Hours = 28*60 / 35 = 48 Miles per hour Answer: option A #### A QUESTION:The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is options: A)1677 B)1683 C)2523 D)3363 E)None of these SOLUTION:Explanation: L.C.M of 5, 6, 7, 8 = 840 therefore Required Number is of the form 840k+3. Least value of k for which (840k+3) is divisible by 9 is k = 2 therefore Required Number = (840 x 2+3)=1683. Answer: B #### B QUESTION:If 7a = 2b = 15, then 42ab = options: A)75 B)125 C)675 D)1100 E)1250 SOLUTION:7a * 2b = 15 * 15 = 225 14 ab = 225 i.e. 42 ab = 675 Answer: Option C #### C QUESTION:Which of the following describes all values of x for which 4–x^2 >= 0? options: A) x >= 1 B) x <= –1 C) 0 <= x <= 1 D) x <= –1 or x >= 1 E) –2 <= x <= 2 SOLUTION:4 - x^2 >=0 means x^2 - 4 <=0 => (x-2)(x+2) <= 0 => -2 <= x <= 2 Answer - E #### E QUESTION:Three numbers are in the ratio 1:3:5 and their H.C.F is 5. The numbers are? options: A)5, 15, 35 B)5, 15, 30 C)5, 15, 25 D)5, 15, 40 E)5, 15, 20 SOLUTION:Let the required numbers be x, 3x and 5x. Then, their H.C.F = x. So, x = 5. The numbers are 5, 15, 25. Answer: C #### C QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money? options: A)1489 B)6845 C)2598 D)1875 E)2600 SOLUTION:P = 75(100/20)5 => P = 1875 Answer: D #### D QUESTION:Tough and Tricky questions: Exponents. If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy? options: A)4, 2, 8, 6 B)4 and 2 C)2 and 8 only D)6 and 4 E)8 and 6 SOLUTION:Only Units digit of X and Y contribute to the Units digit of XY. Finding all values of X for positive values of a When, a=1; X=2 a=2; X=4 a=3; X=8 a=4; X=16 a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4...... Similarly, Finding all values of Y for positive values of b When, b=1; Y=3 b=2; Y= 9 b=3; Y= 27 b=4; Y=81 b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9.... So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y When X=2 and Y=3: Units digit of XY = 6 When X=2 and Y=9: Units digit of XY = 18 When X=2 and Y=7: Units digit of XY = 14 When X=2 and Y=1: Units digit of XY = 2 When X=4 and Y=3: Units digit of XY = 12 When X=4 and Y=9: Units digit of XY = 36 When X=4 and Y=7: Units digit of XY = 28 When X=4 and Y=1: Units digit of XY = 4 When X=8 and Y=3: Units digit of XY = 24 When X=8 and Y=9: Units digit of XY = 72 When X=8 and Y=7: Units digit of XY = 56 When X=8 and Y=1: Units digit of XY = 8 When X=6 and Y=3: Units digit of XY = 18 When X=6 and Y=9: Units digit of XY = 54 When X=6 and Y=7: Units digit of XY = 42 When X=6 and Y=1: Units digit of XY = 6 There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6 Ans: A #### A QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)56 B)50 C)72 D)27 E)25 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B #### B QUESTION:-64*29+468=? options: A)1430 B)1302 C)-2801 D)-1388 E)None of these SOLUTION:=> -64*(30-1)+468; => -(64*30)+64+468; => -1920+532=-1388. Correct Option: D #### D QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many digits does this integer consists of? options: A)150 B)339 C)342 integers D)359 E)362 SOLUTION:1-digit integers Number of 1-digit integers (1 to 9) = 9 - 1 + 1 = 9 Number of digits used = (9)(1) = 9 2-digit integers Number of 2-digit integers (10 to 99) = 99 - 10 + 1 = 90 Number of digits used = (90)(2) = 180 3-digit integers Number of 3-digit integers (100 to 150) = 150 - 100 + 1 = 51 Number of digits used = (51)(3) = 153 TOTAL # of digits uses = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 20 terms of the sequence? options: A)201/100 B)99/100 C)100/101 D)1/10000 E)20/21 SOLUTION:Easy task and accomplish X1=1-1/2 x2=1/2-1/3 x3=1/3-1/4 ..... x20=1/20-1/21 sum=X1+X2+X3+....X20=1-1/2+1/2-1/3+.......1/20-1/21=1-1/21=20/21 E is the answer #### E QUESTION:The average age of a group of 10 students was 24. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group? options: A)22 years B)36 years C)32 years D)44 years E)None of these SOLUTION:The total age of 10 students with average 24 = 240 The total age of 12 students with average 26 = 312 The total age of 2 new students = 72 Their average =36 Correct Option B #### B QUESTION:At what rate percent per annum will a sum of money double in 16years? options: A)10.6% B)3.65% C)6.25% D)8.32% E)11% SOLUTION:Let principle = P S.I. = P T = 16yrs Rate = 100*P/P*16 = 25/4% = 6.25% Answer is C #### C QUESTION:The diagonals of a rhombus are 12 cm and 10 cm. Find its area? options: A)158 B)129 C)150 D)123 E)60 SOLUTION:1/2 * 12 * 10 = 60 Answer:E #### E QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3*1*10+3*10*10 = 330 ANSWER:A #### A QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true? options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6 SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) . ans B #### B QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie? options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9 SOLUTION:There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9 Answer: E #### E QUESTION:A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)29 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 180, so from 2003 to 2005 it increased by (180-140)/140=40/140=2/7=~29%. Answer: E. #### E QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)30 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill? options: A)A)1/8 B)B)1/3 C)C)1/9 D)D)1/2 E)E)1/4 SOLUTION:1/10 + 1/15 = 1/6 * 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 Answer:B #### B QUESTION:2 + 2 + 2 + 2 × 2^2 + 2 × 2^3 + 2 × 2^4 + 2 × 2^5 + 2 × 2^6 + 2 × 2^7 = options: A)2^7 B)2^14 C)2^10 D)2^15 E)2^16 SOLUTION:We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*2^7 we would have: sum=9*(2*2^7)=18*2^7=~2^11, so the actual sum is less than 2^11 and more than 2^7 (option A) as the last term is already more than that. So the answer is clearly C. Answer: C #### C QUESTION:2+2+2²+2³ ... +2^9 options: A)2^9 B)2^10 C)2^16 D)2^35 E)2^37 SOLUTION:2+2=2^2 2^2+2^2=(2^2)*(1+1)=2^3 2^3+2^3=(2^3)*(1+1)=2^4 so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10 Answer B #### B QUESTION:If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil? options: A)9 B)5 C)7 D)8 E)4 SOLUTION:Let the total length be xm Then black part =x/8cm The remaining part=(x-x/8)cm=7x/8cm White part=(1/2 *7x/8)=7x/16 cm Remaining part=(7x/8-7x/16)=7x/16cm 7x/16=7/2 x=8cm Answer is D. #### D QUESTION:Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+34 3x + 6 = x + 34 2x = 28 \inline \therefore x = 14 \inline \therefore Middle number = x + 2 = 14+2 = 16 D #### D QUESTION:At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:If n is an integer greater than 8, which of the following must be divisible by 8 ? options: A)n(n + 5)(n – 6) B)n(n + 2)(n – 1) C)n(n + 1)(n – 4) D)n(n + 3)(n – 5) E)n(n + 5)(n – 6) SOLUTION:If n= 9 , then (n-1) is divisible by 8 . B #### B QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^a*q^b no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:In a dairy farm, 50 cows eat 50 bags of husk in 50 days. In how many days one cow will eat one bag of husk ? options: A)34 days B)40 days C)46 days D)50 days E)None of these SOLUTION:Explanation: Less Cows, More days (Indirect Proportion) Less bags, Less days (Direct Proportion) [Cows1 50 Bags 50 1]::50:x =>x∗50∗1=50∗1∗50 =>x=50 Option D #### D QUESTION:A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 550 ? options: A)249 B)498 C)676 D)823 E)274 SOLUTION:slope of 2 and a y-intercept of 2 y-coordinate is 550 y = 2x + 2 548 = 2x x = 274 Answer: E. 274 #### E QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 * 58 = Rs. 2784. Answer:A #### A QUESTION:The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.90 per metre. options: A)2399 B)3888 C)2999 D)5808 E)6468 SOLUTION:Explanation: Area = (13.86 x 10000) sq.m = 138600 sq.m Circumference = Cost of fencing = Rs. (1320 x 4.90) = Rs. 6468. Answer: E) 6468 #### E QUESTION:60 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)8 days B)6 days C)7 days D)9 days E)12 days SOLUTION:1 women's 1 day work = 1/420 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/420 + 10/140) = 1/12 5 women and 10 children will complete the work in 12 days. Answer: E #### E QUESTION:The average age of a class of 20 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? options: A)40 B)41 C)42 D)45 E)43 SOLUTION:Total age of all students =20×21 Total age of all students + Age of the teacher =21×22 Age of the teacher =21×22−21×20=21(22−20)=21×2=42 Answer is C. #### C QUESTION:What is the smallest number which when diminished by 24, is divisible 5, 10, 15 and 20? options: A)276 B)84 C)88 D)90 E)342 SOLUTION:Required Number = (LCM of 5, 10, 15 and 20) + 24 = 60 + 24 = 84 Option B #### B QUESTION:if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr). options: A)18 kmph B)15.5 kmph C)12.5 kmph D)13.5 kmph E)22.5 kmph SOLUTION:Speed in still water = (16 + 9)1/2 kmph = 12.5 kmph. answer :C #### C QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)20 B)10 C)15 D)5 E)7 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days Answer: A #### A QUESTION:If d<0, which of the following represents a positive number? options: A)d|d| B)|d|d C)|d|/d D)-d|d| E)d/ |d| SOLUTION:Answer : D #### D QUESTION:David covered a distance of 50 miles on his first trip. On a later trip he traveled 75 miles while going six times as fast. His new time compared with the old time was: options: A)twice as much B)three times as much C)the same D)half as much E)a fourth as much SOLUTION:Let t be the time of the first trip. On the later trip, David can travel 300 miles in time t. The trip of 75 miles takes t/4. The answer is E. #### E QUESTION:A man buys 54 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)7.6 % B)7.7 % C)16.21 % D)13.6 % E)7.8 % SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 54 pens = Rs. 46 S.P. of 54 pens = 99% of Rs. 54= Rs. 53.46 Profit % = (Profit /C.P.) x 100 Profit% = (7.46/46) x 100 = 16.21 % ANSWER: C #### C QUESTION:There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3 options: A)I B)II C)III D)II &III E)I &II SOLUTION:Name T = full pool U fills a pool in a days ==> 1 day U fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c 1 day (U+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (U+Y+Z) together fill: T ==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==>d = abc/(ab+bc+ca) d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3 B #### B QUESTION:A train 350 m long passed a pole in 35 sec. How long will it take to pass a platform 650 m long? options: A)100 sec B)89 sec C)85 sec D)16 sec E)15 sec SOLUTION:Speed = 350/35 = 10 m/sec. Required time = (350 + 650)/10 = 100 sec. Answer: A #### A QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)24 B)66 C)55 D)88 E)61 SOLUTION:(15*18)/12 = 24 Answer:A #### A QUESTION:A furniture dealer purchased a desk for $100 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? options: A)40% B)45% C)50% D)55% E)60% SOLUTION:Anyway, in this question, there is no discount but the mark up is given as 40% of the selling price. So it is not 40% of $100 but instead, 40% of Selling price which is obtained by adding mark up to $100. So if selling price is S, 100 + 40% of S = S or 100 = 0.6S therefore S = 100/0.6 = S = Profit = 100/0.6- 100 which is calculated on cost price in % terms. So 40/100 * 100 = 40% is profit. A #### A QUESTION:Dacid obtained 45, 35, 52, 47 and 55 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)79 B)99 C)47 D)89 E)45 SOLUTION:Average = (45+35+ 52+ 47+55)/5 = 234/5 = 47. Answer:C #### C QUESTION:In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi? options: A)1/2 B)1/3 C)2/5 D)2/7 E)3/7 SOLUTION:P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10 P (E or H) = P (E U H) = P (E) + P (H) - P (E ∩ H) = (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5 C #### C QUESTION:A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is : options: A)16000 B)18000 C)20000 D)30000 E)None of these SOLUTION:Explanation: Number of bricks =Courtyard area /1 brick area =(1800×1200 /12×6)=30000 Option D #### D QUESTION:Health insurance Plan Q requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount? options: A)$600 B)$1000 C)$3800 D)$5300 E)$6200 SOLUTION:0.5 * 600 = 300 where Q = B #### B QUESTION:A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:What sum of money put at C.I amounts in 2 years to Rs.7000 and in 3 years to Rs.9261? options: A)4000 B)8877 C)2877 D)2678 E)1011 SOLUTION:7000 ---- 2261 100 ---- ? => 32.3% x *1323/100 * 1323/100 = 7000 x*1.75=7000 x=7000/1.75 => 3999.25 Answer: A #### A QUESTION:A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle? options: A)2.5π B)3π C)5π D)4π E)10π SOLUTION:If a rectangle is inscribed in a circle, then the diagonal of the rectangle = diameter of the circle. In this case, diagonal = (9 + 16)^(1/2) = 5 Hence the radius = 2.5 Circumference = 2πr = 2π*2.5 = 5π Correct Option: C #### C QUESTION:5216 x 51 = ? options: A)266016 B)212016 C)266436 D)216314 E)None of these SOLUTION:Explanation : Normal way of multiplication may take time. Here are one alternative. 5216 x 51 = (5216 x 50) + 5216 = (5216 x 100/2) + 5216 = 521600/2 + 5216 = 260800 + 5216 = 266016. Answer : Option A #### A QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33*100 = 180% of 3.33. Answer: E. #### E QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 30*16=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 90 km/hr? options: A)2.5 sec B)2.9 sec C)3.5 sec D)4 sec E)2.4 sec SOLUTION:Speed = 90 * 5/18 = 25 m/sec Time taken = 100/25 = 4 sec. Answer: D #### D QUESTION:90, 180, 12, 50, 100, 80, ?, 3, 20, 4, 25, 2, 6, 30, 3 options: A)100 B)150 C)180 D)90 E)60 SOLUTION:30*3=90 6*30=180 6*2=12 25*2=50 4*25=100 20*4=80 3*20=60 ans is 60 ANSWER:E #### E QUESTION:When the positive integer c is divided by 11, the quotient is d and the remainder 3. When c is divided by 19, the remainder is also 3. What is the remainder when d is divided by 19? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r where k = LCM (d1,d2) In this case the divisors are 1119 and remainder is 3. so LCM (11,19) = 209 So N= 209+3 = 212 Also c=d1q+3 ; which means d1q=209d1=11 therefore q=19 And ( d divided by 19)19/19 leaves remainder 0. Answer is E #### E QUESTION:The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home? options: A)60% B)50% C)55% D)40% E)33.3% SOLUTION:Increase = 168000-120000 = 48000 % increase = 48000*100/120000 = 40% Answer: option D #### D QUESTION:Jim and Reneey will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneey have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win? options: A)5/6 B)2/3 C)1/2 D)5/12 E)1/3 SOLUTION:1/3 probability of jim winning is basically the sum of three probabilities: probability of jim picking rock and reneey picking scissors = 1/3*1/3 = 1/9 probability of jim picking scissors and reneey picking paper = 1/3*1/3=1/9 probability of jim picking paper and reneey picking rock = 1/3*1/3=1/9 1/9 + 1/9 + 1/9 = 3/9 = 1/3=E #### E QUESTION:The average of 50 numbers id 20. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is : options: A)22.75 B)33.25 C)22.25 D)11.75 E)18.75 SOLUTION:Explanation: Total of 50 numbers = (50×20)=1000 Total of 48 numbers =(1000-(45+55)]=900 Required average = 900/48=18.75 Answer:E #### E QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang two on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)56 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 8P2 = 8!/2! = 56. IMO option C is correct answer.. #### C QUESTION:A train 120 m long passed a pole in 20 sec. How long will it take to pass a platform 780 m long? options: A)150 B)170 C)160 D)100 E)120 SOLUTION:Speed = 120/20 = 6 m/sec. Required time = (120 + 780)/6 = 150 sec. Answer: Option A #### A QUESTION:If a - b =4 and a2+b2=52 , find the value of ab. options: A)8 B)26 C)18 D)42 E)36 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=52−16=36 =>ab=18 Option C #### C QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 11? options: A)44 B)88 C)45 D)176 E)352 SOLUTION:Solution: sequence of 11 lets say sequence is 11n, 11(n+1), 11(n+2), 11(n+3), 11(n+4) so range is 11n+44-11n = 44 if we put the different values of n we will get different but the range will be multiple of 44 and only 45 is not multiple of 44 Answer : C #### C QUESTION:John has taken four (4) tests that have an average of 81. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade? options: A)87 B)90 C)92 D)94 E)99 SOLUTION:87-81=6*4=24 points 2*87=174 174+24=198 points to be scored in the 2 tests. Avg of 2 tests = 198/2=99 Answer: E Traditional Method: Total scored till now 81*4=324 Total score to avg 87 in 6 tests = 87*6=522 Total to be scored on 2 tests = 522-324=198 Avg on 2 tests = 198/2 = 99 Answer E #### E QUESTION:A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse. options: A)2200 B)1800 C)1200 D)1000 E)1500 SOLUTION:Let the C.P of the horse be Rs. X, Then, C.P of the carriage = Rs.(3000- x). 20% of x - 10% of ( 3000-x ) =2% of 3000 = 60, x/5 - ( 3000-x )/10 = 60, 3x - 3000 = 600, 3x =3600, x = 1200. Hence, C.P of the horse = Rs. 1200 ANSWER:C #### C QUESTION:A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr. What is the speed of the boat? options: A)2.5 kmph B)3.5 kmph C)4.5 kmph D)1.5 kmph E)9.5 kmph SOLUTION:speed upstream = 10/3 speed of boat down stream = 10/6 speed of boat = 1/2(10/3 + 10 /6 ) = 2.5 kmph ANSWER:A #### A QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is options: A)70 B)71 C)72 D)73 E)74 SOLUTION:Explanation: Let the second number is x, then first is 2x, and third is 1/3(2x) =>2x+x+2x/3=264 <=>11x/3=264 =>x=72 Answer: Option C #### C QUESTION:Divide Rs. 1300 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)346 B)368 C)375 D)337 E)325 SOLUTION:A+B+C = 1300 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1300 => 325 Answer:E #### E QUESTION:REDO’s manufacturing costs for sets of horseshoes include a $10,500 initial outlay, and $15per set. They can sell the sets $40. If profit is revenue from sales minus manufacturing costs, and the company producessells 500 sets of horseshoes, what was their profit? options: A)$2100 B)$2000 C)$2050 D)$2070 E)$2500 SOLUTION:Total Manufacturing cost = 10500+500*15 = 18000 Total Selling cost = 500*40= 20000 Profit = 20000-18000 = 2000 Answer : B #### B QUESTION:Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: options: A)11:5 B)3 : 2 C)1:2 D)3:5 E)7:8 SOLUTION:Answer: Option B Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. #### B QUESTION:The ratio Q , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio Q, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:(7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = ? options: A)1 B)1 / 5 C)15 / 11 D)3 / 11 E)None SOLUTION:Answer Given expression = (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = (14 + 1) / (10 + 1) =15 / 11 Option: C #### C QUESTION:A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed? options: A)20km/hr B)30km/hr C)40km/hr D)50km/hr E)90km/hr SOLUTION:Let the speed be x km/hr 50x-50* 9/10 *x = 450 50x - 45x = 450 x = 90km/hr Answer is E #### E QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 70% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ? options: A)1/7 m B)1/3 m C)1/4 m D)1/5 m E)1/6 m SOLUTION:After the final transaction: Angela received $(m-n) for t hours; Linda received $(m+n) for 1.5t hours; We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/7. Answer: A. #### A QUESTION:Tough and Tricky questions: Ratios 1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? options: A)1/2 B)2/3 C)7/15 D)23/30 E)4/5 SOLUTION:let total no. of students be 30 students left on a field trip = 1/5(30) =6 thus 24 students left behind 1/3(24)=8 students did not want to go. thus 16 students want to go on the trip 1/2(16)=8 were able to join the other students on the field trip. thus total number of students that went on a field trip =6+8 =14 thus required fraction = 14/30 =7/15 C #### C QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B QUESTION:By selling an article for $180, a person gains $30. What is the gain %? options: A)25% B)30% C)50% D)20% E)10% SOLUTION:S.P. = $180 Gain = $30 C.P. = 180-30 = 150 Gain% = 30/150 * 100 = 20% Answer is D #### D QUESTION:The contents of a certain box consist of 24 carrots and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be carrrots? options: A) 24 B) 26 C) 30 D) 46 E) 50 SOLUTION:carrrots = (carrrots + kiwi + x)*0.3 24 = (30 + 24 + x)*0.3 x = 26. Answer: B. #### B QUESTION:How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3? options: A)3/10 B)4/10 C)6/10 D)7/10 E)9/10 SOLUTION:arrangement = 5!/3!=20 Probability of getting all 3 balls= 3 from 5=5c3 1 from 3 red ball,1 green,1 yellow (3c1*1c1*1c1)/5c3 =3/10 ANSWER:A #### A QUESTION:A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose? options: A)1.4 B)1.5 C)1.6 D)1.8 E)1.0 SOLUTION:Let the speed be 's' and let the distance between rose and poppy be 'x' The problem boils down to: Rose to Poppy: s+3=x/6 ------- 1 Daisy to Rose: s=(x+18)/10------ 2 so from 1 we can re write x as x=6s+18 substitute the value of x in 2 gives us s=1.8 m/s D #### D QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number W of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:Circular arrangements= (n-1)! Hence (4!) = 24=W Answer is C #### C QUESTION:An investment compounds annually at an interest rate of 33.34% What is the smallest investment period by which time the investment will more than triple in value? options: A)1 B)2 C)3 D)5 E)4 SOLUTION:Assume initial amount is x Annual Interest is 34.1% so after 1 year the amount will become x * (100+33.34)/100 => x*4/3 now we need to find n for x * (4/3)^n = 3x or in other words n = 4 E #### E QUESTION:A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected? options: A)1/3 B)2/5 C)2/7 D)3/7 E)3/8 SOLUTION:Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected) = = 2/5 B #### B QUESTION:Today Joelle opened an interest-bearing savings account and deposited $5,000. If the annual interest rate is 4 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account? options: A)$5200 B)$5408 C)$5208 D)$5608 E)$5808 SOLUTION:Interest for 1st year = 5000*4/100 = 200 Interest for 2nd year = 5200 *4/100 = 208 Total =5000+200+208 = 5408 Answer : B #### B QUESTION:Imagine John has 2 blue balls, 3 green balls, 1 black ball and 4 red balls. How many ways can he arrange the balls lining them up? options: A)10!/(2!)2 1! B)10!/2! 1! 3! 1! C)10!/4! 4! D)9!/4! 3! 2! E)10!/4! 3! 2! SOLUTION:n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways. John has 10 balls which are 4 red balls, 3 green balls, 2 blue balls and 1 black ball. Number of arrangements = 9!/(2!)2 3! Answer: E #### E QUESTION:Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D? options: A)(5,10) B)(-3,2) C)(-1,7) D)(-1,2) E)(-3,1) SOLUTION:The slope of the line is -ve, the only point that makes the slope -ve is D. (5 - 2)/(-2 + 1) = 3/-1 Answer - D #### D QUESTION:A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule? options: A)18 B)81 C)56 D)72 E)24 SOLUTION:IMO 'E' is the answer. Matches will be in multiples of 5x+4. The answer that satisfies this condition is E #### E QUESTION:30 liters of a mixture contains milk and water in the ratio 2:1. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be? options: A)3:2 B)3:1 C)4:1 D)5:2 E)2:1 SOLUTION:Quantity of milk in 30 liters if mix = 30*2/3 =20 liters Quantity of milk in 35 liters of new mix = 20+5 = 25 liters Quantity of water in it = 35-25 = 10 liters Ratio of milk and water in new mix = 25:10 = 5:2 Answer is D #### D QUESTION:Deepak can read x pages in 10 minutes. At this rate, how long will it take him to read y pages? options: A)(12/x)*y B)(5/x)*y C)(10/x)*y D)(10x)*y E)(13/x)*y SOLUTION:x page in 10 mins i.e. 1 page in 10/x mins i.e. y pages in (10/x)*y Answer: option C #### C QUESTION:A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)100 B)102 C)104 D)108 E)90 SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 10 = 90 ways. E #### E QUESTION:A tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume. If 6,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 15% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-6,000=4,000 gallons and sodium chloride is 600 gallons (6% of initial solution of 10,000 gallons) then sodium chloride is 600/4,000*100=15% of the remaining solution of 4,000 gallons. Answer: E. #### E QUESTION:Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool? options: A)1400 B)1600 C)1800 D)1500 E)2000 SOLUTION:volume of pool = 80*150*10 cu.ft ,100% full = 60*100*10*1 cu.ft water is available to drain. draining capacity =60 cu.ft /min therefore time taken = 80*150*10*1/ 60 min= 2000 min E #### E QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)6 D)5 E)1 SOLUTION:2x * x = 128 => x = 8 Answer:A #### A QUESTION:A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box? options: A)6 m B)9 m C)10 m D)7 m E)11 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number? options: A)228 B)103 C)286 D)122 E)102 SOLUTION:Explanation: Let the number be x x2 - 732 = 5280 x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609 = 10000 + 2(100)(3) + 32 = (100 + 3)2 x = 100 + 3 = 103. Answer: B #### B QUESTION:An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? options: A)4.04 B)4.02 C)4.01 D)4.05 E)4.06 SOLUTION:Formula for Calculation of Percentage error is: =(x−y−(xy)/100)% =(2+2+(2×2)/100)%=4.04% Answer is A. #### A <<<Examples ends QUESTION:A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route? options: A)12km B)15km C)18km D)24km E)Data Inadequate SOLUTION:time=distance/speed so, let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so, (x/4+y/3)+(y/6+x/4)=6 x+y=12 km. ANSWER:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long? options: A)87 sec B)89 sec C)17 sec D)18 sec E)97 sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 650)/10 = 89 sec. Answer:B #### B QUESTION:The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number? options: A)12 B)20 C)45 D)60 E)52 SOLUTION:Given ratios 5 : 3 4 : 9 20:12:27 The second number = 177/(20+12+27) * 15 = 45 Answer is C #### C QUESTION:In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 9 women? options: A)A)144 B)B)15 C)C)20 D)D)18 E)E)21 SOLUTION:Required number of ways = 4C3*9C2 = 4*36 = 144 Answer is A #### A QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture? options: A)294 B)235 C)350 D)288 E)580 SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:If x = 3 and y = 2, what is the value of 5(x-y)^2 - xy ? options: A)-8 B)-7 C)-1 D)-2 E)-5 SOLUTION:x = 3 and y = 2 x-y = 3 - 2 = 1 x*y = 3 * 2 = 6 Now we apply it in the equation 5(x-y)^2 - xy =5 (1)^2-6 ==>5*1 -6 = 5-6 =-1 Answer : C #### C QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x * 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 13 km/hr downstream and 10 km/hr upstream. options: A)3 kmph B)9 kmph C)4 kmph D)8 kmph E)6 kmph SOLUTION:Speed in still water = (13 + 5)1/2 kmph = 9 kmph. answer :B #### B QUESTION:John found that the average of 15 numbers is 40. If 12 is added to each number then the mean of number is? options: A)52 B)45 C)65 D)78 E)64 SOLUTION:(x+x1+...x14)/15 = 40 52 Option A #### A QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (36 + 36)*5/18 = 4*5 = 20 mps. The time required = d/s = 100/20 = 5 sec. Answer : C #### C QUESTION:For which of the following functions does f(−z)=−f(z) for all real number values of x? options: A)z^8−z^4 B)z^5/(z^2+1) C)z^5/z^7 D)z^9/(z^5+1) E)z^8 SOLUTION:all even root cannot be matched eliminated put z=2 f(−z)=(−2)^5/(−2^)2+1=−32/5, and −f(z)=−2^5/2^2+1=−32/5, for a match. ANSWER: B #### B QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 10 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 10 years = (20 + 10) years =30 years. Answer : A #### A QUESTION:A motorcyclist made 3 roundtrips to the park until he ran out of gas back at home. Te park is 1500 meters away from his home. His speedometer was broke and he wanted to calculate his speed. It took him two and half hours to complete the journey. How fast was the motorcyclist traveling? options: A)25 B)60 C)36 D)45 E)32 SOLUTION:The distance from the park to the motorcyclist home was 15000 meters. He made the trip 3 times in total with each trip being 30000 meters. multiply 3 by 30000 to get 90000 meters or 90km in total. D= ST 90000/2.5 = T which comes to 36000 meters or 36 km per hour Correct answer = 36 #### C QUESTION:A school’s annual budget for the purchase of student computers increased by 70% this year over last year. If the price of student computers increased by 30% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year? options: A)30% B)30.77% C)36% D)37% E)38% SOLUTION:Pick numbers. Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100; This year: budget = $170, price = $1.3 --> the number of computers purchased = 170/1.3 = ~130.77 Increase in the number of computers purchased = 30.77%. Answer: B. #### B QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ? options: A)9/10 B)6/10 C)2/10 D)3/10 E)5/10 SOLUTION:Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20 Let E = event of getting a multiple of 4 or 15 =multiples od 4 are {4, 8, 12, 16, 20} And multiples of 15 means multiples of 3 and 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}. = the common multiple is only (15). => E = n(E)= 6 Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10. Answer is D #### D QUESTION:John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend? options: A)$2,125 B)$1,320 C)$2,000 D)$1,580 E)$2,000.75 SOLUTION:Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125. #### A QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(6200*5*3)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:Two hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:Two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have ALL even (being multiple of 8) Probability of number selected being odd = Total Odd Numbers / Total available numbers Probability = 100/500 = 0.2 = 20% Answer: Option A #### A QUESTION:A and B form a study group and divide a 75 question study guide. If A answer 7 questions per hour, while B answer 5 every hour, what fraction of the study guide is incomplete after 4 hours? options: A)48/75 B)20/75 C)27/75 D)28/75 E)16/75 SOLUTION:Number of questions A can answer per hour: 7 Number of questions B can answer per hour: 5 Number of questions A and B can answer per hour: 7+5=12 Number of questions A and B can answer in 4 hours: 4x12=48 Fraction of the study guide that is incomplete = 1-48/75=27/75 Answer is C #### C QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day? options: A)18 B)9 C)10 D)8 E)11 SOLUTION:We have, M1D1H1 = M2D2H2 So, 9*12*4= 6*D2*8 D2 = 9*12*4/6*8 = 9 ANSWER:B #### B QUESTION:A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 8, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? options: A)20 B)22 C)24 D)27 E)30 SOLUTION:Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes Answer: D. #### D QUESTION:If 7a = 2b = 15, then 42ab = options: A)75 B)125 C)675 D)1100 E)1250 SOLUTION:7a * 2b = 15 * 15 = 225 14 ab = 225 i.e. 42 ab = 675 Answer: Option C #### C QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money? options: A)1500 B)1800 C)2100 D)1950 E)2200 SOLUTION:P = 15(100/10)2 => P = 1500 ANSWER:A #### A QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance? options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr SOLUTION:Total distance traveled = 100+200+300+100 = 700km Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs Average speed = 700/16.67 = 42km/hr approximately ; Answer is B #### B QUESTION:There are 680 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? options: A)425 B)345 C)375 D)380 E)400 SOLUTION:In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 680. Hence 3x + 5x = 680 Solve for x 8x = 680 x = 85 Number of boys 3x = 3 × 85 = 255 Number of girls 5x = 5 × 85 = 425 A #### A QUESTION:A and B are working on an assignment. A takes 6 hours to type 32 pages on a computer, while B takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)2 hours B)5 hours C)6 hours D)8 hours E)3 hours SOLUTION:Number of pages typed by A in one hour=32/6=16/3 Number of pages typed by B in one hour=40/5=8 Number of pages typed by both in one hour=((16/3)+8)=40/3 Time taken by both to type 110 pages=110*3/40=8 hours. Answer : D. #### D QUESTION:There are 3 people A,B & C. Rs.700 is divided among A,B & C so that A receives 1/2 as much as B and B 1/2 as much as C. What is the C's share is? options: A)Rs.100 B)Rs.200 C)Rs.400 D)Rs.500 E)Rs.550 SOLUTION:Let C's share = Rs.x. Then B's share = Rs.x2 And, A's share = Rs.x4 A:B:C = x4:x2:x=1:2:4 Hence, C's share = Rs.(700×47) = Rs.400 C #### C QUESTION:Marge has C candies, where C is an integer such that 20 <C< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children? options: A) 0 B) 1 C) 2 D) 3 E) 4 SOLUTION:If Marge divides the candies equally among 5 children, she will have 2 candies remaining. This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47 If she divides the candies among 6 children, she will have 1 candy remaining. this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49 ONLY 37 is common, so candies are 37 in number.. if 37 is divided in 7 kids, remainder C= 2 C #### C QUESTION:A man can row upstream at 29km/hr and down stream at 15km/hr find mans rate of the current ? options: A)9.8km/hr B)3.6km/hr C)8.9km/hr D)7km/hr E)5.9km/hr SOLUTION:given upstream(u) =29km/hr down stream (v)= 15km/hr rate of the current =1/2(u-v) =1/2(29-15)=7km/hr Answer is (D) #### D QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree. From the diagram, (36−x)2=x2+122(36−x)2=x2+122 ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144 ⇒72x=1296−144⇒72x=1296−144 ⇒x=16 Answer:A #### A QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only? options: A)24 B)27 C)30 D)33 E)36 SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only. Since 10% of students are in both, then 70% of students are in the band which is 84 students. The number of students in the orchestra is (30/70)*84 = 36. The answer is E. #### E QUESTION:If x is a sum of all even integers on the interval 13...55 and y is their number, what is the GCD (x, y)? options: A) 1 B) 21 C) 26 D) 52 E) 1014 SOLUTION:x = 14 + 16 + ... + 54 = (largest + smallest)/2 *(# of terms) = (14 + 54)/2*21= 34*21. GCD of 21 and 34*21 is 21 Answer: B. #### B QUESTION:Ed throws a blue die and a red die. How many combinations are there in which the two dice do not yield the same result and the sum of the results is not 9? options: A)10 B)24 C)26 D)30 E)36 SOLUTION:Total number of combination is 6*6 = 36.. Condition 1: we shouldn't get the same number... (1,1)(2,2)(3,3)(4,4)(5,5)(6,6) - 6 combinations. condition 2: We shouldn't get the 9 as the sum (4,5)(5,4)(3,6)(6,3) - 4 combinations... Total = 36 - 10 = 26. ANS option C. #### C QUESTION:Thompson had the following scores in an exam (out of 100): Social Studies: 60 Science: 89 Art: 62 Music: 69 Spanish:84 Biology: 89 What are his average marks ? options: A)61.5 B)72.5 C)71.5 D)85.5 E)75.5 SOLUTION:Explanation: Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75. Answer: E) 75.5 #### E QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:a dealer buys 4 varieties of wheat costing rs. 20,rs.25,rs.30 and rs.35 per kg in the ratio 6:4:3:1 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of wheat? options: A)30.5 B)31.0 C)32.0 D)33.0 E)34.5 SOLUTION:CP = 20*6+25*4+30*3+35*1=345 SP = 1.4*345=483 Total no.of kgs=6+4+3+1=14 SP per kg=483/14 = 34.50 ANSWER:E #### E QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:If 4 men and 1 boy working together, can do two times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:4M + 1B =2(1M + 1B) 4M + 1B = 2M + 2B 2M = 1B The required ratio of work done by a man and a boy = 1:2 D #### D QUESTION:Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X? options: A)1:1 B)2:3 C)5:2 D)4:3 E)None of these SOLUTION:Explanation : Let,the actual amount of A and B be 4x and 3x respectively. Amount of 1st basic element in the new alloy T is (5/8)*4x + (1/3)*3x = (7x)/2. Similarly, the amount of 2nd basic element in the new alloy T is (3/8)*4x + (2/3)*3x= (7x)/2. So, the ratio of 1st basic element to 2nd basic element is [(7x)/2 ] / [ 7x/2] = 1/1 = 1:1. Answer : A #### A QUESTION:A 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)500 B)350 C)828 D)277 E)122 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/489 = 50/3 3x + 900 = 2400 => x = 500 m. Answer: A #### A QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:Calculate the largest 3 digit number which is exactly divisible by 89? options: A)911 B)969 C)979 D)977 E)971 SOLUTION:Largest 4 digit number is 999 After doing 999 ÷ 89 we get remainder 20 Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 C #### C QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)50 B)78 C)267 D)29 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 500 ---------------- C = 50 Answer: A #### A QUESTION:If p and q are two different prime numbers, which of the following cannot be true? options: A)pq is odd. B)p + q is even. C)p + q is odd. D)pq is even. E)p/q is an integer SOLUTION:A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (p/q=integer means that p is a multiple of q). Answer: E. All other options are possible: A. pq is odd --> p=3 and q=5; B. p + q is even --> p=3 and q=5; C. p + q is odd --> p=2 and q=3; D. pq is even --> p=2 and q=3; E #### E QUESTION:A is 16th position and 29th from down of the people who passed. 5 failed , 6 didn't give . how many boys are there in the class? options: A)52 B)53 C)54 D)55 E)56 SOLUTION:A is 16th position, means = 15 + A 29th from down, means = A + 28 Total passed = A + 15 + 28 = 44 Total failed = 5 Didn't give = 6 Therefore, total boys = 44 + 5 + 6 = 55 ANSWER:D #### D QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60 total S=84 outcomes D #### D QUESTION:In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is : options: A)35 B)38 C)40 D)42 E)44 SOLUTION:Explanation: Let the number of correct answers be X. Number of incorrect answers = (60 – X). 4x – (60 – x) = 140 => 5x = 200 => x = 40 Answer: C #### C QUESTION:The side of a square is increased by 25% then how much % does its area increases? options: A)56.75 % B)56.25 % C)53.85 % D)57.25 % E)56.21 % SOLUTION:a = 100 a2 = 10000 a = 125 a2 = 15625 ---------------- 10000 --------- 5625 100 -------? => 56.25 % Answer:B #### B QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 190 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)19 D)33 E)25 SOLUTION:C 19rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 Thus our anniversary falls on the 19rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### C QUESTION:In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class? options: A)1/2 B)1/3 C)2/3 D)1/4 E)3/4 SOLUTION:(1/2)G=(1/3)(B+G) 3G=2B+2G G=2B B/G=1/2. The answer is A. #### A QUESTION:If E is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of E? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:E = 30! 8 E = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 So we have a total of 14 three's ... Therefore the maximum value of K can be 14 (C) #### C QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)120% B)190% C)100 percent D)200% E)101% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by: I. 12 II. 24 III. 48 options: A)I B)I & III C)II D)II & III E)III SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24. So answer is III Answer : E #### E QUESTION:For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? options: A)18.1 B)21.1 C)36.5 D)42.2 E)84.4 SOLUTION:Let x and z be the smallest and largest of the original set, respectively. z - x = 84.4 The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4. Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1 The answer is B. #### B QUESTION:Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them? options: A)5/7 B)5/3 C)5/1 D)5/6 E)5/2 SOLUTION:P(at least one graduate) = 1 - P(no graduates) = 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6 Answer: D #### D QUESTION:By selling an article for $180, a person gains $30. What is the gain %? options: A)25% B)30% C)50% D)20% E)10% SOLUTION:S.P. = $180 Gain = $30 C.P. = 180-30 = 150 Gain% = 30/150 * 100 = 20% Answer is D #### D QUESTION:Company X provides bottled water to its employees in 5 liter bottles, $2 each. At least how many 5L bottles must Company X buy monthly, so that new contract with $100 fixed monthly rate and $1 for 10L bottle each paid off? (Assume that no other costs apply) options: A) 121 B) 125 C) 132 D) 134 E) 138 SOLUTION:let the no. of 5 liter bottles be x, so the no. of 10l bottles will be x/2 (to equate the vol.) since the total cost will be equal , 2x= 100+x/2 so x= 133.33 or 134. Answer is (D). #### D QUESTION:Pomes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows? options: A)40 minutes. B)1 hour and 30 minutes. C)1 hour. D)1 hour and 40 minutes. E)2 hours and 15 minutes. SOLUTION:Rate =Output/Time Pomes Rate=25/20=5/4 Dylan Rate=25/60=5/12 Combined rate = 5/4+5/12= 20/12 CombinedRate*CombinedTime= CombinedOutput 20/12*t=150 t=90 mins => 1 hr 30 min #### C QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33*100 = 180% of 3.33. Answer: E. #### E QUESTION:The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? options: A)240 B)270 C)295 D)360 E)300 SOLUTION:Explanation: Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Smaller number = 270. ANSWER IS B #### B QUESTION:At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes? options: A)2150 B)2600 C)3120 D)1500 E)1895 SOLUTION:Winner votes = 100-30 = 70 polled votes = [(100*1000)/2*70-100]+100 = 2600 Answer is B #### B QUESTION:When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 14? options: A)7 B)21 C)34 D)8 E)55 SOLUTION:So the number given is N = 143Q + 45 If this number is divided by 13, the remainder would be R[(143Q + 45)/13] Since 143 is divisible by 13 , the product 143Q gives no remainder This means the remainder of 45/13 should be the remainder of the entire number N which is 6 To make it divisible by 13 , the smallest number that can be added = 14 - 6 = 8 Correct Option : D #### D QUESTION:Set #1 = {A, B} Set #2 = {K, L, M, N, O, P} There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel? options: A)1/6 B)1/3 C)7/12 D)2/3 E)5/6 SOLUTION:So Not a vowel in Set-1 : 1/2 And not a vowel in Ser-2:5/6 Now, 1/2∗5/6=5/12 This is for not a vowel. Then for at least one vowel will be = 1−5/12=7/12 Answer will be C. #### C QUESTION:A train 330 m long passed a pole in 11 sec. How long will it take to pass a platform 760 m long? options: A)76 sec B)89 sec C)87 sec D)35 sec E)36 sec SOLUTION:Speed = 330/11 = 30 m/sec. Required time = (330 + 760)/30 = 36 sec. Answer:E #### E QUESTION:The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother? options: A)39 B)41 C)42 D)43 E)44 SOLUTION:Total age of mother and 6 children = avg x n = 9 x (6+1)= 63 If mother is excluded new average is (9 - 5) = 4 so for 6 children = 6 x 4 =24 so mother's age is 63 - 24 =39 Answer: Option A #### A QUESTION:Sheena has a pet frog and it is growing fast and eating more flies each day. When she first brought it home on Monday it ate 3 flies, Tuesday it ate 6, Wednesday it ate 9, and Friday it ate 15. How many flies did her frog eat on Thursday? options: A)12 B)14 C)10 D)11 E)13 SOLUTION:A) 12. The frog started eating 3 more flies each day. 3 +3 =6 6+3=9 9+3=12 12+3=15 #### A QUESTION:Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are options: A)4, 8, 12 B)5, 10,15 C)10, 20, 30 D)12, 24, 36 E)None SOLUTION:Solution Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So x = 12. The numbers are 12, 24, 36. Answer D #### D QUESTION:A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit C on this shipment? options: A)a) $100 B)b) $115 C)c) $125 D)d) $130 E)e) $135 SOLUTION:I recommend one should use fractions to solve this one rather than converting it into decimals Sol: 1500 heads -> $600 1 head -> $600/1500 1 head -> $(2/5) 25% more of (2/5) -> 125/100 * 2/5 = $(1/2) He sold 2/3*1500 = 1000 heads for $(1/2) per head Total revenue by selling 1000 heads = 1000 * 1/2 = $500 Heads left: 500 Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20) Total revenue by selling 500 heads = 9/20 * 500 = 225 Total revenue after selling 1500 cabbage heads - 225+500 = $725 Money spent on the purchase: $600 Profit C= 725-600 = $125 Ans:C #### C QUESTION:A tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume. If 6,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 15% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-6,000=4,000 gallons and sodium chloride is 600 gallons (6% of initial solution of 10,000 gallons) then sodium chloride is 600/4,000*100=15% of the remaining solution of 4,000 gallons. Answer: E. #### E QUESTION:One out of every 600 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment? options: A)60,000 B)5,000 C)10,000 D)50,000 E)52,000 SOLUTION:20 broken glasses indicates that 10*10= 100 defected bulbs are present. 100 defected bulbs indicates that 100*600= 60,000 light bulbs are present. A is the answer #### A QUESTION:Find the odd man out 4, 15, 40, 121, 364, 1093, 3280 options: A)4 B)15 C)121 D)364 E)3280 SOLUTION:1*3+1 = 4 4*3+1 = 13 13*3+1 = 40 40*3+1 = 121 121*3+1 = 364 364*3+1 = 1093 1093*3+1= 3280 ANSWER:B #### B QUESTION:If x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z? options: A)Y2 = xz B)Y2 = xy C)Y2 = Yz D)Y3 = xz E)Y5 = xY SOLUTION:X = (Y*NR)/100 Y = (Z*NR)/100 X/Y = NR/100 Y/Z = NR/100 X/Y = Y/Z Y2 = XZ.Answer:A #### A QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:A soccer coach is preparing his starting lineup of 11 players chosen from 15 players. He considers 8 of his players good at defense and 7 of his players good at offense. If he wants to pick 6 players best at defense and 5 players best at offense, how many different ways can he do this? options: A)264 B)328 C)460 D)588 E)642 SOLUTION:(8c6)*(7c5) [8!/(6!*2!)]*[7!/(5!*2!)] 28*21 588 D #### D QUESTION:√(36)^2 options: A)6 B)14 C)36 D)21 E)None of these SOLUTION:explanation √(36)^2 =? or, ? = 36 Answer C #### C QUESTION:The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 8, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median? I. 3 II. 7 III. 12 options: A)I only B)II only C)III only D)I and III only E)I, II, and III SOLUTION:C for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8 #### C QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)227 B)177 C)120 D)288 E)271 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m.Answer:C #### C QUESTION:If Z = 52 and ACT = 48, then BAT will be equal to options: A)33 B)88 C)77 D)46 E)99 SOLUTION:Explanation: In the given code, A = 2, B = 4, C = 6,.... , Z = 52. So, ACT = 2 + 6 + 40 = 48 and BAT = 4 + 2 + 40 = 46 Answer: D) 46 #### D QUESTION:A box contains 4 chocobars and 4 ice creams. Tom eats 3 of them, by randomly choosing. What is the probability of choosing 2 chocobars and 1 icecream? options: A)9/3 B)1/7 C)2/8 D)2/7 E)4/7 SOLUTION:Probability of choosing 1 chocobar = 4/8 = 1/2 After taking out 1 chocobar, the total number is 7. Probability of choosing 2nd chocobar = 3/7 Probability of choosing 1 icecream out of a total of 6 = 4/6 = 2/3 So the final probability of choosing 2 chocobars and 1 icecream = 1/2 * 3/7 * 2/3 = 1/7 B #### B QUESTION:39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? options: A)9 B)12 C)10 D)13 E)15 SOLUTION:Explanation: Let the required number of days be x More persons, less days (indirect proportion) More hours, less days (indirect proportion) Hence we can write as (persons)39:30 (hours) 5:6}:: x:12 ⇒39×5×12=30 × 6 × x ⇒39×5×2=30 × x ⇒39=3×x ⇒x=13 Answer: Option D #### D QUESTION:A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 85, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? options: A)74 B)75 C)76 D)77 E)78 SOLUTION:ratio is 4:6:5 , numbers are 4x, 6x, 5x total scores of each class is (65*4x + 6x * 85 + 77*5x) = 260x+510x+385x = 1155x total number of students = 15x average = 1155x/15x = 77 D is the answer #### D QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:16, 23, 19, 19, 22, 15, 25, ? What number should replace the question mark? options: A)13 B)11 C)16 D)18 E)19 SOLUTION:B 11 There are two alternate sequences: +3 and –4; #### B QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other? options: A)1.5 hours B)1.27 hours C)1.73 hours D)2 hours E)1.69 hours SOLUTION:The cars travel (145+150=295) miles in one hour. 500 miles/295 miles/hour= 1.69 hours Answer is E #### E QUESTION:A tiger is chasing its prey at a constant speed. It entire body passes a blade of grass in 1 second. It then runs above a fallen tree trunk that is 20 meters long in 5 seconds. What is the length of the tiger? options: A)6 m B)5 m C)4 m D)3 m E)None of the above SOLUTION:Sol. Let the length of the tiger be x metres and its speed be y m/sec. Then, x / y = 1 ⇒ y = x ∴ (x + 20) / 5 = x ⇔ x = 5 m. Answer B #### B QUESTION:The average age 8 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)12 years B)14 years C)18 years D)16 years E)26 years SOLUTION:8 * 2 = 16 years ANSWER:D #### D QUESTION:Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 8 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score? options: A)24 B)30 C)40 D)50 E)60 SOLUTION:One way to do this would be weighted average method.. 1) let the average of 5 mocks be x... so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67... By alligation/weighted average.. the difference in 760 and 726.67 is 5/6 of difference of 760 and x.. 760-726.67 = 5/6 * (760-x) 760-x= 33.33*6/5=40... so x = 720.. the last of mock test will be 720+8+8=736... so ans = 760-736=24 A #### A QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6? options: A)300 B)992 C)772 D)552 E)280 SOLUTION:1/3:1/3:1/6 = 2:2:1 1/5*1400 = 280 560-280 = 280 Answer: E #### E QUESTION:A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute? options: A)1,200 meters / minute B)1,300 meters / minute C)1,450 meters / minute D)1,550 meters / minute E)1,650 meters / minute SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 72 kilometers per hour = 72 km/hr = (72 * 1000 meters) / (60 minutes) = 1,200 meters / minute correct answer A #### A QUESTION:If c is 20% of a and 10% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 200% SOLUTION:Answer = E 20a/100 = 10b/100 b = 20a/10 = 200a/100 = 200% #### E QUESTION:Two numbers when divided by a divisor leave remainders of 238 and 362 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor. options: A)276 B)552 C)414 D)1104 E)2202 SOLUTION:Let x be the divisor. N1 = xa + 238 N2 = xb + 362 N1 + N2 = x(a+b) + 600 = xc + 68 x(c-a-b) = 532 but we know that x>362, thus (c-a-b) must equal 1. The answer is B. #### B QUESTION:The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x? options: A)0.03 B)0.04 C)0.048 D)0.05 E)0.12 SOLUTION:Probability of Brand A defective is x Probability of Brand B defective is 0.06 which 6/100. Which tells you there are 2 defective piece in a lot of 33, for 35 lot it is approx - 2.12 Probability of Brand C defective is 0.08 which 8/100. Which tells you there are 2 defective piece in a lot of 25 Total = 40 + 25 + 25 = 100 Probability of having defective piece in a lot of 100 ( All brands ) = 0.053 Hence 5.3 defective piece out 100 lot. So 40x + 2.12 + 2 = 5.3 x = 0.03 ANSWER :Opt A. #### A QUESTION:a, b, c and d are four consecutive numbers. If the sum of a and dis 111, what is the product of b and c? options: A)2652 B)2578 C)2534 D)3080 E)4234 SOLUTION:Here d = a + 3 a + a + 3 = 111 2a = 108 a = 54 So, numbers are 54, 55, 56 and 57 ∴ b × c= 55 × 56 = 3080 D #### D QUESTION:The forth proportional to 6,8,15 is? options: A)15 B)12 C)18 D)20 E)24 SOLUTION:Let the fourth proportional to 6,8,15 be x then 6:8::15:x 6x = 8*15 x = 20 Answer is D #### D QUESTION:If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true? I. a + b + c > a^3 II. a × b × c < a^3 III. 5b > bc options: A)I only B)II only C)III only D)II and III E)I, II, and III SOLUTION:Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4 Putting the values in the answers only 'A' seems valid. #### A QUESTION:An article is bought for Rs.600 and sold for Rs.500, find the loss percent? options: A)16 2/5% B)16 8/3% C)16 2/7% D)16 2/3% E)12 2/3% SOLUTION:600 ---- 100 100 ---- ? => 16 2/3% Answer: D #### D QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P? options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36 SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house. J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs Answer:B #### B QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 3 days at a time. If A starts they finish the task in exactly 9 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)8 B)6 C)4 D)5 E)9/2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 6No. of days when B works = 3 → 6x + 3y = 1 When B starts: No. of days when A works = 4 No. of days when A works = 5 → 5x + 4y = 1 Solving the above two equations for xy x = 1/9 y = 1/9 → Total work done by AB in a day = 1/9 + 1/9 = 2/9 → No. of days to complete the work when both work together = 9/2; Answer: E #### E QUESTION:A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers? options: A)700; 1100 B)1072; 528 C)1000; 800 D)1200; 800 E)None of the above SOLUTION:The method given above is the one given in the book. However the method I used was (1*x*5)/100 + (1600-x)*6/100 = 1600*5.67/100 Simplifying we get x= 528 B #### B QUESTION:Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 50 years. The age of E is? options: A)50 B)47 C)48 D)49 E)46 SOLUTION:Solution 5 years ago average age of A,B,C,D = 45 years => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years => Total present age of A, B, C, D = 180 + 5x4 = 200 years If E's present age is x years = 200+x/5= 50 x=50 years. Answer A #### A QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:For: (2^(3x+3)+3)/3 Let n = 3x + 3 2^n 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, .... Rule: x^(m+n) = (x^m)(x^n) (2^(3x))(2^3) Rule: x^(mn) = (x^m)^n ((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1. Answer: B #### B QUESTION:A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A options: A)26.2 km B)25.7 km C)23.2 km D)26.67 km E)None of these SOLUTION:Explanation: Distance travelled by each of them is to be made equal. => Distance travelled walking = Distance covered cycling. Let after 4 hours of walking, A walk for x hours more before B catches up with him. => Distance = Speed * Time (4+x)4 = 10x x = 8/3 Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67 ANSWER: D #### D QUESTION:69 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? options: A)20 B)23 C)24 D)25 E)26 SOLUTION:According to the chain rule, M1 x T1 = M2 x T2 Therefore, 69 x 12 x 5 = 30 x 6 x X X = 23 Hence, the number of days = 23. ANSWER:B #### B QUESTION:A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn? options: A) 188 B) 258 C) 376 D) 470 E) 517 SOLUTION:consider 5x acres of land used for bean consider 2x acres of land used for wheat consider 4x acres of land used for corn Total given is 1034 acres 11x =1034 x = 94 land used for corn Y= 4 * 94 = 376 correct option - C #### C QUESTION:Calculate the ratio between x and y if 30% of x equal to 50% of y? options: A)4 : 5 B)3 : 5 C)3 : 7 D)3 : 2 E)4 : 5 SOLUTION:Explanation: 30 x = 50 y x: y = 30: 50 = 3 : 5 Answer:B #### B QUESTION:David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture? options: A)9! B)9×8! C)4x5! D)10!/2! E)10! SOLUTION:In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!*2! ways. Total - Restriction = = 6! - 5!*2! = = 5!(6- 2!) = = 4*5!. Answer: C. #### C QUESTION:What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:the number of 7s in 21!= 21/7=3.. ans B #### B QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 231525, then population in 1978 was? options: A)120000 B)120029 C)187899 D)178968 E)200000 SOLUTION:X * (105/100) * (105/100) * (105/100) = 231525 X = 231525/1.157625 X = 200000 Answer:E #### E QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:5 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this?? options: A)360 B)430 C)510 D)540 E)630 SOLUTION:we have to choose one from each set. 1 from 5 nouns and 1 from 4 verbs and 1 from 3 adjectives. then we have to arrange 3 different sets in 3! ways. so, 5c1*4c1*3c1*3!=360 ANSWER:A #### A QUESTION:A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y? options: A)(320 - y)/(5x) B)(y +220)/(5x) C)5(80 - y)/(4x) D)(y + 400)/(4x) E)(4y + 320)/(5x) SOLUTION:Ans B Plug some numbers Let y = 40 houses and x = 20 then they painted 20 houses per week as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20 = 65 houses per week total time they took = (40/20) + (40/65) = 2.6 weeks Putting the values of x and y in equation B (y +220)/(5x) = (40+220)/5*20 = 260/100 = 2.6 #### B QUESTION:In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:8/7 * 24 = 27.4 The answer is B. #### B QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:A 470 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? options: A)41.1 sec B)64.8 sec C)31.8 sec D)50.4 sec E)none of the above SOLUTION:Speed = 55 Km/hr (to convert km/hr in to M/s) = 55 x 5/18 M/s Distance = 470 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, ) = 990 m Time = Distance / Speed = 990 x 18 / (5 x 55) = 64.8 sec Ans is :B #### B QUESTION:in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 9 people all together .how many people can sit in a bus? options: A)52 B)49 C)95 D)90 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 27*3=81 People can seat in Last Seat = 9 Total People can seat= 81+9=90 ANSWER:D #### D QUESTION:There are 7 players in a bowling team with an average weight of 94 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? options: A)75 Kg. B)80 Kg. C)86 Kg. D)90 Kg. E)92 Kg. SOLUTION:The New average will be= (94*7+110+60)/9= 92 kgs E is the answer #### E QUESTION:The first three terms of a proportion are 3, 9 and 12. The fourth term is? options: A)22 B)28 C)27 D)36 E)88 SOLUTION:(9*12)/3 = 36 Answer:D #### D QUESTION:If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)? options: A)9. B)12. C)15. D)16 E)18. SOLUTION:Expand this to get: (2X + Y)(2Z + W) = 4XZ + 2XW + 2YZ + YW = 4 XZ + YW + 2XW + 2YZ [I rearranged the terms] = 3 + 2XW + 2YZ [replaced 4XZ + YW with 3] = 3 + 2(XW + YZ) factored out a 2 = 3 + 2(6) = 3 + 12 = 15 ANSWER:C #### C QUESTION:In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions? options: A)63 B)48 C)85 D)52 E)47 SOLUTION:In the given word there 6 letters in that there are 2 vowels and 4 consonants no of ways of arranging the vowels=2p2=2 no of ways of arranging the consonants=4p4=24 total number of ways 24*2=48 Answer(B) #### B QUESTION:The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n − 1)(n − 2)...3.2.1 is not divisible by n is options: A)5 B)7 C)13 D)14 E)16 SOLUTION:Explanation : (n-1)! is always divisible by n unless and untill n is a prime number e.g.(5-1)!=4! which is not divisible by 5 bcuz 5 is a prime number Therefore, find all prime numbers in the range of 12 to 40 i.e 13, 17, 19, 23, 29, 31 and 37 Hence, the number of positive integers n is 7. Answer : B #### B QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full? options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes SOLUTION:1/20 - 1/40 = 1/40 40 minutes Answer:C #### C <<<Examples ends QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:If it were a line/column combination/permutation problem, the solution would be : 5! = 120. However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24. ANS:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? options: A)18 B)16 C)26 D)17 E)11 SOLUTION:Explanation: 1500 ---- 390 100 ---- ? => 26% Answer:C #### C QUESTION:The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs. 3. The ratio of the two selling prices is? options: A)52:56 B)52:53 C)52:50 D)54:53 E)52:51 SOLUTION:Let C.P. of the article be Rs. x. Then, required ratio = 108% of x / 106% of x = 108/106 = 54/53 = 54:53 Answer: D #### D QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest? options: A)49% B)90% C)60% D)40% E)41% SOLUTION:8 = (1*20*R)/100 R = 40% Answer:D #### D QUESTION:A and B go around a circular track of length 900m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point? options: A)120 sec B)165 sec C)186 sec D)180 sec E)168 sec SOLUTION:Time taken to meet for the first time at the starting point = LCM { length of the track / speed of A , length of the track / speed of B} = LCM { 900/ (36 * 5/18) , 900/ (54 * 5 /18) } = LCM (90, 60) =180 sec. Answer:D #### D QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: options: A)5:4 B)4:5 C)2:5 D)5:2 E)None of them SOLUTION:Let the third number be x. Then, first number = 120% of x = 120x/100 = 6x/5 Second number = 150% of x = 150x/100 = 3x/2 Therefore, Ratio of first two numbers = (6x/5 : 3x/2) = 12x : 15x = 4 : 5. Answer is B. #### B QUESTION:The average age of a group of 12 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group? options: A)22 years B)30 years C)34 years D)32 years E)None of these SOLUTION:Answer The average age of a group of 12 students is 20. Therefore, the sum of the ages of all 12 of them = 12 * 20 = 240 When two new students join the group, the average age increases by 2. New average = 22. Now, there are 14 students. Therefore, the sum of the ages of all 14 of them = 14 * 22 = 308 Therefore, the sum of the ages of the two new students who joined = 308 - 240 = 68 And the average age of each of the two new students = 68/2 = 34 years. Answer C #### C QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10200 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv) Subtracting (ii) from (iv), we get, P = 4050. P's monthly income = Rs.4050. Answer: A #### A QUESTION:Find the least number must be subtracted from 11070 so that remaining number is divisible by 22. options: A)2 B)3 C)4 D)7 E)8 SOLUTION:On dividing 11070 by 22 we get the remainder 4, so 4 should be subtracted. Answer is A. #### A QUESTION:If x=kc and y=kt,then 2y+x =? options: A)k(t-c) B)k(c-t) C)c(k-t) D)k(2t+c) E)k(1-t) SOLUTION:Just put in the given values of y and x 2y +x =2 kt +kc Now take k common 2y + x = k(2t +c) You get (D) as your answer. #### D QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds? options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these SOLUTION:First cart speed will be 24/3=8 Second cart speed is 120/2=60 So, ratio is 8/60=2/15 ANSWER:A #### A QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E? options: A)60 B)80 C)40 D)120 E)160 SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30 (9/8)x - (3/4)x = 30 x = 80=E Answer: B #### B QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 8 sec, then the speed of each train is? options: A)54 B)77 C)36 D)88 E)21 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/8 => x = 15 Speed of each train = 15 m/sec. = 15 * 18/5 =- 54 km/hr.Answer: A #### A QUESTION:Company A imported 10,500 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 20 percent are painted red and 40 percent are painted blue how many brass widgets painted green were imported? options: A)480 B)840 C)1050 D)420 E)2100 SOLUTION:Answer A. We are told that 10% of all imported widgets are made of brass and of those, 20% are red and 40% are blue. Since we know that there are only three colors, the remaining 40% must be green. 40% blue of 10% brass widgets leads to 4% green brass widgets out of the total 10,550 widgets. 10,500 /100 * 4 = 420. Answer D. #### D QUESTION:Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops? options: A)white − wheat − wheat B)wheat − wheat − rye C)rye − white− wheat D)rye − rye − rye E)rye − rye − white SOLUTION:In a single round Lucy drops 6 morsels. Remainder (2000/6) = 2 Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated Answer: A #### A QUESTION:The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by? options: A)2.0% B)3.2% C)3.9% D)4% E)5.1% SOLUTION:Net growth on 1000 = 32-10 = 20 Net growth on 100 = 20*100/1000 = 2.0% Answer is A #### A QUESTION:A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to options: A)the same as one 45 percent discount B)the same as one 38 percent discount C)the same as one 36 percent discount D)the same as one 30 percent discount E)the same as one 28 percent discount SOLUTION:0.9*0.8*x=0.72x from initial value, meaning 0.28 or 36% discount E #### E QUESTION:Jim and Reneey will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneey have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win? options: A)5/6 B)2/3 C)1/2 D)5/12 E)1/3 SOLUTION:1/3 probability of jim winning is basically the sum of three probabilities: probability of jim picking rock and reneey picking scissors = 1/3*1/3 = 1/9 probability of jim picking scissors and reneey picking paper = 1/3*1/3=1/9 probability of jim picking paper and reneey picking rock = 1/3*1/3=1/9 1/9 + 1/9 + 1/9 = 3/9 = 1/3=E #### E QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C QUESTION:The avg. age of a group of 28 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is? options: A)22 years B)23 years C)24 years D)25 years E)28 years SOLUTION:Total age of 28 students=28*20=560 If total age of 4 students=x Then, (560+x)/(28+4) =(20+1), x=112 So average age of new students=112/4= 28 years ANSWER:E #### E QUESTION:For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive? options: A)None B)One C)Two D)Three E)Four SOLUTION:$ is basically a factorial of a number. So, we are asked to find the number of primes between 7!+2 and 7!+10, inclusive. From each number 7!+k were 2≤k≤102≤k≤10 we can factor out k, thus there are no pries in the given range. For example: 7!+2=2(3*4*5*6*7+1) --> a multiple of 2, thus not a prime; 7!+3=3(2*4*5*6*7+1) --> a multiple of 3, thus not a prime; ... 7!+10=10(3*4*6*7+1) --> a multiple of 10, thus not a prime. Answer: A. #### A QUESTION:How many ways are there for 4 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall? options: A)48 B)12 C)72 D)100 E)720 SOLUTION:So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 4 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 4! different ways, so total 2*4!=48. Answer A. #### A QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday SOLUTION:This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B #### B QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform? options: A)240 B)188 C)177 D)260 E)320 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Length of the train = 20 * 20 = 400 m. Let the length of the platform be x m . Then, (x + 400)/36 = 20 => x = 320. Answer: E #### E QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)1 years B)7 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 36 years. Father's age when Ayesha's brother was born = (38 + 4) = 42 years. Required difference = (42 - 36) = 6 years. Answer: C #### C QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 2050*5=10250 10250-10000=250 Answer E #### E QUESTION:Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%. options: A)429.3 B)270 C)177 D)166 E)111 SOLUTION:Explanation: Cost of each share = (20 + 2.5% of 20) = Rs.20.5 Therefore, number of shares = 8800/20.5 = 429.3 ANSWER:A #### A QUESTION:The first train leaves the station at 7:00 am with a speed of 60 km/hr. The second train leaves at 8:30 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)11:00 am B)12:00 noon C)1:00 pm D)2:00 pm E)3:00 pm SOLUTION:In ninety minutes, the first train travels 90 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train in 4.5 hours. The second train will catch the first train at 1:00 pm. The answer is C. #### C QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)81.6 B)88.6 C)81.1 D)81.5 E)81.2 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer: A #### A QUESTION:A family pays $700 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? options: A)$1,000 B)$1,200 C)$1,500 D)$1,800 E)$2,200 SOLUTION:Assuming the medical expenses are $1000 or more, the family pays $700 + $400 = $1100. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $500 when the medical expenses are $1500. The answer is C. #### C QUESTION:A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color? options: A)49/153 B)18/153 C)49/153 D)40/153 E)24/72 SOLUTION:Explanation: Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random. Therefore, n(S) = 18C2 = 153 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 49/153 ANSWER:A #### A QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination. options: A)15 B)21 C)17 D)19 E)21 SOLUTION:Total Money = Rs. 10350. Let 50 rupees note was X. Then 500 rupees note = 36 - X Now, 50*X + 500 * (36 - X) = 10350 50X + 18000 - 500X = 10350 - 450X = - 7650 X = 17. No. of 50 rupees note = 17. Answer: Option C #### C QUESTION:A and B can do a work in 8 days, B and C can do the same work in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days? options: A)7 B)6 C)5 D)8 E)9 SOLUTION:Let the total units of work be 48. Units of work completed by A and B in one day = 6. Units of work completed by B and C in one day = 4 Units of work completed by A, B, and C in one day = 8. From the above information we get the work completed by A and C in one day is 6 units. Therefore, the number of days taken by A and C to complete the whole work = 48/6 = 8 days. ANSWER:D #### D QUESTION:David invested certain amount in three different schemes. A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B? options: A)5000 B)2787 C)2679 D)2790 E)2712 SOLUTION:Let x, y and z be the amount invested in schemes A, B and C respectively. Then, (x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200 10x + 12y + 15z = 320000 Now, z = 240% of y = 12/5 y And, z = 150% of x = 3/2 x x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y 16y + 12y + 36y = 320000 y = 5000 Sum invested in scheme B = Rs. 5000.Answer: A #### A QUESTION:A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:13 C)23:12 D)11:9 E)11:10 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only. A : B 8000*18 : (8000*8) + (4000*10) 144000 : 104000 A:B = 18:13 ANSWER:B #### B QUESTION:If 75 percent of a class answered the first question on a certain test correctly, 30 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? options: A)25% B)(8) 20% C)30% D)50% E)65% SOLUTION:I didn't understand how to connect 20 percent with the whole equation. Why 20 is out of the percentile diagram (circles) but inside of 100? 20% appeared in the exam; however did not answer Question AQuestion B correctly So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose I am doing it this way: Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both. Now, 100 - [(75 - x) + x + (30 - x)] = 20 .......... values are in percent x = 20 - 100 + 105 x = 25 Ans: A #### A QUESTION:The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will options: A)(a) remain the same B)(b) decrease by 13.64% C)(c) decrease by 15% D)(d) decrease by 18.75% E)(e) decrease by 30% SOLUTION:Length (L) = 12 Breadth (B) = 4 Height (H) = 4 Total Area of Walls = 2(BH + LH) = 2*(4*4 + 12*4) = 2*(16+48) = 128 Then, Finally Length (L) = 2*12 = 24 Breadth (B) = 4/2 = 2 Height (H) = 4/2 = 2 Total Area of Walls = 2(BH + LH) = 2*(2*2 + 24*2) = 2*(4+48) = 104 % change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area i.e. % change in Area of four walls = (104-128)*100 /128=- 18.75% (Decrease) Answer: Option D #### D QUESTION:Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is? options: A)10 B)30 C)40 D)50 E)60 SOLUTION:Let the numbers be 3x,4x and 5x their L.C.M. = 60x 60x =600 x = 10 The numbers are 3*10 , 4*10 , 5*10 Hence required H.C.F. = 10 Answer is A #### A QUESTION:In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:Let x be the number of cars and let y be the number of cars parked illegally. 4%*x = 20%*y y/x = 1/5 = 20% The answer is A. #### A QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)100/3% loss C)50/3% profit D)100/3% loss E)200/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss ANSWER IS A #### A QUESTION:Let N = 18p, where p is a prime number greater than 2. How many odd numbers divide N? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We start by factoring 18. 18 = 2*9 = 6*3 = 2*3*3. Since p is a prime number greater than 2 it must be odd. Therefore 3, 9, and p are the odd numbers that divide N. There are three odd divisors and the answer is therefore C. #### C QUESTION:A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. options: A)45 kmph B)50 kmph C)85 kmph D)60 kmph E)70 kmph SOLUTION:Explanation: Let the speed of the train be x kmph. Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec. Therefore 150/((x+5)×5/18)=6 <=> 30 (x + 5) = 2700 <=> x = 85 Speed of the train is 85 kmph. Answer: Option C #### C QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)22 B)88 C)27 D)20 E)98 SOLUTION:Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D #### D QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 8 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 5 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 8 days; So for 4 days, it will be = 8 x 5 / 4 = 10 So, 10-5 = 5 Answer A #### A QUESTION:If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1, then what is the value of abc/def ? options: A) 27/4 B) 27/8 C) 3/4 D) 3/2 E) 1/4 SOLUTION:Say a = 2. Then: a/b = 1/3 --> b = 6; b/c = 2 --> c = 3; c/d = 1/2 --> d = 6; d/e = 3 --> e = 2; e/f = 1 --> f = 2. abc/def = (2*6*3)/(6*2*2) = 3/2. Answer: D. #### D QUESTION:If two-third of a bucket is filled in one minute then the time taken to fill the bucket completely will be . options: A)90 seconds B)70 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 1 mint 1/3 filled in 1/2 mint thn 2/3+1/3=1 in mint 60 sec+30 sec=90 sec ANSWER:A #### A QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? options: A)10,573 B)11,908 C)12,322 D)13,924 E)14,537 SOLUTION:The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9. The answer is D. #### D QUESTION:Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 res. The ratio in which these two mixtures be mixed to get a new mixture containing milk and a water in the ratio 9:4? options: A)2:8 B)2:1 C)2:2 D)2:3` E)2:7 SOLUTION:Step (i) : Let C.P. of milk be Re.1 Given ratio of mixture in A = 8:5  Milk in 1 lit mixture in A = 8/13 lit  C.P of 1 lit mixture in A = Rs. 8/13 Ratio of Mixture in B = 5:2  milk in 1 litre mixture in B – 5/7 lit  C.P of 1 lit mixture in B = Rs. 5/7 Ratio of new mixture = 9:4  milk in 1 lit mixture = 9/13 C.P of 1 lit mixture = Rs/ 9/13 (Mean price) Step (ii) : By the rule of allegation, i. C.P of 1 liter of mixture in A =8/13 ii. C.P of 1 liter of mixture in B = 5/7 iii. Mean price (p) = 9/13 iv. d – m = 9/13 – 5-7 = 2/91 v. m – c = 9/13 – 8/13 = 1/13  Required ratio = 2/91 : 1/13 = 2:7 Answer:E #### E QUESTION:How many multiples of 5 are there between 50 and 500 ? options: A)128 B)91 C)89 D)61 E)60 SOLUTION:It should be mentioned whether 50 and 500 are inclusive. If 50 and 500 are inclusive, then the answer is (500-50)/5+1=91. If 50 and 500 are NOT inclusive, then the answer is (495-55)/5+1=89. Since OA is C, then we have NOT inclusive case. #### C QUESTION:The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE. If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE? options: A)80 yards B)82 yards C)84 yards D)85 yards E)90 yards SOLUTION:The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question. 1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle. 2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus. 3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle. 4) From (1), we know that x = 202+y2−−−−−−−√202+y2. 5) From (3), we know x = 25 - y. 6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y 7) Solving for y, we get 4.5. 8) 25 - 4.5 = 20.5 = x 9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82. The answer is B, 82 #### B QUESTION:P is 10% more efficient than Q. P can complete a work in 21 days. If P and Q work together, how many days will it take to complete the same work? options: A)7 B)9 C)11 D)13 E)15 SOLUTION:The work done by P in 1 day = 1/21 Let work done by Q in 1 day = q q × (110/100) = 1/21 q = 100/(21×110) = 10/(21×11) The work done by P and Q in 1 day = 1/21 + 10/(21×11) = 21/(21×11)= 1/11 P and Q together can do the work in 11 days. The answer is C. #### C QUESTION:For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 60, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement. options: A)K+35 B)2K+35 C)(60+K)/2 D)(70-K)/2 E)2(70-K) SOLUTION:Say Sue was hired when she was already 60 years old (k=60), then she could retire right away, at the age of 60. Now, plug k=60 in the answer choices and see which yields 60. Only C fits. Answer: C. #### C QUESTION:2. The value of x + x(xx) when x = 2 is: options: A)5 B)10 C)8 D)15 E)20 SOLUTION:x + x(xx) Put the value of x = 2 in the above expression we get, 2 + 2(22) = 2 + 2(2 × 2) = 2 + 2(4) = 2 + 8 = 10 Answer : B #### B QUESTION:If the day before yesterday was Wednesday, what day will be the day after tomorrow? options: A)Sunday B)Monday C)Tuesday D)Friday E)Saturday SOLUTION:Explanation: Day before yesterday was Wednesday =>Yesterday was a Thursday =>Today is a Friday =>Tomorrow is a Saturday =>The day after tomorrow will be a Sunday Answer: Option A #### A QUESTION:Sara works 5 days a week at d dollars per day for m weeks out of the month. Which of the following represents her monthly pay? options: A)m/(5d) B)20d C)5d D)5dm E)20d/m SOLUTION:Total income of Sara in a month = d*5*m dollars. = d*5*m = 5dm Answer is D #### D QUESTION:Jimmy has a pot of soup, and he ate 1/5 of the soup for lunch. If Jimmy ate 1/6 of the remaining soup for dinner, what fraction of the soup was left after dinner? options: A)1/2 B)2/3 C)3/4 D)4/5 E)5/6 SOLUTION:Let x be the amount of soup at the beginning. After lunch, the remaining soup was (4/5)x. After dinner, the remaining soup was (5/6)(4/5)x = (2/3)x. The answer is B. #### B QUESTION:There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)315 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 7C2 Number of ways of selecting 2 non fiction books = 6C2 7C2 * 6C2 = 21 * 15 = 315 Answer: C #### C QUESTION:What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15 options: A)3 B)5 C)7 D)8 E)9 SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Answer: Option A #### A QUESTION:Eight children — A, B, C, D, E, F, G and H — are going to sit in eight chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children? options: A)600 B)720 C)10080 D)14320 E)14800 SOLUTION:for such questions , we can treat both as one then total person=7.. these 7 can be arranged in 7! ways.. but within these 7 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080 ans C #### C QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:Find the highest common factor of 36 and 84. options: A)4 B)6 C)12 D)18 E)19 SOLUTION:36 = 22 x 32 84 = 22 x 3 x 7 H.C.F. = 22 x 3 = 12. Answer: Option C #### C QUESTION:Winson traveled the entire 60 miles trip. If he did the first 10 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour? options: A)20mph B)24mph C)30mph D)32mph E)40mph SOLUTION:Average speed=sum of distance/sum of time. If he travelled the first 10 miles at 20 miles/hr, it would take 0.5 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 60miles/(0.5+1)hrs=40miles/1hr. Therefore, the answer is E. #### E QUESTION:9886 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)2337 E)None of these SOLUTION:Answer x = 13200 - 9886 = 3314 Option: E #### E QUESTION:A division of a company consists of seven men and five women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/9 D)5/12 E)5/33 SOLUTION:First, the denominator. We have twelve different people, and we want a combination of two selected from these twelve. We will use the formula: nC2 = n(n-1)/2 which, for profound mathematical reasons we need not address here, is also the formula for the sum of the first (n – 1) positive integers. Here 12C2=12(11)/2=6*11=66 That’s the total number of pairs we could pick from the twelve employees. That’s our denominator. For the numerator, we want every combination of two from the five female employees. That’s 5C2=5(4)/2=5*2=10 That’s the number of pairs of female employees we could pick from the five. That’s our numerator. probability= 10/66 =5/55 Answer = E #### E QUESTION:A car moves at 80 km/hr. What is the speed of the car in meters per second ? options: A)20 2/9m sec B)22 2/9m sec C)24 2/9m sec D)26 2/9m sec E)28 2/9m sec SOLUTION:Explanation: Speed=(80∗5/18)m/sec =200/9m/sec =22 2/9msec Option B #### B QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock? options: A)20002 B)20000 C)20007 D)200018 E)20012 SOLUTION:Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 400 => x = 20000 Answer:B #### B QUESTION:A farmer spent $33 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined? options: A)$36.30 B)$38.50 C)$39.20 D)$39.50 E)$40.60 SOLUTION:A farmer spent 40% money on chicken feed, so he spent 0.4*$33=$13.2 on chicken feed, thus he spent the remaining 33-13.2=$19.8 on goat feed. Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$13.2 --> x=$16.5. Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 16.5+19.8=$36.3. Answer: A #### A QUESTION:At Bala's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009? options: A)700 B)1000 C)1300 D)1600 E)2000 SOLUTION:At Bala's firm's annual revenue grows twice as fast as its costs. First solve for how much revenue is increasing each year: R2008= R2007*(1+x) R2009= R2007*(1+x)^2=1.44*R2007 (1+x)^2 = 1.44 1+x=1.2 x=0.2 aka revenue increases 20% each year and cost increases 10% annually Next solve for R2007and C2007: R2007= C2007- 1000 1.2*R2007- 1.1*C2007= 0 1.2*[C2007- 1000] - 1.1*C2007= 0 0.1*C2007= 1,200 C2007= 12,000 R2007= 11,000 Finally find 2009 profits: Profit2009= 1.44*11,000 - 1.21*12,000 Profit2009= 15,840 - 14,520 Profit2009= 1320 Answer: C #### C QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 36. What is the value of x? options: A)80 B)96 C)100 D)108 E)120 SOLUTION:y = 0.5*0.5*x = x/4 y%*x = 36 (y/100)*x = 36 (x/400)*x = 36 x^2 = 36*400 x = 120 The answer is E. #### E QUESTION:There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done? options: A)144 B)180 C)192 D)360 E)None of these SOLUTION:Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options. Task 2 can be assigned to 3 or 4 So, there are only 2 options for task 2. So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6. = 2 × 3 × 4 × 3 × 2 × 1 = 144 Answer A #### A QUESTION:Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:t=4p since t = 4p thenevendivisors are: 4p/4p= 1 4p/2p= 2 4p/4= p 4p/2= 2p so the answer is (C) #### C QUESTION:At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate? options: A)134 B)178 C)195 D)166 E)194 SOLUTION:C 195 The number of votes the winning candidate received was 963 + 53 + 79 + 105 /4= 300. The second received 300 – 53 = 247, The third received 300 – 105 = 195. #### C QUESTION:There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks? options: A)5,15 B)4,15 C)5,10 D)4,10 E)5,20 SOLUTION:Assume you have locks 1-5 and keys A-E. Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum. Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D #### D QUESTION:How many different eight letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R? options: A)59 B)11!/(2!*2!*2!) C)56 D)76 E)11!/(3!*2!*2!*2!) SOLUTION:E- -R We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}. We should consider two cases: 1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR. 2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56. Total = 56 + 3 = 76. Answer: D. #### D QUESTION:A and B invests Rs.4000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1 SOLUTION:(4*6 + 8*6): (4*12) 72:48 => 3:2 Answer:C #### C QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-3 < x < 7 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -3 < x < 7 - true because x can be between -3 < x < 7 E. none of the above. Answer: D #### D QUESTION:In a lottery there are 100 prizes and 300 blanks. A lottery is drawn at random. What is the probability of getting a prize? options: A)1/2 B)5/400 C)1/5 D)1/3 E)1/4 SOLUTION:total draws = prizes+blanks= 100+300=400 probability of getting a prize = 100/400 = 1/4 correct option is E #### E QUESTION:A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is options: A)2 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(28-10) kmph = 4 kmph. Answer B #### B QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (36 + 36)*5/18 = 4*5 = 20 mps. The time required = d/s = 100/20 = 5 sec. Answer : C #### C QUESTION:How many times in a day, the hands of a clock are straight? options: A)22 B)44 C)48 D)24 E)36 SOLUTION:The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 'o clock only. Hence the hands point in the opposite directions 22 times in a day. The hands of a clock coincide(0° between them) 11 times in every 12 hours (between 11 and 1, they coincide only once, at 12 o'clock). Hence the hands coincide 22 times in a day. So In 24 hours, the hands come in opposite direction or coincide 44 times. This is already given as a formula and it's is better to learn the answer by heart as 44 which can save time in competitive exams.(However you should know the theory behind). Answer: Option B #### B QUESTION:A circle in the coordinate plane passes through points (-3, -2) and (-1, -4). What is the smallest possible area of that circle? options: A)13π B)26π C)262√π D)52π E)4π SOLUTION:The distance between the two points is sqrt(8) radius = sqrt(8)/2 Area= pi*(sqrt(8)/2)^2 E.4π #### E QUESTION:We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let x be the number of canoes. Then 2x/3 is the number of kayaks. 12x+(2x/3)*18=504 12x+12x=504 24x=504 x=21 (canoes) 2x/3=14 (kayaks) There were 21-14 = 7 more canoes rented out. The answer is C. #### C QUESTION:Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set? options: A) 87 B) 89 C) 90 D) 92 E) 95 SOLUTION:Set X = {11, 13, 17,............., 83, 89, 97} Set Y = {10, 20, 30,..............., 70, 80, 90} Combining two sets, say Set Z Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97} Range = Max Value - Min Value Range (Z) = 97 - 10 = 87 OA A is the answer. #### A QUESTION:Denise is trying to open a safe whose combination she does not know. IF the safe has 3000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one correct combination. options: A)1 B)159/160 C)157/160 D)0.875 E)0.975 SOLUTION:If Denise does not pick the correct combination in first 75 try, then the correct combination is one of remaining 2925. So Probability = 2925/3000 = 0.975. answer is E #### E QUESTION:In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together? options: A)8*9! B)8*8! C)7*9! D)9*8! E)None SOLUTION:Solution: No. of ways in which 10 paper can arranged is 10! Ways. When the best and the worst papers come together, regarding the two as one paper, we have only 9 papers. These 9 papers can be arranged in 9! Ways. And two papers can be arranged themselves in 2! Ways. No. of arrangement when best and worst paper do not come together, = 10!- 9!.2! = 9!(10-2) = 8.9!. Answer A #### A QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage? options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3% SOLUTION:Explanation: Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 33 pens = Rs. 33 Profit% = 33/99 * 100 = 33 1/3% Answer: A #### A QUESTION:(112 x 54) = ? options: A)70000 B)71000 C)72000 D)73000 E)74000 SOLUTION:(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 A) #### A QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)*100}=4% Answer is A. #### A QUESTION:For which of the following values of n is (500+n)/n NOT an integer? options: A) 1 B) 2 C) 3 D) 4 E) 5 SOLUTION:Solution: This problem is easiest solved by plugging in each answer choice. A) (500 + 1)/1 = 501/1 = 501 Answer choice A yields an integer. B) (500 + 2)/2 = 502/2 = 251 Answer choice B yields an integer. C) (500 + 3)/3 = 503/3 = 167, remainder 2 Answer choice C DOES NOT yield an integer. Although we believe answer choice C is correct, we should still test the other answer choices. D) (500 + 4)/4 = 504/4 = 126 Answer choice D yields an integer. E) (500 + 5)/5 = 505/5 = 101 Answer choice E yields an integer. Thus, the correct answer is answer choice C. #### C QUESTION:A train 225 m long passes a man, running at 10km/hr in the same direction in which the train is going, in10 seconds. The speed of the train is: options: A)81 B)90 C)91 D)85 E)96 SOLUTION:Speed of the train relative to man =225/10 m/sec =45/2m/sec. =45/2x18/5km/hr = 81 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 10 = 81 =91km/hr. Answer:C #### C QUESTION:if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr). options: A)18 kmph B)15.5 kmph C)12.5 kmph D)13.5 kmph E)22.5 kmph SOLUTION:Speed in still water = (16 + 9)1/2 kmph = 12.5 kmph. answer :C #### C QUESTION:At what time between 4 & 5 will the hands of a watch point in opposite directions? options: A)50 min past 4 B)42 5/11 min past 4 C)43 min past 4 D)40 min past 4 E)50 4/11 min past 4 SOLUTION:At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30min. spaces apart. Minute hand will have to gain 5 min. spaces. 55min spaces are gained in 60 min. 5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min. Required time = 54 6/11 min. past 4. Answer is E #### E QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches? options: A)25 B)23 C)22 D)15 E)18 SOLUTION:Area of Carol's rectangle = 24*5 = 120 Let width of Jordan's rectangle= w Since , the areas are equal 8w = 120 =>w = 15 Answer D #### D QUESTION:When 4 dice are thrown, what is the probability that the same number appears on each of them? options: A)1/36 B)1/18 C)1/216 D)1/5 E)1/4 SOLUTION:Sample space (Denominator): When 4 dice are thrown simultaneously, then the total number of possible outcomes is 64 = 1296. Event (Numerator): The chances that all the dice show same number (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)} is 6. Probability = Event/ Sample space = 6/64 = 1/63 = 1/216. ANSWER:C #### C QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)4882.40 B)8082.40 C)4002.40 D)4082.40 E)9082.40 SOLUTION:Explanation: Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40 Answer: Option D #### D QUESTION:A student is mixing oil and water as part of an experiment. The student's mixture has a 5:3 oil to water ratio. If the student used 12 more units of oil than water, how many units of water were used? options: A)14 B)18 C)19 D)22 E)24 SOLUTION:Let 5u and 3u be the units of oil and water, respectively 5u - 3u = 12 2u = 12 => u = 6 Water => 3u = 18 Answer: B #### B QUESTION:150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice? options: A)90days B)60days C)67days D)70days E)66days SOLUTION:Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day Let us say 70 men take x days to consume 150 kg. Quantity consumed by each item in x days = 7x/30 kg. Quantity consumed by 70 men in x days = (7x/30)(70)kg (7x/30)(70) = 980 x = (980 * 30)/490 => x = 60 days Answer & Answer: B #### B QUESTION:The average marks of a class of 30 students is 50 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)56.25 B)52.9 C)52.1 D)52.3 E)42.5 SOLUTION:Sum of the marks for the class of 30 students = 30 * 50 = 1500 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 80 students = 1500 + 3000 = 4500 Average marks of all the students = 4500/80 = 56.25 Answer:A #### A QUESTION:Evaluate combination 96C94=96!/(94)!(2)! options: A)6170 B)5560 C)4170 D)4560 E)None of these SOLUTION:Explanation: nCr=n!/(r)!(n−r)! 96C94=96!/(94)!(2)! =96*95*94!/(94)!(2)! =96*95/2∗1 =4560 Option D #### D QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit? options: A)Rs.2329 B)Rs.2380 C)Rs.2329 D)Rs.2320 E)Rs.2328 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 6970 * 14/41 = Rs.2380. Answer: B #### B QUESTION:45 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine? options: A)80 litres B)90 litres C)120 litres D)170 litres E)None of these SOLUTION:Explanatory Answer To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*45 = 60 litres. However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity. i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too. Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*60 = 90 litres. Answer B #### B QUESTION:What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent? options: A)6200 B)3000 C)3000 D)2000 E)1000 SOLUTION:P - 2336 = (P*10*5)/100 P = 6200 Answer: A #### A QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast? options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2 SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes. Answer: C. #### C QUESTION:Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 30ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:If each side is 120 feet..then total perimeter is 150*4=600 poles every 20 feet hence no of poles= 600/20=30 ANSWER:B #### B QUESTION:Of the 70 electronics components that a factory must manufacture, 90 percent would be most e¢ ciently manufactured by Machine A and the remaining 10 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 70 components. If 50 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently? options: A) 30 B) 32 C) 42 D) 35 E) 36 SOLUTION:A can manufacture 90 % of 70 efficiently, which is 63. B can manufacure 10 % of 70 efficiently, which is 7. Now 50 % of 70 are produced by A. This means 35 parts. Since A can produce 63 efficiently, all 35 are produced efficiently. Rest (35) is produced by B, which can produce max. 7 parts efficiently. Hence parts that were produced efficiently = 7+35 = 42. (C). #### C QUESTION:A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 8, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? options: A)20 B)22 C)24 D)27 E)30 SOLUTION:Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes Answer: D. #### D QUESTION:Which of the following is closest to (-7/8)^199？ options: A)-1 B)-1/2 C)0 D)1 E)2 SOLUTION:(-7/8)^4 = 2401/4096 which is already less than 2/3. For larger exponents, the expression will get closer and closer to zero. The answer is C. #### C QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ? options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours SOLUTION:Explanation: We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as Work done for 1 hour without leak = 1/3 Work done with leak = 3 1/2=7/2 Work done with leak in 1 hr=2/7 Work done by leak in 1 hr=1/3=2/7=1/21 So tank will be empty by the leak in 21 hours. ANSWER IS D #### D QUESTION:Shopkeeper rise price by 32% and gives successive discount of 10% and 15%. What is overall % gain or loss? options: A)0.98% B)4.98% C)3.95% D)6.98% E)7.98% SOLUTION:Let d initial price be 100 32 % rise now price = 132/100*100 = 132 10% discount Then price = 132 * 90/100 = 118.8 15 % discount Then price = 118.8 * 85/100 = 100.98 So Gain = 100.98 - 100 = 0.98 Gain % = Gain * 100 /CP ==> 0.98* 100 /100 = 0.98% ANSWER:A #### A QUESTION:AB +BA ___ 121 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)9 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. answer has to be 1 in the units digit.. only 11 fits in.. 2) BA=10B+A, and AB=10A+B.. it is given that BA+AB=121.. or 10B+A +10A+B=121.. 11(A+B)=121.. so A+B=11.. ANSWER:D #### D QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:The cost per pound of green tea and coffee were the same in June. In July, the price of coffee shot up by 100% and that of green tea dropped by 90%. If in July, a mixture containing equal quantities of green tea and coffee costs $3.15 for 3lbs, how much did a pound of green tea cost in July? options: A)$4 B)$0.1 C)$1 D)$3 E)$1.65 SOLUTION:Lets assume price of Coffee in June =100x Price of green Tea in June =100x Price of Coffee in July = 200x (because of 100% increase in price) Price of green Tea in July = 10x (because of 90% Decrease in price) Price of 1.5 pound of Coffee 1.5 pound of green Tea in July will be = 300x + 15x = 315x As per question 315x= 3.15$ x = 0.01S So the Price of green Tea in July = 10x = 10 x 0.01 = 0.1$/pound Answer B #### B QUESTION:The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 30 brand B widgets, 30 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x? options: A)0.02 B)0.095 C)0.03 D)0.0275 E)0.4 SOLUTION:Given probability of defective items in each brand, So, the number of items defective in brand A=x*40, in brand B=0.06*30 and brand C=0.08*30 Total number of widgets=40+30+30=100 the probability that the widget selected is defective is 0.053=(x*40+0.06*30+0.08*30)/100 => 40x+1.8+2.4 =5.3 =>40x=1.1 >x=1.1/40=0.0275 Ans D #### D QUESTION:A group of tourists wants to visit at least three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary. options: A)24 B)36 C)48 D)60 E)64 SOLUTION:The number of ways to choose three cities is 4C3=4. The number of itineraries for each group of 3 cities is 3!. So the number of itineraries to three cities is 4*3!=24. The number of ways to choose four cities is 4C4=1. The number of itineraries for the group of 4 cities is 4!. So the number of itineraries to four cities is 4!=24. The total number of itineraries is 24+24=48. The answer is C. #### C QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5 options: A)134 B)136 C)140 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:A family made a down payment of $300 and borrowed the balance on a set of encyclopedias that cost $750. The balance with interest was paid in 9 monthly payments of $57 each and a final payment of $21. The amount of interest paid was what percent of the amount borrowed? options: A) 6% B) 12% C) 14% D) 18.66% E) 20% SOLUTION:interest paid = 57*9+21 - 450 = 84 % off the balance = (84/450) * 100 = 18.66% Answer is D. #### D QUESTION:If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)? options: A)-f(x) B)f(x) C)2*f(x) D)1/f(x) E)2/f(x) SOLUTION:If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x) answer A #### A QUESTION:Two consecutive traffic signals each show either red or green. How many different arrangements of the two signals are possible? (Note: “Red-green” is different from “green-red.”) options: A)10 B)9 C)8 D)7 E)4 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 2 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 2 signals are possible. Total Options: 4 Final Answer: E #### E QUESTION:The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years, The age of the 15th student is options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Explanation: Age of the 15th student = [15 * 15 - (14 * 7 + 16 * 7)] = 15 years. Answer: E #### E QUESTION:What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years. options: A)2:3 B)2:5 C)1:3 D)2:3 E)None of these SOLUTION:Explanation: Let the principal be P and rate be R then ratio = [(P∗R∗4/100) /(P∗R∗12/100)] =4PR /12PR=1:3 Option C #### C QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? options: A)12 min B)17 min C)19 min D)11 min E)16 min SOLUTION:Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 6 - 1 = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min. Answer: A #### A QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C <<<Examples ends QUESTION:A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? options: A)$330.00 B)$331.00 C)$332.30 D)$333.30 E)$334.60 SOLUTION:The maximum interest in one month is 10%*$300=$30. The combined payment (base plus interest) is $300 + $30 = $330. The greatest possible payment is: 1.01*$330=$333.30. The answer is D. #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons? options: A)17 B)18 C)56 D)21 E)23 SOLUTION:8p2 = 8 x 7 = 56 Answer: C #### C QUESTION:5 3 -2 -5 -3 2....What is the sum of first thirty number sequence? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 => 50-50=0. ANSWER:A #### A QUESTION:If x and y are positive integers, find which of the following CANNOT be the greatest common divisor of 25x and 20y? options: A)5 B)5(x-y) C)20x D)20y E)35x SOLUTION:We are looking for a choice that CANNOT be the greatest common divisor of 25x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer. lets check a. 5 25x/5 = 5x and 20y/5 = 4y both are integers so eliminate b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 25x and 20y ... or 25x/20x = 5/4 which is not a integer. so answer is C. #### C QUESTION:The first train leaves the station at 7:00 am with a speed of 60 km/hr. The second train leaves at 8:30 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)11:00 am B)12:00 noon C)1:00 pm D)2:00 pm E)3:00 pm SOLUTION:In ninety minutes, the first train travels 90 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train in 4.5 hours. The second train will catch the first train at 1:00 pm. The answer is C. #### C QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 19.7%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)26% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 19.70 Let marked price be Rs. x. Then, 95/100 x = 119.70 x = 11970/95 = Rs. 126 Now, S.P. = Rs. 126, C.P. = Rs. 100 Profit % = 26%. Answer: B #### B QUESTION:If the positive integer x is a multiple of 1 and the positive integer y is a multiple of 7, then xy must be a multiple of which of the following? I. 7 II. 2 III. 3 options: A)II only B)I and II only C)I only D)II and III only E)I, II, and III SOLUTION:x=1a y=7b xy=7ab where a,b are integers Hence , xy will always be divisible by 7 . C is the answer. #### C QUESTION:Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? options: A)9 B)10 C)12 D)20 E)8 SOLUTION:Due to stoppages, it covers 9 km less. Time taken to cover 9 km =(9/54x 60)min = 10 min. Answer :B #### B QUESTION:A group of people,dogs, and birds has seventy legs, thirty heads, and twenty tails. How many cats are among this group? (Assume all birds have two legs and a tail.) options: A)0 B)5 C)13 D)15 E)20 SOLUTION:Write P, C, and B for the number of people, dogs, and birds respectively, so that we have 2P + 4C + 2B = 70, P + C + B = 30,C + B = 20: Comparing the last two equations we obtain P = 10, and the first equation simplifies to 4C + 2B = 50, or 2C + B = 25. Therefore, C = (2C + B) -(C + B) = 25- 5 = 5 correct answer B #### B QUESTION:Today is Monday.After 61 days,it will be options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)None of these SOLUTION:Solution Each day of the week is repeated after 7 days So,after 63 days,it will be Monday. ∴ After 61 days,it will be Saturday. Answer B #### B QUESTION:Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? options: A)2 : 3 : 4 B)6 : 7 : 8 C)6 : 8 : 9 D)4 : 6 : 8 E)None of these SOLUTION:Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). (140/100 * 5x), (150/100 * 7x) and (175/100* 8x) 7x, 21x/2 and 14x The required ratio = 7x : 21x/2 : 14x 14x : 21x : 28x 2 : 3 : 4 Answer = A #### A QUESTION:One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field? options: A)120 sq. m B)140 sq. m C)125 sq. m D)130 sq. m E)110 sq. m SOLUTION:Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m Area = 15 x 8 =120 sq. m ANSWER:A #### A QUESTION:If the price of petrol increases by 30, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? options: A)25% B)23% C)16.67% D)33.33% E)None of these SOLUTION:Explanation : let us assume before increase the petrol will be Rs. 100. After increase it will be Rs (100+30) i.e 130. Now, his consumption should be reduced to :- =(130−100)/130 ∗ 100. Hence, the consumption should be reduced to 23%. Answer : B #### B QUESTION:The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row? options: A)15 years B)31 years C)27 years D)82 years E)12 years SOLUTION:Total age seven persons = (28 * 7)years Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively. Age of the person sitting in the middle of the row = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102 = 31 years. Answer: B #### B QUESTION:In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have? options: A)180 B)45 C)60 D)90 E)135 SOLUTION:We can start with the known quantity and then go on to find the others. Shiny igneous ricks are 40. These are (2/3) of total igneous rocks. (2/3)*Total igneous rocks = 40 Total igneous rocks = 40 * (3/2) = 60 Total sedimentary rocks = 2*Total igneous rocks = 2*60 = 120 Total number of rocks = 60 + 120 = 180 Answer (A) #### A QUESTION:9, 16, 18, 25, 36,49 options: A)9 B)16 C)18 D)25 E)36 SOLUTION:Each of the numbers except 18, is perfect square. Answer: Option C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? options: A)250 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Answer: A #### A QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 8:2. If 80% of the Toyota bought and 20% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? options: A)66% B)64% C)68% D)69% E)72% SOLUTION:let total no of Vehicles bought be 100, Toyota 80 and Honda 20, so total number of SUV's bought for Toyota and Honda respectively 80* 80/100=64 and 20* 20/100=4 so total 68 SUV's were bought out of 100 Vehicles bought..so required % is 68% ANSWER:C #### C QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 * 12 = 11 => 2x = 11 => x = 5.5 C #### C QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now? options: A)14years B)15years C)16years D)17years E)18years SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years ANSWER:A #### A QUESTION:The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and three-fourths of the females in the class? options: A)218 B)226 C)234 D)242 E)250 SOLUTION:1/2*2/5 + 3/4*3/5 = 4/20 + 9/20 = 13/20 The number of degrees is 13/20 * 360 = 234 degrees The answer is C. #### C QUESTION:A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees? options: A)$20,200 B)$20,500 C)$20,800 D)$21,000 E)$21,400 SOLUTION:average = 2(19000)+(21000)+3(22000) / 6 = $20,833 The answer is C. #### C QUESTION:What is the greatest positive integer x such that 5^x is a factor of 125^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:125^10 = (5^3)^10 = 5^30 ANSWER:E #### E QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 37.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)50.5 E)67.5 SOLUTION:Total price of six cans = 6*37.5 = 225 Total price of 4 cans = 4*31 = 124 Total rice of two cans = 225 - 124 = 101 Average price of two cans = 101/2 = 50.5 c Another way to do it is this: Assume that the four leftover cans were of 31c each. The avg was 37.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 2*37.5 + 4*6.5 = 101 Avg cost of the two cans = 101/2 = 50.5c Answer (D) #### D QUESTION:If it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed? options: A)400 B)420 C)480 D)500 E)600 SOLUTION:Minimum no of mail to be sent for getting 300 responses at 50% = 300/0.5 = 600 Option E #### E QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rakesh ? options: A)1000 B)1100 C)1125 D)1200 E)1050 SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000 =>4:5:3 =>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...] => 12:5:6 Share of Rajan => 4600*12/23 = 2400 Share of Rakesh => 4600*5/23 = 1000 ANSWER:A #### A QUESTION:An arithemetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 12th member of this sequence? options: A)A)37 B)B)40 C)+ 13 D)D)34 E)+ 13 SOLUTION:Common difference of an arithmetic series is constant. 2p+2-p=4p+3-2p-2 p=1 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 Ans:D #### D QUESTION:How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? options: A)25 B)30 C)99 D)88 E)61 SOLUTION:Speed of train relative to man = 75 - 3 = 72 km/hr. = 72 * 5/18 = 20 m/sec. Time taken to pass the man = 500 * 1/20 = 25 sec. Answer: A #### A QUESTION:A present value of a machine is $2000. Its value depletiation rate is 20% per annum then find the machine value before 2 years? options: A)$3125 B)$2945 C)$3012 D)$2545 E)$3150 SOLUTION:P= $2000 R = 20% T = 2 years Machine value before 2 years = P/[(1-R/100)^T] =2000*5/4 * 5/4 =$3125 Answer is A #### A QUESTION:The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is options: A)3 months B)4 months C)6 months D)8 months E)10 months SOLUTION:Solution S.I on Rs. 1600 = T.D on Rs. 1680. Rs.1600 is the P.W of Rs.1680. Rs.80 is S.I on Rs.1600 at 15%. Time = (100x80 / 600x15) = 1/3 year = 4 months. Answer B #### B QUESTION:The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ? options: A)35 years B)45 years C)51 years D)52 years E)None of these SOLUTION:Explanation: Age of the teacher = (38 * 15 - 37 * 14) years = 52 years. Answer: D #### D QUESTION:The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? options: A)4538 B)2778 C)2608 D)4530 E)2001 SOLUTION:Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs. 4530 Answer:D #### D QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/3*60/55 = 40 min D #### D QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash? options: A)1000 B)3000 C)3500 D)2500 E)2250 SOLUTION:For 20 staffs: 300*100*20 = 60000 for driver and cleaning staff: 300*100*2 =6000 From petty Cash : 1000 Answer is 1000 #### A QUESTION:In a meeting of 4 representatives from each of 6 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place? options: A)250 B)260 C)240 D)270 E)280 SOLUTION:In fact, all 24 people will shake hands with 20 others. So, it SEEMS like the TOTAL number of handshakes = (24)(20) HOWEVER, we need to keep in mind that we have counted each handshake TWICE. To account for this DUPLICATION, we must divide (24)(20) by 2. So, the TOTAL # of handshakes = (24)(20)/2 = 240 Answer : C #### C QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1500 B)2000 C)3000 D)3500 E)2500 SOLUTION:Profit as x since 5% and 95% of x will be divided b/w A and B ration 3:2 =>profit 95x/100 * 3/5 given that A's share is Rs 855 => 95x/100 * 3/5 = 855 hence x = 1500 ANSWER A #### A QUESTION:A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:The area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is? options: A)7 B)7.67 C)8.75 D)8.98 E)8.28 SOLUTION:(4 * 3.5)/2 = 7 Answer:A #### A QUESTION:A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in : options: A)13 1/3 days B)16 days C)15 days D)20 days E)30 days SOLUTION:C alone can finish the work in 80 days. (A + B)can do it in 20 days (A + B)s 1 days wok = 1/20. As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2. A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30 (A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/80) = 1/16 All the three together will finish it in 16 days. ANSWER:B #### B QUESTION:If e<0, which of the following must be true? options: A)–100 < e < 100 B)e ≤ –1 C)e ≤ 1 D)e^2 ≥ 1/4 E)–100 < e < 0 SOLUTION:e is a negative number. A. –100 < e < 100e can be a negative number less than -100 B. e ≤ –1e can be a fraction, in which case it would be greater than -1 C. e ≤ 1must be true since 1 is positive and e is negative D. e^2 ≥ 1/4not true if e is a negative fraction like -1/5 E. –100 < e < 0e can be a negative number less than -100=C #### C QUESTION:If f(x) = 3x^4 - 4x^3 - 2x^2 + 5x , then f(-1) = options: A)-4 B)-2 C)0 D)2 E)4 SOLUTION:f(-1) = 3(-1)^4 - 4(-1)^3 - 2(-1)^2 + 5(-1) = 3+4-2-5 = 0 The answer is C. #### C QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 30 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam. options: A)15 B)30 C)35 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 90(x - 5) 80x - (5 * 30) = 90(x - 5) 300 = 10x => x = 30 ANSWER:B #### B QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)107% C)116.7% D)120% E)140% SOLUTION:Kim purchased 20 gallons of gas. She paid for 5 + 0.9*15 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%. Isabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%. 8 is 8/7.5*100 = 107% of 7.5. Answer: B. #### B QUESTION:Which of the following is an integer? I. 9! / 6! II. 9! / 8! III. 9! / 7!5! options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:9!/6! = 9*8*7 which is an integer. 9!/8! = 9 which is an integer. 9!/7!5! = 9*8 / 5*4*3*2 = 3/5 which is not an integer. The answer is D. #### D QUESTION:How many natural numbers are there which give a remainder of 41 after dividing 1997? options: A)2 B)4 C)6 D)None of these E)Cannot be determined SOLUTION:Solution Let us assume that the quotient is Q and divisor is D. Using the condition given in question, 1997 = QD + 41 ⇒ QD = 1956. Now we will factorize 1956 in two parts such that D (divisor) is more than 41. Answer C #### C QUESTION:Given a collection of points P in the plane a 1-set is a point in P that can be separated from the rest by a line; i.e the pint lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P) . The maximum value of n1(P) over all configurations P of 4 points in the plane is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:maximum no of 1-sets will be the no of points itself...as in even a simple configuration we can separate one point from others to make it 1-set ANSWER:A #### A QUESTION:4,25,121,289,? options: A)345 B)445 C)515 D)529 E)645 SOLUTION:Prime numbers- 2,3,5,7,11,13,17,19,23..... Series - 2^2,5^2,11^2,17^2,23^2 Series- 4, 25, 121, 289, 529. So next term in series is- 529. ANSWER:D #### D QUESTION:Car Z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour? options: A)320 B)384 C)400 D)408.3 E)440 SOLUTION:The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed. The stem tells us that at 45 miles/hour, the car will run 48 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 38.4 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 38.4 miles/gallon * 10 gallons = 384 miles. Answer B. #### B QUESTION:There are 7 players in a bowling team with an average weight of 94 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? options: A)75 Kg. B)80 Kg. C)86 Kg. D)90 Kg. E)92 Kg. SOLUTION:The New average will be= (94*7+110+60)/9= 92 kgs E is the answer #### E QUESTION:On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80? options: A)18% B)21% C)33.35 D)33.3% E)37.5% SOLUTION:let the total no of campers be 100 total amount = (25*110)+(35*80)+(40*65) = 2750+2800+2600= $8150 required percentage = (2800/8150)*100=33.35% C #### C QUESTION:What is the greatest of 3 consecutive integers whose sum is 27 ? options: A)6 B)7 C)8 D)9 E)11 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 27; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: E #### E QUESTION:The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen? options: A)Rs.32 B)Rs.28 C)Rs.36 D)Rs.25 E)None of these SOLUTION:Let the cost of each pen and pencil be 'p' and 'q' respectively. 16p + 8q = 352 --- (1) 4p + 4q = 96 8p + 8q = 192 --- (2) (1) - (2) => 8p = 160 => p = 20 ANSWER:E #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)26 B)22 C)12 D)24 E)20 SOLUTION:Explanation: Let the required number of days be x More men, less days (indirect proportion) Hence we can write as (men) 36 : 27 :: x : 18 ⇒36×18=27 × x ⇒12×18=9 × x ⇒12×2=x ⇒x=24 Answer: Option D #### D QUESTION:A 180 meter long train crosses a man standing on the platform in 9 sec. What is the speed of the train? options: A)72 B)108 C)1266 D)188 E)211 SOLUTION:S = 180/9 * 18/5 = 72 kmph Answer: A #### A QUESTION:What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area? options: A)11 + √5 B)11 + √6 C)11 + 4√7 D)11 + √65 E)11 + 3√17 SOLUTION:We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16) = √65 The perimeter is 11 + √65 The answer is D. #### D QUESTION:The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is: options: A)91 B)910 C)1001 D)1911 E)None of these SOLUTION:Explanation: Required number of students = H.C.F of 1001 and 910 = 91. Answer: A #### A QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)16 km/hr B)17 km/hr C)60 km/hr D)15 km/hr E)19 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer: C #### C QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B QUESTION:John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit as the cost price? options: A)Rs.12 B)Rs.8 C)Rs.16 D)Rs.20 E)None of these SOLUTION:Explanation : CP=20×8.5+35×8.75=170+306.25=476.25Profit=40%SP=(100+Profit%)100×CP=(100+40)100×476.25=140 100×476.25=1404×19.05=35×19.05Total quantity = 20 + 35 = 55 KgSP per Kg=35×19.0555=7×19.0511≈7×1911≈13311≈12 Answer : Option A #### A QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? options: A)1/45 B)1/42 C)1/46 D)1/48 E)1/43 SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42 Answer:B #### B QUESTION:If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price? options: A)Rs.1520 B)Rs.1570 C)Rs.1500 D)Rs.1550 E)Rs.1700 SOLUTION:Let the cost price of an article be Rs. x. (19% of x) - (12% of x) = 105 19x/100 - 12x/100 = 105 => 7x = 105 * 100 => x = 1500 Cost price = Rs.1500 Answer:C #### C QUESTION:If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ? options: A)x-2 B)x-4 C)x+4 D)x-3 E)x-1 SOLUTION:Original Digits=xy i.e. Number=10x+y After reversing the digits: Digits=yx i.e. Number=10y+x 10y+x is 36 more than 10x+y 10x+y+36=10y+x 10x-x+36=10y-y 9x+36=9y x+4=y OR y=x+4 Answer : C #### C QUESTION:The sum of three consecutive even numbers is 42. Find the middle number of the three? options: A)14 B)16 C)18 D)24 E)34 SOLUTION:Three consecutive even numbers (2P - 2), 2P, (2P + 2). (2P - 2) + 2P + (2P + 2) = 42 6P = 42 => P = 7. The middle number is: 2P = 14. ANSWER:A #### A QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true? options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6 SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) . ans B #### B QUESTION:A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 244 passengers. Find the no of passengers in the beginning? options: A)292 B)180 C)276 D)144 E)168 SOLUTION:Let no of passengers in the beginning be X After first station no passengers=(X-X/3)+280=2X/3 +280 After second station no passengers =1/2(2X/3+280)+12 1/2(2X/3+280)+12=244 2X/3+280=2*232 = 464 - 280 = 184 2X/3=184 X=276. So the answer is option C) 276. #### C QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:The expression (5x+2)/(x+3) is equivalent to which of the following? options: A)(5-2)/3 B)5 – (2/3) C)5 – (x)/(x+3) D)5 – (13)/(x+3) E)5 + (17)/(x+3) SOLUTION:Easiest way is to pick any number and put in (5x+2)/(x+3). Then check the options with the same number. I took x=1 and got D as the answer. #### D QUESTION:Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages. options: A)Rs 40, Rs 60 and Rs 260 B)Rs 36, Rs 81 and Rs 243 C)Rs 42, Rs 86 and Rs 232 D)Rs 38, Rs 88 and Rs 234 E)none of these SOLUTION:Let the total work done be 360 units. Therefore, work done by Anil, Bittu and Chintu in single day are 4 units, 9 units and 30 units respectively. Each of them working for 9 days Anil and Bittu will be able to complete 4 units and 9 units of their work on the 9th day but Chintu will be doing remaining 3 units of work. Hence, individual work done by them to complete the whole work is 36 units, 81 units and 243 units till the end of 9th day for each of them. Thus, respective wages on the basis of work done is Rs 36, Rs 81 and Rs 243 respectively for Anil, Bittu and Chintu. ANSWER:B #### B QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. options: A)12 B)14 C)15 D)16 E)17 SOLUTION:d = (D-R)/Q = (109 - 1)/9 = 108/9 = 18 A #### A QUESTION:In how many ways can the letters of the word REPORT be arranged? options: A)1206 B)360 C)2520 D)3000 E)3478 SOLUTION:REPORT has 6 words, but R is repeated two times. Thus ways = 6! / 2! = 360 ways B #### B QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The distance between the nest and the ditch is 250 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 250 = 7500. D = ST 7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km) D) #### D QUESTION:The purchase price of an article is $48. In order to include 30% of cost for overhead and to provide $12 of net profit, the markup should be options: A)15% B)25% C)35% D)40% E)55% SOLUTION:Cost price of article = 48$ % of overhead cost = 30 Net profit = 12 $ We need to calculate % markup Net profit as % of cost price = (12/48)*100 = 25% Total markup should be = 25 + 30 = 55% Answer E #### E QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)22 B)287 C)48 D)277 E)21 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: C #### C QUESTION:A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 B)67 C)108 D)26 E)27 SOLUTION:Length = Speed * time Speed = L/T S = 600/20 S = 30 M/Sec Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 108 Kmph Answer:C #### C QUESTION:If equation |x/2| + |y/2| = 2 encloses a certain region on the coordinate plane, what is the area of this region? options: A)20 B)32 C)100 D)200 E)400 SOLUTION:The equation can be reduced to intercept form as |x/4| + |y/4| = 1, so these are lines in four quadrants with x and y intercept as 14, so it is a rhombus with diagonals of 8 each and hence area = 1/2*d1*d2 = 1/2*8*8 = 32. Answer B. #### B QUESTION:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him? options: A)1/4 B)4/5 C)1/5 D)1/6 E)1/7 SOLUTION:If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E #### E QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 24 times, A has killed: options: A)27 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(24 x 16)/3= 128. Birds killed by A =(5x/24) =(5/24*128)= 27. Answer is A #### A QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:2*6=12.Answer is B. #### B QUESTION:A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)287 B)298 C)350 D)726 E)267 SOLUTION:D = 72 * 5/18 = 25 = 500 – 150 = 350 Answer: C #### C QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A QUESTION:On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every six minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period? options: A)25% B)50% C)75% D)100% E)150% SOLUTION:Dolphin once in 3 min; Beluga once in 6 min; So, dolphin comes up 2 times frequently than beluga, which is 150% (6-3)/2*100. Answer: E. #### E QUESTION:A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a red ball is selected? options: A)x/(x + 4) B)y/(x + 5) C)(x + 5)/(x + y + 9) D)(y + 4)/(x + y + 9) E)(x + 4)/(x + y + 9) SOLUTION:x red balls y green balls x+4+y+5 is the total =x+y+9 x+5 is the number of red balls so (x + 5)/(x + y + 9) the answer is C #### C QUESTION:The cost of an item was reduced from its usual selling price of $23.99 to $16.99. Which of the following is closest to the percent decrease in the price of the item? options: A)17% B)21% C)24% D)29% E)42% SOLUTION:The price decreased by 23.99 - 16.99 = $7. $7 is a bit more than 29% of original price of $24. Answer: D. #### D QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.79 B)5.71 C)5.76 D)5.79 E)5.73 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 Answer: C #### C QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)144° B)150° C)168° D)180° E)none SOLUTION:Solution Angle traced by hour hand in 5 hrs 10 min. = (360/12 x 6)° = 180°. Answer D #### D QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? options: A)1244 B)1532 C)1349 D)1423 E)1543 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)Rs.7000 B)Rs.8000 C)Rs.8500 D)Rs.8600 E)Rs.8700 SOLUTION:The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000. B) #### B QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 15 years? options: A)2:6 B)3:5 C)1:4 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×9/100) /(P×R×15/100)]=9PR/15PR=9/15=3:5 Answer B #### B QUESTION:A two digit number reversed and multiplied by 4 is 3 more than the original digit. what is the digit? options: A)61 B)62 C)63 D)64 E)66 SOLUTION:If no is xy , then 10x+y = 4*(10y+x)-3= 40y +4x-3 6x-39y +3 =0 2x-13y +1 =0 13 y =2x+1 when y=1, x=6 so number is 61. ANSWER:A #### A QUESTION:The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface? options: A)27 B)16 C)12 D)18 E)11 SOLUTION:2 * π * 2r * 3r = 12 πr2 Answer:C #### C QUESTION:If a is an odd integer and b is an even integer which of the following must be an integer : options: A)a/b B)ab C)2a+b D)2(a+b) E)option B C and D SOLUTION:a= odd = e.g 3 b=even = e.g 6 A. odd/even for example 3/6 = 0.5 no even no odd B. odd * even = 3 * 6 = 18 even C. 2*odd + even = even + even even D. 2(even + odd) = 2(odd) even Hence E it is. #### E QUESTION:a man spends $2.6 for parking and $34.4 for petrol to travel in car from monday to friday.if he travel by public transport it costs $1.06,find the percentage of savings? options: A)75.6 B)85.6 C)85.7 D)95.7 E)105.7 SOLUTION:2.6+34.4=37 for 5 days 1.06*5=5.3 37-5.3=31.7 now the required saving percentage is (31.7/37)*100=85.6 ANSWER:B #### B QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale? options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these SOLUTION:Let the original price be x and sale be of y units. Then, the revenue collected initially = x × y Now, new price = 0.8x, new sale = 1.8y Then, new revenue collected = 1.44xy % increase in revenue = 0.44xy/xy×100 = 44% increase Answer A #### A QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true? I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above. options: A)I only B)I and II C)II and III D)I, II, and III E)IV only SOLUTION:This is a very good 'trap question'. Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3 If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'. Ans: E #### E QUESTION:Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities? options: A)3 B)6 C)8 D)9 E)12 SOLUTION:3! = 6 M L S C M S L C L M S C L S M C S M L C S L M C She can visit the cities in any order. Number of ways of arranging the three cities is 3! = 6 ways. Hence B. #### B QUESTION:Concentrated grapes juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated grapes juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:Concentrated grapes juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:If x/y = 5 and (4a - x)/(b - y) = 5, then the value of a/b is? options: A) –3 B) -2 C) 1 D) 5/4 E) 3 SOLUTION:x = 5y 4a - 5y = 5(b - y) 4a - 5y = 5b - 5y 4a = 5b a/b = 5/4 Answer: D #### D QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 145% D) 150% E) 180% SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80 So the approximate answer is E #### E QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? options: A)59020 B)59299 C)59020 D)59300 E)59008 SOLUTION:Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500. Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000. Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P) Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally. Income of A = Twice the income of B (2500 + 18000 + P) = 2(P) P = 20500 Total profit = 2P + 18000 = 2*20500 + 18000 = 59000 Answer: D #### D QUESTION:The points A(0, 0), B(0, 4a - 4) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? options: A)88 B)98 C)108 D)78 E)90 SOLUTION:1/2bh=1/2(2a+1)(2a+6) Now 4a-4=2a+6 2a=10 , a=5 Therefore, A(0,0); B(0,16); C(11,16) 1/2*11*16=88 Answer: A #### A QUESTION:The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot? options: A)77 m B)17 m C)82 m D)28 m E)26 m SOLUTION:Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer: B #### B QUESTION:Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+30 3x + 6 = x + 30 2x = 24 \inline \therefore x = 12 \inline \therefore Middle number = x + 2 = 12+2 = 14 C #### C QUESTION:A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph? options: A)16 km B)87 km C)89 km D)67 km E)20 km SOLUTION:Let the distance between A and B be x km. Total time = x/(9 + 1) + x/(9 - 1) = 3.5 => x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x = 16 km. Answer:A #### A QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B QUESTION:A can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares? options: A)600,400 B)500,500 C)300,700 D)800,1200 E)550,1450 SOLUTION:Ratio of their works A:B = 6:4 Ratio of their wages A:B = 2:3 A's share = (2/5)2000 = 800 B's share = (3/5)2000 = 1200 correct option is D #### D QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:A train 250 m long is running at a speed of 58 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)18 sec E)15 sec SOLUTION:Answer : D. Speed of the train relative to man = (58 - 8) kmph = (50* 5/18) m/sec = (125/9)m/sec Time taken by the train to cross the man = Time taken by It to cover 250 m at 125/9 m / sec = 250 *9/ 125 sec = 18sec #### D QUESTION:The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. options: A)52 minutes B)45 minutes C)30 minutes D)48 minutes E)44 minutes SOLUTION:Explanation: Total time a student spends in college = 4 hours 20 minutes = 260 minutes As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes Hence, the duration of each lecture is = (260 – 20)/5 = 48 minutes ANSWER D #### D QUESTION:In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race? options: A)2min 10 sec B)2min 30 sec C)2min 40 sec D)2min 50 sec E)2min 20 sec SOLUTION:100 m = 15 sec 1 m = 15/100 sec 1000 m = 15/100*1000 =150 sec =2min 30 sec ANSWER:B #### B QUESTION:A man took a loan from a bank at the rate of 10% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was : options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 18,000 D)Rs. 20,000 E)None SOLUTION:Solution Principal = Rs.(100x5400/10x3)= Rs. 18000. Answer C #### C QUESTION:Find the value of a from (15)^2 x 8^3 ÷ 256 = a. options: A)250 B)420 C)440 D)650 E)450 SOLUTION:Given Exp. =(15)^2 x 8^3 ÷ 256 = a = 225 x 512 ÷ 256 = 450 E #### E QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only? options: A)24 B)27 C)30 D)33 E)36 SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only. Since 10% of students are in both, then 70% of students are in the band which is 84 students. The number of students in the orchestra is (30/70)*84 = 36. The answer is E. #### E QUESTION:AB +BA ___ 101 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)10 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. only 10 fits in.. C #### C QUESTION:9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere? options: A)4 cm B)6 cm C)8 cm D)10 cm E)12 cm SOLUTION:Volume of cylinder = pi*r^2*h Volume of a sphere = 4*pi*R^3 / 3 9*4*pi*R^3 / 3 = pi*r^2*h R^3 = r^2*h / 12 = 64 cm^3 R = 4 cm D = 8 cm The answer is C. #### C QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)*(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)*(r+4)/(y+r+6) D)(y+3)/(y+r+7)*(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate? options: A)2 B)4 C)6 D)8 E)12 SOLUTION:To fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible so we will take the base as 12 feet by 8 feet Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less. Therefore the radius of the cylinder will become Diameter 2===>8/2=4 Diameter ANSWER:D #### D QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14×30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×14) Ratio of the capacity of a man and woman =1/(15×14) : 1/(14×30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:The average salary of all the workers in a workshop is $1000. The average salary of 5 technicians is $5000 and the average salary of the rest is $500. The total number of workers in the shop is? options: A)25 B)20 C)15 D)30 E)18 SOLUTION:Let the total number of workers be x 1000x = 5000*5 + 500(x-5) x = 25 Answer is A #### A QUESTION:Jen has a jar of jam, and she ate 1/3 of the jam for lunch. If Jen ate 1/7 of the remaining jam for dinner, what fraction of the jam was left after dinner? options: A)2/7 B)3/7 C)4/7 D)9/14 E)11/14 SOLUTION:Let x be the amount of jam at the beginning. After lunch, the remaining jam was (2/3)x. After dinner, the remaining jam was (6/7)(2/3)x = (4/7)x. The answer is C. #### C QUESTION:Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be options: A)33% less than N B)25% less than N C)equal to N D)20% greater than N E)25% greater than SOLUTION:Correct answer is (A). This year, the price of a tree is price1=P/N. If this price increases by 50% it becomes price2=P/N*1.50 Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.50) i.e. N/1.5 i.e. .67% less* A #### A QUESTION:If you have 4 New Year greeting cards and you want to send them to 2 of your friends, in how many ways can this be done? options: A)360 B)12 C)16 D)24 E)None SOLUTION:Solution We have to find number of permutations of 2 objects out of 4 objects. This number is 4P2=4(4-1)=4*3=12 Answer B #### B QUESTION:The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:EXPLANATION Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. Answer C #### C <<<Examples ends QUESTION:We have 8 people and 5 chairs. In how many ways chairs can be occupy? options: A)1200 B)1450 C)1680 D)1912 E)900 SOLUTION:no. of ways they can be occupy = 8*7*6*5 = 1680 Answer is C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced? options: A)70% B)15% C)20% D)25% E)30% SOLUTION:price of a coat in a certain store = $500 the price of the coat is to be reduced by $350 % change = (Final Value - Initial Value)*100 / Initial Value % Reduction= (Reduction in Price)*100 / Initial Value i.e. % Reduction= (350)*100 / 500 = 70% Answer: Option A #### A QUESTION:how many 1x1x1 cubes can you fit in a 15x16x13 box? options: A)3,200 B)3,150 C)3,448 D)3,120 E)2,980 SOLUTION:The answer is D) 3,120. A 1x1x1 cube has an area of 1. The 15x16x13 box has an area of 3,120. If you divide 3,120 by 1, you get 3,120. Therefore the answer is D. #### D QUESTION:A part-time employee whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? options: A)9 B)13 C)17 D)20 E)33.33 SOLUTION:Let original hourly wage be x and let the no of hours worked be y Total wage will be =x*y After the increment the wage will be=1.5 x Now we need to find number of hours worked so that x*y=1.5x*z i.e z=1/1.5 y = 2/3y %decrease = (y-2/3y)/y *100=100/3=33.33%. Thus my answer is E. #### E QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 60% have red flags, what percentage of children have flags of both the colors? options: A)5% B)10% C)15% D)20% E)It can not be determined SOLUTION:Solution: let the total number of flags be 100(even number) let the total number of 'blue' flags alone be 'a' let the total number of 'red' flags alone be 'b' let the total number of 'both' flags be 'c' We have given, total number of blue flags = 60% = 60 = a+c total number of red flags=55%=55=b+c total number of flags = a+b+c=100 (since all the flags have been utilized) So, substituting for c in the third equation, we have, 60-c+c+60-c=100 c=20 Option D. #### D QUESTION:What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5? options: A)1 B)3 C)2 D)4 E)5 SOLUTION:Only the unit's digit of the product will decide the remainder when divided by 5. Hence, 1*4*3= will give units digit as 2 So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2. Option C #### C QUESTION:The age of Somu is one-third his father's. 8 years back he was one-fifth of his father's age. What is his persent age ? options: A)11 B)13 C)14 D)16 E)10 SOLUTION:Explanation : Let Somu's age be x and that of his father be 3x. So, x - 8 = 3x - 8/5 = x = 16 Answer : Option D #### D QUESTION:If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is: options: A)80% B)90% C)33% D)40% E)10% SOLUTION:Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12. Gain % = 3/9 * 100 = 33% Answer:C #### C QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:What is the remainder of Q= 3^19 when divided by 10? options: A)0 B)1 C)5 D)7 E)9 SOLUTION:I looked for patterns: ^2 - units digit 9 ^3 - units digit 7 ^4 - units digit 1 ^5 - units digit 3 hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9 and we can then see: ^16 - units digit 1, or ^18 - units digit 9 and ^19 - units digit 7 therefore, Q=when divided by 10, the remainder must be 7.D #### D QUESTION:Evaluate:55- 12*3*2 =? options: A)42 B)47 C)62 D)72 E)82 SOLUTION:According to order of operations, 12?3?2 (division and multiplication) is done first from left to right 12**2 = 4* 2 = 8 Hence 55 - 12*3*2 = 55- 8 = 47 correct answer B #### B QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:Perimeter of the backwheel is 9 feet and front wheel is 7 feet at a certain distance. The front wheel gets 10 revolutions more than the back wheel. What is the distance? options: A)305 B)310 C)315 D)320 E)325 SOLUTION:If distance=d Number of revolutions by back wheel=d/9 & front wheel=d/7 (d/7)-(d/9)=10 ,2d=630 ,d=315 ANSWER:C #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)33 B)277 C)40 D)88 E)11 SOLUTION:The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150 Profit(%) = (31150 - 22250)/22250 * 100 = 40% Answer: C #### C QUESTION:A trader sells two brands of petrol; one is Extra Premium and other one is speed. He mixes 12 litres Extra Premium with 3 litres of speed and by selling this mixture at the price of Extra Premium he gets the profit of 9.09. If the price of Extra Premium Rs. 48 per litre, then the price of Speed is: options: A)Rs. 38 per litre B)Rs. 42 per litre C)Rs. 28 per litre D)Rs. 28 per litre E)None of These SOLUTION:Solution: Selling price mix EP, = (CP + 9.09% of CP) 48 = 12/11 of CP CP = 44 No, using Alligation method, MCQ Aptitude Profit and Loss11 4:1 Thus, X = 44 Thus, the price of speed brand is Rs. 28/litre. Answer: Option C #### C QUESTION:Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 25-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs? options: A)60 B)70 C)80 D)100 E)45 SOLUTION:let x be the number of 25 ounce cans. Therefore (x+30) is the number of 15 ounce cans. Total volume is same, therefore 25x=15(x+30) 10x=450 x=45 Ans - E #### E QUESTION:At present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present? options: A)16 B)17 C)10 D)18 E)15 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 2 = 26 => x = 8 Deepak's age = 3x = 18 years. Answer: D #### D QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent? options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these SOLUTION:Let CP of an book = 100 MP of an book = 120 Discount 30 % on 120 = 36 SP of the book = 120 - 36 = 84 loss = 16% Answer : C #### C QUESTION:The length of a rectangle is reduced by 10%. By what % would the width have to be increased to maintain the original area? options: A)10% B)11.1% C)25% D)30% E)35% SOLUTION:Sol. Required change = (10*100)/(100-10)=11.1% B #### B QUESTION:It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? options: A)8:50 a.m B)5:50 a.m C)7:50 a.m D)6:50 a.m E)7:00 a.m SOLUTION:The time it takes Kannan to get to work: time to walk to car park + time to drive 10 + 110 = 120 minutes = 2 hours Kannan needs to get out of the house 2 hours before 9:00 am at 9:00 - 2:00 = 7:00 a.m correct answer E #### E QUESTION:A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is options: A)400 kg B)560 kg C)600 kg D)640 kg E)None SOLUTION:Solution ratio of 1st and 2nd parts = 4 : 6 = 2 : 3. Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg. Answer C #### C QUESTION:Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is? options: A)2777 B)2888 C)8400 D)2882 E)2781 SOLUTION:Ratio of their shares = 22500 : 35000 = 9:14 Deepak's share = 13800 * 14/23 = Rs. 8400. Answer: C #### C QUESTION:If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:P ÷ 44 = 432 => P = 432 * 44 = 19008 P / 31 = 19008 / 31 = 613, remainder = 5 C #### C QUESTION:Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose? options: A)1.25% B)2.1% C)2.25% D)2.65% E)3% SOLUTION:Generally in such cases, there is always loss. So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss. Loss% = Common loss and gain% 2 = x 2 10 10 Therefore, here common loss and gain % = 15% Hence, Loss% = 15 2 = 2.25% C #### C QUESTION:A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target? options: A)175/256 B)451/365 C)312/456 D)156/754 E)164/784 SOLUTION:The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes. So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes. The event of not hitting the target even once is the complement of the event of hitting the target at least once. The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾ Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256 The probability that he will hit the target at least in one of the four shots=1-81/256 =175/256 Ans:A #### A QUESTION:The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ? options: A)12 B)14 C)15 D)16 E)20 SOLUTION:HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D #### D QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 500. What is the manager's monthly salary ? options: A)Rs.16003 B)Rs.16029 C)Rs.1288 D)Rs.16108 E)Rs.12000 SOLUTION:Explanation: Manager's monthly salary Rs. (2000 * 21 - 1500 * 20) = Rs.12000. Answer: E #### E QUESTION:Machine W can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? options: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33 SOLUTION:Let the following be true: W makes x in time t Then the following follows: N makes x in 4t/3 O makes x in 3/2(4t/3) = 2t M:N:O = 1:4/3:2=3:4:6 So N=4/(3+4+6)=4/13=C #### C QUESTION:Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings? options: A)1/2 B)1/4 C)1/6 D)1/8 E)1/16 SOLUTION:Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible). Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8. Answer: D. #### D QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B QUESTION:What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10? options: A)5 B)7 C)4 D)9 E)3 SOLUTION:30,40,50,60,70 total 5 Answer is A #### A QUESTION:If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is options: A)Rs.1820 B)Rs.1040 C)Rs.1120 D)Rs.1680 E)None of these SOLUTION:Explanation: Let the sum of money be x then (x × 4 × 8)/100 = (560 × 12 × 8)/100 x × 4 × 8 = 560 × 12 × 8 x × 4 = 560 × 12x = 560 × 3 = 1680 Answer: Option D #### D QUESTION:If x is an integer and 2.134 × 10^x is less than 21000, what is the greatest possible value for x? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:If x=4 2.134 × 10^4 = 21340 > 21000 So, x = 3 Answer : E #### E QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)288 B)492 C)877 D)278 E)178 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 20 + 21 = 41 T = 12 D = 41 * 12 = 492 Answer: B #### B QUESTION:x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20. Answer: C. #### C QUESTION:Find the value of 72515 x 9999 = m? options: A)345434667 B)246465757 C)465767867 D)725077485 E)645354643 SOLUTION:72515 x 9999 = 72515 x (10000 - 1) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 D #### D QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. options: A)1200 B)1400 C)2660 D)1600 E)1800 SOLUTION:A is a working member and for that, he receive 5% of the profit = 5% of 7400 = 5*7400/100 = 370 Remaining amount = 7400-370 = 7030 Ratio of their investments = 6500*6 : 8400*5 : 10000*3 = 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20 = 13 : 14 : 10 Share of B in the profit = 7030 * (14/37) = 190*14 = 2660 Answer is C #### C QUESTION:A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives options: A)Rs. 8400 B)Rs. 11,900 C)Rs. 13,600 D)Rs. 14,700 E)NONE SOLUTION:Solution: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000. => 3x = 36000. => x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. So A's share = Rs. (35000 x 21/50) = Rs. 14,700. Answer: Option D #### D QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 9 and 10. The larger of the two numbers is: options: A)276 B)299 C)230 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 9) and (23 x 10). Larger number = (23 x 10) = 230. Answer: Option C #### C QUESTION:There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle. options: A)18 B)99 C)12 D)07 E)11 SOLUTION:Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm. a2 = 784 = (4)(196) = (22).(142) a = (2)(14) = 28 a = 2l, l = a/2 = 14 l = (7/3)s Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm. Answer: C #### C QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6? options: A)300 B)992 C)772 D)552 E)280 SOLUTION:1/3:1/3:1/6 = 2:2:1 1/5*1400 = 280 560-280 = 280 Answer: E #### E QUESTION:Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day? options: A)Rs. 120 B)Rs. 150 C)Rs. 250 D)Rs. 400 E)None of these SOLUTION:Solution: Ratio of number of men, women and children, = (18/6): (10/5):(12/3) = 3:2:4 Total (Men +Women +Children) = 18 3X +2X +4X = 18 9X = 18 X = 2 Hence, number of women = 2X = 2*2 = 4 Share of all women = (10*4000)/40 = Rs. 1000 [18+10+12 =40] Thus, share of each woman = 1000/4 = Rs. 250. Answer: Option C #### C QUESTION:One packet of flower seeds was enough to just fill the area of the smaller garden in #3. How many packets of seed are needed for the larger garden? Round each answer to the nearest square foot before continuing. options: A)1 seed packet B)2 seed packets C)3 seed packets D)4 seed packets E)5 seed packets SOLUTION:3.14 x 32 = 28.26 sq. ft. area of small garden 28 sq. ft. rounded 3.14 x 62 = 113.04 sq. ft. area of large garden 113 sq. ft. rounded 113 ÷ 28 = 4.04 or 4 seed packets (rounded) correct answer D #### D QUESTION:The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840.At what rate of interest the same amount of interest can be received on the same sum after 5 years ? options: A)6% B)8% C)9% D)10% E)None SOLUTION:Solution S.I. = Rs. 840,R =5%,T= 8 Years. Principal = Rs.(800x840/5x8)= Rs. 2100. Now,P = Rs. 2100,S.I. = Rs. 840, T = 5 years. ∴ Rate =(100x840/2100x5) = 8%. Answer B #### B QUESTION:A given line L has an equation 3x+4y=5. Which of the following is the equation of line which is parallel to the above line? options: A) 4x + 3y = 5 B) 3x + 4y = 10 C) 3x + 5y = 5 D) 3x + 5y = 3 E) 3x – 4y = 5 SOLUTION:3x+4y=5 --- equation 1 2 lines are parallel if a1/a2 = b1/b2 ≠ c1/c2 Comparing the original line with option B 3x+4y = 10 -- equation 2 From equations 1 and 2 , we get 5=10 which is not possible Hence our answer is 3x + 4y = 10 Answer B #### B QUESTION:Walking at 4/5 of her normal speed, a worker is 10 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is options: A)30 B)35 C)40 D)45 E)50 SOLUTION:Let V be her normal speed and let T be her normal time. D = (4/5)V * (T+10) Since the distance is the same we can equate this to a regular day which is D = V*T V*T = (4/5)V * (T+10) T/5 = 8 T=40 The answer is C. #### C QUESTION:In an exam, Dibi scored 25 percent, Balan scored 38 percent and Cristen 23 percent. The maximum score awarded in the exam is 1200. Find the average mark scored by all the three boys? options: A)322 B)342 C)344 D)328 E)320 SOLUTION:Average mark scored by all the three boys = [25/100 (1200) +38 /100 (1200) + 23/100 (1200)] / 3 300+456+276= 344 Answer: C #### C QUESTION:A coin is weighted so that the probability of heads on any flip is 0.2, while the probability of tails is 0.8. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 B)(0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2 C)(0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2 D)(0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.2 Probability of Tail, P(T) = 0.8 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2*(0.2)^3*(0.8)^2 1 Tail and 4 Heads, Probability = 5C1*(0.2)^4*(0.8)^2 0 Tail and 5 Heads, Probability = (0.2)^5 Required Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 Answer: option A #### A QUESTION:P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last? options: A)5 days B)10 days C)14 days D)22 days E)26 days SOLUTION:Explanation : Work done by P in 1 day = 1/10 Work done by Q in 1 day = 1/6 Work done by P in 2 days = 2 × (1/10) = 1/5 Remaining work = 1 – 1/5 = 4/5 Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15 Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3 Total days = 2 + 3 = 5 Answer : Option A #### A QUESTION:Find 60/42*4 options: A)14.7653 B)0.5897 C)3.6974 D)0.3571 E)1.2587 SOLUTION:Answer=60/42*4 =60/168=0.3571 Option D is correct #### D QUESTION:How many of the positive factors of 17 are not factors of 34? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 17 - 1, 17 factors of 34- 1, 2, 17, 34, Comparing both, we have three factors of 17which are not factors of 34- no factors The answer is A #### A QUESTION:At a meeting of the 8 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 8 Chiefs of Staff be seated around a circular table? options: A)120 B)480 C)960 D)2520 E)5080 SOLUTION:Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E #### E QUESTION:Average of first five multiples of 2 is options: A)9 B)6 C)13 D)15 E)16 SOLUTION:Explanation: Average=2(1+2+3+4+5)5=6 Answer: Option B #### B QUESTION:In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ? options: A)64 B)1/8 C)1 D)4 E)1/64 SOLUTION:Say r=2 => V1 = 1/16 when r=1; V2 = 1/4 V2 = 4*V1. Answer : D #### D QUESTION:The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers? options: A)12/35 B)1/35 C)35/8 D)7/32 E)7/33 SOLUTION:Let the numbers be a and b. Then, a + b = 12 and ab = 35. (a + b)/ab = 12/35 = (1/b + 1/a) = 12/35 Sum of reciprocals of given numbers = 12/35. ANSWER:A #### A QUESTION:Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 8%. What is the approximate interest he pays annually? options: A)1500 B)1750 C)2000 D)3500 E)2500 SOLUTION:An easy way too attempt this is by approximation: For the first quarter, he pays 8% of 10,000 which is $800. So for the four quarters in the year, he will approximately play 800*4=3200 over the entire year. Because of compound interest it will be more than 3200. Approx. option D is correct. Answer :D #### D QUESTION:If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost? options: A)24 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 60 : x 250 * x = (100 * 60) x = (100 * 60) / 250 x = 24 ANSWER: A #### A QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 145% D) 150% E) 180% SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80 So the approximate answer is E #### E QUESTION:The average of 5 quantities is 12. The average of 3 of them is 4. What is the average of remaining 2 numbers? options: A)24 B)10 C)8 D)9.5 E)None of these SOLUTION:ANSWER: A (5x12-3x4)/2=24 #### A QUESTION:The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n? options: A)w– 2n B)w–n + 1 C)w– 2(n– 1) D)n– 6 + w E)w – n/2 SOLUTION:Another method would be to use the concept of Arithmetic Progressions. Consecutive even integers form an AP where the common difference is 2. In an AP, Last term = First term + (n-1)*common difference w = First term + (n-1)*2 First term = w - 2(n-1) ANSWER:C #### C QUESTION:Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week? options: A)$0.00 B)$133.00 C)$250.05 D)$66.74 E)$10000.00 SOLUTION:Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be n/4, n/8, n/16, n/32 So, answer will be D #### D QUESTION:How much water must be added to a 30 quarts of a 75% acid solution to reduce it to a 15% solution of acid? options: A)120 qts B)220 qts C)320 qts D)420 qts E)520 qts SOLUTION:I’m adding water, so we have WATER + WATER = WATER Starting off with 30 quarts and adding x quarts, we should end up with (30 + x) quarts 30 + x = (30 + x) The problem describes the solution in terms of acid, we have set it up in terms of water. So, we have to change the percentages and put them in the problem. .25(30) + x = .85(30 + x) Again, we multiply both sides of the equation by 100 to get rid of the decimal point. 25(30) + 100x = 85(30 + x) 750 + 100x = 2550 + 85x 15x = 1800 x = 120 qts correct answer A #### A QUESTION:A and B started a business with their capitals Rs. 3,00,000 and 18,00,000 respectively. Annual profit will be distributed between them in the ratio options: A)2:5 B)2:3 C)1:3 D)1:6 E)1:9 SOLUTION:3,00,000:18,00,000 Ans. 1:6 ANSWER:D #### D QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: options: A)5% B)8% C)10% D)12% E)6% SOLUTION:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =(80/1600x 100)% = 5%. Answer is A. #### A QUESTION:From a group of 3 boys and 3 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected? options: A)1/10 B)4/9 C)1/2 D)9/15 E)2/3 SOLUTION:The total number of ways to choose 2 children from 6 is 6C2 = 15 The number of ways to choose 1 boy and 1 girl is 3*3 = 9 P(1 boy and 1 girl) = 9/15 The answer is D. #### D QUESTION:A and B invests Rs.4000 and Rs.6000 in a business. After 4 months, A withdraws three-fourth of his capital and 4 months later, B withdraws half of his capital. In what ratio should they share the profits at the end of the year? options: A)2:5 B)3:5 C)4:5 D)3:7 E)5:7 SOLUTION:A : B (4000*4)+(1000*8) : (6000*8)+(3000*4) 24000 : 60000 2 : 5 Answer: A #### A QUESTION:A can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work? options: A)2 1/2days B)4 1/2days C)6 1/2days D)7 1/2days E)10 1/2days SOLUTION:The required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days Answer is B #### B QUESTION:The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students? options: A)52.6 B)52.4 C)52.1 D)69.5 E)52.9 SOLUTION:Sum of the marks for the class of 40 students = 40 * 44 = 1760 Sum of the marks for the class of 45 students = 45 * 70 = 3150 Sum of the marks for the class of 85 students = 2760 + 3150 = 5910 Average marks of all the students = 5910/85 = 69.5.Answer: D #### D QUESTION:If P is a prime number greater than 3, find the remainder when P^2 + 14 is divided by 12. options: A)6 B)1 C)3 D)8 E)7 SOLUTION:Every prime number greater than 3 can be written 6N+1 or 6N-1. If P = 6N+1, then P^2 + 14 = 36N^2 + 12N + 1 + 14 = 36N^2 + 12N + 12 + 3 If P = 6N-1, then P^2 + 14 = 36N^2 - 12N + 1 + 14 = 36N^2 - 12N + 12 + 3 When divided by 12, it must leave a remainder of 3. The answer is C. #### C QUESTION:A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 80 km downstream? options: A)2 hours B)3 hours C)4 hours D)5 hours E)None SOLUTION:Solution Speed Downstream = (13 + 4) km/hr = 17 km/hr. Time taken to travel 80 km downstream =(80 / 17)hrs = 4 hrs 42 minutes. Answer E #### E QUESTION:In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ? options: A)3990 B)1540 C)1995 D)3672 E)None of these SOLUTION:In order that two books on French are never together, we must place all books as under X E X E X E X E X E .....X E X where E denotes the position of an English book and X that of a French book. Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in 22C19 = 22C3 = (22x21x20)/(3x2x1) = 1540 ways Answer B. #### B QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? options: A)1 mins B)3 mins C)8 mins D)6 mins E)4 mins SOLUTION:D = 25 * 60 + 1500 = 3000 m T = 3000/60 * 18/5 = 180 sec = 3 mins Answer: B #### B QUESTION:A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side? options: A)20,25 B)21,25 C)27,23 D)28,25 E)30,25 SOLUTION:Let the two parallel sides of the trapezium be a cm and b cm. Then, a-b = 4 ------ (1) And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2) Solving 1 and 2, we get: a=27,b=23 So, the two parallel sides are 27 cm and 23 cm. C #### C QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)11*10! B)9*8! C)8*7! D)7*6! E)6*5! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=11*10! Ans:A #### A QUESTION:The mean of 1^3,2^3,3^3,4^3,5^3 is? options: A)30 B)45 C)50 D)60 E)75 SOLUTION:1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2 1^3+2^3+3^3+-----+5^3 = (5*6/2)^2 = 225 Required average is = 225/5 = 45 Answer is B #### B QUESTION:A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred. options: A)Rs. 5750 B)Rs. 6000 C)Rs. 5500 D)Rs. 5000 E)Rs. 7000 SOLUTION:The price varies as the square of the weight, P = K x W2 12250 = K x 352 K = 10 Thus, P = 10W2 When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively. Their values should be : 10g piece: 10 x 102 = Rs. 1000; 25g piece: 10 x 252 = Rs. 6250. Total value of stone now, = 1000 + 6250 = Rs. 7250 Loss incurred = 12250 - 7250 = Rs. 5000 ANSWER:D #### D QUESTION:The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday? options: A)39oC B)44oC C)38oC D)41oC E)None SOLUTION:Solution: Average temperature for Wednesday, Thursday and Friday = 40oC Total temperature = 3*40 = 120oC Average temperature for Thursday, Friday and Saturday = 41oC Total temperature = 41*3 = 123oC Temperature on Saturday = 42oC Now, (Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120; Saturday - Wednesday = 3 Wednesday = 42-3 = 39oC. Answer: Option A #### A QUESTION:Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 70, the three numbers in order are? options: A)60, 120, and 30 B)60, 30, and 120 C)30, 60, and 120 D)30, 120, and 60 E)120, 30, and 60 SOLUTION:Let the numbers be 2x, x and 4x (2x + x + 4x)/3 = 70 7x/3 = 70 x = 30 The numbers in order are 60, 30, and 120 The answer is B. #### B QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 160 km/hr? options: A)2.5 sec B)2.9 sec C)2.7 sec D)8.7 sec E)8.5 sec SOLUTION:Speed = 160 * 5/18 = 44 m/sec Time taken = 120/44 = 2.7 sec. Answer: C #### C QUESTION:The smallest 2 digit prime number is? options: A)A)11 B)B)13 C)C)19 D)D)113 E)E)None SOLUTION:The smallest 3-digit number is 10, which is divisible by 2. 10 is not a prime number. 11 is a prime number. Hence 11 is the smallest 2-digit prime number. A) #### A QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? options: A)27 B)50 C)98 D)77 E)51 SOLUTION:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.Answer: B #### B QUESTION:The present average age of a family of five members is 24 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest) options: A)27.5 years B)17 years C)17.5 years D)16.5 years E)15.5 years SOLUTION:Present total age of the members = 24(5) = 120 years. Present age of the youngest member = 10 years Present total age of the remaining four members = 120 -10 = 110 years Their average age at the time of the birth of the youngest member = [110 - (4 * 10)] / 4 = 17.5 years ANSWER:C #### C QUESTION:Rs.12320 were divided among W, X & Y in such a way that W had Rs.640 more than X and Y had Rs 480 more than X . How much was X’s share? options: A)Rs.4590 B)Rs.4610 C)Rs.4620 D)Rs.4630 E)Rs.4640 SOLUTION:Let X gets Rs x. Then We can say W gets Rs (x + 640 ) and Y gets Rs ( x + 560) . x + 640 + x + x + 1120 = 12320 3x = 10560 x = 3520 . C’s share = Rs ( 3520+1120 ) = Rs.4640 E #### E QUESTION:One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number? options: A)4 B)6 C)0 D)9 E)19 SOLUTION:Answer: Option D x/2 – x/3 = 6 => x =6 3 + 6 = 9 #### D QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling? options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr SOLUTION:Number of gaps between 51 telephone posts = 50 Distance traveled in 1 minute = 50*50 = 2500m = 2.5km Speed = 60*2.5=150km/hr Answer is D #### D QUESTION:Complete the series: 16, 06 , 68 , 88 , ? , 98 options: A)L8 B)B6 C)S5 D)E8 E)M5 SOLUTION:A L8 To know why, just read the number series upside down and you will find that the numbers are 91, 90, 89, 88, __, 86 So L8 when read upside down reads as 87. #### A QUESTION:The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is? options: A)6.06% B)6.07% C)6.08% D)6.09% E)6.19% SOLUTION:Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09% ANSWER:D #### D QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%? options: A)20% B)28% C)29% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 86 2/3 SP1 = 86 SP1 = 129 100 --- 29 => 29% Answer:C #### C QUESTION:Today is Tuesday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come? options: A)Saturday B)MONDAY C)TUESDAY D)WEDNESDAY E)FRIDAY SOLUTION:Today is Tuesday after three days--->Friday now, (Friday)after before day--->Thursday then, (Thursday)day after tomorrow--->Saturday ANSWER:A #### A QUESTION:How many bricks, each measuring 125 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm? options: A)1280 B)2400 C)5500 D)7400 E)3400 SOLUTION:Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (125 x 11.25 x 6) = 1280 ANSWER:A #### A QUESTION:Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent? options: A)11 1/8 B)11 1/7 C)11 1/9 D)11 1/1 E)11 1/2 SOLUTION:900 --- 100 100 --- ? => 11 1/9%.Answer: C #### C QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2. options: A)29 B)27 C)28 D)24 E)21 SOLUTION:(4)^11x (7)^5 x (11)^2 = (2 x 2)^11 x (7)^5 x (11)^2 = 2^11 x 2^11 x7^5x 11^2 = 2^22 x 7^5 x11^2 Total number of prime factors = (22 + 5 + 2) = 29. Answer is A. #### A QUESTION:Which number should replace both the asterisks in (* /21) x (*/84) = 1 ? options: A)21 B)42 C)63 D)72 E)168 SOLUTION:Let (y/21) x (y/84) = 1 y^2 = 21 x 84 = 21 x 21 x 4 y = (21 x 2) = 42 The answer is B. #### B QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b? options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given. SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2. Answer: A. #### A QUESTION:The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is: options: A)12 B)24 C)34 D)48 E)54 SOLUTION:Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. So, the numbers 12 and 16. L.C.M. of 12 and 16 = 48.Answer: Option D #### D QUESTION:In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a four or a one on either die, that player wins. What is the probability that a player wins after playing the game once? options: A)1/3 B)4/9 C)5/9 D)2/3 E)3/4 SOLUTION:We're looking for the number of outcomes that include AT LEAST a 1 or a 4. #getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6 #getting a one in 2nd die {(2,1), ...(5,1),(6,1) } = 4 [exclude 1,1 and 4,1] since it will be counted twice #getting a three in 1st die {(3,1), (3,2), ...(3,6) }= 6 #getting a three in 1st die {(2,4), (3,4), ...(6,4) } = 4 [exclude 1,4 and 4,4] since it will be counted twice Total possibities = 20 Probability of rolling at least a 1 or a 4 on two dice: 20/36 = 5/9 C #### C QUESTION:What is the remainder when 3990990900032 is divided by 32 ? options: A)0 B)8 C)4 D)2 E)3 SOLUTION:Though i was unaware of the divisibility test for 32 but i guessed the pattern!! divisibility rule for 4- last two digits must be divisible by 4 divisibility rule for 8- last three digits must be divisible by 8 similarly, divisibility rule for 32 - last five digits must be divisible by 32 Hence, Ans A #### A QUESTION:The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum. options: A)33498 B)17000 C)2665 D)28876 E)313 SOLUTION:The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a. So P = (100 * 10200)/ (30 * 2) = Rs.17000 Answer:B #### B QUESTION:Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed? options: A)10 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:Work done by P in 1 hour = 1/8 Work done by Q in 1 hour = 1/10 Work done by R in 1 hour = 1/12 Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120 Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60 From 9 am to 11 am, all the Printer were operating. Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60 Pending work = 1- 37/60 = 23/60 Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11 which is approximately equal to 2 Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm B #### B QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? options: A)1000 B)817 C)278 D)268 E)280 SOLUTION:2 * 22/7 * 1.75 * x = 11000 x = 1000 Answer: A #### A QUESTION:The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to: options: A)0.04 B)0.004 C)0.4 D)0.0004 E)None of them SOLUTION:Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is A #### A QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 10800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)60000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 10800 ( 18 × 600 = 10800) 100% -------> 60000 votes (100 × 600 = 60000) C #### C QUESTION:In the set of positive integers from 1 to 80, what is the sum of all the odd multiples of 5? options: A)180 B)245 C)320 D)260 E)270 SOLUTION:reduce to 1 - 80 5 - 15 - 25 - 35 - 45--55--65--75 are valid multiples. Add them --> 320 C #### C QUESTION:Each of the integers from 1 to 18 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even options: A)19 B)12 C)11 D)10 E)3 SOLUTION:Out of the 18 integers: 9 are odd and 9 are even. If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case: 1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first 2. 10th number will be the first even number So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even. So, answer will be 10. (D) #### D QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)21% C)21.33% D)22.109% E)23% SOLUTION:Lets say the indicated weight is x for $10 but the trader actually get 1.1x for $10 now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1 so profit % = (12.1-10)/ 10 = 0.21 = 21% ANSWER:B #### B QUESTION:Which is greater than -1? options: A)-5 B)-4 C)-3 D)-2 E)0 SOLUTION:-1 greater than 0. Answer: E #### E QUESTION:Of the 11 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 11 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man? options: A)22 B)35 C)60 D)70 E)105 SOLUTION:another approach : one scenario : [WWWM] now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women. and 6 ways to select one man so 5*4*3*6 = 360 now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways hence 360/3!= 360/6= 60 C #### C QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:1397 x 1397 = ? options: A)1961609 B)1851609 C)1951619 D)1951609 E)1851619 SOLUTION:1397 x 1397 = (1397)^2 = (1400 - 3)^2 = (1400)^2 + (3)^2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer is D. #### D QUESTION:Find the least number of complete years in which a sum of money put out at 15% compound interest will be more than double of itself? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:5 years Answer: A #### A QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:rom the beginning; Initially milk to water is 12l : 8l remove half 6 - 4 add 10l milk 16 - 4 remove half 8 - 2 add 10l milk 18 - 2 18:2 = 9:1 ANSWER:B #### B QUESTION:A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? options: A)37 B)38 C)30 D)77 E)27 SOLUTION:US = 25 DS = 35 M = (35 + 25)/2 = 30 Answer:C #### C QUESTION:A car travels from P to Q at a constant speed. If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance. It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two cities options: A)100 km B)120 km C)150 km D)180 km E)None of these SOLUTION:Explanation : Let the distance between two cities = D, D = x*t (x = usual speed and t is the actual time) D = (X + 20)*(T -2) and D = (X +30)*(T – 2.5) Solve the above equation, u will get T = 5 and X = 30, so distance = 30*5 = 150 km Answer – C #### C QUESTION:If x and y are integers, what is the least positive number of 24x+9y? options: A)1 B)3 C)4 D)6 E)9 SOLUTION:24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1. 8(-1) + 3(3) = 1 Then 3(8x+3y) can have a minimum positive value of 3. The answer is B. #### B QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x? options: A)16 B)28 C)15 D)13 E)18 SOLUTION:HCF x LCM = Product of Numbers 2 x 144 = 16 x x x = (2 x 144) / 16 x = 18 ANSWER : E #### E QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept? Assume there are 82 unique alphanumeric case sensitive characters. options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6) SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways ) =82^4(1+ 82) =82^4 * 83 Answer B #### B QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? options: A)12/489 B)12/452 C)12/455 D)12/429 E)12/292 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When three marbles are drawn, the probability that one is yellow and two are red = (²C₁)(⁴C₂)/¹⁵C₃ = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455 Answer: C #### C QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)11 2/3% loss C)66 2/3% loss D)12 2/3% loss E)17 2/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss Answer: A #### A QUESTION:A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is : options: A)16000 B)18000 C)20000 D)30000 E)None of these SOLUTION:Explanation: Number of bricks =Courtyard area /1 brick area =(1800×1200 /12×6)=30000 Option D #### D QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 8:2. If 80% of the Toyota bought and 20% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? options: A)66% B)64% C)68% D)69% E)72% SOLUTION:let total no of Vehicles bought be 100, Toyota 80 and Honda 20, so total number of SUV's bought for Toyota and Honda respectively 80* 80/100=64 and 20* 20/100=4 so total 68 SUV's were bought out of 100 Vehicles bought..so required % is 68% ANSWER:C #### C QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum z of all the even integers between 99 and 301? options: A)10,100 B)20,200 C)22,650 D)40,200 E)45,150 SOLUTION:I would solve it in a different way. First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101 Average = (301+99)/2 = 400/2 = 200 Sum z= Average*total count = 200*101 = 20,200 Answer is B #### B QUESTION:The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is options: A)17.2 km B)7.2 km C)7.6 km D)17.6 km E)27.2 km SOLUTION:speed of a boat in still water = 15 km/hr Speed of the current = 3 km/hr Speed downstream = (15+3) = 18 km/hr Distance travelled downstream in 24 minutes=(24/60)×18=(2×18)/5 = 7.2 km Answer is B #### B QUESTION:Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work? options: A)13 B)14 C)18 D)11 E)10 SOLUTION:(5 + x)/20 + 5/25 = 1 => x = 11 days Answer:D #### D QUESTION:Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? options: A)129 B)128 C)189 D)187 E)112 SOLUTION:CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135 SP = CP[(100 + profit%)/100] = 135 * [(100 + 40)/100] = Rs. 189. Answer: C #### C QUESTION:In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1? options: A)25 B)45 C)55 D)70 E)30 SOLUTION:Day 1&2 = 80; Only Day 1&2 (80-20) = 60, Day 2&3 = 70; Only Day 2&3 (70-20) = 50, Only Day 1 = 175 - (60+50+20) = 45 Answer:B #### B <<<Examples ends QUESTION:A student can select one of 6 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science. options: A)22 B)72 C)99 D)37 E)01 SOLUTION:6C1×3C1×4C16C1×3C1×4C1 = 6x3x4=72 ways Answer:B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes T, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 6 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15 So, T=15-5 = 10.C #### C QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1). options: A)320 B)350 C)340 D)360 E)400 SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there? 99+(912-9-90*2)/3=340 Answer : C #### C QUESTION:Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L options: A)1/3. B)1/2. C)3. D)2. E)6. SOLUTION:Difference = Average H - L = (H + L)/2, Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2 C #### C QUESTION:A retailer buys 140 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)105 B)155 C)125 D)185 E)285 SOLUTION:let the market price of each pen be $1 then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60 profit %=((102.60*100)/36) %=285% Answer E #### E QUESTION:Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes options: A)18kms B)16kms C)50kms D)30kms E)40kms SOLUTION:total eastward distance= 25kmph*1/4hr=6.25 km total westward distance= 40kmph*1/4hr=10 km total distn betn them= 6.25+10=16.25km ans 16km ANSWER:B #### B QUESTION:In a certain lottery, the probability that a number between 1 and 15, inclusive, is drawn is 1/3 . If the probability that a number 1 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 15 is drawn? options: A)2/3 B)1/3 C)1/4 D)1/6 E)2/5 SOLUTION:You can simply use sets concept in this question. The formula Total = n(A) + n(B) - n(A and B) is applicable here too. Set 1: Number 1 or larger Set 2: Number 15 or smaller 1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or less OR both) 2/3 + P(Set 2) - 1/3 = 1 P(Set 2) = 2/3 Answer A #### A QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? options: A)Rs. 4980 B)Rs. 4991 C)Rs. 4996 D)Rs. 4997 E)Rs. 5000 SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991. B) #### B QUESTION:An apple orchard grows red and green apples. On the first day of harvest, 496 apples are collected. There are three times as many red apples as there are green apples. How many green apples were harvested? options: A)99 B)112 C)118 D)124 E)130 SOLUTION:Let x be the number of green apples. There were 496 total apples; there are three times as many red apples as green apples. Therefore, x + 3x = 496 4x = 496 x = 124 Answer: D #### D QUESTION:What is the probability of drawing a queen from a deck of 52 cards? options: A)4/13 B)1/13 C)4 D)1 E)2/13 SOLUTION:Total number of cards,n(s)=52 Total number of queen cards,n(e)=4 p(e)=n(e)/n(s)=4/52=1/13 Option B is answer #### B QUESTION:A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)120 m B)225 m C)300 m D)360 m E)280 m SOLUTION:Speed = 54 x 5/18 m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/35 = 15 x + 300 = 525 x = 225 m.Answer: Option B #### B QUESTION:The area of a triangle is with base 12m and height 5m? options: A)88 m2 B)30 m2 C)66 m2 D)77 m2 E)31 m2 SOLUTION:1/2 * 12 * 5 = 30 m2 Answer: B #### B QUESTION:A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting? options: A)12 B)22 1/2 C)37 1/2 D)88 E)80 SOLUTION:(16/2) ( 2+3) * 2 = 80=E #### E QUESTION:Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) options: A)27 B)30 C)33 D)36 E)39 SOLUTION:33/4 ÷ 4 = 33/16 pounds in each container 33/16 pounds * 16 ounces / pound = 33 ounces in each container The answer is C. #### C QUESTION:The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher? options: A)30 Years B)49 Years C)51 Years D)55 Years E)57 Years SOLUTION:Total age of students is 32X16 = 512 Years Total age inclusive of teacher = 33X (16+1) = 561 So, Teacher's age is 561-512 = 49 Yrs There is a shortcut for these type of problems Teacher's age is 16+(33X1) = 49 Years B) #### B QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Answer:C #### C QUESTION:Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2500. then his monthly salary is options: A)Rs. 12500 B)Rs. 1000 C)Rs. 8000 D)Rs. 6000 E)Rs. 15000 SOLUTION:Sol. Saving = [100 - (40 + 20 + 10 + 10]% = 20%. Let the monthly salary be Rs. x. Then, 20% of x = 2500 ⇔ 20 / 100x = 2500 ⇔ x = 2500 × 5 = 12500. Answer A #### A QUESTION:A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 5 hour to row to a place and come back, how far is the place? options: A)24km B)30km C)48km D)12km E)15km SOLUTION:Speed of down stream = 10+2 = 12kmph speed of upstream = 10-2 = 8kmph Let the required distance be xkm x/12 + x/8 = 5 2x+3x = 120 x = 24 km Answer is A #### A QUESTION:For which of the following functions f is f(c) = f(1-c) for all c? options: A)f (c) = 1 - c B)f (c) = 1 - c^2 C)f (c) = c^2 - (1 - c)^2 D)f (c) = c^2*(1 - c)^2 E)f (x) = x/(1 - x) SOLUTION:I remember seeing this problem in a GMATprep test. I think choice D should be F(c)=(c^2) (1-c)^2. If that is true then substituting (1-c) for will give us the same function back and the answer choice is D, where the function is multiplicative #### D QUESTION:What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21? options: A)2327 B)2757 C)3147 D)3587 E)3997 SOLUTION:When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150 The answer is C. #### C QUESTION:In how many years will a sum of money double itself at 10% per annum? options: A)2 years 4 months B)4 years 2 months C)8 years 4 months D)10 years 8 months E)None SOLUTION:Sol. Let sum = x. Then, S.I. = x ∴ Time = [100 * S.I. / P*R] = [100 * x / x * 12] years = 8 1/3 years = 8 years 4 months. Answer C #### C QUESTION:A 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec. What is the length of the platform? options: A)500 B)350 C)828 D)277 E)122 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/489 = 50/3 3x + 900 = 2400 => x = 500 m. Answer: A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)240 B)377 C)2908 D)287 E)201 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: A #### A QUESTION:What percent is 20% of 25%? options: A)20% B)30% C)50% D)60% E)80% SOLUTION:Required percentage = 20%/25% * 100 = 20/25 * 100 = 80% Answer is E #### E QUESTION:A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes? options: A)100 m B)150 m C)190 m D)200 m E)220 m SOLUTION:Explanation: Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr Distance covered in 6 minutes =1/60X6km=1/10km=100m Distance between the thief and policeman = (200 – 100) m = 100 m. ANSWER IS A #### A QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ? options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours SOLUTION:Explanation: We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as Work done for 1 hour without leak = 1/3 Work done with leak = 3 1/2=7/2 Work done with leak in 1 hr=2/7 Work done by leak in 1 hr=1/3=2/7=1/21 So tank will be empty by the leak in 21 hours. ANSWER IS D #### D QUESTION:It takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate. If 5 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 1:00 PM, at what time will the machine be complete? options: A)4:30 B)4:45 C)5:00 D)5:15 E)5:30 SOLUTION:3 workers build 1/15 of a machine in one hour. 1 worker builds 1/45 of a machine in one hour. In the first 2 hours, 5 workers build 5*(1/45)*2=10/45 of a machine. From 1:00 to 2:00, 6 workers build another 6/45. The total is 16/45. From 2:00 to 3:00, 7 workers build another 7/45. The total is 23/45. From 3:00 to 4:00, 8 workers build another 8/45. The total is 31/45. From 4:00 to 5:00, 9 workers build another 9/45. The total is 40/45. To build another 5/45, 10 workers need (5/10)*60 minutes which is 30 minutes. The machine is complete at 5:30. The answer is E. #### E QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit? options: A)s.2323 B)s.2380 C)s.2329 D)s.2660 E)s.2312 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 7790 * 14/41 = Rs.2660. Answer: D #### D QUESTION:A train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds. What is the length of the train (in meters)? options: A)190 B)200 C)210 D)220 E)230 SOLUTION:Let the length of the train be x meters. The speed of the train is x / 15. Then, x + 140 = 25*(x / 15) 10x = 2100 x = 210 meters The answer is C. #### C QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)288 B)492 C)877 D)278 E)178 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 20 + 21 = 41 T = 12 D = 41 * 12 = 492 Answer: B #### B QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds? options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these SOLUTION:First cart speed will be 24/3=8 Second cart speed is 120/2=60 So, ratio is 8/60=2/15 ANSWER:A #### A QUESTION:In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class? options: A)1/2 B)1/3 C)2/3 D)1/4 E)3/4 SOLUTION:(1/2)G=(1/3)(B+G) 3G=2B+2G G=2B B/G=1/2. The answer is A. #### A QUESTION:In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old? options: A)231/260 B)117/130 C)51/65 D)23/32 E)11/16 SOLUTION:The number of people younger than 70 years old is 2600-800 = 1800 The number of females older than 70 years old is 0.6*850 = 510 The number of people who are either female or younger than 70 is 1800+510 = 2310. P(a person is younger than 70 or male) = 2310/2600 = 231/260 The answer is A. #### A QUESTION:The height of the wall is 4 times its width and length of the wall is 3 times its height .if the volume of the wall be 10368 cu.m.its width is options: A)4m B)5m C)6m D)7m E)8m SOLUTION:Explanation: Let width = x Then, height=4x and length=12x 12x × 4x × x = 10368 x = 6 Answer: C #### C QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-79)*(50-80)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:In 10 years, P will be as old as Q is now. Twenty years ago, Q was twice as old as P was then. How old is P now? options: A)30 B)35 C)40 D)45 E)50 SOLUTION:Q = P+10 Q-20 = 2(P-20) P-10 = 2P-40 P = 30 The answer is A. #### A QUESTION:There are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? . options: A)75 Kg B)80 Kg C)85 Kg. D)90 Kg E)92 Kg SOLUTION:New average weight= 110+60/2= 85 kgs Since avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85 C is the answer #### C QUESTION:Express the ratio 3 2/3 : 7 1/3 in its simplest form. options: A)1:21 B)1:1 C)2:1 D)1:2 E)2:11 SOLUTION:Solution We first convert the mixed numbers 3 2/3 and 7 1/3 into fractions 3 2/3 = 3*3 / 3 + 2 / 3 = 11 / 3 7 1/3 = 7*3 / 3 + 1 / 3 = 22 / 3 The ratio 3 2/3 : 7 1/3 can be expressed as 11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22 Simplify = 11 / 22 = 1 / 2 The ratio is 1 / 2 or 1:2 ANSWER IS D #### D QUESTION:In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true? I) k=0 II) k=−1 III) k=−3 options: A)I only B)III only C)I and II only D)II and III only E)I and III only SOLUTION:Please format the question properly. Per the question, x^2+kx+1=0 with k=constant. For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges. B is the correct answer. #### B QUESTION:Boy sells a book for Rs. 540 he gets a loss of 10 %, To gain 10%, what should be the SP? options: A)430 B)450 C)550 D)590 E)660 SOLUTION:Cost price = 540/90 x 100 = 600 To gain 10% = 600 x 10/100 = 60 SP = CP + gain = 600 + 60 = 660 Answer :E #### E QUESTION:5% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning? options: A)2988 B)2776 C)4400 D)4675 E)881 SOLUTION:X * (95/100) * (80/100) = 3553 X = 4675 Answer:D #### D QUESTION:We made a down payment of $80 and borrowed the balance on a new cello which cost $500. The balance with interest was paid in 23 monthly payments of $19 each and a final payment of $4. The amount of interest paid was what percent of the amount borrowed? options: A)3.5% B)4% C)4.5% D)5% E)5.5% SOLUTION:We borrowed $420. To pay back this loan, we paid 23*$19 + $4=$441. The interest was $441-$420=$21. The percentage was $21/$420=0.05=5%. The answer is D. #### D QUESTION:If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers? options: A)108 B)99 C)128 D)135 E)143 SOLUTION:Let the 2 positive numbers x and y x+ y = 20 -- 1 x^2 - y^2 = 40 => (x+y)(x-y)=40 -- 2 Using equation 1 in 2 , we get => x-y = 2 -- 3 Solving equation 1 and 3 , we get x= 11 y= 9 Product = 11*9 = 99 Answer B #### B QUESTION:Eggs are sold in packages of six or eleven only. If Doris bought 78 eggs exactly, what could be the number of large packs Doris bought? options: A)6. B)2. C)3. D)5. E)4. SOLUTION:No strategy involved. Simple question demanding fast calculation. 11x6 = 66=> 78-66=12 => 12/6 is an integer Ans A. 6. Good luck #### A QUESTION:The average weight of 5 person's increases by 4 kg when a new person comes in place of one of them weighing 50kg. What is the weight of the new person? options: A)70 B)86.5 C)80 D)88.5 E)75 SOLUTION:Total increase in weight =5 × 4=20 If x is the weight of the new person, total increase in weight = x−50 => 20= x - 50 => x = 20+50= 70 ANSWER:A #### A QUESTION:A retailer buys 100 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? options: A)110 B)175 C)212 D)218 E)220 SOLUTION:let the market price of each pen be $1 then, Cost Price of 100 pens = $ 36 Selling Price of 100 pens =99% of $100=$ 99 profit %=((63*100)/36) %=175% Answer B #### B QUESTION:A man can row his boat with the stream at 19 km/h and against the stream in 11 km/h. The man's rate is? options: A)4 kmph B)2 kmph C)7 kmph D)8 kmph E)3 kmph SOLUTION:DS = 19 US = 11 S = ? S = (19 - 11)/2 = 4 kmph Answer:A #### A QUESTION:At 12:10 o'clock Bill leaves point A towards point B at a speed of 30 Km/h. At 13:40 o'clock Richi leaves from the same point towards point B also, but at a speed of 60 Km/h. At what time will Richi passes over Bill? options: A)14:40. B)15:10. C)16:10 D)15:40 E)15:30 SOLUTION:Distance travelled by Bill in 1hr 30min ( 12:10 to 13:40) = 30kmph*(90/60)hr = 45km Relative speed = Richi's speed ~ Bill's speed = 30kmph Time taken by Richi to cross Bill = 45/30 = 1.5 hrs Time at which Richi will cross Bill = 13:40 + 1:30 = 14:70 = 15:10 hrs Ans. B #### B QUESTION:In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the fifth row? options: A)10 B)11 C)13 D)14 E)16 SOLUTION:Let x be the number of cans in row 1. The total number of cans is x + (x+3) + ... + (x+27) = 10x + 3(1+2+...+9) = 10x + 3(9)(10)/2 = 10x + 135 Since the total is less than 150, x must equal 1. The number of cans in the 5th row is 1 + 3(4) = 13 The answer is C. #### C QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)2/215 B)3/155 C)1/216 D)2/213 E)3/212 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers : options: A)4 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8. Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61. or 5x + 20 = 305 or x = 57. So, required difference = (57 + 8) - 57 = 8 Answer: B #### B QUESTION:On the x-y coordinate plane there is a parabola, y=x(4-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis? I. (1, 4) II. (2, 3) III. (4, 1) options: A)I only B)II only C)III only D)I and II E)I, II, and III SOLUTION:Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive. When x = 1, y = 3 lies on the parabola, so (1, 4) will not be enclosed by the parabola and x axis. When x = 2, y = 4 lies on the parabola, so (2, 3) will lie below it and this point will be enclosed by the parabola and x axis. When x = 4, y = 0 lies on the parabola, so (4, 1) will not be enclosed by the parabola and x axis. The answer is B. #### B QUESTION:Sharmila works 10 hours per day on Monday, Wednesday and Friday, and 8 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $460 per week. How much does she earn in dollars per hour? options: A)8 B)9 C)9.5 D)10 E)11 SOLUTION:So, she works 30 hours in 3 days So, she works 16 hours in 2 days So in a week she works 46 hours ( 30 + 16 ) and earns $460 So, Hourly wage is 460/46 => 10 Hence answer will be (D) 10 #### D QUESTION:The positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true? I. c > a II. c = a III. c < a options: A)I only B)II only C)III only D)I and II only E)II and III only SOLUTION:Let q = 10% then l = 100/11 % let b = 100 then a = 110 after increasing a by l and decreasing b yq we get c= 108 therefore c<a C it is answer #### C QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)8 B)9 C)10 D)20 E)30 SOLUTION:x ------- 6 (x + 10) ---- 3 x * 6 = (x + 10)3 x = 10 ANSWER:C #### C QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:How many numbers amongst the numbers 5 to 30 are there which are exactly divisible by 6 but not by 4? options: A)Nil B)1 C)2 D)3 E)More than 3 SOLUTION:6,12,18,24,30 are divisible by 6. 12, 24 are divisible by 4 also. So there are 3 numbers exactly divisible by 6 but not by 4 ANSWER:D #### D QUESTION:Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between: options: A)40 to 100 B)80 to 140 C)160 to 260 D)220 to 260 E)220 to 300 SOLUTION:260-X+X+300-X+GT60 = 400 =>X = GT 620-400 => X = GT 220 => X >= 220 (Here GT means Greater than) So Min value of X is 220 coming to options D/E X's maximum value cannot exceed 260 as per the venn diagramsince 'W' circle cannot accomodate 'X' More than 260 ANSWER:D #### D QUESTION:Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? options: A)s.10 B)s.2 C)s.5 D)s.3 E)s.4 SOLUTION:2500 = D(100/4)2 D = 4 ANSWER:E #### E QUESTION:If y exceeds x by 25%, then x is less than y by? options: A)20% B)16 3/3% C)16 2/3% D)12 2/3% E)16 1/3% SOLUTION:X=100 y=125 125------25 100-------? => 20% Answer:A #### A QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.15 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost? options: A)1276 B)1200 C)2832 D)1800 E)1236 SOLUTION:Explanation: l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 15 = 1800 Answer: Option D #### D QUESTION:which of the following could be the greatest common factor of positive integers 12 and 16 ? I) 5 II) 4 III) 2 options: A)I only B)I,II only C)II only D)I,III only E)III only SOLUTION:12=2*2*3 16=2*2*2*2 GCF =2*2=4 Answer : C #### C QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:Half of 5 percent written as decimal is options: A)5 B)0.5 C)0.05 D)0.025 E)None of these SOLUTION:Explanation: It will be 1/2(5%) = 1/2(5/100) = 5/200 = 0.025 Answer: Option D #### D QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:A jogger jogs at 1/6 of his usual speed. how much % he has to increase speed to reach normal pace of walking options: A)100 B)200 C)300 D)400 E)500 SOLUTION:suppose usual speed is x, then current speed is x/6. to gain normal speed, he has to gain 5x/6 % increase = 100*(5x/6)/(x/6) = 500% ANSWER:E #### E QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long? options: A)65sec B)70sec C)74sec D)80sec E)85sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 500)/10 = 74 sec. Answer:C #### C QUESTION:A customer pays 30 dollars for a coffee maker after a discount of 20 dollars What is the original price of the coffee maker? options: A)90 B)40 C)70 D)60 E)50 SOLUTION:Let x be the original price. x - 20 = 30 x - 20 + 20 = 30 + 20 x + 0 = 50 x = 50 Answer is E #### E QUESTION:The average of first five multiples of 3 is? options: A)2 B)9 C)8 D)6 E)3 SOLUTION:Average = 3(1 + 2 + 3 + 4 + 5)/5 = 45/5 = 9. Answer:B #### B QUESTION:16, 23, 19, 19, 22, 15, 25, ? What number should replace the question mark? options: A)13 B)11 C)16 D)18 E)19 SOLUTION:B 11 There are two alternate sequences: +3 and –4; #### B QUESTION:If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be options: A)2 B)5 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 5*8820 = 44, 100, which is a square of 210 B #### B QUESTION:A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour? options: A)7 km/hr B)7.2 km/hr C)7.4 km/hr D)7.8 km/hr E)8.9 km/hr SOLUTION:Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B #### B QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21 Ans: B #### B QUESTION:There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female? options: A)75 B)100 C)125 D)175 E)225 SOLUTION:female = x Male = 750-x x/2 + 750-x/4 = 1/3* (750)= 250 x= 250 x/2 = 125 is supposed to be the answer ANSWER:C #### C QUESTION:There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round? options: A)15 B)30 C)120 D)240 E)256 SOLUTION:Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence C. #### C QUESTION:factor: 3y (x-3)-2(x-3) options: A)(x-3)-2(x-3) B)(x-3)power2 C)(x-3)(3y-2) D)3y(x-3) E)x-3 SOLUTION:3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C) #### C QUESTION:With 630 ml mixture of milk & water in the ratio 7:2. How much water mustbe added to make the ratio 7:3? options: A)60 ml B)80 ml C)70 ml D)90 ml E)92 ml SOLUTION:concentration of water in mixture1 =2/9 (since the ratio of milk and water = 7:2) ...(1) concentration of water in pure water= 1 ...(2) Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3 => concentration of water in mixture2 =3/10 By rule of alligation, concentration of water in mixture1 (2/9) concentration of water in pure water (1) Mean concentration (3/10) 1−3/10=7/10 =1:19 => Quantity of water =630×1/9=70 ml C #### C QUESTION:A data set with a mean of 40 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)18 B)36 C)59 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=40-3.5=36.5 to{mean}+{deviation}=40+3.5=43.5. The smallest number within this range from the options is 36. Answer: B. Hope this helps. #### B QUESTION:A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently five spaces behind player B, what is the probability that player B will be frozen after player A rolls? options: A)1/12 B)5/36 C)1/9 D)1/3 E)17/36 SOLUTION:no. of possible outcomes = 6*6 = 36 no. of outcomes that result a total of 5 (as A is 5 spaces behind B) = 4 ( (1,4), (2,3), (3,2), (4,1) ) So, the probability = 1/9 (Option C) #### C QUESTION:if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no. options: A)24 B)25 C)26 D)27 E)28 SOLUTION:25 m^3 = (3+1)(3+1) = 16 then m^4 = (4+1)(4+1)=25 ANSWER:B #### B QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:(112 x 54) = ? options: A)70000 B)71000 C)72000 D)73000 E)74000 SOLUTION:(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 A) #### A QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14×30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×14) Ratio of the capacity of a man and woman =1/(15×14) : 1/(14×30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48. options: A)240/1587 B)240/1545 C)240/1547 D)240/1542 E)240/1512 SOLUTION:P : 2/13 = 5/34 : 7/48 As the product of the means is equal to the product of the extremes. P*7/48 = 2/13 * 5/34 P*7/48 = 10/442 P = 480/3094 => P = 240/1547 Answer: C #### C QUESTION:If w<0, which of the following must be true? options: A)–100 < w < 100 B)w ≤ –1 C)w ≤ 1 D)w^2 ≥ 1/4 E)–100 < w < 0 SOLUTION:w is a negative number. A. –100 < w < 100w can be a negative number less than -100 B. w ≤ –1w can be a fraction, in which case it would be greater than -1 C. w ≤ 1must be true since 1 is positive and w is negative D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5 E. –100 < w < 0w can be a negative number less than -100=C #### C QUESTION:In the new budget, the price of rice rose by 20%. By how much percent must a common man reduce his consumption so that his expenditure on it does not increase? options: A)16.66% B)17% C)15.8% D)12% E)None of these SOLUTION:Explanation : Solution: reduction in consumption = [r/(100+r) * 100]% = (20/120 * 100) = 16.66% Answer : A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train. options: A)150 m B)145 m C)100 m D)135 m E)155 m SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 6 = 100 meter ANSWER: C #### C QUESTION:If a function f is defined by f(x)= (1-x)/x for all non zero numbers x. If f(a) = 1 and f(a/b) = 3 then b= ? options: A)3 B)1/3 C)2 D)1/2 E)-2 SOLUTION:Given that f(x)= (1-x)/x and f(a) = 1, then f(a) =(1-a)/a=1 ===> a=1/2, then backsolve using the answer choices: f(a/b) = f(1/2b) = 3 A) 3 ===> f(1/2*3) = f(1/6) = 5 B) 1/3 ===> f((1/2)/(1/3)) = f(3/2) = (-1/2)/(3/2) = -1/3 C) 2 ===> f(1/2*2) = f(1/4) =3 WINS D) 1/2 ===> f((1/2)/(1/2)) = f(1) = 0 E) -2 ===> f((1/2)/-2) = f(-1/4) = (5/4)/(-1/4) = -5 Answer: C #### C QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:The distance between A&B is 450km. A person is traveling from A to B at 70km/hr started at 9AM and another person is traveling from B to A at 80km/hr and started at same time. Then at what time they meet together.? options: A)A)12PM B)B)4PM C)C)1PM D)D)3PM E)E)5PM SOLUTION:Let x hours be they will meet together distance covered by 1st person+distance covered by 2nd person = 450km 70x+80x = 450 x= 3 hr They will meet = 9AM +3hr = 12PM Answer is A #### A QUESTION:4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there. options: A)6! x 7P4 B)6! x 9P4 C)6! x 5P4 D)6! x 3P4 E)6! x 2P4 SOLUTION:Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways. So total ways are 6! x 7P4 Answer:A #### A QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)200 B)300 C)500 D)600 E)700 SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: Option C #### C QUESTION:The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is options: A)0.4869 B)0.5904 C)0.6234 D)0.5834 E)0.2952 SOLUTION:P(winning prize atleast on one ticket) = 1 - P("Losing on all tickets") = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2) = (1.64)(0.36) = 0.5904 ANSWER:B #### B QUESTION:In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students Q in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get: 0....50k.....100k, 100k, 100k But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done? options: A)572 B)672 C)472 D)372 E)None SOLUTION:Solution: 10C5: when both are not included. 10C4: when one of them is included. Number of ways = 10C5 +10C4+ 10C4 = 672 Answer: Option B #### B QUESTION:An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? options: A)$480 B)$489.60 C)$634.64 D)$800.32 E)$240 SOLUTION:1.04*1.04*6000 = $6489.60 The answer is B. #### B QUESTION:A man spends Rs. 1500 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income? options: A)2075 B)2100 C)2200 D)2300 E)2400 SOLUTION:Explanation: Total expenditure for the first 3 months = 3 × 1500 = 4500 Total expenditure for 4 months = 4 × 1550 = 6200 Total expenditure for 5 months = 5 × 1800 = 9000 Total expenditure and saving (which is income for one year) = 4500 + 6200 + 9000 + 5200 = Rs. 24900 So, Average monthly income = 24900/12 = Rs. 2075 Answer A #### A QUESTION:Three hoses work to fill a tub at at different rate. Hose Q and B, working together, can fill the tub in 6/5 of an hour. Hoses Q and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub? Edited for accurate solution options: A)3/10 B)2/5 C)1/2 D)1 E)6/5 SOLUTION:Convert the given time to rate and you will be able to add it up. Total Rate of Q and B = Rate of Q + Rate of B = 1/(6/5) = 5/6 Total Rate of Q and C = Rate of Q + Rate of C = 1/(3/2) = 2/3 Total Rate of B and C = Rate of B + Rate of C = 1/2 Adding all three, 2(Rate of Q + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2 = 2 Rate of Q + Rate of B + Rate of C = 1 tub/hour Time taken by all three together to fill up the tub is 1 hour=D #### D QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:If a number p is prime, and 2p+4 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:1/6 = 0.1666666... (a repeating pattern one digit long) A #### A QUESTION:John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet? options: A)1/16 B)5/16 C)3/8 D)1/2 E)1/4 SOLUTION:John will run farther if he runs at 5 mph and Amanda runs at 4 mph. P(John runs farther) = 1/4 * 1/4 = 1/16 The answer is A. #### A QUESTION:10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? options: A)2 B)1 C)7 D)6 E)4 SOLUTION:1 women's 1 day work = 1/70 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/10 + 10/140) = (1/14 + 1/14) = 1/7 5 women and 10 children will complete the work in 7 days. Answer:C #### C QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? options: A)480 B)540 C)600 D)720 E)900 SOLUTION:4C2 x 3C3 x 5! = 720 The answer is D. #### D QUESTION:5% of (25% of $1600) is? options: A)$20 B)$30 C)$45 D)$15 E)$60 SOLUTION:5% of (25% of $1600) = 5/100 (25/100 * 1600) = $20 Answer is A #### A QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:16 C)18:10 D)18:14 E)14:11 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer: A #### A QUESTION:the banker's discount on a bill due 4 months hence at 15% is Rs.420. what is the true discount? options: A)41 B)400 C)390 D)380 E)480 SOLUTION:TD= (BD * 100)/(100+TR)= (420 * 100)/100+((4/12)*15)= (420 * 100)/100+((1/3)*15) =(420 * 100)/100+5= (84 * 100)/21 = 4*100=400 correct answer: (B) #### B QUESTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E. #### E QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ? options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9 SOLUTION:Here is how I did it. Probably there may be better way to do it. First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90. That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment. So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17) Number of integers, whose digits add to 1: 1 and 10 = 2 Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4 Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6 Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8 Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10 Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8 Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6 Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4 Number of integers, whose digits add to 16: 79, 88 = 2 So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers Probability B= 50/90 = 5/9 Correct answer E #### E QUESTION:A worker's daily wage is increased by 50% and the new wage is $30 per day. What was the worker's daily wage before the increase? options: A)$15 B)$18 C)$20 D)$22 E)$25 SOLUTION:Let x be the daily wage before the increase. 1.5x = $30 x = $20 The answer is C. #### C QUESTION:The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is options: A)22 B)30 C)99 D)28 E)17 SOLUTION:Explanation: Total age increased = (8 * 2) years = 16 years. Sum of ages of two new men = (21 + 23 + 16) years = 60 years Average age of two new men = (60/2) years = 30 years Answer: B #### B QUESTION:Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 21 have taken the preparatory course and 42 have not taken the course. How many members are there in the swim club? options: A) 40 B) 60 C) 80 D) 90 E) 140 SOLUTION:30% of the members have passed the test, thus 70% have not passed the test. We also know that 42+21=63 members have not passed the test, thus 0.7*Total=63 --> Total=90. Answer: D. #### D QUESTION:Express a speed of 90 kmph in meters per second? options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps SOLUTION:90 * 5/18 = 25 mps Answer:E #### E QUESTION:The two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z? options: A)16 B)3/√2 C)8 D)2√2 E)(√2)/3 SOLUTION:800score Official Solution: The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(3 × 3) = 9/2; so z = 9/2. The next step requires us to find the length of a side of a cube that has a face area equal to 9/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 9/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 9/2. Clearly s = √9/2 = 3/√2 , oranswer choice (B). #### B QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is? options: A)767 km B)975 km C)678 km D)900 km E)546 km SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km. x/40 = (x + 100)/50 50x = 40x + 4000 => x = 400 So, distance between P and Q = (x + x + 100)km =900 km. Answer: D #### D QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half? options: A)44.2 B)47.8 C)50.5 D)53.6 E)56.9 SOLUTION:The average of this half is 154.4/4 = 38.6 This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8 The answer is B. #### B QUESTION:A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)A)300 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 =350 B #### B QUESTION:Which of the following is an integer? I. 9! / 6! II. 9! / 8! III. 9! / 7!5! options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:9!/6! = 9*8*7 which is an integer. 9!/8! = 9 which is an integer. 9!/7!5! = 9*8 / 5*4*3*2 = 3/5 which is not an integer. The answer is D. #### D QUESTION:Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube? options: A)236 B)256 C)216 D)246 E)206 SOLUTION:Volume of the new cube = [ 5(power)3 + 4(power)3 + 3(power)3 ] Cm(power)3 = 125 + 64 + 27 = 216 Cm(power)3 => a(power)3 = 216 Cm(power)3 Answer is C. #### C QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive? options: A)–5040 B)–3600 C)–720 D)–600 E)–120 SOLUTION:Maximize the total product with a -ve sign so -1 * 10 * 9 * 8 = 720 * -1 = -720 Answer is C. #### C QUESTION:If 18!/3^x is an integer, what is the greatest possible value of x? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:18 - 3*3*2 15 - 5*3 12 - 4*3 9 - 3*3 6 - 2*3 3 - 1*3 Hence max of 3^8 is allowed. IMO E. #### E QUESTION:If 4 men and 1 boy working together, can do two times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:4M + 1B =2(1M + 1B) 4M + 1B = 2M + 2B 2M = 1B The required ratio of work done by a man and a boy = 1:2 D #### D QUESTION:The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by? options: A)33 1/3 % B)9 1/11 % C)11 1/9 % D)66 2/3 % E)None SOLUTION:100 75 ------- 75 ------- 25 100 ------ ? => 33 1/3% ANSWER:A #### A QUESTION:What is the leastvalue of x. So that 23x57 is divisible by 3? options: A)3 B)4 C)1 D)5 E)6 SOLUTION:The sum of the digits of the number is divisible by 3, then the number is divisible by3. 2 + 3 + x + 5 + 7 = 17 + x Least value of x may be 1 Therefore 17 + 1 = 18 is divisible by 3. C #### C <<<Examples ends QUESTION:A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent? options: A)5.3 % B)7.6 % C)10.6 % D)12 % E)None of these SOLUTION:Explanation: Let Marked price be Re. 1 each C.P. of 50 pens = Rs. 46 S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50 Profit % = (Profit /C.P.) x 100 Profit% = (3.50/46) x 100 = 7.6 % ANSWER B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: options: A)11:5 B)3 : 2 C)1:2 D)3:5 E)7:8 SOLUTION:Answer: Option B Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. #### B QUESTION:In the exam the average was found to be p mark. After deducting typographical error the average marks of 94 student reduced from 84 to 64 . Due to this the average came down by 18.8 marks. What was the number of students who took the exam? options: A)100 B)120 C)110 D)130 E)160 SOLUTION:Explanation : Number of student = (84-64) * 94/18.8 = 100 Answer : A #### A QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? options: A)20 B)55/4 C)25 D)14 E)13 SOLUTION:After passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles/hour. In those 5 mins the cyclist travels a distance of 5/4 miles. In those 5 mins the hiker travels a distance of 1/3 miles. So the hiker still has to cover 11/12 miles to meet the waiting cyclist. The hiker will need 55/4 mins to cover the remaining 11/12 miles. So the answer is B. #### B QUESTION:If you are given $5, and the amount doubles every day, how much money will you have after 4 days? options: A)$256 B)$512 C)$1024 D)$625 E)$720 SOLUTION:5^4=625 The answer is D #### D QUESTION:Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ? options: A)2150 B)2200 C)2100 D)2250 E)2300 SOLUTION:Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10. Investment x time. Kala = 9 x 12 = 108. Sudha = 12 x 12 = 144. Githa = 10 x 9 = 180. Or Kala : Sudha : Githa => 6 : 8 : 5. Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a. Difference between the profits received by Kala and Sudha 6a – 8a = 2a = 840 or a = 420. Githa = 5a = 5 x 420 = Rs.2100. Option C #### C QUESTION:Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.7 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect? options: A)1/6 B)1/2 C)5/8 D)5/4 E)15/16 SOLUTION:X - fraction of products Jane inspected (1 - X) - fraction of products John inspected 0.7(X) + 0.5(1-X) = 0.75 0.2X = 0.75 - 0.5 X = 0.25/0.2 X = 5/4 Therefore the answer is D: 5/4. #### D QUESTION:What positive number, when squared, is equal to the cube of the positive square root of 17? options: A)64 B)32 C)8 D)4 E)2 SOLUTION:Let the positive number be x x^2 = ((17)^(1/2))^3 =>x^2 = 4^3 = 64 => x = 8 Answer C #### C QUESTION:Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage X. options: A)16.8% B)17.4% C)17.9% D)18.5% E)19.1% SOLUTION:Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20 Selling price of an orange = 10 --> Cost price = 10/1.25 = 8 A > O 23*(A) + 10*(O) = 653 653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0 Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value Between 11 and 21, If A = 11, O = 30 --> Not possible If A = 21, O = 17 --> Possible Cost price = 20*21 + 8*17 = 420 + 136 = 556 Profit = 653 - 556 = 97 Profit% X= (97/556)*100 = 17.4% Answer: B #### B QUESTION:Ayesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? options: A)6 B)40 C)50 D)10 E)20 SOLUTION:Mother's age when Ayesha's brother was born = 42 years. Father's age when Ayesha's brother was born = (58 + 4) years = 62 years. Required difference = (62 - 42) years = 20 years. Answer:E #### E QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:In a right angled triangle, two sides are consecutive whole number in which one side is hypotenuse. what could be the possible length of third side? options: A)277 B)361 C)269 D)171 E)112 SOLUTION:Explanation: Pythagorean triplets are generated with each "odd number" greater than 1 by using a formula. If n is an odd number, then Pythagorean triplet = n,n2−12,n2+12n,n2−12,n2+12. Here 361 is an odd number. So the triplet is 361, 65160, 65161. Answer:B #### B QUESTION:A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)3 B)7.5 C)2.25 D)1.5 E)4 SOLUTION:M = 9 S = x DS = 9 + x US = 9 - x 9 + x = (9 - x)2 9 + x = 18 -2x 3x = 9 x = 3 ANSWER:A #### A QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king? options: A)1/13 B)2/15 C)4/13 D)3/17 E)1/19 SOLUTION:Here, n(S) = 52 There are 13 cards that are diamond (including one king) and there are 3 more kings. Let E = event of getting a diamond or a king. Then, n(E) = (13 + 3) = 16 P (E) = 16 / 52 = 4/13 C #### C QUESTION:A data set with a mean of 40 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)18 B)36 C)59 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=40-3.5=36.5 to{mean}+{deviation}=40+3.5=43.5. The smallest number within this range from the options is 36. Answer: B. Hope this helps. #### B QUESTION:Calculate the circumference of a circular field whose radius is 10 centimeters. options: A)20 π cm B)19 π cm C)28 π cm D)25 π cm E)30 π cm SOLUTION:Circumference C is given by C = 2πr = 2π*10 = 20 π cm Answer: A #### A QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={13,13,13...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)a) k(n+m+mn)+ k B)b) (1+n+m+mn)(k+1) C)c) k^2(mn+n/m) D)d) kmn(k+m+n) E)e) None of the above. SOLUTION:a) how many 2's are included? b) how many 3's are included? and c) how many 11's are included? For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers. NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations. The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together: (mn + m + n + 1)(k + 1). Mike B #### B QUESTION:In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1? options: A)25 B)45 C)55 D)70 E)30 SOLUTION:Day 1&2 = 80; Only Day 1&2 (80-20) = 60, Day 2&3 = 70; Only Day 2&3 (70-20) = 50, Only Day 1 = 175 - (60+50+20) = 45 Answer:B #### B QUESTION:On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 48 centimeters assuming that 1-inch is 2.54 centimeters? options: A)174.2 B)212 C)288.1 D)296 E)302 SOLUTION:1.5 inch = 2.54*1.5 cm. So, 2.54*1.5 represents 24 miles. So for 48 cm.: 48/(2.54*1.5) = x / 24 ---> x = 24*47/(3.81) = 302 Answer will be E. #### E QUESTION:A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? options: A)17% B)25% C)69% D)31% E)19% SOLUTION:Let the price be 100. The price becomes 130 after a 30% markup. Now a discount of 10% on 130. Profit=117-100 17% answer A #### A QUESTION:Tough and Tricky questions: Exponents. If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy? options: A)4, 2, 8, 6 B)4 and 2 C)2 and 8 only D)6 and 4 E)8 and 6 SOLUTION:Only Units digit of X and Y contribute to the Units digit of XY. Finding all values of X for positive values of a When, a=1; X=2 a=2; X=4 a=3; X=8 a=4; X=16 a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4...... Similarly, Finding all values of Y for positive values of b When, b=1; Y=3 b=2; Y= 9 b=3; Y= 27 b=4; Y=81 b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9.... So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y When X=2 and Y=3: Units digit of XY = 6 When X=2 and Y=9: Units digit of XY = 18 When X=2 and Y=7: Units digit of XY = 14 When X=2 and Y=1: Units digit of XY = 2 When X=4 and Y=3: Units digit of XY = 12 When X=4 and Y=9: Units digit of XY = 36 When X=4 and Y=7: Units digit of XY = 28 When X=4 and Y=1: Units digit of XY = 4 When X=8 and Y=3: Units digit of XY = 24 When X=8 and Y=9: Units digit of XY = 72 When X=8 and Y=7: Units digit of XY = 56 When X=8 and Y=1: Units digit of XY = 8 When X=6 and Y=3: Units digit of XY = 18 When X=6 and Y=9: Units digit of XY = 54 When X=6 and Y=7: Units digit of XY = 42 When X=6 and Y=1: Units digit of XY = 6 There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6 Ans: A #### A QUESTION:John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet? options: A)1/16 B)5/16 C)3/8 D)1/2 E)1/4 SOLUTION:John will run farther if he runs at 5 mph and Amanda runs at 4 mph. P(John runs farther) = 1/4 * 1/4 = 1/16 The answer is A. #### A QUESTION:A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process? options: A)4.15 B)4.21 C)4.52 D)4.81 E)4.93 SOLUTION:X is the initial quantity of salt in the water. After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination. So we have: X1=1/3 X X2=1/3 X1 X3=1/3 X2 By multiplying both ends of the equations we get: X1*X2*X3 = (1/3)^3 X*X1*X2 Simplification leaves us with: X3 = (1/3)^3 X X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3) In this case, given X was: X=5 g So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81 Answer: D #### D QUESTION:Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible? options: A)48 B)66 C)72 D)78 E)90 SOLUTION:Total number of 5 digit numbers that can be formed = 5! = 120. Total number of 5 digit numbers in which 3 and 4 are adjacent = 48. This can be calculated by taking 3 and 4 as a pair and considering positions where they can appear. Number of 5 digit numbers in which 3 and 4 are not adjacent = Total number of 5 digit numbers - Total number of 5 digit numbers in which 3 and 4 are adjacent. Ans = 120 - 48 = 72 C #### C QUESTION:A student can select one of 6 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science. options: A)22 B)72 C)99 D)37 E)01 SOLUTION:6C1×3C1×4C16C1×3C1×4C1 = 6x3x4=72 ways Answer:B #### B QUESTION:1.5, 2.3, 3.1, 3.9, ..? options: A)0.6 B)0.8 C)0.4 D)0.24 E)0.15 SOLUTION:1.5+0.8=2.3 2.3+0.8=3.1 3.1+0.8=3.9 3.9+0.8=4.7 ANSWER:B #### B QUESTION:A car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment? options: A)$503 B)$504 C)$505 D)$506 E)$507 SOLUTION:Explanation: Cash price = $21 000 Deposit = 10% × $21 000 = $2100 Loan amount = $21000 − $2100 = $18900 I=p*r*t/100 I=11340 Total amount = 18900 + 11340 = $30240 Regular payment = total amount /number of payments Answer: B #### B QUESTION:529 is a perfect square. When x is added to the square root of 529, the result is also a perfect square. What is x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:529 is 23*23 here A 23+1 = 24 B 23+2 = 25 C 23+3 = 26 D 23+4 = 27 E 23+5= 28 so, B is the only addition that gives a perfect square. so x=3 then the answer is B #### B QUESTION:Find the greatest number of five digits to which if 7143 is added, the final number becomes exactly divisible by 18, 24, 30, 32 and 36. options: A)22391 B)81111 C)27999 D)27711 E)99417 SOLUTION:LCM of 18, 24, 30, 32 and 36 is 1440. 99999 + 7143 = 107142. Dividing 107142 by 1440, the remainder is 582. ∴ Required number = 99999 – 582 = 99417 Alternate Method: Cross check with options. Answer:E #### E QUESTION:Rohit spent 30 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Rohit have left over? options: A)29% B)35% C)46% D)47% E)52% SOLUTION:SayRohit's earning last month was $100. Rohit spent 30 percent of his earning last month on rent --> $30 on rent; 20 percent less than what he spent on rent to purchase a new dishwasher --> $30*0.8=$24 on the dishwasher. Left over amount 100 - (30 + 24) = $46 Answer: C #### C QUESTION:If q and r are even integers, which of the following is an odd integer? options: A)qr + 2 B)q(r − 1) C)q(q + 5) D)3q + 4r E)(q + 3)(r − 1) SOLUTION:If q and r are even integers, then: A. qr + 2: even + even = even B. q(r − 1): even(odd) = even C. q(q + 5): even(odd) = even D. 3q + 4r: even + even = even E. (q + 3)(r − 1): (odd)(odd) = odd. Answer is E. #### E QUESTION:One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met? options: A)38.07 B)40 C)42 D)39 E)40.07 SOLUTION:Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows 9t + 8(t + 1) = 80 9t + 8t + 8 = 80 17t = 72 T = 4.23 (hours) Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A. #### A QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000? options: A)81000 B)81027 C)81089 D)81027 E)28939 SOLUTION:64000* 9/8 * 9/8 = 81000 Answer: A #### A QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b? options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given. SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2. Answer: A. #### A QUESTION:A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? options: A) 16 B) 20 C) 32 D) 44 E) 48 SOLUTION:lets say x ounces of P is mixed with Q. => 67-x ounces of Q is present in the mixture (as the total = 67 ounces) given total almond weight = 15 ounces (20x/100)+(25/100)(67-x) = 15 => x = 35 => 67-35 = 32 ounces of Q is present in the mixture. Answer is C. #### C QUESTION:Submarine M and Submarine N are equipped with sonar devices that can operate within a 4,000 yard range. Submarine M remains in place while Submarine N moves 3,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West options: A)I,II only B)II,III only C)II only D)I and III only E)III only SOLUTION:It's evident if we make a diagram for the Movement of N respect to M. From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range. Thus it can only move north or west or anything in that curve. Answer : D #### D QUESTION:I purchased a superb bike and like my bike my number plate is also superb. The number plate is a five digit number plate and its water image is 78633 more than the number plate. Also all digits are unique. Whats is my number plate number ? options: A)10935 B)10968 C)23984 D)13725 E)11332 SOLUTION:B 10968 Water image is 89601 #### B QUESTION:One out of every 4000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch? options: A)450 B)900 C)90,000 D)1800,000 E)900,000 SOLUTION:(D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 4000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/4000 = 450/y. Solve for y and you will get the total number of chips in the batch: 1800,000. The answer is (D). #### D QUESTION:A ladies hostel had provision of food for 200 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is: options: A)28.97 B)28.0 C)28.47 D)27.47 E)29.47 SOLUTION:Explanation : After 10 days : 200 women had food for 25 days. Suppose 175 women had food for x days. Now, Less women, More days (Indirect Proportion) 175 : 200 :: 25 : x => 175 x x = 200 x 25 => x = 200 x 25 / 175 => x =28.47 Answer : C #### C QUESTION:A man watched his wife run around the neighborhood block 4 times. He was curious how fast she was running. Each block is 500 meters and she ran the distance in one hour. How fast was his wife running in kilometers per hour? options: A)3 B)1 C)2 D)4 E)5 SOLUTION:The distance of each block was 500 meters. She made the roundtrip 4 times. Multiply 4 by 500 to get 2000 meters or 2 km. Because it took her one hour to run the distance the answer is already in kilometers per hour. Correct answer is 2km/hour #### C QUESTION:Kira's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ? options: A)7cdx/100 B)d + 7cx/100 C)7d + xc/100 D)7d + 7xc/100 E)7cdx SOLUTION:Answer is D. #### D QUESTION:The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range: options: A)30 < x < 36 B)30 < x < 37 C)31 < x < 37 D)31 < x < 38 E)32 < x < 38 SOLUTION:f(n) = number of perfect squares less than n 1,4,9,16,25,36 f(25) = 4 f(26)=f(27)=...=f(35)=f(36) = 5 f(37) = 6 g(n) = number of prime numbers less than n 2,3,5,7,11,13,17,19,23,29,31,37 g(31)=10 g(32)=g(33)=...=g(36)=g(37) = 11 g(38)=12 f(x)+g(x)=16 implies that f(x)=5 and g(x)=11. So, x = 32,33,34,35,or36. Answer C, 31 < x < 37. #### C QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color? options: A)24/78 B)24/709 C)24/76 D)24/71 E)24/72 SOLUTION:Explanation: Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 2 marbles are drawn from 13 marbles at random. Therefore, n(S) = 13C2 = 78 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 24/78 ANSWER:A #### A QUESTION:Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/6. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)25. B)24. C)23. D)20. E)16. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 6,5 and 10 Lets take LCM of three balls 6,5 and 10 = 30. The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS. Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls. IMO option E is correct. #### E QUESTION:Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178? options: A)2277 B)2669 C)2200 D)2766 E)2998 SOLUTION:Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178. => (90%) of (110%) of x = Rs. 2178. => (90/100)(110/100)x = 2178 => x = (2178 * 100)/(9 * 11) => x = Rs. 2200 Answer: C #### C QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x*4x=900 x^2= 225 x= 15 Length= 4*15= 60 difference= 60-15= 45 E is the answer #### E QUESTION:In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg? options: A)5/6 B)3/9 C)5/0 D)5/3 E)5/9 SOLUTION:Explanation: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6 Answer: Option A #### A QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:Seller selling an apple for Rs.18, a Seller loses 1/6th of what it costs him. The CP of the apple is? options: A)10 B)12 C)19 D)18 E)20 SOLUTION:SP=18Loss=CP19Loss=CP−SP=CP−18⇒CP19=CP−18⇒18 CP19=18⇒CP19=1⇒CP=19 C #### C QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/38 C)18/34 D)18/31 E)18/30 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35. Answer:A #### A QUESTION:How many cubes of 5cm edge can be cut out of a cube of 20cm edge options: A)36 B)64 C)216 D)484 E)None of these SOLUTION:Explanation: number of cubes=(20 x 20 x 20) / (5 x 5 x 5) = 64 Answer: B #### B QUESTION:The product of two numbers a and b equals one-quarter their average. What is a in terms of b? options: A)a= b/(8b-1) B)a= b/(7b-1) C)a= b/(8b) D)a= b/(8b-4) E)a= 2b/(8b-1) SOLUTION:a*b = ( a+b)/8 8ab =a+b a= b/(8b-1) ANSWER:A #### A QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)3600 C)8900 D)9000 E)5000 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 ANSWER A #### A QUESTION:A man can row upstream at 22 kmph and downstream at 42 kmph, and then find the speed of the man in still water? options: A)29 B)92 C)30 D)32 E)23 SOLUTION:US = 22 DS = 42 M = (42 + 22)/2 = 32 Answer:D #### D QUESTION:The price of lunch for 10 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? options: A)11.73 B)12 C)13.8 D)14 E)18 SOLUTION:Clearly E is the answer I used POE here Lets consider option (E) 10*18= 180 now 180(115/100)=207 => possible ANSWER IMO E #### E QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)28% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 121.60 Let marked price be Rs. x. Then, 95/100 x = 121.60 x = 12160/95 = Rs. 128 Now, S.P. = Rs. 128, C.P. = Rs. 100 Profit % = 28%. Answer: B #### B QUESTION:Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let x be the number of shelves. 11x - 30 = 7(x-1) + 5 4x = 28 x = 7 The answer is C. #### C QUESTION:If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)9 E)18 SOLUTION:Let length of rectangle = L 6^2 = L*4 => L = 36/4 = 9 Answer D #### D QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)19% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer: C #### C QUESTION:If (-12x)^(4x) = 12x^(15 - x) and x is an integer, what is the value of x ? options: A)5 B)4 C)3 D)2 E)-2 SOLUTION:Since x is an integer, (-12x)^(4x) is always positive. So, 12x^4x = 12x^(15 - x) 4x = 15 - x 5x = 15 x = 3 Answer: C #### C QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:Dacid obtained 45, 35, 52, 47 and 55 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)79 B)99 C)47 D)89 E)45 SOLUTION:Average = (45+35+ 52+ 47+55)/5 = 234/5 = 47. Answer:C #### C QUESTION:In 24 minutes, the hour hand of a clock moves through an angle of: options: A)60° B)24° C)12° D)5° E)None SOLUTION:12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚ Answer: C #### C QUESTION:Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point? options: A)20sec B)15sec C)30sec D)24sec E)1min SOLUTION:They meet every 360/7+8 = 24sec Answer is D #### D QUESTION:In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum? options: A)1 1/4 B)1 1/6 C)1 1/0 D)1 1/5 E)1 5/1 SOLUTION:Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10% Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.Answer: A #### A QUESTION:The ratio 3 : 5 expressed as a percent equals options: A)60% B)40% C)80% D)125% E)None SOLUTION:Solution 3 : 5 = 3/ 5 = (3 / 5 x 100)%. = 60 %. Answer A #### A QUESTION:What is the rate percent when the simple interest on Rs.1000 amount to Rs.400 in 4 Years? options: A)5% B)6% C)2% D)95% E)10% SOLUTION:Interest for 4yrs = 400 Interest for 1yr = 100 Interest rate = 100/1000 x 100 = 10% Answer : E #### E QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 8480, what is the length of the plot in metres? options: A)20 B)200 C)300 D)90 E)140 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 8480 [4L - 40] = 8480 / 26.50 = 320 4L = 360 L = 360/4= 90 meters. Answer: D #### D QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age? options: A)22 B)15 C)77 D)21 E)182 SOLUTION:Present age is 4x and 3x, => 4x + 6 = 34 => x = 7 So Deepak age is = 3(7) = 21 Answer: D #### D QUESTION:In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year? options: A)74 B)75 C)76 D)77 E)78 SOLUTION:let the age is 'x' so after 1st yr 2x=40 and x=20 after 2nd year (now age become 21) 2*21+ 20=62 grades after 3rd year(now age becomes 22) 2*22+31=75 ANSWER:B #### B QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many digits does this integer consists of? options: A)150 B)339 C)342 integers D)359 E)362 SOLUTION:1-digit integers Number of 1-digit integers (1 to 9) = 9 - 1 + 1 = 9 Number of digits used = (9)(1) = 9 2-digit integers Number of 2-digit integers (10 to 99) = 99 - 10 + 1 = 90 Number of digits used = (90)(2) = 180 3-digit integers Number of 3-digit integers (100 to 150) = 150 - 100 + 1 = 51 Number of digits used = (51)(3) = 153 TOTAL # of digits uses = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:Find the middle one when The sum of three consecutive even numbers is 36? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:3 consecutive numbers can be a - 1, a, a + 1 So sum of numbers = 3a = 36. Hence a = 12. B #### B QUESTION:CONVERT 2.5 hectares in ares options: A)130 ares. B)160 ares. C)180 ares. D)230 ares. E)250 ares. SOLUTION:2.5 hectares in ares 1 hectare = 100 ares Therefore, 2.5 hectares = 2.5 × 100 ares = 250 ares. ANSWER- E #### E QUESTION:Anne bought doughnuts for a class breakfast party. She bought 12 chocolate doughnuts, 12 coconut doughnuts, and 10 jam-filled doughnuts. How many doughnuts did Anne buy in all? options: A)25 B)34 C)39 D)21 E)11 SOLUTION:Add the numbers of doughnuts. 12 + 12 + 10 =34. Answer is B. #### B QUESTION:The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year? options: A)5% B)6% C)7% D)2% E)8% SOLUTION:increase = 262500 - 175000 = 87500 % increase in 10 yrs = 87500/175000*100 = 50% avg = 50/10 = 5% ANSWER A #### A QUESTION:if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)11x/y B)10x/y C)x/11y D)11/xy E)xy/11 SOLUTION:Answer is B. The rate of running hards: 10 minutes per y hards. Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y #### B QUESTION:In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the fifth row? options: A)10 B)11 C)13 D)14 E)16 SOLUTION:Let x be the number of cans in row 1. The total number of cans is x + (x+3) + ... + (x+27) = 10x + 3(1+2+...+9) = 10x + 3(9)(10)/2 = 10x + 135 Since the total is less than 150, x must equal 1. The number of cans in the 5th row is 1 + 3(4) = 13 The answer is C. #### C QUESTION:If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:A shopping mall give 40% sale on T-shirts and increase 25% price of pants. The cost price of pants and T-shirts are 1500 and 400 respectively. Overall they makes a? options: A)200 B)250 C)300 D)215 E)180 SOLUTION:Let the SP of the pants and T-shirts be Rs. p and Rs. t respectively. p = 1500(1 + 25/100) = 1500 + 375 t = 400(1 - 40/100) = 400 - 160 Total SP - Total CP = p + t - (1500 + 400) = 375 - 160 = Rs. 215 As this is positive, an overall profit of Rs. 500 was made. Answer: D #### D QUESTION:There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season? options: A)A)55% B)B)60% C)C)80% D)D)72% E)E)70% SOLUTION:There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 30% chance that Federer will not play at all in the whole season We can also infer that there is 70% chance that Federer will play. Answer E #### E QUESTION:The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of options: A)20% B)19% C)18% D)11% E)10% SOLUTION:Say the original price of the TV was $p, then the final price would be (0.9p)∗0.9=0.81p. Therefore the original price was discounted by 19%. Answer: B. #### B QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost? options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800 SOLUTION:1.4x = 2500 x=2500/1.4 so, 1.5X = 2500*1.5/1.4= 2478 Answer:- D #### D QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,200 sedans in Anytown, how many motorcycles are there? options: A)1260 B)2100 C)3600 D)3200 E)5200 SOLUTION:Let the total number of trucks = 3x total number of sedans = 7x total number of motorcycles = 2x total number of sedans = 11200 => 7x = 11200 => x = 1600 total number of motorcycles =2x = 2*1600 =3200 Answer D #### D QUESTION:A certain number X when divided by 253 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81? options: A)17 B)27 C)27 D)47 E)57 SOLUTION:Least possible value of the number is 253 + 98 = 351 Further it is given the number must be divisible by 81 . 351/81 = Gives remainder as 27 So, 27 must be subtracted from the number , answer is (C) #### C QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow? options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10% So 8100+15100⋅x+10100⋅(8100−x)=9100 Therefore 8100+320x+110(8100−x)=9100 120x=190 x=3800 Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres correct answer is D)4370 lt #### D QUESTION:For which of the following values of n is (500+n)/n NOT an integer? options: A) 1 B) 2 C) 3 D) 4 E) 5 SOLUTION:Solution: This problem is easiest solved by plugging in each answer choice. A) (500 + 1)/1 = 501/1 = 501 Answer choice A yields an integer. B) (500 + 2)/2 = 502/2 = 251 Answer choice B yields an integer. C) (500 + 3)/3 = 503/3 = 167, remainder 2 Answer choice C DOES NOT yield an integer. Although we believe answer choice C is correct, we should still test the other answer choices. D) (500 + 4)/4 = 504/4 = 126 Answer choice D yields an integer. E) (500 + 5)/5 = 505/5 = 101 Answer choice E yields an integer. Thus, the correct answer is answer choice C. #### C QUESTION:A cab driver 5 days income was $250, $400, $750, $400 , $500. Then his average income is? options: A)$440 B)$450 C)$460 D)$470 E)$480 SOLUTION:avg = sum of observations/number of observations avg income=(250+400+750+400+500)/5 = 460 Answer is C #### C QUESTION:For 15 people each has to pay Rs.20.For 20 people each has to pay Rs.18. For 40 people--how much has each to pay? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:15-->20 20-->18 25-->16 30-->14 35-->12 40-->10 ANSWER:B #### B QUESTION:Average of first five multiples of 3 is options: A)9 B)11 C)13 D)15 E)17 SOLUTION:Explanation: Average=3(1+2+3+4+5) / 5=45 / 5=9 Option A #### A QUESTION:What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.? options: A)Rs. 8908.42 B)Rs. 9720 C)Rs. 10123.20 D)Rs. 10483.20 E)None SOLUTION:Amount = [22000 * (1 + 12/100)3] = 22000 * 28/25 * 28/25 * 28/25 = Rs. 30908.42 C.I. = (30908.42 - 22000) = Rs. 8908.42 ANSWER:A #### A QUESTION:Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid? options: A)D + 40 B)D + H – 1 C)D + 2H D)6.93H E)1.21D SOLUTION:before Discount price was: 1.4D+1.5H After Discount: 1.4D +1.5H-.42D-.45H substitute D=6H final value: 6.93H Ans Is D #### D QUESTION:If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ? options: A)(a) 4/10 B)(b) 4/9 C)(c) 1/2 D)(d) 6/10 E)(e) 5/9 SOLUTION:Here is how I did it. Probably there may be better way to do it. First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90. That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment. So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17) Number of integers, whose digits add to 1: 1 and 10 = 2 Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4 Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6 Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8 Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10 Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8 Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6 Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4 Number of integers, whose digits add to 16: 79, 88 = 2 So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers Probability B= 50/90 = 5/9 Correct answer E #### E QUESTION:A company has 2 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director? options: A)500 B)720 C)4500 D)20 E)55 SOLUTION:atleast one means exactly one and more than one. different committees with 5 people can be chosen having at least 1 director is (2c1*5c4) + (2c2*5c3) = 20; Hence D. #### D QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:If it were a line/column combination/permutation problem, the solution would be : 5! = 120. However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24. ANS:C #### C QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: options: A)No profit, no loss B)5% C)8% D)10% E)11% SOLUTION:Explanation: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =80/100X100%=5% ANSWER IS B #### B QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint? options: A)9 B)16 C)19 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 * 12/17=9/17.. 35 pints will require 9/17 * 35= 19 pints.. C #### C QUESTION:Entry fee in a zoo is $10. Later this was reduced by 50% which increased the sale by 40%. The percentage increase in the number of visitors is? options: A)100% B)50% C)180% D)200% E)150% SOLUTION:Let the total original sale be $1000 Then original number of visitors = 100 New number of visitors = 1400/5 = 280 Increase % = 180% Answer is C #### C QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? options: A)62.5 B)62.8 C)62.1 D)62.9 E)32.5 SOLUTION:Explanation: CP = 47.50 SP = 47.50*(125/100) = 59.375 MP*(95/100) = 59.375 MP = 62.5 Answer: A #### A QUESTION:The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is? options: A)7 B)4 C)5 D)3 E)1 SOLUTION:Explanation: P(1 + 20/100)n > 2P or (6/5)n > 2 Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years. Answer:B #### B QUESTION:If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72? options: A)24 B)36 C)12 D)18 E)16 SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. 72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12 C #### C QUESTION:2 friends A n B running up hill and then to get down length of road 440 yads A on his return journey met B going up at 20 yards from top if A has finished race 5 minute earlier than B then how much time A had taken to complete the race ? options: A)100 minute B)110 minute C)120 minute D)130 minute E)140 minute SOLUTION:total journey= 440*2=880 A meet B 20 yards from top in getting down it means he has covered 440+20=460 yards while B is 420 yards.so he is 40 yards ahead of B which is equals to 5 minute. so 40 yards in 5 min 880 yards will be in 5*880/(40)=110 minute ANSWER:B #### B QUESTION:he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)0 B)1 C)10 D)19 E)8 SOLUTION:Average of 20 numbers = 0. Sum of 20 numbers (0 x 20) = 0. It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a). Answer: Option D #### D QUESTION:A sum of money is sufficient to pay B's wages for 12 days and C's wages for 24 days. The same money is sufficient to pay the wages of both for? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Let the total money be $x B's 1day work = $ x/12 C's 1day work = $ x/24 A+B 1day work = $ x/8 Money is sufficient to pay the wages of both for 8days Answer is C #### C QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)120% B)190% C)100 percent D)200% E)101% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate? options: A)100 B)50 C)Cannot be determined D)105 E)25 SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position. Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C QUESTION:A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number M is options: A)74 B)M=75 C)M=175 D)M=680 E)690 SOLUTION:I solved this question by plugging in numbers from the answer choices. A.) 74 Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5. B.) 75 I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7. 15-7 = 8 so I know the correct answer isB #### B QUESTION:A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 18 = 6 + 12 - {Both} + 0; {Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: A. #### A QUESTION:Set X consists of 10 integers and has median of 30 and a range of 20. What is the value of the greatest possible integer that can be present in the set? options: A)32 B)37 C)C.40 D)43 E)50 SOLUTION:Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle. Quick check of each option starting from the largest: (E) 50 Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median. (D) 43 Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median. (C) 40 Range of 20 means the smallest integer will be 20. 20 can lie in between such as: 20, 20, 20, 20, 20, 20, 20, 20, 20, 50 This is possible. Hence it is the greatest such number. Answer (E) #### E QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 20 years = (20 + 20) years =40 years. Answer : C #### C QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 175, how many coins of each type are there? options: A)20 coins B)30 coins C)50 coins D)100 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 175 ⇒ 1.75x = 175 ⇒ x = 100 coins Answer D #### D QUESTION:The area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:L * W = 750 : area , L is the length and W is the width. 2 L + 2 W = 110 : perimeter L = 55 - w : solve for L (55 - W) * W = 750 : substitute in the area equation W = 25 and L = 30 correct answer E #### E QUESTION:Three different containers contain 496 litres, 403 litres and 713 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ? options: A)29 litres B)31 litres C)35 litres D)19 litres E)26 litres SOLUTION:M1 = 496 litres M2 = 403 litres M3 = 713 litres Required measurement = H.C.F. of M1,M2,M3 = 31 litres Answer is B #### B QUESTION:At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? options: A)5 B)10 C)720 D)32 E)120 SOLUTION:Has to be C. Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle hence (7-1)! = 6!= 720 #### C QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)50 SOLUTION:Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec t=500*3/50=30sec ANSWER:B #### B QUESTION:If f(x)=x^2 and x is a positive integer, which of the following will not be the value of f(f(x))? options: A)1 B)16 C)81 D)256 E)144 SOLUTION:f(x)=x^2 f(f(x)) = (x^2)^2 =x^4 A. 1 , x=1 B. 16 , x=2 C. 81 , x=3 E. 144 f(x)=12 Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) . D. 256 , x=4 Answer E #### E QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5 of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students. options: A)200 B)210 C)220 D)230 E)240 SOLUTION:210 ANSWER:B #### B QUESTION:What least number should be subtracted from 13605 such that the remainder is divisible by 87 ? options: A)27 B)29 C)28 D)30 E)33 SOLUTION:13605 ÷ 87 = 156, remainder = 33 Hence 33 is the least number which can be subtracted from 13605 such that the remainder is divisible by 87 Answer is E #### E QUESTION:Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations X of project assignments are possible? options: A)252 B)1,680 C)2,340 D)362,880 E)592,704 SOLUTION:The ways to select three employees out of 9 for first project = 9C3 The ways to select three employees out of Remaining 6 for Second project = 6C3 Third Project already has the group of three to be assigned to it so need to select that So total ways to assign 3 employees to each of 3 projects X= 9C3 * 6C3 * 1 = 1,680 Answer: Option B #### B <<<Examples ends QUESTION:The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is ? options: A)96 litres B)98 litres C)100 litres D)102 litres E)None SOLUTION:Answer Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12 Average = ( 110 x 7 + 86 x 5 ) / 12 =(1200 / 12 = 100 liters Correct Option: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is : options: A)3 M^9 B)3 M^2 C)3 M^6 D)3 M^1 E)3 M^7 SOLUTION:Explanation: We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. . Answer: B) 3 M^2 #### B QUESTION:The operation # is defined for all nonzero x and y by x#y = x + x/y. If S>0, then 1#(1#S) = options: A)S B)S+1 C)S/(S+1) D)(S+2)/(S+1) E)(2S+1)/(S+1) SOLUTION:x#y = x + x/y. If S>0, then 1#(1#S) = You can see that a stands for y and 1 stands for x. I like to work with numbers so I did x=1 S=2 and S=y so y=2 1#S= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3 So now you can check by filling in S, which is 2: A. S --> 2 B. S+1 --> 2+1=3 C. S/(S+1)-->2/(2+1)=2/3 D. (S+2)/(S+1)-->(2+2)/(2+1)=4/3 E. (2S+1)/(S+1)-->(2*2+1)/(2+1)=5/3 So E is the answer. #### E QUESTION:The difference between the ages of two persons is 10 years.Fifteen years ago ,the elder one was twice as old as the younger one.The present age of the elder person is : options: A)25 years B)35 years C)45 years D)55 years E)75 years SOLUTION:Solution Let their ages be x year and (x + 10) years respectively. Then,(x + 10) - 15 = 2 (x - 15) ⇔ x-5 = 2x-30 ⇔ x =25. ∴ Present age of the elder person =(x + 10) =35 years. Answer B #### B QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)196 E)200 SOLUTION:185 Answer is B #### B QUESTION:The price of 10 bat is equal to that of 4 balls. The price of 15 balls and 2 bats together is Rs. 4000. The total price of 12 chairs and 3 balls is: options: A)Rs. 3200 B)Rs. 3500 C)Rs. 3700 D)Rs. 3900 E)Rs. 4000 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. D) #### D QUESTION:What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 10%? options: A)20% B)29% C)10% D)35% E)90% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 90 2/3 SP1 = 90 SP1 = 135 100 --- 35 => 35% Answer: D #### D QUESTION:The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? options: A)4 B)8 C)16 D)17 E)None of these SOLUTION:Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) = 2x = 8. Answer:B #### B QUESTION:What will come in place of the x in the following Number series? 1, 2, 12, 7, 23, 12, 34, x options: A)14 B)15 C)16 D)17 E)18 SOLUTION:There are two series here 1, 12, 23, 34, ... (Increase by 11) 2, 7, 12, ... (Increase by 5) Hence, next term is 12 + 5 = 17 Correct Answer Choice is D #### D QUESTION:Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop? options: A)128 B)64 C)32 D)16 E)8 SOLUTION:Before stop 3, there were 2 passengers on the bus. Before stop 2, there were 4 passengers on the bus. Before stop 1, there were 8 passengers on the bus. The answer is E. #### E QUESTION:A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)235 m B)245 m C)247 m D)249 m E)252 m SOLUTION:length of the bridge = x meter Total distance covered = 130+x meter total time taken = 30s speed = Total distance covered /total time taken = (130+x)/30 m/s = 45 × (10/36) = (130+x)/30 = 45 × 10 × 30 /36 = 130+x = 45 × 10 × 10 / 12 = 130+x = 15 × 10 × 10 / 4 = 130+x = 15 × 25 = 130+x = 375 = x = 375-130 =245 #### B QUESTION:When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item? options: A)$1,600 B)$1,850 C)$2,250 D)$2,400 E)$2,750 SOLUTION:Let the value of the item be $x, then 0.07(x−1,000)=87.5--> x−1,000=1,250x−1,000=1,250 --> x=2,250. Answer: C. #### C QUESTION:Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg options: A)2:0 B)2:3 C)2:1 D)2:2 E)2:8 SOLUTION:By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind Required ratio = 60 : 90 = 2 : 3 Answer: B #### B QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)7 1/2 years B)20 years C)15 years D)38 years E)30 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years ANSWER:B #### B QUESTION:The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages. options: A)30% B)32.50% C)33 1/3% D)40% E)50% SOLUTION:Explanation: The gain is 4 out of 12 articles. Therefore, gain percentage = 4x100/12 = 100/3 = 33 1/3% Answer: Option C #### C QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:If x is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ? options: A)1 B)2 C)3 D)6 E)12 SOLUTION:Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey x=4n, if it really wanted to convey so. From other questions that I have seen, proper wordings could be: If x is three times as large as n OR simply, If x is three times n.C #### C QUESTION:The banker's discount on Rs.1800 at 48% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time? options: A)1 months B)4 months C)5 months D)6 months E)7 months SOLUTION:Solution S.I on Rs.1800 = T.D on Rs.1872. P.W on Rs.1872 is Rs.1800. Rs.72 is S.I on Rs. 1800 at 48%. Time =(100x72 / 48x1800) = 1/12 year = 1 months. Answer A #### A QUESTION:A and B can do a piece of work in 11 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? options: A)15.5 days B)19.5 days C)17.5 days D)9.2 days E)18.5 days SOLUTION:C = 1/5 – 1/11 = 6/55 => 9.2 days ANSWER:D #### D QUESTION:If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before? options: A)A)3/22% B)B)10% C)1/9 % D)1/11 % E)% SOLUTION:100 – 12 = 88 88------12 100------? => 11 3/22% ANSWER:A #### A QUESTION:The price of 24 apples is equal to that of 28 oranges. The price of 45 apples and 60 oranges together is Rs.1350. The total price of 30 apples and 40 oranges is options: A)850 B)900 C)750 D)950 E)800 SOLUTION:Let the price of one apple = a and price of one orange = b Price of 24 apples is equal to that of 28 oranges 24a = 28b => 6a = 7b ⇒b=6a/7 -----(Equation 1) price of 45 apples and 60 oranges together is Rs.1350 => 45a + 60b = 1350 => 3a + 4b = 90 ⇒3a+4(6a)/7=90 (∵ Substituted the value of b from equation 1) ⇒a+4(2a)/7=30 => 7a + 8a = 30 × 7 = 210 => 15a = 210 ⇒a=21015=423=14 b=6a7=(6×14)/7=6×2=12 Total price of 30 apples and 40 oranges = 30a + 45b = (30 × 14) + (40 × 12) = 420 + 480 = 900 Answer is B. #### B QUESTION:If 2994 ÷ 14.5 = 179, then 29.94 ÷ 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.9 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 179 in the place of 2994/14.5 ] = 179/10 = 17.9 Answer is E. #### E QUESTION:What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 6), (x, 6)? options: A)64 B)81 C)125 D)196 E)225 SOLUTION:To find the area of a square, knowing the length of one side is sufficient. From the coordinates given, we can see that one side equals 14. The area is 14*14 = 196. The answer is D. #### D QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Solution Radius = Area / Semi perimeter = [Area x 2 / Area] = 2. Answer B #### B QUESTION:A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? options: A)29% B)17% C)44% D)46% E)21% SOLUTION:g% = 10 + 10 + (10*10)/100 = 21% Answer: E #### E QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled? options: A)80 B)81 C)82 D)83 E)84 SOLUTION:Solution: Mabel handled 90 transactions Anthony handled 10% more transactions than Mabel Anthony = 90 + 90 × 10% = 90 + 90 × 0.10 = 90 + 9 = 99 Cal handled 2/3rds of the transactions than Anthony handled Cal = 2/3 × 99 = 66 Jade handled 15 more transactions than Cal. Jade = 66 + 15 = 81 Jade handled = 81 transactions. Answer: B #### B QUESTION:A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 15% less than B, and C costs 20% less than A,and D costs 25% less than C what percent of B's cost is D? options: A)40% B)38% C)44% D)46% E)51% SOLUTION:Soln:- B=100 A 15% less than B = 85 C 20% less than A = 68 D 25% less than C = 51 D is what percent of B = D/B * 100 = 51/100 * 100 = 51% ANSWER:E #### E QUESTION:Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 3 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? options: A)1/24 B)1/8 C)1/4 D)1/3 E)3/8 SOLUTION:I hope you are familiar with basic probability fundas - Let's say you have just ONE letter and TWO envelopes ONE of which is correctly addressed and the other addressed incorrectly. What's the probability of putting the Letter in the correctly addressed envelope - To answer this question - we see IN HOW MANY WAYS can the letter be put into the envelope - you could put it (assuming you don't know which envelope is which) in either of the two - so in total you have TWO ways of shoving the letter in. However, there's only ONE way in which it can go into the correctly addressed envelope - so 1/2 is the prob of putting in correct envelope. This is easy. Now in our current problem - let's say we have just ONE letter but FOUR envelopes. Only one of these envelopes has the address corresponding to the letter. The remaining three envelopes are incorrectly addressed. So the probability that you will put the letter correctly is 1/4. Right? What happens if i ask you the reverse question? what is the prob for putting it in the incorrect envelope. Suddenly you have three envs that are incorrect so you can put the letter incorrectly with a prob of 3/4. Right? The whole problem can be broken down into Four Events that will fulfill the requirement of the question Event 1 - E1 We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the first letter goes into the correct envelope) we have the remaining THREE Letters and THREE envelopes. Event 2 - E2 Let's take letter number 2 now - what is the probability that it LANDS in the INCORRECT envelope. Again by the same logic as above - there are 3 envelopes remaining out of which ONLY ONE has the correct address for LETTER number 2. The remaining 2 have INCORRECT address and LETTER NUMBER 2 could go in either of these 2 to meet our condition. Thus the probability of this event is 2/3 So till now what we have done is - we have calculated the prob of shoving Letter number 1 in correct env -- 1/4 we have calculated the prob of shoving Letter number 2 in INcorrect env --- 2/3 Event 3 - E3 Now let's take letter number 3 - again according to question we want to shove this in the WRONG envelope. There are 2 remaining envelopes and hence the prob of shoving this in the wrong env (or equally in the RIght env) is 1/2. Finally we come to event E4 - the Letter number 4. This has only one way of going in so its probability of being put into the WRONG envelope is 1. ok so we can see that our grand event is actually a combination of FOUR EVENTS happening - each with a probability of its own. So to calculate the total probability of the Grand Event itself we just multiply the individual probabilities since each event happens INDEPENDENTLY of each other Egrand = 1/4 * 2/3 * 1/2 * 1/1 = 1/12 However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result. If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 and worked thru the remaining letters, we could have equally well started out with letter L2 or L3 or L4. Thus since each of these events ARE MUTUALLY EXCLUSIVE, meaning THEY CAN NEVER HAPPEN ALL THE SAME TIME BUT ONLY ONE LETTER AT A TIME, to calculate the TOTAL PROBABILITY of we will add the individual probabilities 1/12 + 1/12 + 1/12 + 1/12 which works out to 1/8. B #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)86400 D)153603 E)153604 SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1200 or x = 120. Length = 360 m and Breadth = 240 m. Area = (360 x 240) m2 = 86400 m2. Answer: C #### C QUESTION:If the height of a right cone C is 3 and the diameter of the base of C is 8, what is the distance from the apex of C to any point on the circumference of the base of C? options: A)3√2 B)5 C)5√2 D)√(67) E)√(73) SOLUTION:height of cone=3 radius of base=4 so the distance from the apex of C to any point on the circumference of the base of C will be a right angled triangle Hence the distance is sqrt(3^2+4^2)= 5 ANSWER:B #### B QUESTION:In a business Ram invests Rs.60,000. After 6 months his uncle invests Rs.40,000. After one year they got a profit of Rs.12,000. Then uncle gets his share as options: A)Rs.2500 B)Rs.2000 C)Rs.1000 D)Rs.3000 E)Rs.4000 SOLUTION:ram=60,000(12months) uncle=(40000)(6months) 60000*12 : 40000*6 3 : 1 uncle share= (1/3+1)(12000)=3000 ANSWER:D #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)11% B)25% C)87% D)19% E)12% SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 10P pots? options: A)M/10 B)6/M C)600M D)M/6 E)10M SOLUTION:The time it takes to wash 10P pots is 10M minutes which is 10M / 60 = M/6 hours. The answer is D. #### D QUESTION:Two trains, one from Hyderabd to Bangalore and the other from Bangalore to Hyderabad, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is ? options: A)2 : 3 B)3 : 2 C)3: 4 D)1 : 2 E)4 : 3 SOLUTION:Let us name the trains as A and B. Then, (A's speed) : (B's speed) = √b : √a = √16 : √9 = 4:3 Answer : E #### E QUESTION:Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is? options: A)10 B)30 C)40 D)50 E)60 SOLUTION:Let the numbers be 3x,4x and 5x their L.C.M. = 60x 60x =600 x = 10 The numbers are 3*10 , 4*10 , 5*10 Hence required H.C.F. = 10 Answer is A #### A QUESTION:A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n? options: A)8/7 B)8 C)9/8 D)7 E)5 SOLUTION:Say each floor worker is paid $x, then the manager is paid $xn. Total salary would be 9x+xn and we are told that it equals to 9xn: 9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9 n = 9/8 Answer: C #### C QUESTION:The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 32,000 locusts? options: A)2 B)4 C)6 D)8 E)9 SOLUTION:- 4 hours: 1,000 -2 hours: 2,000 Now: 4,000 + 2 hours: 8,000 + 4 hours: 16,000 + 6 hours: 32,000 Answer : C #### C QUESTION:What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5? options: A)1 B)3 C)2 D)4 E)5 SOLUTION:Only the unit's digit of the product will decide the remainder when divided by 5. Hence, 1*4*3= will give units digit as 2 So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2. Option C #### C QUESTION:There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted? options: A)6 B)7 C)8 D)2 E)9 SOLUTION:Let xx be the number of roses. Then the number of birches is 24−x24−x, and the number of boys is 3×(24−x)3×(24−x). If each girl planted 3 roses, there are x3x3 girls in the class. We know that there are 24 students in the class. Therefore x3+3(24−x)=24x3+3(24−x)=24 x+9(24−x)=3⋅24x+9(24−x)=3⋅24 x+216−9x=72x+216−9x=72 216−72=8x216−72=8x 1448=x1448=x x=18x=18 So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches. Answer:A #### A QUESTION:A circle graph shows how the budget of a certain company was spent: 60 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation? options: A)18° B)36° C)54° D)72° E)90° SOLUTION:The percent of the budget for transportation is 100 - (60+9+5+4+2)= 20% 100% of the circle is 360 degrees. Then (20%/100%)*360 = 72 degrees The answer is D. #### D QUESTION:It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number X? options: A)a. 2^96 + 1 B)b. 2^16 - 1 C)c. 2^16 + 1 D)d. 7 * 2^33 E)e. 2^64 + 1 SOLUTION:a³ + b³ =(a+b)(a² -ab +b²) Now, let (2^32 + 1) be (a+b) a³ + b³ = (2^96 + 1) Now, as mentioned in formula above, a³ + b³ is always divisible by (a+b) So any factor of X=(a+b) is a factor of (a³ + b³) Henca A #### A QUESTION:If the simple interest on Rs.3100 amount to Rs. 632.40 in 2 Years, What is the rate percent? options: A)11.2% B)10.2% C)12.2% D)13.2% E)18.2% SOLUTION:$632.40 = (3100*2*R)/100 R = 10.2% Answer: B #### B QUESTION:A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 5 games? options: A)x + 3y/(n + 3) B)x + y/(n + 3) C)(x + 3y)/(n + 3) D)(nx + 3y)/(n + 5) E)(3x + ny)/(n + 3) SOLUTION:Total points in first n games = nx Total marks in next 3 games is 3y So, Average marks in n + 5 games = (nx+3y)/(n+5) Hence, correct answer will be (D) #### D QUESTION:At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number W of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:Circular arrangements= (n-1)! Hence (4!) = 24=W Answer is C #### C QUESTION:If each digit in the set A = {1, 2, 3, 4, 5} is used exactly once, in how many ways can the 5 digits be arranged? options: A)6 B)24 C)72 D)96 E)120 SOLUTION:Use the slot method for all the possible arrangements: we have 5 options for the 1st slot, 4 for the 2nd, 3 for 3rd , 2 for 4th and 1 for the 5th, giving the total number of arrangements = 5*4*3*2*1 = 120, E is the correct answer. #### E QUESTION:Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) options: A)8/3 B)3/8 C)8/5 D)12/5 E)5/3 SOLUTION:Distance traveled by Eddy = 540 km Time taken by Eddy = 3 hours Average speed of Eddy = 540/3 = 180 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 180/75 = 12/5 Answer D #### D QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.723 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. options: A)22200 B)21897 C)28799 D)30000 E)32782 SOLUTION:P(11/10)^4 - P(6/5)^2 = 723 P = 30000 Answer: D #### D QUESTION:If three sides of the triangle are 8 , 15 and A respectively then the how many values can A ? options: A)[A] 6 B)[B] 7 C)[C] 8 D)[D]9 E)[E] infinite number of values SOLUTION:Needed: How many Values can A take Concept: Sum of any two sides of a triangle is greater then the third side. Case 1: 8+5 > A => A<13 Case 2: 5+A > 8 => A >3 Case 3: 8+A > 5 => A > -3 (Always true since A is one side of a Triangle) Finally, 3 < A < 13. So, we can have infinite number of sides between 3 and 13. Answer = E PS: If question said A can take only integer value, the A = 9. Answer choice D. #### D QUESTION:if log 2 = 0.30103, the number of digits in 2128 is options: A)22 B)39 C)88 D)28 E)11 SOLUTION:Explanation: log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4 ie, its characteristic = 38 Hence, number of digits in 2128 = 38+1 = 39 Answer: Option B #### B QUESTION:A third of Arun’s marks in mathematics exeeds a half of his marks in english by 80.if he got 240 marks In two subjects together how many marks did he got inh english? options: A)120,60 B)180,60 C)180,90 D)120,40 E)None of them SOLUTION:Let Arun’s marks in mathematics and english be x and y Then 1/3x-1/2y=30 2x-3y=180……>(1) x+y=240…….>(2) solving (1) and (2) x=180 and y=60 Answer is B. #### B QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40 SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35 P(at least one graduate) = 1- 1/35 = 34/35 The answer is D. #### D QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)299 B)277 C)266 D)992 E)188 SOLUTION:(800*3*3)/100 = 72 920 + 72 = 992 Answer:D #### D QUESTION:If each digit in the set of A = {1,2,3,4,5,6,7,8} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent? options: A)8! / 7! B)8! - 7! C)6*7! D)8!/2! E)7! SOLUTION:The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent). The number of ways to arrange 8 units is 8! If we think of 2 and 5 as one single unit, the number of arrangements is 7! Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*7! The total number of valid arrangements is 8! - 2*7! = 8*7! - 2*7! = 6*7! The answer is C. #### C QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively? options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these SOLUTION:Y:Z = 70000 : 30000 = 7:3. ANSWER:C #### C QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)22 B)98 C)60 D)88 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is options: A)91 B)910 C)61 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 671 and 610. ‹=› 61. Answer C #### C QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11 SOLUTION:Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify. As for your question, it is very simple and straightforward with number plug in. Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E QUESTION:What is the least integer that is a sum of four different prime numbers each greater than 50? options: A)232 B)234 C)236 D)238 E)240 SOLUTION:The sum of the four smallest primes greater than 53+59+61+67=240. The answer is E. #### E QUESTION:Average between two sets of numbers is closer to the set withmore numbers? options: A)70 B)80 C)90 D)95 E)98 SOLUTION:If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86. Here, 90 has a weight of 3 => it occurs 3 times. Whereas 80 has a weight of 2 => it occurs 2 times. So the average is closer to 90 than to 80 as we have just calculated. B #### B QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:9 B)8:7 C)8:1 D)8:2 E)8:8 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8 : 7 Answer:B #### B QUESTION:Find the third proportional to 63 and 29.9? options: A)14.09 B)14.29 C)14.19 D)14.16 E)None of these SOLUTION:Explanation: Formula = Third proportional = (b × b)/a A = 63 and B = 29.9 (29.9 × 29.9)/ 63 = 894.01/63 = 14.19 Answer: Option C #### C QUESTION:The average age of a group of persons going for picnic is 16 years. Twelve new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is options: A)5 B)10 C)12 D)40 E)50 SOLUTION:Solution Let the initial number of persons be x. Then 16x + 12 x 15 = 15.5(x+20) = 0.5x = 6 x = 12. Answer C #### C QUESTION:If the product of the integers from 1 to n is divisible by 378, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:378 = 2 x 3 x 3 x 3 x 7 N must include at least 3, 2*3, and 3*3. The answer is C. #### C QUESTION:Felix earned 30% more per month than Oscar. If Felix’s salary is decreased 10% and Oscar’s salary is increased by 10%, then Felix would be earning what percent more than Oscar? options: A)10% B)9.09% C)7% D)6.36% E)It cannot be determined from the information given. SOLUTION:the very first step requires taking some numbers for each.. ONE should be 100... it is easy to take 70 and 100 here.. but the BASE is 100 here, so the salary can be 100 and 130.. 100 increases 10% =110.. 130 decreases 10%=117.. so the increase is 7.. again the BASE is 110, so answer 7/110 * 100= 6.36% D without calculations, answer cannot be equal to or greater than 7, as 7 is on 110.. so D is the only one left ANSWER:D #### D QUESTION:How much is 80% of 40 is greater than 4/5 of 25? options: A)15 B)57 C)16 D)12 E)73 SOLUTION:(80/100) * 40 – (4/5) * 25 32 - 20 = 12 Answer: D #### D QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C QUESTION:A person travels equal distances with speeds of 8 km/hr, 9 km/hr and 10 km/hr and takes a total time of 47 minutes. The total distance is? options: A)6 km B)3 km C)7 km D)5 km E)2 km SOLUTION:Let the total distance be 3x km. Then, x/8 + x/9 + x/10 = 47/60 x/3 = 47/60 => x = 2.33. Total distance = 3 * 2.33 = 6.99 km. Answer:C #### C QUESTION:9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90.5% B)87.5% C)80.5% D)77.5% E)70.5% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.212; 10+0.3} = {9.788; 10.212}. From the 8 listed numbers, 7 are within this range so 6/8=87.5%. Answer: B. #### B QUESTION:What is the sum of all three digit integers formed using the digits 1, 2, and 3 (repetition is allowed) options: A)4443 B)5980 C)5992 D)5990 E)5994 SOLUTION:n = 3*3*3 = 27 <x> = (333 + 111) / 2 = 222 Sum = number of integers x average value n * <x> = 27 * 222 = 5994 answer = E #### E QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? options: A)289 B)132 C)279 D)277 E)278 SOLUTION:2 * 22/7 * 14 = 88 88 * 1 1/2 = Rs.132 Answer: B #### B QUESTION:The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24. ANS :C #### C QUESTION:A 6 faced die is thrown. The probability that the die will land on the number 4 is what? options: A)1/6 B)1/2 C)1/12 D)1/4 E)1/5 SOLUTION:There are six sides to the die and only one side has a 4 on it, so the probility is 1/6 Answer:A #### A QUESTION:A six-sided die is rolled once. What is the probability that the number rolled is greater than 3? options: A)2 / 3 B)1 / 2 C)3 / 3 D)4 / 5 E)2 / 4 SOLUTION:Only 4, 5 & 6 so, 3 / 6 = 1/2 correct answer B #### B QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)76.5 B)36.5 C)46.5 D)16.5 E)26.5 SOLUTION:Explanation: Correct Sum = (36 * 50 + 48 - 23) = 1825. Correct mean = = 1825/50 = 36.5 Answer: B #### B QUESTION:Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is: options: A)0.20887 B)0.3887 C)0.33487 D)0.20833 E)0.38222 SOLUTION:Explanation: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x \therefore Cultivated land of village = 384000x \therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833 Answer: D #### D QUESTION:How many different possible permutations can be made from the word ‘VULLAT’ such thatthe vowels are never together? options: A)120 B)200 C)240 D)260 E)270 SOLUTION:The word ‘BULLAT’ contains 6 letters of which 1 letter occurs twice = 6! / 2! = 360 No. of permutations possible with vowels always together = 5! * 2! / 2! = 120 No. of permutations possible with vowels never together = 360-120 = 240. C #### C QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:A car traveled 75% of the way from town A to town B at an average speed of 60 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ? options: A)10 B)20 C)25 D)30 E)37.5 SOLUTION:Total distance = 100 miles (easier to work with %) 75% of the distance = 75 miles 25% of the distance = 25 miles 1st part of the trip → 75/60 = 1.25 2nd part of the trip → 25/S = t Total trip → (75+25)/40 = 1.25 + t » 100/40 = 1.25 + t » 2.5 = 1.25 + t » t = 1.25 Back to 2nd part of the trip formula: 25/S = 1.25 » S = 20 Ans B #### B QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is? options: A)22772 B)24000 C)23877 D)23789 E)28222 SOLUTION:Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs. 24000 Answer: B #### B QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is: options: A)8% B)6% C)9% D)10% E)11% SOLUTION:Rs 1552 income = Rs 128 By investing Rs 97 income = 128/1552*97 = Rs 8 Divdend = 8% ANSWER A #### A QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:What is the average of xx,2x2x,and 66? options: A)x+2 B)x+2x C)x+2x+2 D)2x+2 E)x+2x-2 SOLUTION:By the definition of an average, we get: x+2x+63=3x+63x+2x+63=3x+63 =3(x+2)3=x+2.=3(x+2)3=x+2. Hence, the answer is x+2x+2 or Option C #### C QUESTION:On the number line, if x is halfway between -8 and 4, and if y is halfway between -4 and 6, what number is halfway between x and y? options: A)-1.5 B)-0.5 C)0.5 D)1.5 E)2.5 SOLUTION:x= -2 and y = 1. The answer is B. #### B QUESTION:The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)227 B)299 C)276 D)600 E)211 SOLUTION:Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 20 è x = 20 * 60 / 2 = 600 Answer: D #### D QUESTION:In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary options: A)42,000 B)43,000 C)44,000 D)45,000 E)46,000 SOLUTION:as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned) Rest amounts are in the form of greater than or lesser than , Hence C $45000 answer is D #### D QUESTION:In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old? options: A)231/260 B)117/130 C)51/65 D)23/32 E)11/16 SOLUTION:The number of people younger than 70 years old is 2600-800 = 1800 The number of females older than 70 years old is 0.6*850 = 510 The number of people who are either female or younger than 70 is 1800+510 = 2310. P(a person is younger than 70 or male) = 2310/2600 = 231/260 The answer is A. #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform? options: A)338 B)240 C)287 D)400 E)191 SOLUTION:Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m. Answer: D #### D QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C QUESTION:For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3). If 3y = –30, then y = options: A) –15 B) –6 C) -3 D) 6 E) 15 SOLUTION:(3+2)(y-3)=-30.. x-3=-6.. x=-3 C #### C QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230 m B)210 m C)260 m D)320 m E)330 m SOLUTION:Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B #### B QUESTION:A machine P completes a certain amount of work in 12 hrs and machine Q completes the same work in x hrs if both machines works together to complete the same work in 8 hrs then what is x? options: A)12 hrs B)18 hrs C)24 hrs D)32 hrs E)34 hrs SOLUTION:Explanation: P’s 1hr work = 1/12 Q’s 1 hr work = 1/x (A+B)’s 1 hr work = 1/8 = 1/12+1/x => x = 24 hrs Answer: Option C #### C QUESTION:One boy forgot the last digit of a 7 digit no. If he randomly dialthe final 3 digits aftercorrectly dialing the 1st 4, then what is the chance of dialing the correct no.? options: A)1/890 B)2/465 C)1/1000 D)1/3453 E)2/1454 SOLUTION:it is given that last 3 digits are randomly dialed Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability = 1/(10)3 = 1/1000 C #### C QUESTION:How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)65 B)69 C)30 D)31 E)32 SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: Option C #### C QUESTION:A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? options: A)1 day B)10 days C)30 days D)32 days E)34 days SOLUTION:Explanation: C = 1/5 – 1/6 = 1/30 => 30 days Answer: C #### C QUESTION:217 + 2.017 + 0.217 + 2.0017 = ? options: A)229.3657 B)229.7563 C)229.6357 D)229.5637 E)221.2357 SOLUTION:217 2.017 0.217 + 2.0017 -------- 221.2357 --------- Answer is E. #### E QUESTION:A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:if average of 3 is 9 so sum of 3 should be 27 3 recording can be from 0-10 inclusive to find one smallest other two should be highest so, lets assume three var are a,b,c say a is smallest and give b and c greatest readings say 10 and 10 so a has to be 7 E #### E QUESTION:The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? options: A)4 B)8 C)9 D)2 E)9 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is options: A)50 liters B)55 liters C)60 liters D)70 liters E)75 liters SOLUTION:Quantity of milk = 60 x 2 litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres. Then, milk : water = 40 . 20 + x Now, 40 = 1 20 + x 2 20 + x = 80 x = 60. Quantity of water to be added = 60 liters. C #### C QUESTION:A and B started a business with their capitals Rs. 3,00,000 and 18,00,000 respectively. Annual profit will be distributed between them in the ratio options: A)2:5 B)2:3 C)1:3 D)1:6 E)1:9 SOLUTION:3,00,000:18,00,000 Ans. 1:6 ANSWER:D #### D QUESTION:Whats the reminder when 58,458,965,231,457,895,684,525,465,985,445 is divided by 16 options: A)5 B)7. C)2. D)3 E)9 SOLUTION:A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16. Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it. 58,458,965,231,457,895,684,525,465,985,445 = 58,458,965,231,457,895,684,525,465,980,000+5,445 The first number is divisible by 16. You just have to find the remainder when you divide 5445 by 16. That will be the remainder when you divide the original number by 16. 5445/16 gives remainder 5. Answer (A) #### A QUESTION:A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village? options: A)10km B)50km C)30km D)25km E)20km SOLUTION:Average speed = 2xy/x+y = 2*25*4/25+4 = 200/29km/hr Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km Distance of the post office from the village = 40/2 = 20km Answer is E #### E QUESTION:Based on this year's costs, a builder budgets P dollars for planing N new buildings next year. If the average cost of building each building were to increase 10% from this year's cost, then the greatest number of buildings that the builder could build next year using P dollars would be: options: A)9% less than N B)11% less than N C)Equal to N D)9% greater than N E)11% greater than N SOLUTION:Correct answer is (A). This year, the price of a building is price1=P/N. If this price increases by 50% it becomes Price2=P/N*1.1 Then with P dollars, you can build P/Price2 buildings i.e. P/(P/N*1.1) i.e. N/1.1 i.e. 0.91*N Which is 9% less than N. #### A QUESTION:A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 5 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled? options: A)5.2 hrs B)2.9 hrs C)1.9 hrs D)7.5 hrs E)1.4 hrs SOLUTION:Net part filled in 1 hour = (1/3 - 1/5) = 2/15 The cistern will be filled in 15/2 hrs i.e., 7.5 hrs. Answer:D #### D QUESTION:The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is: options: A)1439 B)1440 C)1459 D)1449 E)1549 SOLUTION:LCM = 1440 1440 - 1 = 1439 ANSWER:A #### A QUESTION:A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00? options: A)$ 14.00 B)$ 11.20 C)$ 14.40 D)$ 16.00 E)$ 18.00 SOLUTION:For retail price = $25 First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5 Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14 Answer: Option A #### A QUESTION:A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute? options: A)1,200 meters / minute B)1,300 meters / minute C)1,450 meters / minute D)1,550 meters / minute E)1,650 meters / minute SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 72 kilometers per hour = 72 km/hr = (72 * 1000 meters) / (60 minutes) = 1,200 meters / minute correct answer A #### A QUESTION:Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles? options: A)2000 B)2781 C)2278 D)2081 E)2721 SOLUTION:Explanation: (10*10)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer: A #### A QUESTION:At 12:10 o'clock Bill leaves point A towards point B at a speed of 30 Km/h. At 13:40 o'clock Richi leaves from the same point towards point B also, but at a speed of 60 Km/h. At what time will Richi passes over Bill? options: A)14:40. B)15:10. C)16:10 D)15:40 E)15:30 SOLUTION:Distance travelled by Bill in 1hr 30min ( 12:10 to 13:40) = 30kmph*(90/60)hr = 45km Relative speed = Richi's speed ~ Bill's speed = 30kmph Time taken by Richi to cross Bill = 45/30 = 1.5 hrs Time at which Richi will cross Bill = 13:40 + 1:30 = 14:70 = 15:10 hrs Ans. B #### B QUESTION:The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size? options: A)6 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Side of smallest cube = L.C.M of 5,10,20 = 20cm Volume of the cube = (20 x 20 x 20)cm3 = 8000 cm3 Volume of the block= (5 x 10 x 20) cm3 = 1000 cm3 Number of blocks = (8000/1000) = 8 Answer: B #### B QUESTION:In how many ways can five boys, three girls and a teacher sit in a row such that all boys sit together? options: A)A)10000 B)B)12100 C)C)14400 D)D)1097 E)E)2781 SOLUTION:Treat all boys as one unit. Now there are four students and a teacher and they can be arranged in 5! ways. Again five boys can be arranged among themselves in 5! ways. Required number of arrangements = 5! * 5! = 120 * 120 = 14400. Answer:C #### C QUESTION:A set of numbers has the property that for any number t in the set,t+3 is in the set. If -1 is in the set, which of the following must also be in the set? I. 2 II. 5 III. 7 options: A)II only B)I only C)I,II only D)II,III only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+3 must be there. if -1 is the starting element the sequence is as follows. S ={-1,2,5,8,11....} if -1 is not the starting element the sequence is as follows S = {...-4,-1,2,5,8,11...} By observing the above two sequences we can say that 2,5 must be there in set S. Answer : C #### C QUESTION:A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in options: A)18 sec B)12 sec C)15 sec D)20 sec E)13.5 sec SOLUTION:Length of train = 12 × 15 = 180 m. Then, speed of train = 180⁄18 = 10 m/s Now, length of train = 9 × 15 = 135m ∴ Required time = 135⁄10 = 13.5 sec. Answer E #### E QUESTION:Find 60/42*4 options: A)14.7653 B)0.5897 C)3.6974 D)0.3571 E)1.2587 SOLUTION:Answer=60/42*4 =60/168=0.3571 Option D is correct #### D QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)6 SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours Answer: option E #### E QUESTION:Tough and Tricky questions: Exponents. If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy? options: A)4, 2, 8, 6 B)4 and 2 C)2 and 8 only D)6 and 4 E)8 and 6 SOLUTION:Only Units digit of X and Y contribute to the Units digit of XY. Finding all values of X for positive values of a When, a=1; X=2 a=2; X=4 a=3; X=8 a=4; X=16 a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4...... Similarly, Finding all values of Y for positive values of b When, b=1; Y=3 b=2; Y= 9 b=3; Y= 27 b=4; Y=81 b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9.... So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y When X=2 and Y=3: Units digit of XY = 6 When X=2 and Y=9: Units digit of XY = 18 When X=2 and Y=7: Units digit of XY = 14 When X=2 and Y=1: Units digit of XY = 2 When X=4 and Y=3: Units digit of XY = 12 When X=4 and Y=9: Units digit of XY = 36 When X=4 and Y=7: Units digit of XY = 28 When X=4 and Y=1: Units digit of XY = 4 When X=8 and Y=3: Units digit of XY = 24 When X=8 and Y=9: Units digit of XY = 72 When X=8 and Y=7: Units digit of XY = 56 When X=8 and Y=1: Units digit of XY = 8 When X=6 and Y=3: Units digit of XY = 18 When X=6 and Y=9: Units digit of XY = 54 When X=6 and Y=7: Units digit of XY = 42 When X=6 and Y=1: Units digit of XY = 6 There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6 Ans: A #### A QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds? options: A)4 B)9 C)39 D)48 E)63 SOLUTION:Given: z=s^2+2s for 0≤s≤7 z(4) = 4^2 + 2*4 = 24 z(7) = 7^2 + 2*7 = 63 Therefore z(7) - z(3) = 63 - 24 = 39 km/hr Option C #### C QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 5-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5 Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6 Ratio: 5 to 1 Answer : D #### D QUESTION:If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is options: A)5 km/hr B)4 km/hr C)2 km/hr D)1 km/hr E)None of these SOLUTION:Explanation: Rate upstream = (15/3) kmph Rate downstream (21/3) kmph = 7 kmph. Speed of stream (1/2)(7 - 5)kmph = 1 kmph Answer: D #### D QUESTION:A sum of Rs. 2730 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum? options: A)1629 B)1680 C)1677 D)1698 E)1679 SOLUTION:(x*8*3)/100 = ((2730 - x)*3*5)/100 24x/100 = 40950/100 - 15x/100 39x = 40950 => x = 1050 Second sum = 2730 – 1050 = 1680 Answer:B #### B QUESTION:A "word" is defined as a sequence of three dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed? options: A)3 B)5 C)6 D)8 E)9 SOLUTION:there are two ways of possibilities.. 1) all three same colour- YYY or BBB- 2 ways 2) two of one colour and one of different colour- 3!/2!-3ways.. now two /one could be Y/B or B/Y.... so 3*2=6.. total 6+2=8 ans D #### D QUESTION:In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:In the xy-coordinate system, what is the slope of the line that goes through point (2, 4) and is equidistant from the two points P = (9, 3) and Q = (5, 9)? options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:First, get the middle coordinate between (9,3) and (5,9). x = 9 + (5-9)/2 = 7 y = 3 + (9-3)/2 = 6 Second, get the slope of (7,6) and (2,4). m = 6-4 / 7-2 = 2/5 = 0.4 Answer: D #### D QUESTION:The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices. options: A)220. B)205. C)250 D)105 E)225 SOLUTION:different ways.. 1) EASIEST approach.. lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220... Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15.. total = 220-15 = 205 ANSWER:B #### B QUESTION:The area of the largest circle that can be drawn inside a square of side 98 Cm in length is: options: A)8600 B)3646 C)7546 D)7636 E)1606 SOLUTION:Radius of required circle = 49 Cm its area = 22/7 × 49 × 49 154 × 49 = 7546 Cm(power)2 Answer is C. #### C <<<Examples ends QUESTION:Simple interest on a sum at 5% per annum for 2 years is Rs.120. The C.I. on the same sum for the same period is? options: A)81.6 B)81.9 C)121.5 D)121.3 E)121.1 SOLUTION:SI = 60 + 60 CI = 60 + 60 + 1.5= 121.5 Answer: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Sum of the numbers from 1 to 25 is options: A)210 B)325 C)320 D)105 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 25. So S20=25×26/2=325 Correct Option: B #### B QUESTION:For 15 people each has to pay Rs.20.For 20 people each has to pay Rs.18. For 40 people--how much has each to pay? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:15-->20 20-->18 25-->16 30-->14 35-->12 40-->10 ANSWER:B #### B QUESTION:An article is bought for Rs.560 and sold for Rs.340, find the loss percent? options: A)36% B)38% C)16% D)39% E)12% SOLUTION:560 ---- 220 100 ---- ? => 39% Answer:D #### D QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Solution Radius = Area / Semi perimeter = [Area x 2 / Area] = 2. Answer B #### B QUESTION:If x, y, and z are all factors of 35, which of the following must be true? options: A)The product xyz > 35 B)Either x = y, y = z, or x = z C)x – y – z = even D)The product xyz is odd E)yz/x is an integer SOLUTION:All the factors of 35 are odd numbers. The product of odd numbers is odd. The answer is D. #### D QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was? options: A)160000 B)228788 C)266891 D)267689 E)127791 SOLUTION:X * (105/100) * (105/100) * (105/100) = 185220 X = 185220/1.157625 X = 160000 Answer:A #### A QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be: options: A)5:2 B)7:3 C)9:2 D)13:4 E)3:4 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 ANSWER:B #### B QUESTION:The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? options: A)4 years B)8 years C)6 years D)5 years E)1 years SOLUTION:Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 => x = 4. Age of youngest child = x = 4 years. Answer: A #### A QUESTION:A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price options: A)Rs.450/- B)Rs.451/- C)Rs.440/- D)Rs.455/- E)Rs.445/- SOLUTION:Loss = 500*10/100 = 50 S.P = C.P - Loss = 500- 50 =Rs.450/- Answer : A #### A QUESTION:There are 4 copies of 5 different jeans. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different jeans.20!/((4!)^5) Answer - C #### C QUESTION:A man purchased 3 blankets @ Rs.100 each, 2 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? options: A)278 B)900 C)278 D)450 E)772 SOLUTION:10 * 150 = 1500 3 * 100 + 2 * 150 = 600 1500 – 600= 900 Answer:B #### B QUESTION:If the cost price is 96% of sp then what is the profit % options: A)4.07% B)4% C)4.7% D)4.17% E)4.27% SOLUTION:Sol. sp=Rs100 : then cp=Rs 96:profit =Rs 4. Profit={(4/96)*100}%=4.17% Answer is D. #### D QUESTION:What is the smallest possible common multiple of three integers, all larger than 53? options: A)27. B)54. C)846. D)19,656. E)21,924. SOLUTION:The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54. Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer B. #### B QUESTION:The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Solution Let the toatl number of workers be x. Then 8000x=(12000 x 7) + 6000 (x -7) 2000x =42000 x= 21. Answer B #### B QUESTION:In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same) options: A)1:2 B)3:5 C)1:1 D)3:7 E)2:4 SOLUTION:C 1:1 This is a very simple probability question in a software interview. This question might be a little old to be ever asked again but it is a good warm up. Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method. Number of girls = 0*(Probability of 0 girls) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + … Number of girls = 0*(C*1/2) + 1*(C*1/2*1/2) + 2*(C*1/2*1/2*1/2) + … Number of girls = 0 + C/4 + 2*C/8 + 3*C/16 + … Number of girls = C (using mathematical formulas; it becomes apparent if you just sum up the first 4-5 terms) The proportion of boys to girls is 1 : 1. #### C QUESTION:Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 100 + 280 = 380m. The time required = d/s = 380/20 = 19 sec. Answer:E #### E QUESTION:The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year? options: A)12300 B)12350 C)12000 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 120/100 = 12000 C #### C QUESTION:Joshua is fifth from the bottom in a queue of 100 boys. What is the position of Joshua from the top of the queue? options: A)51 B)52 C)53 D)54 E)55 SOLUTION:Solution: 51 Explanation: The position of boys higher than Joshua in the queue is 100 - 50 = 50. Therefore, the position of Joshua from the top is 50 + 1 = 51. Answer A #### A QUESTION:A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? options: A)5.79 B)5.71 C)5.76 D)5.79 E)5.73 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 Answer: C #### C QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 21,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 147% D) 150% E) 225% SOLUTION:The percent increase is (21947-8902)/8902=13045/8902=1.47 So the approximate answer is C #### C QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? options: A)22 B)25 C)66 D)77 E)91 SOLUTION:800 --- 200 100 --- ? => 25% Answer: B #### B QUESTION:A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |Y|<3? options: A)1/7 B)3/7 C)2/5 D)3/11 E)4/7 SOLUTION:|X||X| can take 7 values. To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x ⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases = 3/7 B #### B QUESTION:A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet? options: A)6.37 p.m B)6.20 p.m C)6.30 p.m D)6.38 p.m E)6.10 p.m SOLUTION:D = 50 * 1 ½ = 75 km RS = 75 – 50 = 25 T = 75/25 = 3 h 3.30 + 3 h = 6.30 p.m. Answer: C #### C QUESTION:The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? options: A)81 : 121 B)81 : 127 C)81 : 191 D)81 : 161 E)81 : 182 SOLUTION:Explanation: Ratio of the sides = ³√729 : ³√1331 = 9 : 11 Ratio of surface areas = 92 : 112 = 81 : 121 Answer: Option A #### A QUESTION:A certain characteristic in a large population has a distribution that is symmetric about the mean a. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than a+d? options: A) 16% B) 32% C) 48% D) 84% E) 92% SOLUTION:16% ________________________________________________ a+d 34% ________________________________________________ a 34% ________________________________________________ a-d 16% since 68% lies one standard deviation from mean a, => 50% of 68% lies on either side as it is symmetric about a. thus 16% lie below a-d and 16% lie above a+d now below a+d = 16+34+34 = 84% hence D #### D QUESTION:Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.? options: A)28 B)60 C)32 D)36 E)44 SOLUTION:the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13. using the elimination method look for a number that is both divisible by 7 and 13, of all the options only 60 is divisible by 4 and 20. [ 60/4=15 and 60/20=3] answer :B #### B QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3600 C)Rs. 3900 D)Rs. 4000 E)Rs. 4100 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C #### C QUESTION:In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots? options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours. The answer is A. #### A QUESTION:A start walking from a place at a uniform speed of 5 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B. options: A)4.7 kmph B)5.6 kmph C)4 kmph D)7 kmph E)5.3 kmph SOLUTION:Distance covered by A in 30 min = 1 Km B covers extra 1km in 1 hour 48 minutes (9/5 hr) i.e. Relative speed of B over A = 1/(9/5) = 5/9 So the speed of B = Speed of A + 5/9 = 5 + 5/9 = 5.55 Answer B #### B QUESTION:A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$333.33 C)$100.25 D)$277.78 E)$377.00 SOLUTION:Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 ) $25000 is 60% of total amount. So total amount = 25000 * 100/60 Remaining amount is 40% of total amount. 40% of total amount = 25000 * (100/60) * (40/100) = 50000/3 This amount has to be divided by 50( remaining people are 50 ) So per head amount is 50000/3 / 50 = 32000/180 = 333.33; ANSWER:B #### B QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ? options: A)13500 B)10500 C)9423 D)8500 E)None of these SOLUTION:Explanation: Simran : Nanda =(50000×36):(80000×30)=(50000×36):(80000×30) =3:4=3:4. Simran's share = Rs. (24500×37)(24500×37) = Rs. 10500. ANSWER IS B #### B QUESTION:It takes Jim three hours to wash the gym and it takes Julia two hours to wash the gym. Working together, how many minutes will it take them to wash the gym? options: A)70 B)72 C)74 D)76 E)78 SOLUTION:Jim can wash (1/3) of the gym per hour. Julia can wash (1/2) gym per hour. Together they can wash 1/3+1/2=5/6 of the gym per hour. 1 gym / (5/6) of the gym per hour = 6/5 hours = 72 minutes. The answer is B. #### B QUESTION:Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ??? options: A)a,b B)a,c C)b,c D)a,d E)b,d SOLUTION:a. 3i+2j and c. 2i-3j are orthogonal pair. as the dot product of two vectors is zero;so they are orthogonal. ANSWER:B #### B QUESTION:An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity? options: A)7/18 B)9/18 C)2 D)18/7 E)18/5 SOLUTION:Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D. #### D QUESTION:The proportion of water to alcohol in Solution A is 5:4 and the proportion of water to alcohol in Solution B is 6:5. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? options: A)40.9% B)41.9% C)42.9% D)43.9% E)44.9% SOLUTION:Let V be the total volume of the new solution. Then a volume of V/2 was added from each solution A and B. The amount of alcohol added to the new solution was: (4/9)(V/2)+(5/11)(V/2)=2V/9+5V/22=89V/198. The concentration of alcohol is 89/198=44.9% The answer is E. #### E QUESTION:Horse started to chase a dog as it relived stable two hours ago. And horse started to ran with average speed of 22kmph, horse crossed 10 meters road and two ponds with depth 3 meters and it crossed 2 small streets with 200 meters length. After travelling 6 hours, 2 hours after the sunset it got dog. Compute the speed of dog? options: A)16.5 kmph B)16.6 kmph C)16.4 kmph D)16.9 kmph E)16.2 kmph SOLUTION:In an average speed of 22 kmph horse got dog in 6 hours So distance=speed*time distance=22*6=132km Dog takes 8 hours to travel 132 km. So the speed if dog is speed=distance/time speed=132/8=16.5 kmph Answer: 16.5 kmph Answer A #### A QUESTION:The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994? options: A)5N B)7N C)10N D)15N E)20N SOLUTION:In 1992, the company's assets were N. In 1993, the company's assets were N + 4N = 5N. In 1994, the company's assets were 5N + 5N = 10N. The answer is C. #### C QUESTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, is options: A)131 B)176 C)274 D)405 E)495 SOLUTION:The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}. 6 times 40 something is approx north of 240 Hence the answer is (C) 274 #### C QUESTION:If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b = options: A) −48 B) −2 C) 2 D) −7 E) 48 SOLUTION:a(a + 7) = 18 and b(b + 7) = 18 => a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively => a+b = -7 Ans: D #### D QUESTION:A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum? options: A)337 B)268 C)198 D)697 E)168 SOLUTION:1200 = P [1 + (12*6)/100] P = 697' Answer:D #### D QUESTION:A sum amounts to Rs.8820 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? options: A)s.4000 B)s.5000 C)s.4500 D)s.4800 E)s.8000 SOLUTION:CI=8820,R=5,N=2 CI=P[1+R/100]^2 =P[1+5/100]^2 8820=P[21/20]^2 8820[20/21]^2 8000 ANSWER:E #### E QUESTION:Entry fee in a zoo is $10. Later this was reduced by 50% which increased the sale by 40%. The percentage increase in the number of visitors is? options: A)100% B)50% C)180% D)200% E)150% SOLUTION:Let the total original sale be $1000 Then original number of visitors = 100 New number of visitors = 1400/5 = 280 Increase % = 180% Answer is C #### C QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? options: A)2000 B)2200 C)3000 D)3400 E)3500 SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans Alternative 100+105+110+115=12900 430=12900 100=12900/(430)X100=3000 C #### C QUESTION:At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate? options: A)134 B)178 C)195 D)166 E)194 SOLUTION:C 195 The number of votes the winning candidate received was 963 + 53 + 79 + 105 /4= 300. The second received 300 – 53 = 247, The third received 300 – 105 = 195. #### C QUESTION:What is the rate percent when the simple interest on Rs.1000 amount to Rs.400 in 4 Years? options: A)5% B)6% C)2% D)95% E)10% SOLUTION:Interest for 4yrs = 400 Interest for 1yr = 100 Interest rate = 100/1000 x 100 = 10% Answer : E #### E QUESTION:Two vessels contains equal number of mixtures milk and water in the ratio 5:2 and 6:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained? options: A)1:3 B)9:13 C)5:11 D)11:3 E)15:4 SOLUTION:The ratio of milk and water in the new vessel is = (5/7 + 6/7) : (2/7 + 1/7) = 11/7 : 3/7 = 11:3 Answer is D #### D QUESTION:Average of first five multiples of 3 is options: A)9 B)11 C)13 D)15 E)17 SOLUTION:Explanation: Average=3(1+2+3+4+5) / 5=45 / 5=9 Option A #### A QUESTION:The price of rice falls by 10%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously? options: A)5 kg B)15 kg C)25 kg D)30 kg E)None SOLUTION:Solution: Let Rs. 100 be spend on rice initially for 20 kg. As the price falls by 10%, new price for 20 kg rice, = (100 -10% of 100) = 90 New price of rice = 90/20 = Rs. 4,5 per kg. Rice can bought now at = 100/4,5 = 22,22 kg. Answer: Option E #### E QUESTION:Convert the 8/36 m/s into kilometers per hour? options: A)0.8 kmph B)9.9 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:8/36 m/s = 8/36 * 18/5 = 8/10 = 0.8 kmph. Answer: A #### A QUESTION:When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8? options: A)3 B)4 C)5 D)6 E)2 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 24) 3n = 3(6) =18, which leaves a remainder of 2 when divided by 8. Answer E #### E QUESTION:The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 15 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1? options: A)28% B)40% C)68% D)70% E)72% SOLUTION:Let initial price be 1000 Price in day 1 after 10% discount = 900 Price in day 2 after 15% discount = 765 Price in day 3 after 20% discount = 612 So, Price in day 3 as percentage of the sale price on day 1 will be = 612/900*100 => 68% Answer will definitely be (C) #### C QUESTION:For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 1*3*5*7*9*...*99 g(97) = 1*3*5*7*9*...*97 g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98 hence:A. #### A QUESTION:Out of a classroom of 7 boys and 4 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions? options: A)2/165 B)4/165 C)7/165 D)2/33 E)5/33 SOLUTION:The number of ways to choose three people is 11C3=165. The number of ways to choose three girls is 4C3=4. P(only girls are chosen)=4/165 The answer is B. #### B QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? options: A)20% B)40% C)50% D)60% E)70% SOLUTION:70 + 55 + 35 = 160% The number is 60% above 100% because 60% of the counties were counted twice. The answer is D. #### D QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.723 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. options: A)22200 B)21897 C)28799 D)30000 E)32782 SOLUTION:P(11/10)^4 - P(6/5)^2 = 723 P = 30000 Answer: D #### D QUESTION:If 1 = 3 2 = 6 3 = 9 4 = 12 5 = 15 Then 9 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)3 D)4 E)5 SOLUTION:C 3 As stated 3=9 => 9=3 Answer is C #### C QUESTION:The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? options: A)Rs.200 B)Rs.250 C)Rs.300 D)Rs.450 E)None of these SOLUTION:Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.150 15x + 5x = Rs.150 X = 150/20 = 7.50 :. Cost of 1 pen = 5x = 5 x 7.50 = 37.50 :. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450 Answer: Option D #### D QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 24*5= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 24*5 + 2y =124 then y=2 24*4 + 2y = 124 then y=14 24*3 +2y = 124 then y= 26 24*2 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join? options: A)4 months B)5 months C)6 months D)7 months E)8 months SOLUTION:Explanation: Assume that C was there in the business for x months A:B:C =40000×12:60000×10:120000 × x =40×12:60×10:120x =40:5×10:10 x =8:10:2x =4:5:x C's share =375000 x/ 9+x=375000 x/9+x ⇒375000 x/9+x=150000 ⇒375x9+x=150 ⇒15x=6(9+x) ⇒5x=18+2x ⇒3x=18 ⇒x=6 It means C was there in the business for 6 months. Given that B joined the business after 2 months. Hence C joined 4 months after B joined. Answer: Option A #### A QUESTION:In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent X of his family’s total income? options: A) 15% B) 17% C) 24% D) 30% E) 33% SOLUTION:Lets suppose the Total Family income in Feb = 100x Wilson's earning in Feb = 40% of 100x = 40x Earnings of remaining family in Feb = 100x - 40x = 60x Wilson's earning in March = 75% of Wilson's Feb earnings = 75% of 40x = 30x Earnings of remaining family in March = Earnings of remaining family in Feb = 60x Thus Wilson's earning as % of Total family income in March X= 30x/ (30+60)x = 30x/90x = 33.33% Thus Answer is E #### E QUESTION:When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.15, what is the value of y? options: A)96 B)60 C)48 D)25 E)12 SOLUTION:Guys, one more simple funda. 5/2= 2.5 now .5 x2 =1 is the remainder 25/4 = 6.25 now .25x4=1 is the remainder 32/5=6.4 now.4x5 = 2 is the remainder given x/y = 96.15 and remainder is 9 So .15 X y = 9 hence y= 60 Ans B #### B QUESTION:Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 4 = f(3x – 6) options: A)3 B)4 C)6 D)7 E)13 SOLUTION:Answer = A = 3 f(x) = 3x – 5 2*[f(x)] – 4 = f(3x – 6) 2(3x-5) -4 = 3 (3x-6) - 5 6x - 14 = 9x - 23 x = 3 #### A QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000 SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager. Average company salary * Number of employees = Total company salary >>> $80,000 * 10 = $800,000 Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000) >>> $800,000 - $300,000 - $240,000 = $260,000. The correct answer is C. #### C QUESTION:4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 weavers in 10 days? options: A)10 B)15 C)20 D)25 E)30 SOLUTION:1 weaver can weave 1 mat in 4 days. 10 weavers can weave 10 mats in 4 days. 10 weavers can weave 25 mats in 10 days. The answer is D. #### D QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers? options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 8 is 8!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!6!. # of arrangements when 3 boys do not sit together would be: 8!-3!6!. Answer: B). #### B QUESTION:The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria options: A)10 B)12 C)14 D)16 E)18 SOLUTION:The question basically asks how many minutes it takes for a population to increase by factor 50(50,000 / 1,000 = 50). Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes: 2^x >= 50, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^6 = 64, i.e. the population has to double 6 times. Since it takes the population 2 minutes to double once it takes 6*2 minutes = 12 minutes to double nine times. Thus, solution B = 12 is correct. #### B QUESTION:Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? options: A)a) 3y(7x+2xy) B)b) 3x+12y C)c) 3xy(7x+2) D)d) 3x(2y+7) E)e) 17x+6xy SOLUTION:Payment of a week for 2 days a week = $2x Payment of 4 weeks for 2 days a week = $2x*4 = $8x Payment of a week for y days overtime a week = $3x+$2xy Payment of 3 weeks for y days overtime a week = ($3x+$2xy)*3 Total Earnings = $8x + ($3x+$2xy)*3 = 17x+6xy Answer: option E #### E QUESTION:A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is options: A)250 B)276 C)280 D)285 E)None SOLUTION:Solution since the month begins with a sunday , so there will be five sundays in the month. Required Average = (510x5+240x25 / 30) = (8550 / 30) = 285 Answer D #### D QUESTION:Pipes A and B can fill a cistern in 10 and 90 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full? options: A)13 B)12 C)16 D)18 E)19 SOLUTION:: 1/10 + 1/90 = 1/9 9 * 2 = 18.Answer:D #### D QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)226 B)Rs.992 C)665 D)771 E)211 SOLUTION:(800*3*3)/ 100 = 72 920 + 72 = 992 Answer: B #### B QUESTION:In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned? options: A)3:16. B)2:3. C)4:9 D)3:4. E)2:5. SOLUTION:1st statement : ratio of pants Store A : Store B 10x : 30x X:3X Price : 4y:3y Total revenue 4xy : 9xy 4:9 Answer : C #### C QUESTION:There are 3 people and 3 chairs. In how many different ways people can occupy the chairs? options: A)6 B)15 C)24 D)36 E)120 SOLUTION:number of ways =3! = 6 Answer is A #### A QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90.5% B)87.5% C)80.5% D)77.5% E)70.5% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.212; 10+0.3} = {9.788; 10.212}. From the 8 listed numbers, 7 are within this range so 6/8=87.5%. Answer: B. #### B QUESTION:A man has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? options: A)110 B)115 C)120 D)125 E)130 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 640 16x = 640 x = 40. Hence, total number of notes = 3x = 120 ANSWER :C #### C QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast? options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2 SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes. Answer: C. #### C QUESTION:1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus? options: A)98 B)99 C)97 D)96 E)95 SOLUTION:Let x be the no of initial passenger no of passengr left in 1st stop (2x/3)+30 no of passenger in the 2nd stop 3/4((2x/3)+30) + 12 which is equal to 84 (passngr on last stop) so final eqn....3/4((2x/3)+30) + 12 = 84 Ans x = 99 ANSWER:B #### B QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides? options: A)3 B)6 C)5 D)9 E)1 SOLUTION:S = (1 + 2 + 7)/2 = 5 Answer:C #### C QUESTION:Two numbers N and 12 have LCM = 48 and GCF = 8. Find N. options: A)24 B)34 C)44 D)54 E)32 SOLUTION:The product of two integers is equal to the product of their LCM and GCF. Hence. 12 × N = 48 × 8 N = 48 × 8 / 12 = 32 correct answer E #### E QUESTION:Evaluate 28% of 550 + 45% of 280 options: A)232 B)242 C)252 D)262 E)280 SOLUTION:Explanation: = (28/100) * 550 + (45/100) * 280 = 154 + 126 = 280 Answer: Option E #### E QUESTION:Ravi and sunil are partners in a business. Ravi invests Rs.12,000 for 4 months and Sunil invested Rs.10000 for 5 months then after one year ratio of their profits will be options: A)1:3 B)2:3 C)24:25 D)20:22 E)3:4 SOLUTION:=(12000*4):(10000*5) =48000:50000 =24:25 ANSWER:C #### C QUESTION:Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3? options: A)2/5 B)2/7 C)33/83 D)51/250 E)100/249 SOLUTION:SOLUTION The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250. Answer: D #### D QUESTION:At a circular table for nine will sit seven adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the nine people be arranged around the table. options: A)120 B)240 C)480 D)600 E)720 SOLUTION:Consider the two parents and two children as one unit. Then there are five adults and one family unit. The number of ways 6 can form a line is 6! Around a circular table, there would be 6 rotations so we divide this number by 6. There are 5! ways for 6 to sit around the circular table. Then the two children have two options and the two parents have two options. Then the total number of ways is 5!*2*2= 480 The answer is C. #### C QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 * 11 * 7 = 154 ANSWER:B #### B QUESTION:Three hoses work to fill a tub at at different rate. Hose Q and B, working together, can fill the tub in 6/5 of an hour. Hoses Q and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub? Edited for accurate solution options: A)3/10 B)2/5 C)1/2 D)1 E)6/5 SOLUTION:Convert the given time to rate and you will be able to add it up. Total Rate of Q and B = Rate of Q + Rate of B = 1/(6/5) = 5/6 Total Rate of Q and C = Rate of Q + Rate of C = 1/(3/2) = 2/3 Total Rate of B and C = Rate of B + Rate of C = 1/2 Adding all three, 2(Rate of Q + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2 = 2 Rate of Q + Rate of B + Rate of C = 1 tub/hour Time taken by all three together to fill up the tub is 1 hour=D #### D QUESTION:Rectangular tile each of size 60cm by 56cm must be laid horizontally on a rectangular floor of size 560cm by 240cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: options: A)50 B)54 C)47 D)40 E)45 SOLUTION:Area of tile = 60*56 = 3360 Area of floor = 560*240 = 134400 No of tiles = 134400/3360 = 40 So, the no of tile = 40 ANSWER:D #### D QUESTION:A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? options: A)1/3 B)1/4 C)1/5 D)1/6 E)1/10 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 5*4*1=20. P(dispensing one of each color)=20/120=1/6. The answer is D. #### D QUESTION:How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3? options: A)14 B)13 C)12 D)11 E)10 SOLUTION:The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers. The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form. So, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number. We get a total of 19−5=1419−5=14 numbers. Answer A #### A QUESTION:There are 22 students in a class. In how many different ways can a committee of 3 students be formed? options: A)1180 B)1320 C)1540 D)1760 E)1920 SOLUTION:22C3 = 22*21*20 / 6 = 1540 The answer is C. #### C QUESTION:From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 13 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ? options: A)38 B)39 C)40 D)41 E)42 SOLUTION:Soln:- 13x=45 --> 87/77*x=45 --> x=45*77/87=677/17=~40. Answer: C. #### C QUESTION:Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$824.32 C)$954.26 D)$2472.96 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 30000*(1 + 2/100)^4 = 30000 * 51/50 * 51/50 * 51/50 * 51/50 = $32472.96 C.I. = 32472.96-10000 = $2472.96 Answer is D #### D QUESTION:In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters? options: A)125.5 meters B)126.5 meters C)127.5 meters D)128.5 meters E)None of these SOLUTION:Explanation: When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters. Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters. So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C. So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters. Answer: C #### C QUESTION:A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the work ? options: A)10 hours B)12 hours C)16 hours D)18 hours E)None of these SOLUTION:ExplanaƟon: Work done by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12 Work done by B in 1 hour = (7/12)�(1/2) = 1/12 => B alone can complete the work in 12 hour Answer: B #### B QUESTION:judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 6th position from either end of the row. Can you find out how many girls are practicing together? options: A)4 B)9 C)11 D)6 E)8 SOLUTION:As judith is 6th from either end of the row, it means that 5 girls are on one of her sides and 5 are present on the other. 5 + 5 + 1(judith herself) = 11. Hence, 11 girls are practicing the dance together. correct answer is C)11 #### C QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 11 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 * 12 = 11 => 2x = 11 => x = 5.5 C #### C QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? options: A)610 B)720 C)825 D)920 E)None of these SOLUTION:Explanation : The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA). Hence we can assume total letters as 5. and all these letters are different. Number of ways to arrange these letters = 5! = [5 x 4 x 3 x 2 x 1] = 120 All The 3 vowels (OIA) are different Number of ways to arrange these vowels among themselves = 3! = [3 x 2 x 1] = 6 Hence, required number of ways = 120 x 6 = 720. Answer : Option B #### B QUESTION:Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? options: A)10liters B)15liters C)20liters D)18liters E)22liters SOLUTION:Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters Let x liters of pure milk be added. Then, 0.5/(10+x) = 2/100 2x = 30 x=15 liters Answer is B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 B)240 C)288 D)267 E)211 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 24)m = 360 m. Let the length of the platform be x meters. Then, (x + 360)/36 = 15 ==> x + 360 = 540 ==> x = 180 m.Answer: A #### A QUESTION:Find the product of the localvalue and absolutevalue of 4 in 20468? options: A)1000 B)1100 C)1200 D)1300 E)1600 SOLUTION:Local value of 4 = 4 x 100 = 400 Place value of 4 = 4 There fore = 4 x 400 = 1600 E #### E QUESTION:60 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple? options: A)47 B)46 C)54 D)58 E)67 SOLUTION:orange+mango-apple=7 mango+apple-orange=10 apple=60 orange+mango+apple=4 60+10+4-7=67 like apple ANSWER:E #### E QUESTION:Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 120 players took part in that tournament. How many matches were played? options: A)99 matches. B)88 matches. C)77 matches. D)66 matches. E)119 matches. SOLUTION:Solution: 119 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 119 matches were played. Answer E #### E QUESTION:A train 124 m long running at 68 kmph crosses a platform in 19 sec. What is the length of the platform? options: A)338 B)234 C)240 D)881 E)271 SOLUTION:D = 68 * 5/18 = 19 = 358 – 124 = 234 Answer: B #### B QUESTION:A chair is bought for Rs.200/- and sold at Rs.310/- find gain or loss percentage options: A)15% loss B)20% gain C)25% gain D)30% gain E)55% gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (310- 200)/200= 55% gain E #### E QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following numbers? options: A)4 B)3 C)7 D)6 E)9 SOLUTION:Let the consecutive even integers are n and (n + 2) difference of the squares = (n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4 = 4(n + 1) which is divisible by 4 Answer is A #### A QUESTION:A division of a company consists of four men and eight women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)7/11 B)7/33 C)14/33 D)7/66 E)14/66 SOLUTION:The total number of ways to choose two representatives is 12C2=66. The number of ways to choose two females is 8C2=28. P(choosing two female representatives)=28/66=14/33 The answer is C. #### C QUESTION:495 x 495 = ? options: A)250000 B)250025 C)5000 D)245025 E)240000 SOLUTION:495 x 495 = (495 )2 = (500 - 5)2 = (500)2 + (5)2 - (2 x 500 x 5) = 250000+ 25 - 5000 = 250025 - 5000 =245025. D) #### D QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)16 SOLUTION:1. We need to find out the time taken by 7 workers after day 1. 2. total no.of wokers * total time taken = time taken by 1 worker 3. Time taken by 1 worker = 16*8 = 128 days 4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job. 5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7* total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days. 6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days. The answer is choice E #### E QUESTION:The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 5 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 18 seconds? options: A)18 miles per hour B)90 miles per hour C)216 miles per hour D)324 miles per hour E)5400 miles per hour SOLUTION:Since Velocity is proportional to Time Velocity =k*Timewhere k is the constant of proportionality Time= 5 seconds Velocity = 5k = 90 miles per Hour i.e. k = 18 i.e. The relation between Velocity and Time becomes Velocity =18*Time Time= 18 seconds Velocity = 18*18 = 324 miles per hour Answer: Option D #### D QUESTION:S is a set containing 8 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? options: A) The median of S is prime. B) The median of T is prime C) The median of S is equal to the median of T. D) The sum of the terms in S is prime. E) The sum of the terms in T is prime. SOLUTION:Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? (A) The median of S is prime. Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime. (B) The median of T is prime. Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number. (C) The median of S is equal to the median of T. Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true. (D) The sum of the terms in S is prime. Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime. (E) The sum of the terms in T is prime. Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime. C #### C QUESTION:Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together? options: A)17 1/7 B)17 1/9 C)17 1/2 D)17 1/7 E)17 1/5 SOLUTION:1/30 + 1/40 = 7/120 120/7 = 17 1/7 days Answer: A #### A QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)56 B)28 C)45 D)24 E)45 SOLUTION:D 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### D QUESTION:Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? options: A)654 B)655 C)656 D)588 E)658 SOLUTION:total cost 840 840*30/100=252 so the cut in amount is 252 the less amount to be spend is 840-252=588 ANSWER:D #### D QUESTION:A train 350 m long passed a pole in 35 sec. How long will it take to pass a platform 650 m long? options: A)100 sec B)89 sec C)85 sec D)16 sec E)15 sec SOLUTION:Speed = 350/35 = 10 m/sec. Required time = (350 + 650)/10 = 100 sec. Answer: A #### A QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(6200*5*3)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 * 12 = 9 => 2x = 9 => x = 4.5 A #### A QUESTION:A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time? options: A)75 m. B)80 m. C)150 m. D)100 m. E)None of the above SOLUTION:ratio of speeds of a and b is 2:1 b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b the time taken for a to cover 50m is 50/1=50m so the total time taken by a and b to reach =2*50=100m ANSWER:D #### D QUESTION:An athlete runs 200 metres race in 24 seconds. His speed is : options: A)20 km/hr B)24 km/hr C)28.5 km/hr D)30 km/hr E)None of these SOLUTION:Speed = 200/24 m/sec=25/3 m/sec=(25/3*18/5)km/hr=30 km/hr. Correct Option: D #### D QUESTION:There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle. options: A)18 B)99 C)12 D)07 E)11 SOLUTION:Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm. a2 = 784 = (4)(196) = (22).(142) a = (2)(14) = 28 a = 2l, l = a/2 = 14 l = (7/3)s Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm. Answer: C #### C QUESTION:Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey? options: A)67.0 km /hr B)67.2 km /hr C)69.0 km /hr D)69.2 km /hr E)None SOLUTION:Solution Required average speed =(2xy / x+y)km/hr = 2 x 84 x 56 /(84 + 56) = (2 x 84 x 85 /140) = 67.2 km/hr. Answer B #### B QUESTION:The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)18 years B)88 years C)77 years D)10 years E)17 years SOLUTION:Let their ages be x and (x + 20) years. 5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10. Their present ages are 30 years and 10 years Answer:D #### D QUESTION:A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. options: A)15/7 B)4/17 C)7/18 D)19/6 E)7/15 SOLUTION:Let S be the sample space Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45 Let E=event of getting both balls of same colour Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4) =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21 P(E)=n(E)/n(S)=21/45=7/15 Option E #### E QUESTION:A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose? options: A)22 B)77 C)877 D)99 E)88 SOLUTION:3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters=525 cm = 5 × 5 × 3 × 7 Hence common factors are 3 and 7 Hence LCM = 3 × 7 = 21 Hence largest size of square tiles that can be paved exactly with square tiles is 77 cm. Answer:B #### B QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 11 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)64 B)72 C)80 D)90 E)99 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 11 and the total number of coins is 9k = 99. The answer is E. #### E QUESTION:Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $45,000 higher than Store B's revenues. In the second month, Store A's revenues were $8,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue? options: A) $14,000 B) $15,000 C) $42,000 D) $47,000 E) $50,000 SOLUTION:Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +45 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +8 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T): (45 + 8 + T)/3 = 2 53 + T = 6 T = -47 Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -47 represents a $47,000 advantage in favor of Store B. Choice (D) is correct. #### D QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 4 cm. What is the length of the wire? options: A)116 cm B)144 cm C)168 cm D)173 cm E)189 cm SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(4)^2 * h = (4/3)π (12)^3 => h = 144 cm Answer:B #### B QUESTION:What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected? options: A)76 ways B)66 ways C)30 ways D)56 ways E)43 ways SOLUTION:The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5 = 30 ways. Answer: C #### C <<<Examples ends QUESTION:Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina Works independently at the job for 8 hours and then Ann works independently, how many hours will it take Ann to complete the remainder of the jobs? options: A)2/3 B)3/4 C)1 D)2 E)3 SOLUTION:Work done by Tina in 1 hr=1/12 Work done by Tina in 8 hr=1/12*8 which is 2/3 Now,the remaining work is 1/3 which is completed by Ann in 1/3*9 which is 3hr ANSWER:E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)15,2 B)15, 4 C)15, 8 D)15, 5 E)15,7 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer:D #### D QUESTION:√(36)^2 options: A)6 B)14 C)36 D)21 E)None of these SOLUTION:explanation √(36)^2 =? or, ? = 36 Answer C #### C QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)198 E)200 SOLUTION:185 Answer is B #### B QUESTION:A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$333.33 C)$100.25 D)$277.78 E)$377.00 SOLUTION:Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 ) $25000 is 60% of total amount. So total amount = 25000 * 100/60 Remaining amount is 40% of total amount. 40% of total amount = 25000 * (100/60) * (40/100) = 50000/3 This amount has to be divided by 50( remaining people are 50 ) So per head amount is 50000/3 / 50 = 32000/180 = 333.33; ANSWER:B #### B QUESTION:The cube root of what integer power of 2 is closest to 50? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Integer powers of 2 = 2 , 2^2, 2^3, 2^4, 2^5, 2^6, 2^7 etc. Let, Cube root of x is closest to 50 i.e. x is closest to cube of 50 = 50*50*50 = 125000 But x must be equivalent to an Integer power of 2 2^10 = 1024 2^7 = 128 i.e. 2^17 = 128*1024 = 128000 (approx.) i.e. 2^18 = 256*1024 = 256000 (approx.) i.e. 2^16 = 64*1024 = 64000 (approx.) i.e. 2^17 which is closest to 125000 i.e. Integer power of 2 must be 7 Answer: option B #### B QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:If r and t are positive integers, rt + r + t cannot be options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let rt + t + r = x Add 1 on both sides: rt + t + r + 1 = x + 1 t(r + 1) + r + 1 = x + 1 (r + 1)(t + 1) = x + 1 Minimum value of (r + 1) = 2 Minimum value of (t + 1) = 2 Hence x + 1 cannot be prime Substitute x from the given options: 6 + 1 = 7 --> prime --> rt + t + r cannot be 6 Answer: B #### B QUESTION:A sum of money at simple interest amounts to $ 980 in 3 years and to $1024 in 4 years. The sum is: options: A)$153 B)$848 C)$398 D)$549 E)$675 SOLUTION:B $848 S.I. for 1 year = $(1024 - 980) = $44. S.I. for 3 years = $(44 x 3) = $132. Principal = $(980 - 132) = $848. #### B QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? options: A)7/17 B)7/22 C)7/18 D)7/19 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ⁸C₂ ways. P = 7C2/¹15C2 + 8C2/15C2 = 7/15 Answer: E #### E QUESTION:It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? options: A)10 hours B)17 hours C)19 hours D)16 hours E)27 hours SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:A red ant is sitting on one side of a table (point X) and a black ant is sitting on the opposite side of the table (point Y). Now both of them decides to exchange their places and starts crawling. On the way, both of the ants meet and after that, it takes 20 seconds for the Red ant to move to point Y and it takes 5 seconds for the Black ant to reach point X. Find out the total time taken by the Red and the Black ant to make the journey. options: A)30 and 15 seconds B)10 and 15 seconds C)20 and 15 seconds D)25 and 15 seconds E)5 and 15 seconds SOLUTION:Solution: Let the speed of red ant be R. Speed of Black ant be B. Time at which they cross their paths be T. Now we will apply the basic formula of distance Distance = Speed * Time The Red ant travels R * T distance before meeting and R * 20 after meeting. The Black ant travels B * T distance before meeting and B * 5 after meeting. Now as per the question, The distance traveled by red ant before they both meet will be equal to the distance covered by black ant after they meet. We can say the same for the vice versa case as well. Thus R * T = B * 5 and B * T = R * 20 Using both the quations T = 10 Thus the red ant will require 10 + 20 = 30 seconds to travel the distance. And the black ant will take 10 + 5 = 15 seconds to travel the distance. Answer A #### A QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 *12=45,000*8 1:1 Madhu's share=1/2*60,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b? options: A)5 B)6 C)11 D)16 E)19 SOLUTION:The number of possible permutation without 2 in the first digit is 4X4X3X2X1=96 ways. The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways. 18c1/96c1 = 18/96= 3/16= > a+b=19. ANSWER:E #### E QUESTION:A person starting with Rs.64 and making 6 bets, wins 3times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is? options: A)Rs.37 B)Rs.45 C)Rs.47 D)Rs.53 E)Rs.59 SOLUTION:As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order). The overall resultant will remain same. So final amount with the person will be (in all cases): =64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727 Hence the final result is: 64−27=3764−27=37: A loss of Rs.37 A #### A QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:How many integers between 500 and 1000 are there such that their unit digit is even? options: A)250 B)150 C)500 D)100 E)200 SOLUTION:500 numbers between - 500 and 1000 Out of which half would be even, half odd. Number of even unit digit number = 250. correct option is A #### A QUESTION:If r is a positive integer and r^2 is divisible by 12, then the largest positive integer that must divide r ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since r is an integer so r cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making r^2 as a multiple of 12)) r^2 is divisible by 12 (12 = 2*2*3), So, r should have at least one 2 and one 3 so that r^2 has a 2^2 and two 3 So, r will have a 2 and a 3. Or r will be a multiple of 6 So, largest possible integer than should divide r^3 is 6^3 So, Answer will be D #### D QUESTION:A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week? options: A)605 B)505 C)105 D)100 E)200 SOLUTION:earning 35 surveys using her cell phone = 13*35 = 455 balance 15 surveys = 10 x 15 = 150 Total = 455+150 = 605 Answer : A #### A QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 24 times, A has killed: options: A)27 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(24 x 16)/3= 128. Birds killed by A =(5x/24) =(5/24*128)= 27. Answer is A #### A QUESTION:Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible? options: A)48 B)66 C)72 D)78 E)90 SOLUTION:Total number of 5 digit numbers that can be formed = 5! = 120. Total number of 5 digit numbers in which 3 and 4 are adjacent = 48. This can be calculated by taking 3 and 4 as a pair and considering positions where they can appear. Number of 5 digit numbers in which 3 and 4 are not adjacent = Total number of 5 digit numbers - Total number of 5 digit numbers in which 3 and 4 are adjacent. Ans = 120 - 48 = 72 C #### C QUESTION:1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:1/5 , 1/2 , 1/3 1/5*2 , 1/2*2 ,1/3*2 1/5*3 , 1/2*3 ,1/3*3 1/5*4 , 1/2*4 ,1/3*4 so 1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,2 ANSWER:B #### B QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)18 sec B)28 sec C)48 sec D)29 sec E)24 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed? options: A)5 B)4 C)3 D)2 E)0 SOLUTION:= 147,000 = 147 x 1000 = (3) x (7 x 7) x (2x2x2) x (5x5x5) = 2^3 x 3^1 x 5^3 x 7^2 red = 7^2 = 49 ANSWER:D #### D QUESTION:Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 4 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)18 D)12 E)6 SOLUTION:21-12 < no of hrs < 21-6 9< no of hrs < 17. D #### D QUESTION:Of the science books in a certain supply room, 40 are on botany, 45 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same area science? options: A)186 B)225 C)294 D)302 E)314 SOLUTION:The worst case scenario is to remove all the books on botany, zoology, and geology. Also we can remove 79 books each from physics and chemistry. The total is 40 + 45 + 50 + 79 + 79 = 293. The next book removed must either be physics or chemistry, ensuring 80 books in that subject. The answer is C. #### C QUESTION:A ship sails out to a mark at the rate of 15 kmph. and sails back at the rate of 10 kmph. The average rate of sailing is ? options: A)5 km/hr B)12 km/hr C)12.5 km/hr D)25 km/hr E)None SOLUTION:Answer Average = ( 2uv / u +v ) km/hr = ( 2 x 15 x 10 ) / (15 +10 ) km/hr. = 12 km/hr. Correct Option: B #### B QUESTION:Number A is randomly selected from a set of all primes between 10 and 40, inclusive. Number K is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that A+K is odd? options: A) 1/2 B) 2/3 C) 3/4 D) 4/7 E) 5/8 SOLUTION:All primes except 2 are odd, thus A must be odd. For A + K = odd + K to be odd, K must be even. There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd. Therefore the probability that A + K is odd is 4/7. Answer: D. #### D QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2 SOLUTION:42/360 * 22/7 * 12 * 12 = 52.8 m2 Answer: C #### C QUESTION:Bob finishes the first half of an exam in one-thirds the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam? options: A)20 B)24 C)27 D)30 E)40 SOLUTION:Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/3's the time of the second half (3/3's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 1:5 and the second half is 3:5). With each fifth of an hour being 15 minutes (60/4), the first half of the exam would have taken 30 minutes. Correct answer is D. #### D QUESTION:Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 12 machines produce in 6 minutes? options: A)1344 B)3360 C)8400 D)5040 E)67200 SOLUTION:8 machines produce 560 in 1 min 8 machines produce 560* 6 in 6 min 12 machine produce 560*6*(12/8) in 6 minutes 560*6*12/8=5040 answer is D. #### D QUESTION:Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: options: A)2:3 B)4:3 C)7:3 D)9:3 E)4:2 SOLUTION:Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3. #### B QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 * 2600 = Rs.1200 Answer: A #### A QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value D of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] D=z-x = x+9-x= 9 Ans:D #### D QUESTION:A boat goes 100 km downstream in 10 hours, and 80 km upstream in 20 hours. The speed of the stream is? options: A)4km/h B)3km/h C)2km/h D)(1/2) km/h E)E)None SOLUTION:100 --- 10 DS = 10 ? ---- 1 80 ---- 20 US = 4 ? ----- 1 S = (10 - 4)/2 = 3 kmph ANSWER:B #### B QUESTION:A rectangular box of volume x has width, depth and height in the ratio of 5:1:2 (in that order). What is the width as a function of x? options: A)(4x/12)^(1/2) B)(10x/4)^(1/2) C)(5x)^(1/2) D)(2x/5)^(1/2) E)(4x/3)^(1/2) SOLUTION:We are given width = 5, depth = 1, height = 2 Then Volume x = Width x Depth x Height = 5*1*2 = 10 i.e. x = 10 i.e. The correct option should result in 5 (the width) on substituting the value of x=10 Checking options with x=10 A) (4x/12)^(1/2) = (4*10/12)^(1/2) = (40/12)^(1/2) INCORRECT ANSWER B) (10x/4)^(1/2) = (10*10/4)^(1/2) = 25^(1/2) = 5 CORRECT ANSWER C) (5x)^(1/2) = (5*10)^(1/2) = 50^(1/2) INCORRECT ANSWER D) (2x/5)^(1/2) = (2*10/5)^(1/2) = 4^(1/2) = 2 INCORRECT ANSWER E) (4x/3)^(1/2) = (4*10/3)^(1/2) = 40/3^(1/2) INCORRECT ANSWER Answer: Option B #### B QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)3 B)2.5 C)2.25 D)1.5 E)4 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 - x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 ANSWER:B #### B QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/6. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)25. B)24. C)23. D)20. E)16. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 6,5 and 10 Lets take LCM of three balls 6,5 and 10 = 30. The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls. The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls. The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS. Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls. IMO option E is correct. #### E QUESTION:A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is options: A)280 B)285 C)290 D)295 E)275 SOLUTION:Explanation: As the month begin with sunday, so there will be five sundays in the month. So result will be: =(510×5+240×25 / 30)=(8550 / 30)=285 Option B #### B QUESTION:In Plutarch Enterprises, 60% of the employees are marketers, 30% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? options: A)$80,000 B)$130,000 C)$260,000 D)$290,000 E)$320,000 SOLUTION:For sake of ease, let's say there are 10 employees:6 marketers, 3 engineers, and 1 manager. Average company salary * Number of employees = Total company salary >>> $80,000 * 10 = $800,000 Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (3 * $80,000) >>> $800,000 - $300,000 - $240,000 = $260,000. The correct answer is C. #### C QUESTION:Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children? options: A)60 B)180 C)240 D)360 E)720 SOLUTION:If we wanted, we could make this one extremely difficult, counting out all kinds of possibilities in several different cases. Instead, we are going to make this ridiculously easy. First of all, with absolutely no restrictions, how many ways can the six children be arranged on the six chairs? That’s a permutation of the 6 items —- 6P6 = 6! = 720. That’s the total number of arrangements with no restrictions. Of course, those 720 arrangements have all kinds of symmetry to them. In particular, in all of those arrangements overall, it’s just as likely for E to be to the left of F as it is for E to be to the right of F. Therefore, exactly half must have E to the right of F, and exactly half must have E to the left of F. Therefore, exactly (1/2)*720 = 360 of the arrangements have E to the left of F. Answer = D. #### D QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres? options: A)20 B)200 C)300 D)400 E)100 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 9540 [4L - 40] = 9540 / 26.50 = 360 4L = 400 L = 400/4= 100 meters. Answer: E #### E QUESTION:During the months May through October, Teddy the bear triples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976? options: A)9m−1300 B)9m−300 C)4m−1200 D)3m−300 E)m−1300 SOLUTION:Nov ' 73 = m April ' 74 = m - 100 Oct ' 74 = 3m - 300 April' 75 = 3m - 400 Oct' 75 = 9m - 1200 April'76 = 9m - 1300 Hence answer will be (A) 9m - 1300 #### A QUESTION:The average (arithmetic mean) of the integers from 100 to 400, inclusive, is how much greater than the average of the integers from 50 to 250, inclusive? options: A) 100 B) 175 C) 200 D) 125 E) 300 SOLUTION:For an AP the mean or average of series is average of first and last term. So, average of numbers between 100 to 400, inclusive = (100+400)/2 = 250 average of numbers between 50 to 250, inclusive = (50+250)/2 = 150 difference = 250 - 150 = 100 Answer is A #### A QUESTION:A can give B 70 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? options: A)139.78 B)139.13 C)139.22 D)111.0 E)111.12 SOLUTION:A runs 1000 m while B runs 930 m and C runs 800 m. The number of meters that C runs when B runs 1000 m, = (1000 * 800)/930 = 860.21 m. B can give C = 1000 - 860.21 =139.78m. Answer:A #### A QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)106 C)110 D)120 E)130 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C QUESTION:What is the remainder when 25472 is divided by 2? options: A)3 B)1 C)8 D)7 E)0 SOLUTION:If the digit in unit place is even, the number will be divisible by 2. 2 is an even number,so the number is divisible by 2 ANSWER:0 #### E QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a - b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:a = 2n (n>=3), b = 2n - 2, c = 2n - 4 a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E ANSWER:E #### E QUESTION:The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)22 seconds B)65 seconds C)78 seconds D)12 seconds E)21 seconds SOLUTION:Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 60/5 = 12 seconds. Answer:D #### D QUESTION:What percent of 180 is 45? options: A)0.25% B)4% C)25% D)40% E)250% SOLUTION:Here's an algebraic approach. Let p = the required percent. This means p/100 = the percent as a fraction. So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45 Or: (p/100)(180) = 45 Divide both sides by 180 to get: p/100 = 45/180 Simplify right side: p/100 = 1/4 Multiply both sides by 100 to get: p = 25 ANSWER:C #### C QUESTION:A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long? options: A)38 sec B)35 sec C)44 sec D)40 sec E)50 sec SOLUTION:Explanation: Speed = 45 km/hr = 45×(10/36) m/s = 150/12 = 50/4 = 25/2 m/s Total distance = length of the train + length of the platform = 360 + 140 = 500 meter Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds Answer: Option D #### D QUESTION:Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $45,000 higher than Store B's revenues. In the second month, Store A's revenues were $8,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue? options: A) $14,000 B) $15,000 C) $42,000 D) $47,000 E) $50,000 SOLUTION:Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +45 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +8 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T): (45 + 8 + T)/3 = 2 53 + T = 6 T = -47 Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -47 represents a $47,000 advantage in favor of Store B. Choice (D) is correct. #### D QUESTION:In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B? options: A)4 : 9 B)5 : 8 C)7 : 11 D)4 : 7 E)None of these SOLUTION:Explanation : Assume that investment of C = x Then, investment of A =2x A receive 48000 Then C will receive = 48000/2 = 24000 And B receive = 180000 - (24000+48000) = 108000 Ratio of investment between A and B = 48000 : 108000 = 4 : 9 Answer : Option A #### A QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers? options: A)1 B)5 C)7 D)8 E)9 SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6 y = mx + b => 12 2/3 = -22*5/6 + b => b = 31 y = -5x/6 + 31 Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point. A #### A QUESTION:A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in one hour? options: A)6 metre B)12 metre C)120 metre D)1200 metre E)2200 metre SOLUTION:Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600 :. Distance moves = (600 *20) cms = 12000 cms In metres = 120 metre Answer: C #### C QUESTION:there are two cubes with ratio between volume is 125:64. then what is the value of length of each cube? options: A)25:16 B)16:25 C)4:5 D)5:4 E)150:96 SOLUTION:given 6a12:a22=150:96 then a12:a22=25:16 a1:a2=5:4 so the answer is D #### D QUESTION:When m is divided by 9, the remainder is 8. When m is divided by 13, the remainder is 1. If 1 < m < 200, what is the greatest possible value of m? options: A)47 B)65 C)103 D)117 E)170 SOLUTION:Looking at the choices, options BD can be eliminated as they are divisible by 13 Starting from the highest number 164; 170 = 162 + 8 (162 divisible by 9) 170 = 169 + 1 (169 divisible by 13) it fits the result Answer = E #### E QUESTION:What is the perimeter of a square field whose diagonal is 8√2? options: A)82 m B)32 m C)27 m D)26 m E)76 m SOLUTION:4a = 32 m Answer: B #### B QUESTION:Entry fee in a zoo is $10. Later this was reduced by 50% which increased the sale by 40%. The percentage increase in the number of visitors is? options: A)100% B)50% C)180% D)200% E)150% SOLUTION:Let the total original sale be $1000 Then original number of visitors = 100 New number of visitors = 1400/5 = 280 Increase % = 180% Answer is C #### C QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)19.7 C)20 D)21.1 E)23 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 50 years. The age of E is? options: A)50 B)47 C)48 D)49 E)46 SOLUTION:Solution 5 years ago average age of A,B,C,D = 45 years => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years => Total present age of A, B, C, D = 180 + 5x4 = 200 years If E's present age is x years = 200+x/5= 50 x=50 years. Answer A #### A QUESTION:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.) options: A)4 B)5 C)6 D)12 E)24 SOLUTION:Let's start with 4 minimum number of colors So single color code we can make 4 nos. Now if we need to make 2 color combination out of 4 we can do so in 4!/2!*2! or 4*3/2 or 6 So total we can make 4+6=10 color combinations but we have 12 boxes So let's look at 5 we get 5 single color codes and out 5 color choices, we can choose 2 in 5!/2!*3! ways or 10 ways. So total we can have 5+10=15 color combinations. So, minimum number we need will be 5 Ans is B....... #### B QUESTION:Due to 10% decrease in the price of sugar and John can buy 4kg more sugar in Rs100 , then find the CP of sugar? options: A)s. 1(2/9) B)s. 2(7/9) C)s. 2(1/9) D)s. 3(2/7) E)s. 4(2/9) SOLUTION:Here r = 10 % ,x = 100 and A = 4 kg Actual price of sugar = 10*100/((100-10 )*4) = Rs. 2(7/9) B #### B QUESTION:An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)144° B)150° C)168° D)180° E)none SOLUTION:Solution Angle traced by hour hand in 5 hrs 10 min. = (360/12 x 6)° = 180°. Answer D #### D QUESTION:There are 5 boxes in a cargo. The weight of the 1st box is 200 KG, the weight of the 2nd box is 20% higher than the third box, whose weight is 25% higher than the 1st box weight. The 4th box which weighs 350 KG is 30% lighter than the 5th box. Find the difference in average weight of the 4 heaviest boxes and the four lightest boxes. options: A)22 B)75 C)25 D)70 E)11 SOLUTION:weight of 1st box=200 weight of 3rd box=(125/100)*200=250 weight of 2nd box=(120/100)*250=300 weight of 4th box =350 weight of 5th box=(10/7)*350=500 average of 4 highest weighted boxes=(500+350+300+250)/4=350 average of 4 lightest boxes=(350+300+250+200)/4=275 therefore difference=350-275=75 Answer:B #### B QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:In a class of 150 students 55 speak English;85 speak Telugu and 30 speak neither English nor Telugu How many speak both English and Telugu? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Total=150 English=55 Telugu=85 none/ neither English nor Telugu=30 No. of Students who speak only one or both=150-30=120 so, 120 stud's can speak english or telugu or both. then, No. of Stud's speak only English= 120-85(telugu)=35 " " " " " Telugu= 120-55=65 Remaining 120-(65+35)=20 stud's can speak both. B) #### B QUESTION:The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought? options: A)42. B)38. C)33. D)22. E)20. SOLUTION:Let X pizzas of 2 slices and Y pizzas of 4 slices. 2X + 4Y. Lets check options wise. A. 42 => 2(15) + 4(3) B. 38 => 2(15) + 4(2) C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out. D. 22 => 2(10) + 4(3) E. 20 => 2(6) + 4(2) Answer: correct option is C #### C QUESTION:In a group of 3 boys and 2 girls can be formed out of a total of 4 boys and4 girls? options: A)20 B)22 C)24 D)26 E)29 SOLUTION:Solution: Total number of ways = (select 3 boys from group of 4 boys) * (2 girls from group of 4 girls) => (4c3) * (4c2) = 24 C #### C QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? options: A)18 B)16 C)26 D)17 E)11 SOLUTION:Explanation: 1500 ---- 390 100 ---- ? => 26% Answer:C #### C QUESTION:What is the sum of all the composite numbers up to 12? options: A)21 B)20 C)36 D)40 E)49 SOLUTION:Explanation: 4 + 6 + 8 + 9 + 10 +12 = 37 Answer: E #### E QUESTION:In how many ways the word "KIT" can be arranged? options: A)6 B)8 C)18 D)21 E)24 SOLUTION:Explanation : The required number of ways = 3! = 6 Answer : A #### A QUESTION:Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $3 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans? options: A)9% B)56.6% C)11% D)12% E)15% SOLUTION:You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So 3(15) = 45 - Fox 2(18) = 36 - Pony The total discount discount is $3 and you are asked to find the percent discount of pony jeans, so 45(18 - X)/100 + 36(X)/100 = 3 or 45*18 -45*x + 36*x =3*100 or 9x = -3*100 +45*18 x= 510/9 = 56.6% B #### B QUESTION:Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following Q must be true? I. At least 50% of the numbers in Z are smaller than the median. II. Less than 50% of the numbers in Z are greater than the median. III. The median of Z is greater than the average of the largest and smallest numbers in Z. options: A)I only B)II only C)III only D)I and III only E)Q=None of the above SOLUTION:Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3. Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect. Even if not, we can rule them both out. So, E. #### E QUESTION:A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)276 m B)279 m C)240 m D)207 m E)285 m SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 39 = 15 x + 300 = 585 x =285m. Answer: E #### E QUESTION:Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute). options: A)2 hours 2 minutes B)3 hours 5 minutes C)4 hours 6minutes D)5 hours 7 minutes E)7 hours 9 minutes SOLUTION:In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill 1/5 + 1/8 = 13 / 40 of a tank Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving (13/40) t = 1 t = 40 / 13 = 39/13 + 1/13 hours = 3 hours and (1/13)*60 minutes = 3 hours 5 minutes (rounded to the nearest minute) correct answer B #### B QUESTION:If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in options: A)2 days B)1 day C)3 days D)5 days E)7 days SOLUTION:The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day. B) #### B QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer:A #### A QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)60 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 105 ⇒ 1.75x = 105 ⇒ x = 60 coins Answer D #### D QUESTION:The first republic day of the India was celebrated on 26th January,1950. It was options: A)221 B)28 C)276 D)20 E)22 SOLUTION:1-1-1 AD fall on Monday. We calculate the number of odd days till 24th december, 1995. Number of odd days till 1600 years = 0 1601 to 1700 = 5 1701 to 1800 = 5 1801 to 1900 = 5 49 years contains = 37 normal + 12 leap years =12 × 2 + 37 = 61 odd days = 61/7 = 5 odd days 25th January 1950 = 25/7 = 4 odd days Total odd days =15 + 5 + 4 = 24/7 = 3 odd days So 26th January,1950 is Thursday Answer:B #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is options: A)277 B)668 C)119 D)177 E)121 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer: C #### C QUESTION:The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is: options: A)377 B)267 C)268 D)750 E)271 SOLUTION:Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 .Answer: D #### D QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction? options: A)5hours B)40hours C)8hours D)20hours E)30hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 40 =20 hours Answer is D #### D QUESTION:In 110 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: options: A)20 m B)25 m C)22 m D)9 m E)12 m SOLUTION:Distance covered by B in 9 sec. = 110/45 x 9 m = 22 m. A beats B by 20 metres. Answer: Option C #### C QUESTION:Sum of 42 odd numbers is? options: A)1764 B)1774 C)1784 D)1794 E)1754 SOLUTION:sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 42 odd numbers = 42^2 = 1764 ANSWER:A #### A QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 6*8.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (5*27) - (4*25) = 135-100 = 35 Answer: Option A #### A QUESTION:Two 6 faced dice are thrown together. The probability that all the three show the same number on them is? options: A)1/32 B)1/6 C)1/33 D)1/38 E)1/34 SOLUTION:The three dice can fall in 6 * 6 = 36 ways. Hence the probability is 6/36 = 1/6 Answer: B #### B QUESTION:The successive discounts 20% and 15% are equal to a single discount of? options: A)43% B)72% C)32% D)44% E)29% SOLUTION:C 32% Let the CP of an article be Rs. 100 Given that successive discounts are 20% and 15%. SP = 85% of 80% of 100 = (85/100)(80/100)(100) => SP = Rs. 68 Clearly, single discount is 32%. #### C QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is options: A)70 B)71 C)72 D)73 E)74 SOLUTION:Explanation: Let the second number is x, then first is 2x, and third is 1/3(2x) =>2x+x+2x/3=264 <=>11x/3=264 =>x=72 Answer: Option C #### C QUESTION:Less than half of a committee that is to be formed out of certain group, are to be men. If there are 100 possible ways of forming the committee, then the number of men in the committee can be, options: A)2 B)3 C)4 D)5 E)cannot be determined SOLUTION:1. Let there be m men and w women out of which the committee is formed. 2. mCn * wCr = 100, where n is the number of men chosen and r is the number of women chosen 3. The possible products for LHS of (2) are, 100 * 1, 50 * 2, 25 * 4, 20 * 5, 10 * 10 4. Since the number of women is greater than the number of men, the first three products in (3) can be rejected as they would not satisfy this condition. 5. In the case of the fourth product, 20 * 5 may be given by 6C3 * 5C1. Though this may satisfy the condition with 3 women and 1 man, 1 man is not in the choices given. 6. The last product 10 * 10 may be given by 5C2 * 5C3 with 2 men and 3 women. This satisfies the condition and also 2 men is one of the choices given. Therefore the answer is choice A. #### A QUESTION:How many ONE letter words are formed using the letters of the word WALK? options: A)1 B)16 C)7 D)4 E)2 SOLUTION:The number of letters in the given word is 4. The number of ONE letter words that can be formed using these four letters is 4P1=4*1=4 Answer:D #### D QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:Find the third proportional to 63 and 29.9? options: A)14.09 B)14.29 C)14.19 D)14.16 E)None of these SOLUTION:Explanation: Formula = Third proportional = (b × b)/a A = 63 and B = 29.9 (29.9 × 29.9)/ 63 = 894.01/63 = 14.19 Answer: Option C #### C QUESTION:The average of first four prime numbers greater than 50 is? options: A)50 B)57 C)89 D)56 E)60 SOLUTION:53 + 59 + 61 + 67 = 240/4 = 60 Answer: E #### E QUESTION:What distance (in meters) will be covered by a bus moving at 54 km/hr in 15 seconds? options: A)175 B)200 C)225 D)250 E)275 SOLUTION:54 km/hr = 54 * 5/18 = 15 m/s distance = 15 * 15 = 225 meters The answer is C. #### C QUESTION:Ben is driving on the highway at z miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(z/y) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of z miles per hour, Ben covers z miles, so 5,280z feet. The number of revolutions = distance/circumference = 5,280z/y. Answer: A. #### A QUESTION:The probability that A speaks truth is 15/23 and that of B speaking truth is 17/29. What is the probability that they agree in stating the same fact? options: A)182/395 B)129/289 C)197/353 D)479/667 E)None of these SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 15/23 * 17/29 + 14/23 * 16/29 = 255/667 + 224/667 = 479/667 ANSWER:D #### D QUESTION:The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly options: A)24.64 B)24.69 C)24.62 D)24.6 E)24.61 SOLUTION:Explanation: For 1st year S.I =C.I. Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200 i.e S.I on the principal for 1 year is Rs.200 Principle = = Rs.2500 Amount for 2 years, compounded half-yearly C.I = Rs.424.64 Also, Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64 Answer:A #### A QUESTION:One day a car rental agency rented 3/4 of its cars, including 4/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players? options: A)23/40 B)17/30 C)12/25 D)7/15 E)3/10 SOLUTION:The cars with CD players which were not rented is (1/5)(3/5) = 3/25 of all the cars. The cars which were not rented is 1/4 of all the cars. The percent of non-rented cars which had CD players is (3/25) / (1/4) = 12/25 The answer is C. #### C QUESTION:Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share? options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164 SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B #### B QUESTION:Josh spends a total of $5.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following? options: A)99 B)100 C)101 D)109 E)140 SOLUTION:Let x be the number of single bubblegums and y be the number of bubblegum pack. then 5x+50y=550 or x+10y=110 or x=110-10y Now, let y=0, then x= 110 and N=x+y or N=0+110 =110. let y=1, then x=100 and N=100+1= 101 (given in the options) let y=2, then x= 90 and N=92 the value will further decrease and hence we do not need to calculate anymore values. ANSWER:- C #### C QUESTION:There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 20% of all the students at Morse have cars, how many students are in the three lower grades? options: A)600 B)900 C)1200 D)1350 E)1500 SOLUTION:Let x be the number of students in the lower three grades. 0.1x + 150 = 0.2(x+300) 0.1x = 900 x = 900 The answer is B. #### B QUESTION:A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream? options: A)6 hr B)2 hr C)4 hr D)1 hr E)None of these SOLUTION:Explanation : Speed downstream = 96⁄8 = 12 kmph Speed of current = 4 km/hr Speed of the boatman in still water = 12-4 = 8 kmph Speed upstream = 8-4 = 4 kmph Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B #### B QUESTION:A group of men decided to do a work in 20 days, but 8 of them became absent. If the rest of the group did the work in 28 days, Find the original number of men? options: A)60 B)28 C)40 D)50 E)25 SOLUTION:Original number of men = 8*28 / (28-20) = 28 Answer is B #### B QUESTION:1/3, 1/2, 1/4, 2 1/3, 3 1/2, 4 1/4, 4 1/3, 6 1/2, ? options: A)8 1/4 B)9 1/4 C)8 1/2 D)8 1/3 E)6 1/4 SOLUTION:there are 3 series--- 1/3,2 1/3,4 1/3. 1/2,3 1/2,6 1/2. 1/4,4 1/4,? ans 8 1/4 ANSWER:A #### A QUESTION:Which of the following equations has a root in common with x^2−3x+2=0 ? options: A)x^2-2x+1=0 B)x^2-2x-1=0 C)x^2-x+1=0 D)x^2-3x+3=0 E)x^2-7x=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-2)= 0 so the two roots are 1 and 2. Now put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. A is the answer. #### A QUESTION:In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 6 metres then what will be the area of the square so formed? options: A)Cannot be determined B)2600 cm2 C)5184 cm2 D)3025 cm2 E)None of these SOLUTION:Let the side of the square be x m. ∴ Perimeter of the square = 48 × 6 = 4x ∴ x = 72 m ∴ Area = (72)2 = 5184 m2 Answer C #### C QUESTION:The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average? options: A)69 B)70 C)71 D)72 E)75 SOLUTION:Sum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled. The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72. ANSWER:D #### D QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)12:17 C)17:12 D)21:32 E)15:19 SOLUTION:Here capital is not the same. Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =(20000×6+15000×6) Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio =(30000×4+50000×4) Suresh : Kiran =(20000×6+15000×6) :(30000×4+50000×4) =(20×6+15×6):(30×4+50×4) =(20×3+15×3):(30×2:50×2) =105:160 =21:32 Answer is D. #### D QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 35 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)45 E)01 SOLUTION:Explanation: As there is meal for 70 adults and 35 have their meal, the meal left can be catered to 35 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 35 adults = 45 children Hence, the meal can be catered to 45 children. ANSWER: D #### D QUESTION:In how many different ways can the letters of the word 'CAREER' be arranged? options: A)10 ways B)20 ways C)180 ways D)60 ways E)40 ways SOLUTION:Totally there are 6 letters on the word CAREER. it contains 1C,1A,2R,2E. The no of ways is 6!/2!2!=180 ways. ANSWER:C #### C QUESTION:Find the missing in the series: 70, 54, 45, 41,___ options: A)22 B)287 C)2679 D)2767 E)2771 SOLUTION:Answer:B #### B QUESTION:In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive? options: A)None B)One C)Two D)Three E)Four SOLUTION:Non - Negative ( zero to positive infinity ) Solution to the question : -4,-3,-2,-1,0 , 1,2,3 Hence ans is 3 ..option D #### D QUESTION:Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ? options: A)2 B)5 C)1 D)9 E)4 SOLUTION:4-3=1. Answer is C #### C QUESTION:Last year, the price per transaction of certain company increases P percent from the year before, and the number of transactions increase N percent from the year before. Total revenue is simply the number of transactions times the price per transaction. Assume this one transaction is this company's only source of revenue. Which of the following is the percent increase in revenue last year, from the year before? options: A)P∗N % B)(P+N) C)(P+N+P∗N/100) % D)(P+N-P∗N/100) % E)(P+N+P∗N/100)^2 % SOLUTION:Assume x = price per transaction for previous year y = price per transaction for this year Relationship between x and y y =x (1+P/100) Similarly, if n1= no. of transactions for last year n2 = no. of transactions for this year n2 = n1(1+N/100) Now, the question is [(n2y- n1x) /n1x] * 100 n2y = n1x(1+P/100)(1+N/100) So, [(n2y - n1x)/n1x] * 100 = (n1x[(1+P/100) (1+N/100) - 1]/ n1x) * 100 D is the answer. #### D QUESTION:Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved? options: A)56% B)64% C)62.2% D)68% E)61% SOLUTION:If initial cost is Rs 100, then Final cost will be 100*0.7*0.6*0.9 = Rs. 37.8 savings = 100-37.8=62.2 so 62.2% ANSWER:C #### C QUESTION:Mark drove for 1/2 of the trip, and Justin drove for 1/4 of the trip. Gina and Kaitlyn divided the rest of the driving evenly between them. If the entire trip was 128 miles, how many miles did Kaitlyn drive? options: A)26 miles B)16 miles C)20 miles D)18 miles E)17 miles SOLUTION:1/2 x 128 = 64 miles Mark drove 1/4 x 128 = 32 miles Justin drove 64 + 32 = 96 miles driven 128 - 96 = 32 miles left 32 ÷ 2 = 16 miles driven by Kaitlyn correct answer B #### B QUESTION:Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other? options: A)300 kms from A B)280 kms from A C)305 kms from A D)295 kms from A E)265 kms from A SOLUTION:DETAILED SOLUTION Bus A Travels 200km @ 40kmph the next 200km @ 50kmph and the final 200km @ 60kmph So, Bus A will be at a distance of 200km from city M after 5 hours, and at a distance of 400km after 9 hours, and reach N after 12 hours and 20 mins Bus B Travels at an overall average speed of 50kmph, so will take 12 hours for the entire trip. So, Bus B will travel 160 kms in the first 4 hours 200 kms in the next 4 hours and 240 in the final 4 hours So, both buses cross each other when they are in their middle legs. After 5 hours, bus A will be at a position 200kms from city M. At the same time, bus B will be at a distance 210kms from city N (4 * 40 + 50). The distance between them will be 190kms (600 - 200 - 210). Relative speed = Sum of the the two speeds = 50 + 50 = 100 kmph. Time taken = 190/100 = 1.9 hours. = 1 hour and 54 minutes. So, the two buses will meet after 6 hours and 54 minutes. Bus B will have travelled 210 + 95 = 305 kms. So, the two buses will meet at a point that is 305 kms from City N and 295 kms from city A. CORRECT ANSWER D #### D QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? options: A)1000 B)817 C)278 D)268 E)280 SOLUTION:2 * 22/7 * 1.75 * x = 11000 x = 1000 Answer: A #### A QUESTION:A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and B leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost? options: A)3 2/3 B)5 2/3 C)6 2/3 D)4 2/3 E)7 2/3 SOLUTION:x/10 + 2/15 + 4/20 = 1 x = 40/60*10 = 6 2/3 Answer: C #### C QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 6 years ago? options: A)152460 B)214560 C)131632 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^6 Answer is C #### C QUESTION:√[200√[200√[200……..∞]]] = ? options: A)200 B)10 C)1 D)20 E)2 SOLUTION:Let √[200√[200√[200……..∞]]] = x ; Hence √200x = x Squaring both sides 200x = x² Þ x (x – 200) = 0 Þ x = 0 or x – 200 = 0 i.e. x = 200 As x cannot be 0, x = 200. ANSWER:A #### A QUESTION:Which number should replace both the asterisks in (* /18) x (*/162) = 1 ? options: A)27 B)36 C)54 D)72 E)90 SOLUTION:Let (y/18) x (y/162) = 1 y^2 = 18 x 162 = 18 x 18 x 9 y = (18 x 3) = 54 The answer is C. #### C QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)27% B)25% C)21% D)85% E)24% SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer:B #### B <<<Examples ends QUESTION:A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? options: A)Rs. 4980 B)Rs. 4991 C)Rs. 4996 D)Rs. 4997 E)Rs. 5000 SOLUTION:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991. B) #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country? options: A)166 2/7 B)166 2/1 C)166 2/2 D)166 2/3 E)166 2/8 SOLUTION:5% - 2% = 3% 3% ---- 5 100% ---- ? => 166 2/3 Answer:D #### D QUESTION:X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 54 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is : options: A)34 B)43.2 C)40 D)38 E)29 SOLUTION:Solution: Average speed = 2XY / X+Y = 2*54*36 / 54+36 = 43.2 Answer : B #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is : options: A)22 B)21 C)88 D)37 E)29 SOLUTION:Explanation: Lot the total number of workers be v Then, 8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21 Answer: B) 21 #### B QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)820 SOLUTION:The word ‘ORANGE’ contains 6 different letters. Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time =6P6 = 6! = 6*5*4*3*2*1 = 720 ANSWER:B #### B QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents. Answer: C. #### C QUESTION:A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred. options: A)Rs. 5750 B)Rs. 6000 C)Rs. 5500 D)Rs. 5000 E)Rs. 7000 SOLUTION:The price varies as the square of the weight, P = K x W2 12250 = K x 352 K = 10 Thus, P = 10W2 When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively. Their values should be : 10g piece: 10 x 102 = Rs. 1000; 25g piece: 10 x 252 = Rs. 6250. Total value of stone now, = 1000 + 6250 = Rs. 7250 Loss incurred = 12250 - 7250 = Rs. 5000 ANSWER:D #### D QUESTION:The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)35 kmph D)23 kmph E)14 kmph SOLUTION:S = (10 + 60)/2 = 35 kmph Answer:C #### C QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream? options: A)60/18 B)30/29 C)60/12 D)60/13 E)30/82 SOLUTION:Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 120/26 = 60/13 hours. Answer:D #### D QUESTION:If 4x + y = 8 and −2x + y = 13, then what is the value of 2x + 2y? options: A)1/7 B)3 C)15 D)21 E)60/7 SOLUTION:4x + y = 8 −2x + y = 13 Adding both the equations --> 2x + 2y = 21 Answer: D #### D QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? options: A)6 hrs 21 min B)6 hrs 71 min C)6 hrs 32 min D)6 hrs 27 min E)6 hrs 23 min SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs. Number of stoppages = 600/75 - 1 = 7 Total time of stoppages = 3 * 7 = 21 min Hence, total time taken = 6 hrs 21 min. Answer:A #### A QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. #### C QUESTION:If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:0.003^5= (3*10^-3)^5 = 243*10^-15 = 0.243*10^-12 which would have 12 zeros to the right of the decimal point. The answer is D. #### D QUESTION:Two friends run the New York City marathon, one friend finishes the marathon in 400 minutes while the second friend finishes the marathon in 625 minutes. What is the ratio of their speed? options: A)10 : 12 B)1 : 2 C)5 :10 D)20 : 25 E)None SOLUTION:Solution Let us name the friends as A and B. = ( Friend A'S speed) : (Friend B's speed) =√b : √a = √400 : √625 = 20 : 25 Answer D #### D QUESTION:In a colony of 70 residents, the ratio of the number of men and women is 5: 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony? options: A)A)1:5 B)B)1:1 C)C)1:8 D)D)1:9 E)E)1:3 SOLUTION:Number of men in the colony = 5/7 * 70 = 50. Number of women in the colony = 2/7 * 70 = 20. Number educated women in the colony = 1/5 * 30 = 6. Number of uneducated women in the colony = 4/5 * 50 = 24. Number of educated persons in the colony = 8 /35 * 70 = 16. As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 50 - 10 = 40. Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4. Answer:A #### A QUESTION:Suganya and Suriya are partners in a business. Suganya invests Rs. 38,000 for 8 months and Suriya invests Rs.40,000 for 10 months. Out of a profit of Rs.31,570. Suganya's share is options: A)Rs.1435 B)Rs.12,628 C)Rs.1685 D)Rs.18,942 E)None SOLUTION:Solution Ratio of their shares =(35000×8):(42000×10) = 2 : 44. Suganya's share = Rs.(31570 ×2/44) = Rs.1435. Answer A #### A QUESTION:8k8 + k88 -------- 1,6w6 If k and w represent non-zero digits within the integers above, what is w? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16w6 Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and w=6. Answer: A. #### A QUESTION:In an examination a pupil's average marks were 63 per paper. If he had obtained 26 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination? options: A)8 B)9 C)10 D)14 E)12 SOLUTION:Let the number of papers be x. Then, 63x + 26 + 2 = 65x = 2x = 28 = x = 14. ANSWER:D #### D QUESTION:There are 50 students in a class. If 10 % are absent on a particular day, find the number of students present in the class. options: A)43 B)36 C)28 D)45 E)11 SOLUTION:Number of students absent on a particular day = 10 % of 50 i.e., 10/100 × 50 = 5 Therefore, the number of students present = 50 - 5 = 45 students. Answer:D #### D QUESTION:A is 16th position and 29th from down of the people who passed. 5 failed , 6 didn't give . how many boys are there in the class? options: A)52 B)53 C)54 D)55 E)56 SOLUTION:A is 16th position, means = 15 + A 29th from down, means = A + 28 Total passed = A + 15 + 28 = 44 Total failed = 5 Didn't give = 6 Therefore, total boys = 44 + 5 + 6 = 55 ANSWER:D #### D QUESTION:Median H of price of the car is 52,000. which could be the median of the other two. 35000, 44000, x, y, 57000. options: A)38000 B)47000 C)48000 D)51,000 E)56,000 SOLUTION:Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits H is 56,000.E #### E QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)6 D)5 E)1 SOLUTION:2x * x = 128 => x = 8 Answer:A #### A QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.450 B)Rs.500 C)Rs.550 D)Rs.640 E)Rs.650 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)12% B)19% C)15% D)14% E)22% SOLUTION:Original price = 100 CP = 80 S = 80*(140/100) = 112 100 - 112 = 12% Answer:A #### A QUESTION:Which of the following is(are) true for a@b=b@a? I. a@b=b+ba II. a@b=(a+b)(a-b) III. a@b=(a/b)+(b/a) options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X). If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O). If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O). Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A QUESTION:After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day? options: A)$1.25 million B)$80,000 C)$750,000 D)$27,000 E)$10,000 SOLUTION:Let sales in previous month = X 1.25 X=2,000,000 5/4 X= 2,000,000 ..........> X=2,400,000 sales per day= 2,400,000/30= less than 80,000 Answer:B #### B QUESTION:A starts a business with a capital of Rs. 9,000. B joins in the business with Rs.18,000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? options: A)2 months B)6 months C)7 months D)8 months E)None of these SOLUTION:Explanation : Let B joins for x months. Then A:B = 9000*12 : x* 18000 = 3 : 1 => 9*12 : 18x= 3 : 1 => 9*12/ 18x = 3/1 = 3 => 9*4 /18x = 1 => 2/x = 1 => x = 2. Answer : Option A #### A QUESTION:David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house? options: A)$96,000 B)$94,000 C)$88,000 D)$75,000 E)$40,000 SOLUTION:Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer. #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is? options: A)65 B)21 C)78 D)67 E)51 SOLUTION:Let the total number of workers be x. Then, 8000x = (12000 * 7) + 6000(x - 7) = 2000x = 42000 = x = 21. Answer: B #### B QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 14 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)17 E)72 SOLUTION:Explanation: As there is meal for 70 adults and 14 have their meal, the meal left can be catered to 56 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 56 adults = 72 children Hence, the meal can be catered to 72 children. ANSWER: E #### E QUESTION:Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)18 sec B)70 sec C)21 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 120 + 280 = 400 m. The time required = d/s = 400/20 = 20 sec. Answer: D #### D QUESTION:The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 25 feet on a side. What will be the volume of the new building in cubic feet? options: A)3,937,500 cubic feet B)15,750 cubic feet C)11550√3 cubic feet D)7,160,947 cubic feet E)3,937,500√3 cubic feet SOLUTION:Volume of the Hexagon with side 200 and height 70 = Area * height = 6*(sqrt(3)/4)(200^2)(70) Volume of the center bull's eye that is similar in shape of a hexagon but side 25 = 6 * (sqrt(3)/4)(25^2)*70 Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(25^2)*70=7,160,947 Answer is D #### D QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 5-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5 Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6 Ratio: 5 to 1 Answer : D #### D QUESTION:If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar? options: A)45 B)67 C)75 D)83 E)150 SOLUTION:We are told that 15 percent discount from the original price is more than $10: 0.15*{price} > 10; {price} > 1,000/15; {price} > 66 2/3. Answer: B. #### B QUESTION:A train 280 m long passed a pole in 28 sec. How long will it take to pass a platform 660 m long? options: A)52 B)94 C)71 D)68 E)88 SOLUTION:Speed = 280/28 = 10 m/sec. Required time = (280 + 660)/10 = 94 sec. Answer: B #### B QUESTION:If the productivity of a brigade grows by 40% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade? options: A)1.51 B)0.82 C)1.2 D)1.21 E)1.44 SOLUTION:B = 10-men brigade p = increase in the productivity = 40% Solution: B x p = B x 1.4 = 1.4B -------> the productivity of 11 men brigade 1.4B x p = 1.4B x 1.1 = 1.51B -----> the productivity of 12 men brigade The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.51B/B = 1.51 A #### A QUESTION:Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year? options: A)142% B)150% C)165% D)176% E)188% SOLUTION:Let last year's salary be x. Last year, Sandy save 0.1x This year, Sandy saved 0.15*1.1x = 0.165x 0.165x / 0.1x = 1.65 = 165% The answer is C. #### C QUESTION:If p, q, and r are positive numbers such that (p/(p+q))(10) + (q/(p+q))(20)=r and if p<q which of the following could be the value of r? options: A)10 B)12 C)15 D)18 E)30 SOLUTION:The answer is D. For any positive p and q, r is a number between 10 and 20. Since p < q, weight of 10 is inferior of weight of 20 -> r is > 15 -> 18 is the answer. #### D QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)288 B)492 C)877 D)278 E)178 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 20 + 21 = 41 T = 12 D = 41 * 12 = 492 Answer: B #### B QUESTION:If an amount of Rs 41,800 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1900 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41800/22 = Rs 1900 Answer A #### A QUESTION:In case N is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)O and P E)T and U SOLUTION:O and P should serve on A ANSWER:D #### D QUESTION:Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 9 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)32/9 C)15/4 D)10/3 E)17/5 SOLUTION:Rate(1)=1/6 Rate(2)=1/9 Combined = 5/18 Work done in 2 days=5/9 Work left = 4/9 Rate * Time = Work left 1/8 * Time = 4/9 Time=32/9 B #### B QUESTION:The divisor is 12, the quotient is 4 and the remainder is 1. What is the dividend? options: A)48 B)49 C)96 D)97 E)72 SOLUTION:D = d * Q + R D = 12 * 4 + 1 D = 48 + 1 D = 49 Answer: B #### B QUESTION:A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen? options: A)119 B)1,200 C)3,240 D)3,600 E)14,400 SOLUTION:To meet the conditions we can have only 2 cases: 2 officers and 3 civilians: C25∗C39=840 3 officers and 2 civilians: C35∗C29=360 Total: 840+360=1,200. Answer: B. #### B QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 4, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit? options: A)23/24 B)31/36 C)55/64 D)65/81 E)75/121 SOLUTION:P(no even digits) = 2/3*2/3*2/3*2/3 = 16/81 P(at least one even digit) = 1 - 16/81 = 65/81 The answer is D. #### D QUESTION:A "word" is defined as a sequence of three dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed? options: A)3 B)5 C)6 D)8 E)9 SOLUTION:there are two ways of possibilities.. 1) all three same colour- YYY or BBB- 2 ways 2) two of one colour and one of different colour- 3!/2!-3ways.. now two /one could be Y/B or B/Y.... so 3*2=6.. total 6+2=8 ans D #### D QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase? options: A)80% B)90% C)70% D)60% E)50% SOLUTION:Ans. Let previous income = Rs. 100 Previous savings = 10% of Rs. 100 = Rs. 10 Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120 Increased savings = 15% of Rs. 120 = Rs. 18 Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8 Therefore, Percent increase in savings = 8/10 x 100 = 80% Answer A #### A QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)19% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer: C #### C QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? options: A)1000 B)817 C)278 D)268 E)280 SOLUTION:2 * 22/7 * 1.75 * x = 11000 x = 1000 Answer: A #### A QUESTION:Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? options: A)289 B)132 C)279 D)277 E)278 SOLUTION:2 * 22/7 * 14 = 88 88 * 1 1/2 = Rs.132 Answer: B #### B QUESTION:The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this triangle. options: A)15° ,45° ,110° B)15° ,45° ,130° C)15° ,45° ,110° D)15° ,35° ,110° E)25° ,45° ,110° SOLUTION:Solution If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence x + 3x + 8x = 180 Solve for x 12x = 180 x = 15 The measures of the three angles are x = 15° 3x = 3 × 15 = 45° 8x = 8 × 15 = 120° ANSWER IS C #### C QUESTION:3,8,18,38,78,__ options: A)158 B)156 C)154 D)150 E)148 SOLUTION:8=3*2+2 18=8*2+2 38=18*2+2 78=38*2+2 158=78*2+2 ANSWER:A #### A QUESTION:Peter's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Peter makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0? options: A) 15 B) 24 C) 25 D) 26 E) 13 SOLUTION:day 0- payment of $7 is made in the morning (after 12 am midnight) day 1 onwards(after 12 am midnight) internet service will begin and will run for 7*2=14 days i.e. at the end of day 15 balance will be zero. now Peter can still use the internet till her debt reaches $5 which means total of 5*2=10 days. now the question states for how many days, including today, will she be connected to the internet without any additional paymentsi.e. we will have to include day0 also in our final answer. therefore total no. of days =1+14+10=25=C #### C QUESTION:A monkey ascends a greased pole 12 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ? options: A)21st B)22nd C)23rd D)24th E)None of these SOLUTION:In 2 minutes, he ascends = 1 metre ∴ 10 metres, he ascends in 20 minutes. ∴ He reaches the top in 21st minute. Answer B #### B QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money? options: A)1489 B)6845 C)2598 D)1875 E)2600 SOLUTION:P = 75(100/20)5 => P = 1875 Answer: D #### D QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:A train leaves Delhi at 9 a.m. at a speed of 35 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet? options: A)229 B)288 C)600 D)888 E)1400 SOLUTION:D = 35 * 5 = 175 RS = 40 – 35 = 5 T = 175/5 = 35 D = 40 * 35 = 1400 km Answer: E #### E QUESTION:The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i options: A)70 B)72 C)75 D)78 E)80 SOLUTION:Income of 6 months = (6 × 85) – debt = 510 – debt Income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ Income of 10 months = 780 Average monthly income = 780 ÷ 10 = 78 Answer D #### D QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)25 B)30 C)40 D)45 E)35 SOLUTION:Speed of the train relative to man = (63 - 3) km/hr = 60 km/hr =(60 x(5/18)) m/sec =50/3 m/sec. Therefore Time taken to pass the man =(500 x(3/50))sec = 30 sec. Answer :B #### B QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)81.6 B)88.6 C)81.1 D)81.5 E)81.2 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer: A #### A QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire? options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 120,000 m : C is the circumference C = 5 meters correct answer C #### C QUESTION:31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 12 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates? options: A)A)11 B)B)23 C)C)24 D)D)29 E)D)36 SOLUTION:lets solve by creating equation.. W = 31.. Total = 50.. Not W = 50 -31= 19.. Now let people who were neither be x, so out of 19 who won Nobel = x+3.. so x+x+3=19 or x=8.. so who won Nobel but not Wolf = x+3 = 11.. But people who won BOTH W and N = 12.. so total who won N = 11+12 = 23.. B #### B QUESTION:he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person ? options: A)75 kg B)55 kg C)80 kg D)85 kg E)25 kg SOLUTION:Explanation: Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (60 + 20) kg = 80 kg. Answer: C #### C QUESTION:What is the HCF of 2/3, 5/9 and 6/5 options: A)1/45 B)2/45 C)4/15 D)8/45 E)9/45 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 5, 6)/(LCM of 3, 9, 5) = 1/45 Answer: Option A #### A QUESTION:Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 seconds. What is the length of the fast train? options: A)23 m B)23 (2/9)m C)38 (8/9)m D)29 m E)28 m SOLUTION:Relative speed = (40 - 20) km/hr = (20 x(5/18))m/sec = (50/9)m/sec. Therefore Length of faster train = ((50/9) x 7) m = (350/9)m = 38 (8/9) m. C #### C QUESTION:From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? options: A)756 B)700 C)600 D)500 E)450 SOLUTION:We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only). Required number of ways = (7C3 x 6C2) + (7C4 x 6C1) + (7C5) = (525 + 210 + 21) = 756. ANSWER A #### A QUESTION:Robert's salary was decreased by 60% and subsequently increased by 60%. how much percentage does he lose? options: A)10% B)20% C)25% D)36% E)50% SOLUTION:let original salary be $100 Salary after decreasing 60% = 100 - 100 x 60/100 = $40 Salary after increasing 60% on $40 = 40 + 40 x 60/100 = $64 Percentage of loss = 100 - 64 = 36% Answer : D #### D QUESTION:What is the number of integers from 1 to 100 (inclusive) that are divisible by neither 5 nor by 6? options: A)35 B)47 C)58 D)26 E)34 SOLUTION:In 100 consecutive numbers, number of multiples of 5 = 100/5 = 20 (Ignore decimals) In 100 consecutive numbers, number of multiples of 6 = 100/6 = 16 Number of multiples of 5*6 i.e. 30 = 100/30 = 3 Number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - (29 + 16 - 3) {Using the concept of sets here) = 58 Answer is C #### C QUESTION:What approximate value should come in plce of question mark (?) in the following equations ? 728.038 x 54.978 - 72.016 x 85.250 = ? options: A)31400 B)32700 C)33900 D)34400 E)32400 SOLUTION:Explanation : ? = 728 x 55 - 72 x 85.25 = 40040 - 6138 = 339900 Answer : Option C #### C QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 15000, then find his savings? options: A)3600 B)3607 C)3608 D)3602 E)3000 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 15000 => x = 3000 Savings = Income - expenditure = 5x - 4x = x So, savings = Rs. 3000. Answer:E #### E QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 21% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? options: A)40% B)45% C)55% D)60% E)63.5% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 63.5%. E #### E QUESTION:Which of the following has the most number of divisors? options: A)99 B)101 C)176 D)182 E)179 SOLUTION:Explanation: 99 = 1 x 3 x 3 x 11 101 = 1 x 101 176 = 1 x 2 x 2 x 2 x 2 x 11 182 = 1 x 2 x 7 x 13 So, divisors of 99 are 1, 3, 9, 11, 33, .99 Divisors of 101 are 1 and 101 Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176 Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Hence, 176 has the most number of divisors. Answer: C #### C QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? options: A) 4 B) 2 C) 2 D) 10 E) 12 SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. Answer A #### A QUESTION:If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average R (arithmetic mean) annual increase in the index over this period? options: A) (x + 100)/18 B) x/18 C) (100 − x)/18 D) (x − 100)/18 E) 100x/18 SOLUTION:CPI in end of 1967 = 100 CPI in end of 1985 = x Number of years = 18 Average annual increase in CPI R= (x-100)/18 Answer D #### D QUESTION:The banker's discount on Rs.1800 at 48% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time? options: A)1 months B)4 months C)5 months D)6 months E)7 months SOLUTION:Solution S.I on Rs.1800 = T.D on Rs.1872. P.W on Rs.1872 is Rs.1800. Rs.72 is S.I on Rs. 1800 at 48%. Time =(100x72 / 48x1800) = 1/12 year = 1 months. Answer A #### A QUESTION:An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)144° B)150° C)168° D)180° E)none SOLUTION:Solution Angle traced by hour hand in 5 hrs 10 min. = (360/12 x 6)° = 180°. Answer D #### D QUESTION:The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)1752 B)1799 C)1719 D)1750 E)1800 SOLUTION:Speed = [216 * 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 60 è x = 60 * 60 / 2 = 1800 Answer: E #### E QUESTION:Two numbers when divided by a divisor leave remainders of 238 and 362 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor. options: A)276 B)552 C)414 D)1104 E)2202 SOLUTION:Let x be the divisor. N1 = xa + 238 N2 = xb + 362 N1 + N2 = x(a+b) + 600 = xc + 68 x(c-a-b) = 532 but we know that x>362, thus (c-a-b) must equal 1. The answer is B. #### B QUESTION:a dealer buys 4 varieties of wheat costing rs. 20,rs.25,rs.30 and rs.35 per kg in the ratio 6:4:3:1 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of wheat? options: A)30.5 B)31.0 C)32.0 D)33.0 E)34.5 SOLUTION:CP = 20*6+25*4+30*3+35*1=345 SP = 1.4*345=483 Total no.of kgs=6+4+3+1=14 SP per kg=483/14 = 34.50 ANSWER:E #### E QUESTION:A number consists of 3 digit whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is: options: A)22 B)24 C)77 D)26 E)81 SOLUTION:Explanation: Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 * 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. Answer: B #### B QUESTION:When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y? options: A)560 B)616 C)672 D)728 E)784 SOLUTION:ans B 616... remainders = .32=32/100=8/25=16/50 and so on.. so two digit remainders are 16+24+32+....+96.. W=8(2+3+4....+12)=616 #### B QUESTION:A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month? options: A)6/25 B)5/16 C)4/9 D)3/7 E)2/5 SOLUTION:Let x be the fraction of her take-home pay that the worker saved. Let P be the monthly pay. 12xP = 8(1-x)P 12xP = 8P - 8xP 20xP = 8P x = 2/5 The answer is E. #### E QUESTION:What is the sum of all the composite numbers up to 12? options: A)21 B)20 C)36 D)40 E)49 SOLUTION:Explanation: 4 + 6 + 8 + 9 + 10 +12 = 37 Answer: E #### E QUESTION:The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? options: A)14 years B)17 years C)18 years D)12 years E)11 years SOLUTION:9 * 2 = 181 Answer:C #### C QUESTION:A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following? options: A)1/6 B)1/9 C)1/18 D)1/24 E)1/36 SOLUTION:There are 6*6 = 36 possibilities. Bob has 2 chances so the probability is 2/36 = 1/18. The answer is C. #### C QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show? options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30 SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour. The two clocks show 2:00 at 2 0'clock At 3:00 - Clock B is at 3:00 Clock A is at 3:20 (1 hour + gains 20 minutes) AT 4:00 - Clock B is at 4:00 Clock A is at 4:40 (2 hours + gains 40 minutes) In 4 hours the clock A gains 4*20=80 minutes or 1 hour 20 minutes If clock A is at 7:20 the clock B is at 6:00 Answer is B #### B QUESTION:A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze? options: A)1298 B)1228 C)1210 D)1782 E)1762 SOLUTION:π (232 – 122) = 1210 Answer:C #### C QUESTION:The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? options: A)9% B)4% C)6% D)3% E)5% SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer:B #### B QUESTION:A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B? options: A)7 B)14 C)21 D)28 E)35 SOLUTION:In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice. With 36 liters of milk, we need a total of 48 liters of juice to make drink B. We need to add 21 liters of juice. The answer is C. #### C QUESTION:Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){2, 10} B){16, 16} C){10, 18} D){9, 11} E){7, 13} SOLUTION:answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is one unit. therefore accepted answer is D mean is 10 and S.D decreases minimum. D #### D QUESTION:The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit? options: A)Rs. 2000 B)Rs. 2200 C)Rs. 2400 D)Data inadequate E)Cannot be determined SOLUTION:Explanation : Let the C.P. of the article be Rs. x Given that % profit earned by selling article at Rs. 1920 = % loss incurred by selling article at Rs. 1280 (1920−x/x)∗100 = (x−1280/x)∗100 => 1920 - x = x - 1280 => 2x = 3200 => x = 1600 S.P. for 25% profit = Rs. 1600 + 25% of Rs. 1600 = Rs. 1600*(125/100) = Rs. 2000 Answer : A #### A QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ? options: A)95 B)110 C)20 D)None of these E)Cannot be determined SOLUTION:Solution 2/5of 350 - 4/7of 210 = 20. Answer C #### C QUESTION:A pair of articles was bought for $50 at a discount of 50%. What must be the marked price of each of the article? options: A)$25 B)$12.50 C)$29.65 D)$35.95 E)$45.62 SOLUTION:S.P. of each of the article = 50/2 = $25 Let M.P = $x 50% of x = 25 x = 25*.5 =$12.50 Answer is B #### B QUESTION:Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 10 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 50 will be in team A 50 will be in team B The larger diff is 70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10. Answer choice C #### C QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend? options: A)$2,125 B)$1,320 C)$2,000 D)$1,580 E)$2,000.75 SOLUTION:Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125. #### A QUESTION:A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is? options: A)1250m B)1750m C)950m D)1000m E)1300m SOLUTION:Speed = 15*5/18 = 15/18 m/sec Distance covered in 35 minutes = 15/18 *35 *60 = 1750 m Answer is B #### B QUESTION:A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is options: A)83.33 ml B)83.03 ml C)93.33 ml D)63.03 ml E)82.33 ml SOLUTION:Explanation: Profit (%) = 9.09 % = \inline \frac{1}{11} Since the ratio of water and milk is 1 : 11, Therefore the ratio of water is to mixture = 1:12 Thus the quantity of water in mixture of 1 liter = \inline 1000\times \frac{1}{12} = 83.33 ml] Answer: A) 83.33 ml #### A QUESTION:A division of a company consists of six men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/11 D)5/12 E)7/15 SOLUTION:Total number of ways to select 2 members = 11C2 = 55 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/55 = 2/11 The answer is C. #### C QUESTION:In how many ways can six members be selected from a group of ten members? options: A)10C6 B)10C8 C)10C4 D)10C3 E)10C1 SOLUTION:Six members can be selected from ten members in 10C6 = 10C4 ways. Answer: B #### B QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 6*6 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers? options: A)180 B)128 C)276 D)297 E)236 SOLUTION:Let the five numbers be P, Q, R, S and T. => P + Q + R + S + T = 655. (P + Q)/2 = 85 and R = 125 P + Q = 170 and R = 125 P + Q + R = 295 S + T = 655 - (P + Q + R) = 360 Average of the last two numbers = (S + T)/2 = 180. Answer:A #### A QUESTION:For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2? options: A)5 B)3 C)2 D)1 E)0 SOLUTION:4”2= 4 - 4=0 Answer: E #### E QUESTION:A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 550 ? options: A)249 B)498 C)676 D)823 E)274 SOLUTION:slope of 2 and a y-intercept of 2 y-coordinate is 550 y = 2x + 2 548 = 2x x = 274 Answer: E. 274 #### E QUESTION:Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points? options: A)25 B)29 C)48 D)26 E)54 SOLUTION:A 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. #### A QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)228 B)200 C)279 D)480 E)221 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480.Answer:D #### D QUESTION:The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall’s revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n? options: A)100n/(150 – n) B)200n/(250-n) C)200n/(300-n) D)250n/(400-n) E)300n/(500-n) SOLUTION:Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold. Total revenue= Revenue due to A + Revenue due to B = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B) = n *1 + (100-n) *1.5 = n + (150-1.5n) --- (1) 2. But we know, revenue due to A = m%. of the total revenue --- (2) 3. To express m in terms of n we need to relate (1) and (2) 4. m% = n / ( n + (150-1.5n)) or m= 100n / 150-0.5n = 200n/(300-n) ANSWER:C #### C QUESTION:Three unbased coins are tossed. the probability of getting at least two head is ? options: A)1/4 B)1/2 C)3/4 D)2/3 E)2/5 SOLUTION:S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH} E be the event of getting at least two head is {THH,HTH,HHT,HHH} P(E)=n(E)/n(S)=4/8=1/2 Answer(B) #### B QUESTION:A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)3 B)7.5 C)2.25 D)1.5 E)4 SOLUTION:M = 9 S = x DS = 9 + x US = 9 - x 9 + x = (9 - x)2 9 + x = 18 -2x 3x = 9 x = 3 ANSWER:A #### A QUESTION:A numberais squared and then multiplied by negative 3. The result of this operation Q is equal to three times the sum of three timesaand two. What is one possible value ofa? options: A)-3 B)-2 C)1 D)2 E)3 SOLUTION:Q=-3*a^2=3(3a+2) a= -2 or -1 a=-2=B #### B QUESTION:If y is an integer, then the least possible value of |23 - 4y| is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We know that 4y is a multiple of 4, so let’s first look at the multiples of 4 closest to 23. We have “20” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 4y = 20, y is 5 and when 4y = 24, y is 5. Let’s start with letting y = 4. |23-4(5)| |23-20| |3| = 3 Next, let’s let y equal 5. |23-4(6)| |23-24| |-1| = 1 We see that the smallest possible value of |23-4y| is 1. Answer A. #### A QUESTION:If a/b = 6/5, Then (5a + 4b) / (5a - 4b) = ? options: A)4 B)7 C)5 D)3 E)6 SOLUTION:Answer Dividing numerator as well as denominator by b, we get Given Exp. = (5a + 4b) / (5a - 4b) = (5a/b + 4) / (5a/b - 4) Since a/b = 6/5 this implies that =[(5*6)/5 +4]/[(5*6)/5 -4)] = (6 + 4) / (6 - 4) = 5 Option: C #### C QUESTION:Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many straight lines can be formed by joining them ? options: A)124 B)144 C)134 D)142 E)143 SOLUTION:The number of straight lines formed joining the 18 points, taking 2 at a time = 18C2=153. Number of straight lines formed by joining the 5 points, taking 2 at a time =5C2=10. But 5 collinear point, when joined pairwise give only one line. Required number of straight lines =153-10+1 =144. Answer :B #### B QUESTION:In what ratio should a variety of oil costing Rs. 9 per ltr be mixed with another variety of oil costing Rs. 17.25 per ltr to obtain a mixture costing Rs. 11.75 per ltr? options: A)4 : 1 B)1 : 3 C)3 : 1 D)1 : 2 E)2 : 1 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (17.25 - 11.75) / (11.75 - 9) = 22/11=2/1 ANSWER:E #### E QUESTION:Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 22 boys and 38 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic. Table method is shown above; here is how you will use logic: There are 6 happy boys. There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys. We have 6 happy boys and 6 sad boys. Total we have 22 boys. So 22 - 6 - 6 = 10 boys must be neither happy nor sad. Answer (E) #### E QUESTION:A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 15% less than B, and C costs 20% less than A,and D costs 25% less than C what percent of B's cost is D? options: A)40% B)38% C)44% D)46% E)51% SOLUTION:Soln:- B=100 A 15% less than B = 85 C 20% less than A = 68 D 25% less than C = 51 D is what percent of B = D/B * 100 = 51/100 * 100 = 51% ANSWER:E #### E QUESTION:Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 50 yr. How old is E? options: A)50 yr B)40 yr C)45yr D)64 yr E)NOne SOLUTION:Solution: Total present age of A, B, C and D, = (45*4)+(4*5) = 200 yr; Total age present age of A, B, C, D and E, = 50*5 = 250 yr. So, age of E = 50 yr. Answer: Option A #### A QUESTION:Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube? options: A)22 B)77 C)28 D)18 E)19 SOLUTION:93 + 123 + 153 = a3 => a = 18 Answer: D #### D QUESTION:A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color? options: A)50 B)8 C)60 D)42 E)32 SOLUTION:in the first case the lady takes up 32 red colour then he takes up 24 y (cause he should take up pair) then he takes up 1y+1blue then 2blue(cause to make sure he has a pair of each color in hand) 32+24+2+2=60 ANSWER:C #### C QUESTION:A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? options: A)A)182 B)B)208 C)C)220 D)D)224 E)E)302 SOLUTION:If x is the original number of employees, then after 13% reduction in employees number is .87x but we are given .87x = 181 x = 208 So the original number of employees is 208 Correct Answer - B #### B QUESTION:By selling an article for $180, a person gains $30. What is the gain %? options: A)25% B)30% C)50% D)20% E)10% SOLUTION:S.P. = $180 Gain = $30 C.P. = 180-30 = 150 Gain% = 30/150 * 100 = 20% Answer is D #### D QUESTION:An plane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of ? options: A)100 B)720 C)1100 D)940 E)860 SOLUTION:We know Distance = speed * time = 240 * 5 = 1200 km Now to cover 1200 km in 5/3 hrs , speed = distance / time = 1200 / (5/3) = 720 KMPH Ans- B #### B <<<Examples ends QUESTION:A certain computer manufacturing firm last year produced 80 percent of its computers using parts made by its subsidiary company. If the remaining 10,000 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether? options: A)60000 B)60100 C)60500 D)50000 E)70000 SOLUTION:80% parts used of subsidary company, so 20% parts used of other companies. Now, 20% parts = 10,000 computers So, 1% parts = 10,000/20 Or, 100% parts = 50,000 computers. Hence answer is (D) #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? options: A)45 B)33 1/3 C)27 D)16 2/3 E)15 SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x: 1.5/x = 1/20 x = 30 Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution. Answer is A. #### A QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 7? options: A)56 B)112 C)224 D)448 E)425 SOLUTION:Solution: sequence of 7 lets say sequence is 7n, 7(n+1), 7(n+2), 7(n+3), 7(n+4) so range is 7n+28-7n = 28 if we put the different values of n we will get different but the range will be multiple of 28 and only 425 is not multiple of 28 Answer : E #### E QUESTION:As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found? options: A)14 B)18 C)15 D)10 E)20 SOLUTION:E 20 If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14. #### A QUESTION:A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. options: A)220 B)222 C)223 D)224 E)225 SOLUTION:distance = speed x time Let time taken to travel the first half = x hr then time taken to travel the second half = (10 - x) hr Distance covered in the the first half = 21x Distance covered in the the second half = 24(10 - x) But distance covered in the the first half = Distance covered in the the second half => 21x = 24(10 - x) => 21x = 240 - 24x => 45x = 240 => 9x = 48 => 3x = 16 ⇒x=16/3 Hence Distance covered in the the first half = 21x=21×16/3=7×16=112 km Total distance = 2×112=224 km Answer is D. #### D QUESTION:The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x? options: A)0.03 B)0.04 C)0.048 D)0.05 E)0.12 SOLUTION:Probability of Brand A defective is x Probability of Brand B defective is 0.06 which 6/100. Which tells you there are 2 defective piece in a lot of 33, for 35 lot it is approx - 2.12 Probability of Brand C defective is 0.08 which 8/100. Which tells you there are 2 defective piece in a lot of 25 Total = 40 + 25 + 25 = 100 Probability of having defective piece in a lot of 100 ( All brands ) = 0.053 Hence 5.3 defective piece out 100 lot. So 40x + 2.12 + 2 = 5.3 x = 0.03 ANSWER :Opt A. #### A QUESTION:Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 7 hours? options: A)675 B)750 C)1,800 D)5,900 E)1,575 SOLUTION:8 machines/ 360 cans = 5 machines/ x cans 8x= 1800 x=225 (225)(7 hours)= 1575 cans. The answer is E. #### E QUESTION:The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article? options: A)1:3 B)2:5 C)3:2 D)9:4 E)4:2 SOLUTION:Explanation: Let C.P. = Rs. 5x and S.P. = Rs. 7x. Then, Gain = Rs. 2x Required ratio = 2x : 5x = 2:5 Answer: Option B #### B QUESTION:Mohit sold an article for Rs. 18000. Had he offered a discount of 25% on the selling price, he would have earned a profit of 8%. What is the cost price of the article? options: A)12500 B)27767 C)16688 D)26678 E)19987 SOLUTION:Let the CP be Rs. x. Had he offered 25% discount, profit = 8% Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 25/100(18000) = Rs. 13500 => 1.08x = 13500 => x = 12500 \Answer: A #### A QUESTION:Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4, find P (E|F) and P(F|E)? options: A)1/4 B)1/7 C)3/7 D)4/9 E)5/11 SOLUTION:Here, E and F are events P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1 P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4. A) #### A QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 The total amount of Fuel paid by the company during the given period is approximately what percent of the total amount of salary paid during this period? options: A)A)0.5% B)B)1% C)C)1.25% D)D)3% E)E)4% SOLUTION:Required percentage = (288 + 342 + 324 + 336 + 420) = [ 17 x 100 ] % 1710 ~= 1%. Answer : B #### B QUESTION:The H.C.F. of two numbers is 59 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is: options: A)678 B)944 C)456 D)323 E)899 SOLUTION:: Explanation: Clearly, the numbers are (59 x 13) and (59 x 16). {\color{Blue} \therefore } Larger number = (59 x 16) = 944. Answer: B)944 #### B QUESTION:If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p? options: A)p B)2p C)5p D)7p E)p^2 SOLUTION:Y=30p other number is 5p then GCF(30p,5P)=5P; C is the correct answer #### C QUESTION:Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price? options: A)$1 B)$1.84 C)$1.92 D)$2.13 E)$2.15 SOLUTION:Ordering the data from least to greatest, we get: $1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11 The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.) B #### B QUESTION:In how many different number of ways 5 boys and 4 girls can sit on a bench? options: A)700 B)710 C)720 D)362880 E)740 SOLUTION:npn = n! 9p9 = 9 X 8 X 7 X 6 × 5 × 4 × 3 × 2 × 1 = 362880 D #### D QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only? options: A)24 B)27 C)30 D)33 E)36 SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only. Since 10% of students are in both, then 70% of students are in the band which is 84 students. The number of students in the orchestra is (30/70)*84 = 36. The answer is E. #### E QUESTION:A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week? options: A)605 B)505 C)105 D)100 E)200 SOLUTION:earning 35 surveys using her cell phone = 13*35 = 455 balance 15 surveys = 10 x 15 = 150 Total = 455+150 = 605 Answer : A #### A QUESTION:A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? options: A)1/7 B)2/9 C)1/12 D)4/17 E)2/3 SOLUTION:Total number of balls = 7+2 = 9 n(S) = 9C3 = 9*8*7 / 3*2 = 84 n(E) = 2C2* 7C1 = 7 Probability = 7/84 = 1/12 Answer is C #### C QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 5*60/60 = 5*1/1 = 5 New time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:If (2^13)(25^S) = 5(10^m) what is the value of m ? options: A)7 B)13 C)15 D)16 E)23 SOLUTION:given 2^13 * 25^s = 5 * 10^2 => 2^13 * 5^(2s) = 2^m * 5^(m+1) Ans B on comparing the power of 2 => m=13 #### B QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50 SOLUTION:Others equal 5650. Answer D #### D QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse? options: A)27 B)98 C)27 D)80 E)71 SOLUTION:CP = SP + 1CP = SP - g 620 + x = 860 - 2x 3x = 240 => x = 80 Answer:D #### D QUESTION:There is a certain relation between two given words on one side of : : and one word is given on another side of : : while another word is to be found from the given alternatives, having the same relation with this word as the given pair has. options: A)Landslides B)Strains C)Resistances D)Volcanoes E)Volcanoe1 SOLUTION:Explanation: Seismography is an instrument to measure the intensity of an earthquake. Similarly, taseometer is an instrument to measure strains. Answer: B) Strains #### B QUESTION:If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)7/3 E)9/7 SOLUTION:70 Workers = 3 hours then, 1 Worker = 3*70 Hours 30 Workers = (3*70) /(30) = 7 ANSWER:C #### C QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6 SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2 Answer:B #### B QUESTION:A disease has infected an ant colony that consists of "workers" and "soldiers": 30% of the soldiers and 14% of the "workers" were infected. If that colony is inhabited by 7000 ants, out of which 1700 are infected, how many "workers" inhabit the colony? options: A)1500 B)2500 C)2750 D)3000 E)3250 SOLUTION:From two question we get wo equations: (1) 0,3s + 0,14w = 1700 (2) s + w = 7000 From (2) we get w=7000-s In (1) 0,3s + 980-0,14s= 1700 0,16s=720 72000:16= 4500 =s In (2) 4500 + w = 7000 w= 2500 ANSWER:B #### B QUESTION:A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible? options: A)230 B)360 C)420 D)840 E)5,040 SOLUTION:we have 6 letters out of which 3 are of one kind, 2 are of another kind.. so total ways = 6!/2!1!=360 ans B #### B QUESTION:If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was options: A)Rs 1.56 B)Rs 2.40 C)RS 3.00 D)Rs 3.80 E)Rs 4.20 SOLUTION:first 1/5 mile costs = 1.00 remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14, hence 14*0.20=2.80 total fare = 2.80 + 1.00 =3.80 ANSWER:D #### D QUESTION:Find the one which does not belong to that group ? options: A)237 B)232 C)223 D)426 E)111 SOLUTION:Explanation: 525 => 5 52, 39 => 3 32, 24 => 2 22, 636 => 6 62. The above pattern is not followed in 426. Answer: D #### D QUESTION:There are 50 students in a class. If 10 % are absent on a particular day, find the number of students present in the class. options: A)43 B)36 C)28 D)45 E)11 SOLUTION:Number of students absent on a particular day = 10 % of 50 i.e., 10/100 × 50 = 5 Therefore, the number of students present = 50 - 5 = 45 students. Answer:D #### D QUESTION:John is filling out the office space for his employees. There are 8 people in his office, and he must assign 8 employees to the following positions: 2 next to his cabin, 2 near the gate, 2 in center, and 2 near coffee machine. Only 2 employees are secretary and can sit next to his cabin, and they cannot sit anywhere else. The other employees can sit anywhere they like. How many different groupings are possible? options: A)100 B)90 C)80 D)70 E)60 SOLUTION:Secretary can sit in 2C2 ways = 1 Near the gate we can have 6C2 combinations (2 secretaries are already having a place) In the center we can have 4 C2 employees as 4 already have a place Near coffee machine we can have 2C2 employees as all other place are taken Number of selection = 2C2 * 6C2 * 4C2 * 2C2 = 90 Ans: B #### B QUESTION:In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is? options: A)11 B)20 C)28 D)17 E)13 SOLUTION:Explanation: It is the same as a person with 20 years more age replaces an existing person of the group ( or village) Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village. Alternatively : ( n x 42 ) + 20 = ( n x 43 ) => n=20 Answer: B #### B QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job? options: A)4 days B)6 days C)8 days D)2 days E)9 days SOLUTION:Sandy can do 1/6 of the job each day. Molly can do 1/12 of the job each day. The combined rate is 1/6 + 1/12 = 1/4 of the job each day. The job will take 4 days. The answer is A. #### A QUESTION:If e is an integer, what is the greatest possible value for e that would still make the following statement true: 11*10^e < 1/10 ? options: A) –4 B) –3 C) –2 D) –1 E) 0 SOLUTION:Just putting values, the LHS becomes e=0 --> 11 e=-1 --> 11/10 e=-2 --> 11/100 e=-3 --> 11/1000 Anything lower will be smaller than 11/1000. e=-2, equality does not hold but it does for e=-3. Answer is B. #### B QUESTION:If 2m + n = 7 and m + 2n = 5, then (2m + n)/2 = options: A) 1 B) 7/2 C) 17/5 D) 18/5 E) 4 SOLUTION:2*(m+2m = 5) equals 2m+4n=10 2m+4n=10 - 2m + n= 7 = 3n=3 Therefore n = 1 Plug and solve... 2m + 1 = 7 2m=6 m=3 (6+1)/2= 7/2 B #### B QUESTION:The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area? options: A)10000 B)2777 C)2657 D)2876 E)2868 SOLUTION:100 * 100 = 10000 125 * 80 = 10000 No change Answer: A #### A QUESTION:It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)142 B)144 C)3680 D)3280 E)3680 SOLUTION:Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th . Now, number of even places = 3. Number of girls to occupy the even places = 3. Even places can be filled = P (3, 3) ways. Number of boys = 4. The remaining 4 places can be filled by 4 boys = P (4, 4) ways By the fundamental principle of counting: The required number of seating arrangements P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144 ANSWER:B #### B QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? options: A)3.25 B)3.6 C)4.2 D)4.4 E)6 SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours Answer: option E #### E QUESTION:The banker's discount on Rs.1800 at 48% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time? options: A)1 months B)4 months C)5 months D)6 months E)7 months SOLUTION:Solution S.I on Rs.1800 = T.D on Rs.1872. P.W on Rs.1872 is Rs.1800. Rs.72 is S.I on Rs. 1800 at 48%. Time =(100x72 / 48x1800) = 1/12 year = 1 months. Answer A #### A QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled 3 min--------1/30 parts x min--------- 1 part(full) x=90 min =1 hour 30 min ANSWER:C #### C QUESTION:Two taps can separately fill a cistern 8 minutes and 12 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? options: A)7 B)8 C)6.5 D)9 E)5 SOLUTION:1/8 + 1/12 - 1/x = 1/18 x = 72/11 = 6.5 Answer: C #### C QUESTION:If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series? options: A)26 B)29 C)35 D)40 E)48 SOLUTION:Ans: A Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 24*5= 120 so number of 24 can't be more than 5 so D=24x +2y = 124 24*5 + 2y =124 then y=2 24*4 + 2y = 124 then y=14 24*3 +2y = 124 then y= 26 24*2 +2y =124 then y = 38 24 +2y = 124 then y= 50 26 is the ans.A #### A QUESTION:A train 200 m long passed a pole in 20 sec. How long will it take to pass a platform 610 m long? options: A)46 B)54 C)92 D)76 E)81 SOLUTION:Speed = 200/20 = 10 m/sec. Required time = (200 + 610)/10 = 81 sec. Answer: E #### E QUESTION:The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream? options: A)19 B)88 C)14 D)12 E)17 SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 57/3 = 19 kmph. Answer:A #### A QUESTION:Let N = 18p, where p is a prime number greater than 2. How many odd numbers divide N? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We start by factoring 18. 18 = 2*9 = 6*3 = 2*3*3. Since p is a prime number greater than 2 it must be odd. Therefore 3, 9, and p are the odd numbers that divide N. There are three odd divisors and the answer is therefore C. #### C QUESTION:Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B QUESTION:Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her nine kids? options: A)8 B)9 C)3 D)7 E)10 SOLUTION:cost of each apple = 4 dollars Apples that Benny can buy with the amount she has=360/4 = 90. Apples that each kid gets evenly = 90/9 =10 Apples. So the answer is E=10 #### E QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)7508 C)7528 D)7527 E)7232 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 Answer:A #### A QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)190/827 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways Total ways of getting outcome on two dice =6*6=36 Probability of getting sum as 10 in any attempt =3/36=1/12 Probability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12 Probability of losing game =(11/12)*(11/12)*(11/12)=637/827 I.e. Probability of wining game = 1-(637/827) = 190/827 Answer : Option C #### C QUESTION:If Jenee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased? options: A)1/4 B)1/5 C)1/10 D)3/50 E)1/20 SOLUTION:Perhaps it is also easy to just translate the % into fractions: 6%: 6/100 = 3/50 7%: 7/100 8%: 8/100 = 4/50 =2/25 9%: 9/100 Only 3/50 exists in the answer choices, so ANS D #### D QUESTION:John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist? options: A)6 B)9 C)36 D)120 E)144 SOLUTION:First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places Second Place, Physics Book - in 4 ways Third Place, Math Book - in 2 ways (only 2 books left) Fourth Place, Physics - in 2 ways (only 2 Physics book left) Rest two places can be arranged in one way only. Total no of ways = 4*3*3*2*2*1*1 = 144 ways E #### E QUESTION:In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ? options: A)8% B)5% C)7% D)12% E)19% SOLUTION:A 8% of student hate all four subjects. #### A QUESTION:In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y = options: A)6 B)7 C)5 D)8 E)3 SOLUTION:Line k passes through the origin and has slope 1/7 means that its equation is y=1/7*x. Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6. Answer: A #### A QUESTION:Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics? options: A)7/12 B)4/9 C)5/9 D)1/4 E)2/3 SOLUTION:Lets pick smart numbers. Total number of students: 12 Biology (1/2): 6 Chemistry (1/3): 4 Physics (1/6): 2 After leaving school Biology: 4 Chemistry: 4 Physics: 1 New Total number of students: 9 Biology and Physics: 5 Answer 5/9 or C #### C QUESTION:The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers? options: A)1500 B)1600 C)1400 D)1200 E)1000 SOLUTION:Sum of first n even numbers = n(n+1) =1640 Sum of first n odd numbers = n^2 = 40*40 = 1600 (here n=40) Answer : B #### B QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/38 C)18/34 D)18/31 E)18/30 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35. Answer:A #### A QUESTION:A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.2 km long? options: A)2 mins 14 sec B)2 mins 34 sec C)162 sec D)244 sec E)2 mins 44 sec SOLUTION:D = 25 * 60 + 1200 = 2700 m T = 2700/60 * 18/5 = 162 sec ANSWER:C #### C QUESTION:A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ? options: A)115 B)117 C)116 D)114 E)112 SOLUTION:Explanation: Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117. Answer IS B #### B QUESTION:In honor of the year 2013, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive? options: A)18 B)36 C)42 D)52 E)56 SOLUTION:All options other than 'D' are factors of 2013. Hence, 'D' is the answer #### D QUESTION:In how many different number of ways a Committee of 4person of can be selected from 4boys and 4girls such that at least 1 girl is included in the committe options: A)70 B)69 C)67 D)68 E)65 SOLUTION:1G 3B 2G 2B 3G 1B 4G =(4C1*4C3)+(4C2*4C2)+(4C3*4C1)+4C4 = (4*4)+(6*6)+(4*4)+1 = 16+36+16+1=69 Total 4M 4W 8C4=70 4C4=1 At least one girl = total - with out girl At least one girl =70-1=69 B) #### B QUESTION:Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 10000 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×5400 / 12×3) => Rs. 15,000. Answer : C #### C QUESTION:There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women? options: A)8/12 B)6/16 C)4/16 D)6/10 E)4/10 SOLUTION:w = m+4 w+m = 20 m+4+m = 20 2m = 16 m = 8 w = 12 ratio:8:12 Ans: A #### A QUESTION:Fourthty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club? options: A) 60 B) 70 C) 100 D) 120 E) 140 SOLUTION:40% of the members have passed the test, thus 60% have not passed the test. We also know that 30+12=42 members have not passed the test, thus 0.6*Total=42 --> Total=70. Answer: B. #### B QUESTION:A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in? options: A)12 B)13 C)13 5/7 D)13 ¾ E)None of these SOLUTION:Explanation: (A+B)’s 2 day work = 1/16 + 1/12 = 7/18 work done in 6 pairs of days=7/48 x 6 = 7/8 remaining work = 1/8 work done by A on 13th day =1/16 remaining work = 1/16 on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day total time taken =13 ¾ days Answer: Option D #### D QUESTION:If n is a positive integer, then n(n+1)(n+2) is +ve and options: A)divisible by 4 whenever n is even B)divisible by 3 only when n is odd C)odd whenever n is odd D)even only when n is odd E)even only when n is even SOLUTION:n*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 3,4,&5) A #### A QUESTION:There are 12 cans in the refrigerator. 8 of them are red and 4 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. options: A)460 B)490 C)493 D)455 E)424 SOLUTION:Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator = total ways to pick 4 can out of 12 - ways to pick 4 red out of 8 red - ways to pick 4 blue out of 4 blue 12C4−8C4−4C4=495−70−1=424 ANSWER:E #### E QUESTION:If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x? options: A)-1 B)2 C)1 D)-2 E)0 SOLUTION:If we solve the question, we get x=-2. Option: D #### D QUESTION:A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A. options: A)Rs.240 B)Rs.350 C)Rs.340 D)Rs.390 E)Rs.370 SOLUTION:Explanation: (3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 630 = 240 ANSWER IS A #### A QUESTION:If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 5. II. x is an integer multiple of 3 III. x is an integer multiple of 6 options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6. Let us take example n, n+1, n+2 as 3 three consecutive positive integers. In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12 Hence in a product of 3 consecutive integers, the product is always divisible by 3. Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also. Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even Answer E #### E QUESTION:When a 192 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ? options: A)52 B)68 C)62 D)67 E)69 SOLUTION:Answer No. of pieces = Total length / Length of each piece = 192/3.2 = 60 Option: D #### D QUESTION:A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth? options: A)80 B)28 C)90 D)26 E)11 SOLUTION:Explanation: SP of 1m of cloth = 8925/85 = Rs. 105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 105 - Rs. 25 = Rs. 80. Answer: A #### A QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is: options: A)22 B)50 C)99 D)35 E)12 SOLUTION:Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr.Answer: D #### D QUESTION:If x and y are integers, what is the least positive number of 24x+9y? options: A)1 B)3 C)4 D)6 E)9 SOLUTION:24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1. 8(-1) + 3(3) = 1 Then 3(8x+3y) can have a minimum positive value of 3. The answer is B. #### B QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)767 E)408 SOLUTION:1h ----- 2 ? ------ 60 12 h RS = 16 + 18 = 34 T = 12 D = 34 * 12 =408 Answer: E #### E QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:1) Draw a simple cube 2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes. 3) Remember that the OUTSIDE of the cube is the part that's painted.... The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. J=4 + 4 + 4 = 12. Answer A #### A QUESTION:If a and b are prime numbers, which of the following CANNOT be (x + y)? options: A)5 B)9 C)13 D)16 E)23 SOLUTION:All answer choices but E are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd. Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers. Answer: E. #### E QUESTION:A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work? options: A)6 days B)2 days C)4 4/5 days D)3 days E)9 days SOLUTION:Work done by A in 2 days = 2/10 = 1/5 Remaining work = 4/5 Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6 Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days. Answer: C #### C QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 2 months and 7 months respectively. What was the ratio of their investments? options: A)10:12:14 B)12:24:28 C)20:22:12 D)5:49:16 E)None of these SOLUTION:Explanation : Ratio in which A,B and C shared the profit = 5 : 7 : 8 Assume that the ratio of their investment = a:b:c Then 14a : 2b : 7c = 5 : 7 : 8 Good to go, we got the equation. Now it's a matter of time to find a, b and c 14a/2b = 5/7 => 98a = 10b => b = 98a/10 = 49a/5 ---(1) 14a/7c =5/8 => 2a/c =5/8 => 16a = 5c => c = 16a/5 ---(2) a : b : c = a : 49a/5 : 16a/5 = 1 : 49/20 : 16/5 = 5 : 49 : 16. Answer : Option D #### D QUESTION:If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:t=4p since t = 4p thenevendivisors are: 4p/4p= 1 4p/2p= 2 4p/4= p 4p/2= 2p so the answer is (C) #### C QUESTION:The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half? options: A)44.2 B)47.8 C)50.5 D)53.6 E)56.9 SOLUTION:The average of this half is 154.4/4 = 38.6 This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8 The answer is B. #### B QUESTION:A and B started a business with their capitals Rs. 3,00,000 and 18,00,000 respectively. Annual profit will be distributed between them in the ratio options: A)2:5 B)2:3 C)1:3 D)1:6 E)1:9 SOLUTION:3,00,000:18,00,000 Ans. 1:6 ANSWER:D #### D QUESTION:The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen? options: A)Rs.32 B)Rs.28 C)Rs.36 D)Rs.25 E)None of these SOLUTION:Let the cost of each pen and pencil be 'p' and 'q' respectively. 16p + 8q = 352 --- (1) 4p + 4q = 96 8p + 8q = 192 --- (2) (1) - (2) => 8p = 160 => p = 20 ANSWER:E #### E QUESTION:Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar? options: A)2288 B)2677 C)6000 D)2700 E)2881 SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x 10 * 20 * 90 = 15 * 2 * x => x = 6000 Answer: C #### C QUESTION:85% of a number is added to 24, the result is the same number. Find the number? options: A)28 B)288 C)279 D)160 E)232 SOLUTION:(85/100) * X + 24 = X 3X = 480 X = 160 Answer:D #### D QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)28% D)68% E)48% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make an orange juice. How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice. options: A)25 B)34 C)50 D)67 E)100 SOLUTION:A =25 1 oz concentrate + 3 oz ofwater = 4 oz jucie 300 oz concentrate +900 oz of waer = 1200 oz juice no of cans==300/12=25 Ratio of juice to water ===> 1:3 total 200*6 ounces 12 ounce juice cans ==> 1200/12 == 100*1/4 (ratio of jiuce to total) == 25 #### A QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $25. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet) options: A)9/(25xy) B)xy/225 C)225/(xy) D)225xy E)25xy/9 SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 9. The price per square yard is 25 / (xy/9) = 225/(xy). The answer is C. #### C QUESTION:Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages. options: A)Rs 40, Rs 60 and Rs 260 B)Rs 36, Rs 81 and Rs 243 C)Rs 42, Rs 86 and Rs 232 D)Rs 38, Rs 88 and Rs 234 E)none of these SOLUTION:Let the total work done be 360 units. Therefore, work done by Anil, Bittu and Chintu in single day are 4 units, 9 units and 30 units respectively. Each of them working for 9 days Anil and Bittu will be able to complete 4 units and 9 units of their work on the 9th day but Chintu will be doing remaining 3 units of work. Hence, individual work done by them to complete the whole work is 36 units, 81 units and 243 units till the end of 9th day for each of them. Thus, respective wages on the basis of work done is Rs 36, Rs 81 and Rs 243 respectively for Anil, Bittu and Chintu. ANSWER:B #### B QUESTION:Which of the following fractions is the largest? options: A)7/8 B)7/7 C)7/2 D)7/5 E)7/6 SOLUTION:L.C.M of 8, 16, 40 and 80 = 80. 7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80 Since, 70/80 > 63/80 > 65/80 > 62/80, So, 7/8 > 63/80 > 13/16 > 31/40 So, 7/8 is the largest. Answer: A #### A QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:The ratio of boys to girls is 6:4.60% of the boys and 40% of girls take lunch in the canteen.What % of class takes lunch? options: A)51% B)52% C)53% D)54% E)55% SOLUTION:let total no of students 100, boy 60 and girl 40, so lunch taken by boy and girl respectively 60* 60/100=36 and 40* 40/100=16 so total 52 students takes lunch out of 100 students..so required % is 52% ANSWER:B #### B QUESTION:A person crosses a 1800 m long street in 12 minutes. What is his speed in km per hour? options: A)4.1 B)4.5 C)4.8 D)5.4 E)9 SOLUTION:Speed = 1800/(12x60) m/sec = 2.5 m/sec. Converting m/sec to km/hr =2.5 x(18/5) km/hr = 9 km/hr. ANSWER :E #### E QUESTION:A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Number = ( 779 x a) + 47, where "a" is the quotient = (19 x 41 x a) + (19 x 2) + 9 = 19 x (41a + 2) + 9 = 19 x (New quotient) + 9 \inline \fn_jvn \therefore Required remainder = 9 Answer:A #### A QUESTION:A basketball coach is choosing her starting lineup from a team of 11 girls. 7 of the girls are post players and 4 are guards. If she chooses 3 post players and 2 guards, how many different lineups can be made? options: A)210 B)220 C)240 D)260 E)270 SOLUTION:(7c3)*(4c2) [7!/(3!*4!)]*[4!/(2!*2!)] 35*6 210 A #### A QUESTION:If the sum of 5 consecutive integers is x, which of the following must be true? I. x is an even number II. x is an odd number III. x is a multiple of 5 options: A)I only B)II only C)III only D)I and III E)II and III SOLUTION:I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true. II. Same as above. This need not be always true. III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4) = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases. Therefore C is the answer. #### C QUESTION:How many 9 digit numbers are possible by using the digits 1, 2, 3, 4, 5 which are divisible by 4 if the repetition is allowed? options: A)77 B)26 C)88 D)27 E)99 SOLUTION:: If A number has to be divisible by 4, the last two digits must be divisible by 4. So possibilities are, 12, 24, 32, 44, 52. And the of the remaining 7 places, each place got filled by any of the five digits. So these 7 places got filled by 5 x 5 x .....(7 times) = 5757 ways. So total ways are 5 x 5757 = 5/8 Answer:A #### A QUESTION:In the class of 50 students, 30 speak Tamil and 30 speak Telugu. What is the lowest possible number of students who speak both the languages? options: A)A)8 B)B)10 C)C)20 D)D)30 E)E)32 SOLUTION:let the student who speaks tamil-x let the student who speaks telugu-y as (xuy)-(xny)=total 30+30-(xny)=50 =10 B) #### B QUESTION:The sides of a cube are in the ratio 1:2 the ratio of their volume is? options: A)1:9 B)1:5 C)1:8 D)1:1 E)1:2 SOLUTION:1:8 Answer: C #### C QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)? options: A)2 B)4 C)7 D)9 E)10 SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3. Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9. The answer is D. #### D QUESTION:3 of the 4 expressions (1), (2), (3) & (4) given below are exactly equal . Which of the expression is not equal to the other four expressions? options: A)(A + B)2 - 4AB B)(A – B)2 + 4AB C)A2 + B2 - 4AB + 2AB D)A2 – B2 + 2B(B – A) E)None of these SOLUTION:1) (A + B)2 – 4AB = A2 + 2AB + B2 - 4AB = A2 + B2 - 2AB 2) (A – B)2 + 4AB = A2 – 2AB + B2 + 4AB = A2+ B2 + 2AB 3) A2 +B2 – 4AB + 2AB = A2 + B2 - 2AB 4) A2 – B2 + 2B(B – A) = A2 – B2 + 2B2 – 2AB = A2 + B2 – 2AB Therefore, (1) = (3) = (4) ≠ (2) Therefore, expression (2) is wrong ANSWER IS B #### B QUESTION:In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 45 percent of the vote. How many additional votes would James have needed to win the election? options: A)901 B)989 C)990 D)891 E)1,001 SOLUTION:James = (0.5/100)*2000 = 10 Votes to win = (45/100)*Total Votes +1 = (45/100)*2000 +1 = 901 Remaining Voted needed to win election = 901 - 10 = 891 Answer: option D #### D QUESTION:What is the value of m and n ? if log3m/log3n=log 52 options: A)1,5 B)2,5 C)3,5 D)4,5 E)2,3 SOLUTION:log (base a) b=log(base n)b/log(base n)a here base are same in reverse way of formula so log(base n)m=log(base 5) 2 hence n=5,m=2 ANSWER:B #### B QUESTION:N, a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is options: A)(a) 61250 B)(b) 65525 C)(c) 42455 D)(d) 62525 E)(e) 55425 SOLUTION:The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question. To start, we're given information on the sub-sets of numbers: -The 1st set has 1 number -The 2nd set has 2 numbers -The 3rd set has 3 numbers Etc. So the 50th set will have 50 numbers in it. Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching... The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers Etc. This pattern will continue all the way down to... The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'... So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive... Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)... 25(1226+1275) = 25(2501) = 62525 D #### D QUESTION:In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school? options: A)150 B)100 C)280 D)360 E)496 SOLUTION:Explanation: Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 +2/3 of 48 80/100x=80 x=100 Answer: B #### B QUESTION:Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 7.5 km apart, if they walk in the same direction? options: A)12 hrs B)14 hrs C)15 hrs D)17 hrs E)None SOLUTION:Sol. to be 0.5 km apart, they take 1 hour. To be 7.5 km apart, they take [1/0.5 * 7.5] hrs = 15 hrs. Answer C #### C QUESTION:Which of the following must be subtracted from 2^96 so that the resulting integer will be a multiple of 3? options: A)2 B)5 C)3 D)1 E)4 SOLUTION:{4^1} / 3 =4/3 remainder 1 {4^2} / 3 = 16/3 remainder 1 {4^3} / 3 = 64/3 remainder 1 {4^4} / 3 = 256/3 remainder 1 Actually the same remainder keeps repeating ..... Try with a diff no, say 2 {2^1}/3 = remainder 2 {2^2}/3 = remainder 1 {2^3}/3 = remainder 2 {2^4}/3 = remainder 1 Answer : D #### D QUESTION:Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money? options: A)1489 B)6845 C)2598 D)1875 E)2600 SOLUTION:P = 75(100/20)5 => P = 1875 Answer: D #### D QUESTION:If 10^(z-1)< 0.000125 <10^z, what is the value of an integer z? options: A)-4 B)-3 C)-2 D)3 E)4 SOLUTION:-> Multiply 10^6- > (10^6){10^(z-1)}<125<(10^6)(10^z) -> 125 is bigger than 100 -> (10^6)(10^(z-1))=100 -> 10^(6+z-1)=10^2, z+5=2 -> z=-3 Thus, the answer is B #### B QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 25 years and that for 40 years? options: A)5:8 B)7:5 C)3:8 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×25/100) /(P×R×40/100)]=25PR/40PR=25/40=5:8 Answer A #### A QUESTION:If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer? I. w + t + 2 II. w^2 + 2wt + t^2 III. w^2 + t^2 options: A)None B)I only C)II only D)III only E)I, II, and III SOLUTION:w^2–t^2 is an odd integer means that either w is even and t is odd or w is odd and t is even. Check all options: I. w + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard; II. w^2 + 2wt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard; III. w^2 + t^2 --> even+odd=odd or odd+even=odd. Discard. Answer: A. #### A QUESTION:Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? options: A)4 B)6 C)8 D)9 E)1 SOLUTION:There are five letters in the given word. Consider 5 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways. The number of words = 3! = 6. Answer: B #### B QUESTION:Two letters from the word KYANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant? options: A)14/27 B)15/28 C)27/28 D)16/28 E)30/28 SOLUTION:There are 6 consonants and 2 vowels in KYANTKAR . probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels) Probability of both vowels = 2C2/8C2 = 1/28 So,Answer is 1 - 1/28 = 27/28 Answer : C #### C QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers? options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89 SOLUTION:(5x-25):(7x-25) = 35:59 x = 12 => 60,84 Answer:D #### D QUESTION:If 5a + 7b = t, where a and b are positive integers, what is the largest possible value of t for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5*a1 + 7*b1 = t 5*a2 + 7*b2 = t 5*(a1 - a2) = 7*(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,200 sedans in Anytown, how many motorcycles are there? options: A)1260 B)2100 C)3600 D)3200 E)5200 SOLUTION:Let the total number of trucks = 3x total number of sedans = 7x total number of motorcycles = 2x total number of sedans = 11200 => 7x = 11200 => x = 1600 total number of motorcycles =2x = 2*1600 =3200 Answer D #### D QUESTION:A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9 Probability to become a secretary = (9/10 * 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:Find the invalid no.from the following series 15 46 63 71 75 77 78 options: A)32 B)35 C)46 D)49 E)67 SOLUTION:In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46 C #### C QUESTION:If a and b are positive integers and x = 4^a and y = 5^b, which of the following is a possible units digit of xy? options: A)0 B)4 C)5 D)7 E)8 SOLUTION:The units digit of 4^a is either 4 or 6. The units digit of 5^b is 5. 4*5 = 20 and 6*5 = 30. The units digit of xy is 0. The answer is A. #### A QUESTION:Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet? options: A)15 B)18 C)21 D)24 E)27 SOLUTION:Let K and T be the speeds of Karen and Tom respectively. t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles. Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours Thus the distance traveled by Tom when Karen is 4 miles ahead of him Y: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer. #### D QUESTION:Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in. options: A)40 min B)25 min C)54 min D)65 min E)58 min SOLUTION:Distance = Speed * time 3*20/3= 20km New Speed = 18 kmph Therefore time = 20/18 = 10/9= 54min Answer : C. #### C QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:Calculate the circumference of a circular field whose radius is 10 centimeters. options: A)20 π cm B)19 π cm C)28 π cm D)25 π cm E)30 π cm SOLUTION:Circumference C is given by C = 2πr = 2π*10 = 20 π cm Answer: A #### A QUESTION:The editor of an anthology of short stories will select authors from a pool of 12 authors, of which 5 are female. If the anthology is to include the work of 7 authors of which at least 2 are female, in how many ways can the editor select the authors? options: A)734 B)745 C)756 D)767 E)778 SOLUTION:12C7 = 792 The number of ways to select 7 males is 7C7 = 1 The number of ways to select 6 males and 1 female is 7C6*5C1 = 35 792 - 1 - 35 = 756 The answer is C. #### C QUESTION:A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)? options: A)1250 B)1280 C)1320 D)1340 E)1450 SOLUTION:Explanation: Speed = 5 km/hr Time = 15 minutes = 1/4 hour Length of the bridge = Distance Travelled by the man = Speed × Time = 5×1/4 km = 5 × 1/4 × 1000 metre=1250 metre Answer: Option A #### A QUESTION:If x is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ? options: A)1 B)2 C)3 D)6 E)12 SOLUTION:Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey x=4n, if it really wanted to convey so. From other questions that I have seen, proper wordings could be: If x is three times as large as n OR simply, If x is three times n.C #### C QUESTION:Zeeshan having a certain number of one rupee,fifty paise and twenty five paise coins are in the ratio of 3:2:4, add up to Rs 75. Then how many 1 rupee coins he have? options: A)10 B)20 C)45 D)128 E)49 SOLUTION:Explanation : Given ratio = 3:2:4. Let us assume that there are 3 one rupee coins,2 fifty paise coins and 4 twenty-five paise coins in all. Their value=(3*1)+(2*.50)+(4*.25)=3+1+1=Rs 5 If the total is Rs 5, number of 1 rupee coins are 3. If the total is Rs 75, number of 1 rupee coins would be 75*3/5=45. Answer : C #### C QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)11*10! B)9*8! C)8*7! D)7*6! E)6*5! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=11*10! Ans:A #### A <<<Examples ends QUESTION:If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased? options: A)8% B)7% C)10% D)6% E)9% SOLUTION:Explanation: Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol, such that Benson buys 1 litre of petrol After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125 Since Benson spends additional 15% on petrol, amount spent by Benson = 100× (100+15)/100 = Rs.115 Hence Quantity of petrol that he can purchase = 115/125 Litre Quantity of petrol reduced = (1−115/125) Litre Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8% Answer: Option A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In a division, divident is 725, divisior is 36 and quotient is 20. Find the remainder. options: A)A)4 B)B)3 C)C)2 D)D)5 E)E)6 SOLUTION:Explanation: 725 = 36 x 20 + r 725 = 720 + r r = 725 - 720 = 5 Answer: Option D #### D QUESTION:A present value of a machine is $400. Its value depletiation rate is 25% per annum then find the machine value after 2 years? options: A)$125 B)$100 C)$200 D)$215 E)$225 SOLUTION:P= $400 R = 25% T = 2 years Machine value after 2 years = P[(1-R/100)^T] =400*3/4 * 3/4 =$225 approximately Answer is E #### E QUESTION:An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length. options: A)12sec B)20sec C)15sec D)18sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec Answer : E #### E QUESTION:Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in? options: A)6 B)12 C)28 D)42 E)21 SOLUTION:The part of the tank filled by three pipes in one hour = 1/14 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/14= 1/21. The tank can be filled in 21 hours. Answer:E #### E QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test. You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it? options: A)48% B)55% C)60% D)71% E)80% SOLUTION:C 60% In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability. In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already. Therefore, P(Second/First) = P (First and Second)/ P (First) = 0.25/0.42 =0.60 =60 % #### C QUESTION:It will take 16 days for Mary to complete a certain task alone. She worked for 8 days before she was joined by her sister. both of them completed the remaining task in 2 and half days. if her sister had joined her when she started the task, how many days would it have taken? options: A)6 B)8 C)2 D)5 E)4 SOLUTION:Explanation: Mary and her sister complete half work in 2.5 days => they can complete whole work in 5 days Answer: Option D #### D QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B QUESTION:When 2/3 of the garments in the shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 80 percent of the garments in the shipment pass? options: A)6 B)9 C)8 D)7 E)5 SOLUTION:B = 9 2/3x= 20 x=30 for 80% approval we need 24 garments approved. already approved = 18 we need 6 more. Answer : A #### A QUESTION:If n = 2.0254 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n? options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0046 E) 0.0153 SOLUTION:n*=2.03 n*-n=2.03-2.0254 0.0046 Answer: D #### D QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)2/215 B)3/155 C)1/216 D)2/213 E)3/212 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 32,000 locusts? options: A)2 B)4 C)6 D)8 E)9 SOLUTION:- 4 hours: 1,000 -2 hours: 2,000 Now: 4,000 + 2 hours: 8,000 + 4 hours: 16,000 + 6 hours: 32,000 Answer : C #### C QUESTION:In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate? options: A)100 B)50 C)Cannot be determined D)105 E)25 SOLUTION:Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position. Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points. #### C QUESTION:Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount? options: A)$1200 B)$1400 C)$1600 D)$1800 E)$2000 SOLUTION:0.7(x-600)=0.6(x-400) 0.1x=420-240 x=1800 The answer is D. #### D QUESTION:Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 11220, how much money did he borrow? options: A)11000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 11220 18x + 45x + 39x = (11220 * 100) 102x = 1122000 => x = 11000. Answer:A #### A QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)99 B)277 C)48 D)99 E)22 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer:C #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. ANSWER:D #### D QUESTION:Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit? options: A)Rs.10528 B)Rs.10521 C)Rs.10511 D)Rs.10411 E)Rs.10500 SOLUTION:Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 24500 * 3/7 = Rs.10500 Answer: E #### E QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)767 E)408 SOLUTION:1h ----- 2 ? ------ 60 12 h RS = 16 + 18 = 34 T = 12 D = 34 * 12 =408 Answer: E #### E QUESTION:The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)22 seconds B)65 seconds C)78 seconds D)12 seconds E)21 seconds SOLUTION:Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 60/5 = 12 seconds. Answer:D #### D QUESTION:In certain code 'TWICE' is written as '34$5δ' and 'WEARS' is written as '4δ29%'. How is 'SEAT' written in that code? options: A)22 B)23 C)697 D)66P E)82 SOLUTION:Answer: Option B #### B QUESTION:If shares of two persons in profits are Rs.600 and Rs.1000 then ratio of their capitals is options: A)3:5 B)2:3 C)4:3 D)1:3 E)1:2 SOLUTION:profit=time*capital so 600:1000=3:5 ANSWER:A #### A QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 27 cm * 16 cm. What is the perimeter of the square? options: A)140 B)240 C)340 D)144 E)122 SOLUTION:Area of the square = s * s = 3(27 * 16) => s = 9 * 4 = 36 cm Perimeter of the square = 4 * 36 = 144 cm. Answer: D #### D QUESTION:If P represents the product of the first 13 positive integers, which of the following must be true? I. P is an odd number II. P is a multiple of 24 III. P is a multiple of 23 options: A)I only B)II only C)III only D)None of the above E)All of the above SOLUTION:The correct answer is B. #### B QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 4x+ 4y > 4z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 4x+ 4y > 4z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B #### B QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have? options: A)27 B)32 C)43 D)54 E)77 SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys 49 - 5 = 44 for Tom and Bob If distributed equally, each one will have 44 / 2 = 22 toys Bob has 5 more toys than Tom, so Bob has 22 + 5 = 27 toys correct answer A #### A QUESTION:A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job? options: A)6 B)8 C)3 D)4 E)0 SOLUTION:Explanation: Use formula For a work Members × days = constant 8 × 3 = 4 × a a = 6 so answer is 6 days Answer: A #### A QUESTION:Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit? options: A)s.2323 B)s.2380 C)s.2329 D)s.2660 E)s.2312 SOLUTION:Kamal : Sameer = (9000 * 12) : (8000 * 7) = 108:56 = 27:14 Sameer's share = 7790 * 14/41 = Rs.2660. Answer: D #### D QUESTION:For each positive integer,the quantitySn is defined such thatSn+1=(Sn)^2 -S(n+1).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! A #### A QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 7? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The numbers should be of the form 7c+3. The minimum is 3 when c=0. The maximum is 45 when c=6. There are 7 such numbers. The answer is C. #### C QUESTION:The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 360 metres, what is its area? options: A)1320 sq.metres B)4260 sq.metres C)6870 sq.metres D)7875 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 360 ⇒ x = 15 Area = 7 × 15 × 5 × 15 = 7875 sq.m. Answer D #### D QUESTION:Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.9 hour B)2.1 hour C)4.7 hour D)2.4 hour E)3.2 hour SOLUTION:Part filled by pipe A in 1 hour =1/8 Part filled by pipe B in 1 hour =1/4 Part filled by pipe C in 1 hour =1/24 Part filled by pipes A,B,C together in 1 hour=1/8+1/4+1/24=10/24 i.e, pipes A,B,C together can fill the tank in = 24/10 hr =2.4 hour. ANSWER:D #### D QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:A pharmaceutical company received $2 million in royalties on the first $20 million in sales of and then $9 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales? options: A)8% B)15% C)45% D)52% E)56% SOLUTION:(9/108)/(2/20) = 30/54 = 55,5% it means that 9/108 represents only 83,3%. Therefore a decrease of 15%. Answer B #### B QUESTION:A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son? options: A)23 Years B)21 Years C)20 Years D)25 Years E)22 Years SOLUTION:Let present age of the son =x=x years Then, present age the man =(x+24)=(x+24) years Given that, in 22 years, man's age will be twice the age of his son ⇒(x+24)+2=2(x+2)⇒x=22 ANSWER:E #### E QUESTION:When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? options: A)17% increase B)44% decrease C)60% increase D)66% increase E)66% decrease SOLUTION:if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater. ANSWER:A #### A QUESTION:A two digit number reversed and multiplied by 4 is 3 more than the original digit. what is the digit? options: A)61 B)62 C)63 D)64 E)66 SOLUTION:If no is xy , then 10x+y = 4*(10y+x)-3= 40y +4x-3 6x-39y +3 =0 2x-13y +1 =0 13 y =2x+1 when y=1, x=6 so number is 61. ANSWER:A #### A QUESTION:If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production? options: A)4% B)10% C)14% D)15% E)18% SOLUTION:Let Cost of PROD for 1 ticket = 1 So COP for n tickets = n So for selling n tickets, SP = 1.2 * n = 1.2n So SP of 1 ticket = 1.2 SP of 95% tickets = 1.2 * 0.95n So profit % = (1.2 * 0.95n - n)/n * 100 = 0.14 * 100 = 14% Answer - C #### C QUESTION:If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board? options: A)1136 B)1268 C)1244 D)1296 E)1308 SOLUTION:Here m = 9, n = 9 Hence, number of rectangles that can be formed = mC2 × nC2 = 9C2 × 9C2 = (9C2)^2 = 36^2 =1296 Ans-D #### D QUESTION:If 63 percent of a class answered the first question on a certain test correctly, 49 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? options: A)22% B)24% C)26% D)28% E)32% SOLUTION:63% answered the first question correctly and 20% answered neither correctly. Then 17% missed the first question but answered the second question correctly. Then the percent who answered both correctly is 49% - 17% = 32%. The answer is E. #### E QUESTION:A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 2. Find his average after 17th inning. options: A)36 B)39 C)42 D)45 E)None of the above SOLUTION:Let the average after 17th inning = x. Then, average after 16th inning = (x – 2). ∴ 16(x – 2) + 87 = 17x or x = (87 – 32) = 55. Answer E #### E QUESTION:Alex age after 13years will be 10 times his age 10years back. What is the present age of Alex? options: A)15 B)13 C)20 D)21 E)26 SOLUTION:Let Alex's present age be x Alex's age after 17 years = x+17 Alex's age 10 years back = x-10 x+17= 10(x-10) x = 13 Rajeev's present age = 13 years Answer is B #### B QUESTION:In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats? options: A)12 B)302 C)1 D)250 E)286 SOLUTION:Total number of hats = 13 Possible number of formations = 13C3 = 286 Correct answer is E #### E QUESTION:The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z? options: A)35 B)33 C)28 D)21 E)15 SOLUTION:The smallest possible product is 33 which is 3*11. All other products are too big. The answer is B. #### B QUESTION:For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 1*3*5*7*9*...*99 g(97) = 1*3*5*7*9*...*97 g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98 hence:A. #### A QUESTION:The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year? options: A)12300 B)12350 C)12000 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 120/100 = 12000 C #### C QUESTION:Jemma takes 2 hours to swim the 4 miles from buoy A to buoy B. Tired from her swim, she then continues to buoy C at half her previous speed. If buoy C is 6 miles away from buoy B, how many more hours will pass before Jemma reaches Buoy C? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Time taken for Jemma to reach buoy B is 2 hours. The distance between the buoys is 4 miles. Distance travelled/time taken = Average speed Hence the average speed to travel the distance is 2m/hr Now, she would have to travel 6 miles . However as she is tired the speed is half or 1m/hr Hence, it will take her 6 hours (Option C) #### C QUESTION:A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 m B)200 m C)240 m D)320 m E)450 m SOLUTION:Sol. Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x metres. Then, x + 300 / 50 = 15 ⇔ x + 300 = 750 ⇔ x = 450 m. Answer E #### E QUESTION:In a manufacturing plant, it takes 48 machines 4 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders? options: A)3 B)6 C)8 D)9 E)12 SOLUTION:the choices give away the answer.. 48 machines take 4 hours to fill 8 standard orders.. in next eq we are doubling the machines from 48 to 72, but the work is not doubling(only 1 1/2 times), = 4*48/72*12/8 =4 Ans A #### A QUESTION:If x-y=8, which of the following must be true? I. Both x and y are positive II. If x is positive, y must be positive III. If x is negative, y must be negative options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:The best way to approach such questions is to plug in values for x and y Given: x-y=8 I. Both x and y are positive: Let x=10 and y=2 x-y=8 But, Let x=6 and y=-2 x-y=8 Therefore, NOT TRUE II. If x is positive, y must be positive Let x=10 and y=2 x-y=8 But, Let x = 6 and y=-2 x-y=8 Therefore, NOT TRUE III. If x is negative, y must be negative If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number! Therefore, TRUE Ans: 'C' #### C QUESTION:If (a-3)(b-2) =0, which of the following must be true ? I. a=3 and b=2 II. if a is not = 3, then b=2 III. if a=3, then b is not=2 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:(a-3)(b-2)=0 So either a=3 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true. The answer is B. #### B QUESTION:Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? options: A)5/5 B)5/9 C)3/4 D)5/7 E)5/2 SOLUTION:In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27 The probability = 27/36 = 3/4. Answer: C #### C QUESTION:A six-sided die is rolled once. What is the probability that the number rolled is greater than 3? options: A)2 / 3 B)1 / 2 C)3 / 3 D)4 / 5 E)2 / 4 SOLUTION:Only 4, 5 & 6 so, 3 / 6 = 1/2 correct answer B #### B QUESTION:A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? options: A)35 hours B)25 hours C)20 hours D)Cannot be determined E)None of these SOLUTION:Suppose the efficiencies of pipes C, B and A are 4K, 2K and K. Since, the tank is filled in 5 hours by the three pipes having combined efficiency equal to 7K, the time required to fill the tank by A alone = 7K×5 /K=35hours Answer A #### A QUESTION:The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle? options: A)8m. B)6m. C)4m. D)2m. E)5m. SOLUTION:Explanation: Let the sides of the rectangle be l and b respectively. From the given data, (√l2 + b2) = (1 + 108 1/3 %)lb => l2 + b2 = (1 + 325/3 * 1/100)lb = (1 + 13/12)lb = 25/12 lb => (l2 + b2)/lb = 25/12 12(l2 + b2) = 25lb Adding 24lb on both sides 12l2 + 12b2 + 24lb = 49lb 12(l2 + b2 + 2lb) = 49lb but 2(l + b) = 28 => l + b = 14 12(l + b)2 = 49lb => 12(14)2 = 49lb => lb = 48 Since l + b = 14, l = 8 and b = 6 l - b = 8 - 6 = 2m. Answer: Option D #### D QUESTION:Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between: options: A)40 to 100 B)80 to 140 C)160 to 260 D)220 to 260 E)220 to 300 SOLUTION:260-X+X+300-X+GT60 = 400 =>X = GT 620-400 => X = GT 220 => X >= 220 (Here GT means Greater than) So Min value of X is 220 coming to options D/E X's maximum value cannot exceed 260 as per the venn diagramsince 'W' circle cannot accomodate 'X' More than 260 ANSWER:D #### D QUESTION:A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. options: A)1200 B)1400 C)2660 D)1600 E)1800 SOLUTION:A is a working member and for that, he receive 5% of the profit = 5% of 7400 = 5*7400/100 = 370 Remaining amount = 7400-370 = 7030 Ratio of their investments = 6500*6 : 8400*5 : 10000*3 = 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20 = 13 : 14 : 10 Share of B in the profit = 7030 * (14/37) = 190*14 = 2660 Answer is C #### C QUESTION:A and B finish the job in 15 days.while A,B and C can finish it in 12 days . C alone will finish the job in options: A)40 days B)30 days C)60 days D)70 days E)50 days SOLUTION:Explanation: 12 = (15 * x)/(15 + x) 180+12x=15x 3x=180 X=60 Answer: Option C #### C QUESTION:Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 30 are on geology, and 100 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? options: A)81 B)159 C)166 D)285 E)304 SOLUTION:I solve it using the tough luck technique: According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject. 80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=100>80 Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives. We picked: 50 Botany Books 65 Zoology Books 30 Geology Books Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!! Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick 79*2+1 books Because, we could have picked the books in following order; 1st book picked: Physics 2nd book picked: Chemistry 3rd book picked: Physics Thus, Total= 50+65+30+79*2+1=145+1+158=304 Ans:E #### E QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced? options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None SOLUTION:Explanation : Time = 80*4 / 60 = 5 hours 33 mins Answer – B #### B QUESTION:An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of: options: A)2200 kmph B)1800 kmph C)1900 kmph D)2100 kmph E)none SOLUTION:Explanation: Distance = (1500 x 2) = 3000 km. Speed = Distance/Time Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours] Required speed = 3000 x 3/5 km/hr = 1800 km/hr. Answer: Option B #### B QUESTION:Ravi and Kavi start a business by investing ₹ 4000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year. options: A)2 : 28 B)5 : 28 C)7 : 18 D)1 : 18 E)3 : 18 SOLUTION:Ratio of profit = Ratio of investments = 4000 : 72000 = 1 : 18 Answer : D #### D QUESTION:8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work? options: A)5 days B)15 days C)28 days D)4 days E)7 days SOLUTION:Explanation: 1 man’s 1 day’s work = 1/8 × 12 = 1/96 10 men’s 1 day’s work = 1 × 10/96 = 5/48 1 woman’s 1 day’s work = 1/192 20 women’s 1 day’s work = 1/192 × 20 = 5/48 1 child’s 1 day’s work = 1/240 10 children’s 1 day’s work = 1/24 Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24 =1/4 The required No. of days = 4 days Answer: Option D #### D QUESTION:The ages of Smirthi and Samantha vary by 16 years, Six years ago, Deepika’s age was three times as that of Smirthi’s, find their current ages. options: A)20 B)50 C)40 D)30 E)45 SOLUTION:D 30 Let Smirthi’s age = A years So, Deepika’s age = (A + 16) years Also, 3(A – 6) = A + 16 – 6 or, A = 14 Smirthi’s age = 14 years and, Deepika’s age = 14 + 16 = 30 years #### D QUESTION:A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? options: A)4:7 B)4:0 C)4:3 D)4:1 E)4:2 SOLUTION:12:9 = 4:3 Answer: C #### C QUESTION:The length of a side of a hexagon is 2 inches. What is the perimeter? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Hexagon. It means 6 equal sides. p = 2 + 2 + 2 + 2 + 2 + 2 = 4 + 4 + 4 = 8 + 4 = 12 inches Answer B #### B QUESTION:If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $81, how much does one shirt cost? options: A)$10 B)$12 C)$13.20 D)$21 E)$16.80 SOLUTION:3J + 2S = 69 2J + 3S = 81 ---------------- 5J + 5S = 150 ----(divide by 5)---> J + S = 30 3J + 2S = J + 2(J + S) = J + 60 = 69 ---> J = 9 3*9 + 2S = 69 27 + 2S = 69 2S = 42 S = 21 Answer: D #### D QUESTION:The breadth of a rectangular hall is two-thirds of its length. If the area of the hall is 2400 sq metres, what is the length in metres? options: A)120 B)80 C)60 D)40 E)None of these SOLUTION:Let the length of the rectangular hall be ‘x’ m, then the breadth of the rectangular hall = 2x⁄3 m. Area of hall = 2x⁄3 × x = 2x2⁄3 or, 2x2⁄3 = 2400 or x = 60 m Answer C #### C QUESTION:12,31,68,129,220,? options: A)129 B)220 C)387 D)347 E)520 SOLUTION:2*2*2 + 4 = 12 3*3*3 +4 = 31 4*4*4 + 4 = 68 5*5*5 + 4 = 129 6*6*6 + 4 = 220 7 *7 *7 + 4 = 347 ANSWER : D #### D QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work? options: A)2 days B)76 days C)8 days D)6 days E)4 days SOLUTION:1 man's 1 day work = 1/108 12 men's 6 day's work = 1/9 * 6 = 2/3 Remaining work = 1 - 2/3 = 1/3 18 men's 1 day work = 1/108 * 18 = 1/6 1/6 work is done by them in 1 day. 1/3 work is done by them in 6 * 1/3 = 2 days. Answer: A #### A QUESTION:A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? options: A)9/30 B)14/30 C)4/9 D)3/5 E)6/25 SOLUTION:I guess it's mean that square B is placed within rectangle A entirely. Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16; Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30. Answer: B. #### B QUESTION:A and B together can do a work In 4 days. A alone can do it in 12 days. What time B will take to do the work alone? options: A)6 days B)8 days C)12 days D)10 days E)5 days SOLUTION:Explanation: A and B 1day's work = 1/6 A alone can do 1day's work = 1/12 what time B will take to do the work alone? B = (A+B) - A = (1/6) - (1/12) = 12 Days Answer: Option C #### C QUESTION:Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil. options: A)12 B)10 C)15 D)19 E)20 SOLUTION:Let the cost of a pen ands a pencil be Rs. X and Rs. Y respectively. Then, 2x + 3y = 86 ….(i) and 4x + y =112. Solving (i) and (ii), we get: x = 25 and y = 12. Cost of a pen =Rs. 25 and the cost of a pencil =Rs. 12. Answer is A. #### A QUESTION:A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: options: A)5% B)8% C)10% D)12% E)6% SOLUTION:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =(80/1600x 100)% = 5%. Answer is A. #### A QUESTION:In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other? options: A)24 B)48 C)56 D)72 E)96 SOLUTION:These 5 people can be arranged in 5! ways. These are the total number of ways you get. Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!. Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72 ANSWER:D #### D QUESTION:A coin is tossed 6 times. What is the probability of getting exactly 5 heads? options: A)3/8 B)3/16 C)5/16 D)3/32 E)7/64 SOLUTION:The number of possible outcomes is 2^6 = 64 There are 6 ways to get exactly 5 heads. P(exactly 5 heads) = 6/64 = 3/32 The answer is D. #### D QUESTION:For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? options: A)18.1 B)21.1 C)36.5 D)42.2 E)84.4 SOLUTION:Let x and z be the smallest and largest of the original set, respectively. z - x = 84.4 The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4. Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1 The answer is B. #### B QUESTION:A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. #### C QUESTION:Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.? options: A)8 kmph B)11 kmph C)12 kmph D)14 kmph E)16 kmph SOLUTION:Explanation: Let the distance travelled by x km. Then, x/10-x/15=2 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr =60/10 hrs= 6 hrs. So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60/5kmph= 12 kmph ANSWER IS C #### C QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:The function f is defined for all the positive integers d by the following rule: f(d) is the number of positive integers each of which is less than d and has no positive factor in common with d other than 1 . if p is a prime number then f(p)? options: A)p-1 B)p-2 C)(p+1)/2 D)(p-1)/2 E)2 SOLUTION:The moment you put a prime number in the function f(d), notice that all the numbers lesser than d have no divisor clashing with divisor of d since d is prime!!. For instance f(7)= {6, 5, 4, 3, 2, 1} Thus for f(p) number of integers falling under this set will be p-1 Answer :- A #### A QUESTION:An elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children? options: A)40: 20 B)42: 21 C)50: 100 D)15: 25 E)It cannot be determined by the information given. SOLUTION:While you can figure out most of this question, there is not enough information to completely tell. the answer is E. #### E QUESTION:If x is an integer, then x(x – 1)(x – k) must be evenly divisible by six when k is any of the following values EXCEPT options: A)-4 B)-2 C)-1 D)2 E)5 SOLUTION:We have the product of 3 integers: (x-1)x(x-k). Note that the product of 3 integers is divisible by 6 if at least one multiple is divisible by 6. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 6 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 6. Next, if k=2 then we'll have (x-1)x(x-2)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 6. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 6. Answer: D. #### D QUESTION:If x is an integer and y = 3x + 5, which of the following CANNOT be a divisor of y? options: A)4 B)12 C)2 D)7 E)6 SOLUTION:For any value of x, the expression 3x + 5 would never be divisible by 3,6,9...... onwards So answer = 6 = E #### E QUESTION:The income derived from a Rs. 100, 13% stock at Rs. 105, is : options: A)Rs. 5 B)Rs. 8 C)Rs. 13 D)Rs. 18 E)Rs. 19 SOLUTION:Solution Income on Rs. 100 stock = Rs. 13. Answer C #### C QUESTION:The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.4 kg. The weight of the new student is options: A)22 kg B)21.6 kg C)22.4 kg D)10 kg E)None of these SOLUTION:Exp . The total weight of 29 students = 29* 28 The total weight of 30 students = 30* 27.4 Weight of the new student = ( 30*27.4 – 29*28) = 822 - 812 = 10 Answer:D #### D QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? options: A)671.5 B)600 C)672.5 D)673 E)773.5 SOLUTION:Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds; Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours; So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time). Answer: B. #### B QUESTION:If “GREEN” is given number code as 49, what is the difference between the number codes of “VIOLET” and “PINK” ? options: A)55 B)45 C)33 D)60 E)40 SOLUTION:Explanation: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26 GREEN = 7 + 18 + 5 + 5 + 14 = 49 Thus we get, VIOLET = 22 +9 +15+12 + 5 + 20 = 83 PINK = 16 + 9 + 14 + 11 = 50 Thus, difference is 83 – 50 = 33. ANSWER C #### C QUESTION:If x is 20 percent greater than 98, then x = options: A)68 B)70.4 C)86 D)105.6 E)117.6 SOLUTION:x=98*1.2=117.6 So the answer is E. #### E QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities? options: A)48 B)72 C)96 D)120 E)192 SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again Rate x time = distance. For the initial trip lets the distance Q to the midpoint be represented by P. EQN1: R x 2 = P For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by: Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5 EQN2: R x 2.5 = P + 24 EQN2-EQN1 : 0.5R=24 R=48 So the distance is rate x time = 48 x 4 = 192. ANS = E #### E QUESTION:If x+|x|+y=4 and x+|y|-y=6 what is x+y=? options: A)11 B)-1 C)3 D)5 E)13 SOLUTION:If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0. If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases). Answer: C. Adding both eqn we get 2x +IxI+IyI = 13 Now considering X <0 and y>0 2x-x +y = 13 we get x+y =11 Hence answer should be A #### A QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:If, 1 * 3 * 5 = 16 3 * 5 * 7 = 38 Then find, 15 * 17 * 19 =? options: A)89 B)49 C)68 D)38 E)338 SOLUTION:E 338 (19 * 17) + 15 = 338 #### E QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:220% of a number X is 44. What is 44% of X. options: A)8.8 B)8.9 C)6.6 D)7.7 E)None SOLUTION:Solution: Given, 220% of X = 44 Or, X = 20. Thus, 44% of 20 = (44 *20) /100 = 8.8 Answer: Option A #### A QUESTION:A train running at the speed of 36 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)286 B)278 C)90 D)150 E)287 SOLUTION:Speed=(36 * 5/18) m/sec = (10) m/sec Length of the train = (Speed x Time) = (10 * 9) m = 90 m. Answer:C #### C QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? options: A)5040 B)2520 C)360 D)120 E)42 SOLUTION:6! = 720 720/2=360 half the time carmelo is in front, vice versa Answer: (C) 360 #### C QUESTION:A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. options: A)40 B)50 C)62 D)45 E)56 SOLUTION:Let the average after 11th inning = x Then, average after 10th inning = x-5 10(x-5)+100 = 11x x = 100-50 = 50 Answer is B #### B QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work? options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work .. Therefore, Y will do the remaining 1/10 th work alone.. As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job... ans 10 E #### E QUESTION:Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 7 meters, and the interior of tank B has a height of 7 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? options: A)70% B)80% C)100% D)120% E)125% SOLUTION:The radius of tank A is 7/(2*pi). The capacity of tank A is 10*pi*49 / (4*pi^2) = 245 / (2*pi) The radius of tank B is 10 / (2*pi). The capacity of tank B is 7*pi*100 / (4*pi^2) = 350 / (2*pi) Tank A / Tank B = 245/350 = 7/10 = 70% The answer is A. #### A QUESTION:The average marks scored by Ganesh in English, Science, Mathematics and History is less than 18 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him? options: A)72 B)50 C)60 D)Data inadequate E)None of these SOLUTION:E+H+G+M/4−E+S+M+H/4=18 ⇒ G - S = 72 Answer A #### A QUESTION:Find the product of the localvalue and absolutevalue of 4 in 20468? options: A)1000 B)1100 C)1200 D)1300 E)1600 SOLUTION:Local value of 4 = 4 x 100 = 400 Place value of 4 = 4 There fore = 4 x 400 = 1600 E #### E QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? options: A)10 B)15 C)8 D)12 E)20 SOLUTION:4n+7 > 1 4n> -6 n > -(3/2) n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity) From second constraint 4n+7 < 60 4n< 53 n < 13. 25 n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13) Combining the two -1.5 < n<13.25 n = 1 to 13 (48 integers) and n = -1 and 0 so 15 integers. B #### B QUESTION:A person crosses a 1800 m long street in 12 minutes. What is his speed in km per hour? options: A)4.1 B)4.5 C)4.8 D)5.4 E)9 SOLUTION:Speed = 1800/(12x60) m/sec = 2.5 m/sec. Converting m/sec to km/hr =2.5 x(18/5) km/hr = 9 km/hr. ANSWER :E #### E QUESTION:For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| = options: A)ab-4 B)2b-ab-4 C)ab+4 D)ab-2b+4 E)4-ab SOLUTION:Given: |ab| = -ab and |a| = -a Question: |b-4| + |ab-b| = ? **** Looking at |ab| = -ab tells us that either one of a or b is negative. **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: b is positive Let a=-1 and b=1 |b-4| + |ab-b| = |1-4| + |-1-1| = 5 Test a) |ab-4| = |(1)(-1)-4| = |-5|=5 Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1 Test c) ab+4 = -1 + 4 = 3 Test d) ab-2b+4 = -1-2(1)+4=1 test e) 4-1=3 ANSWER=A #### A QUESTION:In how many ways letters of the word LEADER be arranged? options: A)5 B)78 C)69 D)58 E)120 SOLUTION:LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways E #### E QUESTION:In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ? options: A)13/40 B)13/80 C)2/13 D)Data inadequate E)None SOLUTION:Answer Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp. ∴ 2/13 of total number of students took part in the camp. Correct Option: C #### C QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:The ratio 25:50 expressed as percent equals to options: A)50 % B)85 % C)25 % D)75 % E)None of above SOLUTION:Explanation: Actually it means 25 is what percent of 50, which can be calculated as, (25/50)*100 = 25 * 2 = 50 Answer: Option A #### A QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ? options: A)1/26 B)1/20 C)1/25 D)1/29 E)1/23 SOLUTION:Let E1 be the event of drawing a red card. Let E2 be the event of drawing a king . P(E1 ∩ E2) = P(E1) . P(E2) (As E1 and E2 are independent) = 1/2 * 1/13 = 1/26.Answer: A #### A QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse? options: A)A)5 B)B)8 C)C)10 D)D)15 E)E)30 SOLUTION:Total number of ways to choose 6 chairs from 5= 6C2=15 Total number of combination=150 That means we need get 10 combinations from the selection of tables.... Screening through the answers.... 5C3=10..... 10*15=150 Answer is 5... A #### A QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? options: A)336 B)425 C)275 D)235 E)689 SOLUTION:B 425 (68 ÷ 16) × 100 #### B QUESTION:A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 60% have red flags, what percentage of children have flags of both the colors? options: A)5% B)10% C)15% D)20% E)It can not be determined SOLUTION:Solution: let the total number of flags be 100(even number) let the total number of 'blue' flags alone be 'a' let the total number of 'red' flags alone be 'b' let the total number of 'both' flags be 'c' We have given, total number of blue flags = 60% = 60 = a+c total number of red flags=55%=55=b+c total number of flags = a+b+c=100 (since all the flags have been utilized) So, substituting for c in the third equation, we have, 60-c+c+60-c=100 c=20 Option D. #### D QUESTION:If a truck is traveling at a constant rate of 54 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters) options: A)18 B)24 C)30 D)36 E)40 SOLUTION:Speed = 54 Km/hr => 54,000 m/hr In one minute => 54000/60 = 900 meters In one sec => 900/60 = 15 meters Time = Total distance need to be covered / Avg. speed => 600/ 15 =40 and hence the Answer : E #### E QUESTION:If A got 70 marks and B got 60 marks, then what percent of A's mark is B's mark? options: A)A)60% B)B)85.7% C)C)65% D)D)75% E)of these SOLUTION:A's marks = 70 ; B's marks = 60. Let x% of A = B => x/100 *70 = 60 => x = (60 * 100)/80 = 85.7 B's marks is 85.7% of A's marks. ANSWER:B #### B QUESTION:A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 300,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes? options: A)a) 500 B)b) 750 C)c) 1,000 D)d) 1,250 E)e) 1,500 SOLUTION:Since N = 2F, no of Florida zip codes (F) will be N/2. Since N = 4A, no of Arizona zip codes (A) will be N/4 Since N = (4/3)C, no of California zip codes (C) will be 3N/4 N + N/2 + N/4 + 3N/4 = 5N/2 = 250 N = 100 C = 3N/4 = 75 No of orders is 25% of 300,000 = 75,000 So required ratio = 75,000/75 = 1000 Answer C #### C QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)22 B)45 C)66 D)88 E)12 SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer: B #### B QUESTION:Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)80% C)100% D)180% E)200% SOLUTION:We can use fractional equivalents here to solve the problem 80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears 10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours Now we come to productivity Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour Hence the productivity is double with the assistant i.e. the increase in productivity is 180% D #### D QUESTION:What is the sum of odd integers from 35 to 55, inclusive? options: A)495 B)1,500 C)1,240 D)1,120 E)1,100 SOLUTION:Number of odd integers = (55-35)/2 + 1 = 20/2 + 1 = 11 Sum of odd integers = (35+55)/2 * 11 = 495 Answer A #### A QUESTION:When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ? options: A)11 B)44 C)24 D)25 E)22 SOLUTION:the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44 0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44. Only option A-11 satisfies this for remainder 11, A=236 and B=25 Ans - D #### D QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr Answer :D #### D QUESTION:In 24 minutes, the hour hand of a clock moves through an angle of: options: A)60° B)24° C)12° D)5° E)None SOLUTION:12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚ Answer: C #### C QUESTION:The diagonals of a rhombus are 12 cm and 10 cm. Find its area? options: A)158 B)129 C)150 D)123 E)60 SOLUTION:1/2 * 12 * 10 = 60 Answer:E #### E QUESTION:Find the total number of divisors of 1728(including 1 and 1728) options: A)28 B)29 C)30 D)31 E)32 SOLUTION:1728=2^6*3^3 no. of divisors = (6+1)*(3+1)=28 ANSWER:A #### A QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? options: A)12/489 B)12/452 C)12/455 D)12/429 E)12/292 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When three marbles are drawn, the probability that one is yellow and two are red = (²C₁)(⁴C₂)/¹⁵C₃ = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455 Answer: C #### C QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)22 B)88 C)27 D)20 E)98 SOLUTION:Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D #### D <<<Examples ends QUESTION:P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings? options: A)1:8 B)1:6 C)2:1 D)1:1 E)1:7 SOLUTION:Ratio of investments of P and Q is 2 : 5 Total salary claimed by P = 12 * 5000 = Rs. 60000 Total profit = Rs. 2 lakhs. Profit is to be shared = Rs. 140000 Share of P = (2/7) * 140000 = Rs. 400000 Share of Q = Rs. 100000 Total earnings of P = (60000 + 40000) = Rs. 100000 Ratio of their earnings = 1:1 Answer:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back? options: A)$4,040 B)$4,120 C)$1,960 D)$4,920 E)$1,400 SOLUTION:In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost. So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost. Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $5,000-$880=$4,120. Answer: B. #### B QUESTION:Excluding stoppages,the speed of the bus is 54kmph and including stoppages,it is 27kmph. For how many minutes does the bus stop per hr options: A)12 min B)11 min C)13 min D)20 min E)30 min SOLUTION:Due to stoppages,it covers 27km less. time taken to cover 27 km is [27/54 *60] min = 30min Answer is E. #### E QUESTION:A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 5 games? options: A)x + 3y/(n + 3) B)x + y/(n + 3) C)(x + 3y)/(n + 3) D)(nx + 3y)/(n + 5) E)(3x + ny)/(n + 3) SOLUTION:Total points in first n games = nx Total marks in next 3 games is 3y So, Average marks in n + 5 games = (nx+3y)/(n+5) Hence, correct answer will be (D) #### D QUESTION:The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? options: A)18/35 B)18/38 C)18/34 D)18/31 E)18/30 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35. Answer:A #### A QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? options: A)480 B)540 C)600 D)720 E)900 SOLUTION:4C2 x 3C3 x 5! = 720 The answer is D. #### D QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)267 B)240 C)166 D)111 E)121 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B #### B QUESTION:The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 19,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263. What is the difference between the areas of Russia and China? options: A)5,476,811 kilometers squared B)9,500,148 kilometers squared C)9,843,123 kilometers squared D)1,878,965 kilometers squared E)4,787,900 kilometers squared SOLUTION:he difference between the areas of Russia and China is given by 19,098,242 - 9,598,094 = 9,500,148 kilometers squared correct answer B #### B QUESTION:If the sum of 5 consecutive integers is x, which of the following must be true? I. x is an even number II. x is an odd number III. x is a multiple of 5 options: A)I only B)II only C)III only D)I and III E)II and III SOLUTION:I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true. II. Same as above. This need not be always true. III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4) = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases. Therefore C is the answer. #### C QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent? options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these SOLUTION:Let CP of an book = 100 MP of an book = 120 Discount 30 % on 120 = 36 SP of the book = 120 - 36 = 84 loss = 16% Answer : C #### C QUESTION:What is the range of all the roots of |x^2 - 5| = x ? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:we get 2 quadratic equations here .. 1) x^2-x-5=0 ....... roots 2 , -1 2) x^2+x-5=0 ........ roots -2, 1 Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations . So value of x for given equation .... x=5 or x=1 I guess range is 5-1 =4 A #### A QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work? options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work .. Therefore, Y will do the remaining 1/10 th work alone.. As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job... ans 10 E #### E QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.8 sec C)8.5 sec D)2.2 sec E)4.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. Answer:A #### A QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions? options: A)287 m B)704 m C)278 m D)298 m E)286 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m Answer:B #### B QUESTION:Two employees X and Y are paid a total of Rs. 800 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.200.63 B)s.250.63 C)s.290.63 D)s.300.63 E)s.363.63 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 800 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 800 ⇒ y[12/10 + 1] = 800 ⇒ 22y/10 = 800 ⇒ 22y = 8000 ⇒ y = 8000/22 =Rs.363.63 E) #### E QUESTION:Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)16.80 × 4.50 + 4.4 B)1600 ÷ 40 + 16 × 2 C)5.5 × 8.4 + 34.6 D)1620 ÷ 20 – 1 E)1856.95 – 1680.65 – 96.3 SOLUTION:Others equal 80 whereas (c) equals 80.8. Answer C #### C QUESTION:If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)9 E)18 SOLUTION:Let length of rectangle = L 6^2 = L*4 => L = 36/4 = 9 Answer D #### D QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? options: A)9 B)18−3√3 C)18 D)18+3√3 E)27 SOLUTION:The altitude of an equilateral triangle is side*√3/2. As perimeter of triangle ACD is 9+3√3, AC + CD + AD = (side+side/2+side*√3/2) = 9 + 3√3 or side =6. Perimeter of equilateral triangle, ABC is 3(side) or 18. Answer:(OptionC) #### C QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 7*1+1 (7*1+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ? options: A)120ways B)220ways C)420ways D)720ways E)520ways SOLUTION:By kept 3boys together(1) and arranging 4 girls with them 5! = 5*4*3*2*1 = 120ways. (i.e., 4+1 =5) Possible arrangements of 3 boys in following ways 3! = 3*2*1 = 6ways Now, arrange all with the boys together 120*6 = 720ways ANSWER:D #### D QUESTION:Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations R are there for the children? options: A)240 B)480 C)720 D)1440 E)3600 SOLUTION:MAGOOSHOFFICIAL SOLUTION: First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats? X X X _ _ _ _ _ X X X _ _ _ _ _ X X X _ _ _ _ _ X X X _ _ _ _ _ X X X There are five different “three in a row” locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B — just those two orders. This means the total number of configurations for these three children is 5*2 = 10. Now, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats — that’s a permutation of the 4 items —- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats. Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations R of 24*10 = 240. Answer = A #### A QUESTION:The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 10800 sq. m, the cost of fencing the field @ 25 paise per metre is options: A)Rs. 55.50 B)Rs. 67.50 C)Rs. 86.50 D)Rs. 105.00 E)None of these SOLUTION:Solution Let length = (3x) metres and breadth = (4x) metres. Then, 3x × 4x = 10800 ⇔ 12x2 = 10800 ⇔ x2 =900 ⇔ x = 30. So, length = 90 m and breadth = 120 m. Perimeter = [2(90 + 120)] m = 420 m. ∴ Cost of fencing = Rs. (0.25 × 420) = Rs. 105.00. Answer D #### D QUESTION:597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred’s and ten’s places are respectively: options: A)3 and 6 B)7 and 9 C)2 and 6 D)4 and 7 E)None SOLUTION:Solution : Let the given number be 597xy6. Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3 And, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0 => y=x+3 27+x+y) =>(27+x+x+3) =>(30+2x) => x = 3 and y = 6. Answer A #### A QUESTION:The average score of a cricketer in 2 matches is 30 and in other 3 matches is 40. Then find the average score in all the 5 matches? options: A)25 B)27 C)30 D)35 E)36 SOLUTION:Average in 5 matches = (2*30 + 3*40)/2+3 = 60+120 / 5 = 180/5 = 36 Answer is E #### E QUESTION:A man can row upstream at 10kmph and downstream at 18 kmph. The speed of the stream is options: A)2.5 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(18 -10) kmph = 4 kmph. Answer B #### B QUESTION:When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country? options: A)166 2/7 B)166 2/1 C)166 2/2 D)166 2/3 E)166 2/8 SOLUTION:5% - 2% = 3% 3% ---- 5 100% ---- ? => 166 2/3 Answer:D #### D QUESTION:If the productivity of a brigade grows by 40% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade? options: A)1.51 B)0.82 C)1.2 D)1.21 E)1.44 SOLUTION:B = 10-men brigade p = increase in the productivity = 40% Solution: B x p = B x 1.4 = 1.4B -------> the productivity of 11 men brigade 1.4B x p = 1.4B x 1.1 = 1.51B -----> the productivity of 12 men brigade The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.51B/B = 1.51 A #### A QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? options: A)4 min B)8 min C)9 min D)6 min E)1 min SOLUTION:S = 600/40 = 15 mps S = 3600/15 = 240 sec = 4 min Answer:A #### A QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years? options: A)2500 B)2800 C)3500 D)3600 E)2050 SOLUTION:P = 4032 R = 20% Required population of town = P/(1 + R/100)^T = 4032/(1 + 20/100)^2 = 4032/(6/5)^2 = 2800(approximately) Answer is B #### B QUESTION:what is next number in sequence 212 427 303 336 394 ? options: A)123 B)345 C)560 D)567 E)245 SOLUTION:E 245 space them properly as 21 24 27 30 33 36 39 42 45 ? #### E QUESTION:A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? options: A)29% B)17% C)44% D)46% E)21% SOLUTION:g% = 10 + 10 + (10*10)/100 = 21% Answer: E #### E QUESTION:A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 35% impurities to the product. Find the net profit percentage of the dealer? options: A)44% B)40% C)68.75% D)56.25% E)36% SOLUTION:The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight. It means that he is selling $4 worth of product for $5. The dealer then further added 35% impurities to the product. It means that he is selling $5 worth of product for $6.75. So his profit is $6.75-$4 = $2 and his profit percent is (2.75/4)*100 = 68.75% Answer:- C #### C QUESTION:Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm. options: A)221 cm2 B)211 cm2 C)231 cm2 D)236 cm2 E)241 cm2 SOLUTION:Given: length = 17 cm, breadth = 13 cm Perimeter of rectangle = 2 (length + breadth) = 2 (17 + 13) cm = 2 × 30 cm = 60 cm We know that the area of rectangle = length × breadth = (17 × 13) cm22 = 221 cm2 ANSWER :A #### A QUESTION:If the cost price is 96% of the selling price, then what is the profit percent? options: A)4.17% B)5% C)6.12% D)3.25% E)5.75% SOLUTION:Let S.P. = $100 C.P. = $96 Profit = $4 Profit% = 4/96 * 100 = 25/6 = 4.17% Answer is A #### A QUESTION:The number which exceeds 16% of it by 63 is : options: A)75 B)52 C)58 D)60 E)62 SOLUTION:Solution Solution Let the number be x. x-16% of x =63 x-16/100x =63 x-4/25x=63 21/25x=63 x=(63x25/21)= 75 Answer A #### A QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:The function f is defined by subtracting 25 from the square of a number and the function v is defined as the square root of one-half of a number. If v(f(x))=10, then which of the following is a possible value of x? options: A)-15 B)-5 C)0 D)5 E)25 SOLUTION:f(x) = x^2-25 v(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number). v(f(x)) = 10 v(x^2-25) =10 sqrt((x^2-25)/2) = 10 => (x^2-25)/2 = 100 =>x^2 = 225 => x = 15 or -15 Answer is A. #### A QUESTION:When positive integer N is divided by positive integer P, the quotient is 20, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 2. What is the value of N? options: A)107 B)331 C)511 D)691 E)871 SOLUTION:N/P=10 7/P= 20P+7 N/(P+2)=15 2/(P+2)=15P+30+2 solving these two equations we get P=5 N= 107 answer is A. #### A QUESTION:A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day 5 miles per hour for 6 hours. How many miles in total did she walk? options: A)68 B)44 C)58 D)60 E)62 SOLUTION:First day - 18 miles with 3 miles per hours then total - 6 hours for that day Second day - 4 miles per hour and 5 hours - 20 miles Third day - 5 miles per hour and 6 hours - 30 miles Total 18+20+30 = 68 Answer: option A. #### A QUESTION:The total cost of 100 paper plates and 200 paper cups is $7.50 At the same rates what is the total cost of 20 of the plates and 40 of the cups? options: A)$.90 B)$1.00 C)$1.20 D)$1.50 E)$1.60 SOLUTION:U dont need to go through all this What u have with u is 100 P + 200 C = $7.50 Just divide the equation by 5 and you will get what u are looking for 20P + 40 C = $1.50 Therefore OA is D #### D QUESTION:The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ? options: A) 10^9 B) 10^8 C) 10^2 D) 10^6 E) 10^5 SOLUTION:P = 2*3*5*7 ~ 10^ 2 Answer : C #### C QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? options: A)18 B)16 C)26 D)17 E)11 SOLUTION:Explanation: 1500 ---- 390 100 ---- ? => 26% Answer:C #### C QUESTION:Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary? options: A)Rs.3500 B)Rs.4000 C)Rs.4500 D)Rs.5000 E)None SOLUTION:Explanation: Let salary be Rs.x. Then, x-15% of x -30% of 85% of x = 2380 or x- 15x/100−30×85×x/100×100=2380 or 200x-30x-51x=2380×2002380×200 or 119x = 2380×2002380×200 or x 2380×200/119=4000 Correct Option: B #### B QUESTION:Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? . options: A)20 B)30 C)50 D)80 E)100 SOLUTION:150 employees 80 are full-time 100 have worked at company X for at least a year 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? 150-80=70 employees not full time 70-20= 50 employees not full time who worked over a year 100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year ANSWER:C #### C QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent E of the list price is the lowest possible sale price? options: A)20 B)25 C)30 D)40 E)50 SOLUTION:Let the list price be 2x for min sale price, the first discount given should be 50%, 2x becomes x here now, during summer sale additional 20% off is given ie sale price becomes 0.8x it is given lise price is $80 => 2x = 80 => x = 40 and 0.8x = 32 so lowest sale price is 32, which E is 40% of 80 hence, D is the answer #### D QUESTION:The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km? options: A)300 B)400 C)250 D)350 E)450 SOLUTION:50 kmph consumption is 1 lt/hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance. 1 lt costs $30 so 8 lt costs $240 extra expenses for 1 hr - $20 8 hrs - $160 total expense - $240 + $160= $400 Answer : B #### B QUESTION:The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is options: A)1677 B)1683 C)2523 D)3363 E)None of these SOLUTION:Explanation: L.C.M of 5, 6, 7, 8 = 840 therefore Required Number is of the form 840k+3. Least value of k for which (840k+3) is divisible by 9 is k = 2 therefore Required Number = (840 x 2+3)=1683. Answer: B #### B QUESTION:The ratio of two quantities is 1 to 2. If each of the quantities is increased by 15, what is the ratio of these 2 new quantities? options: A)5:6 B)25:27 C)15:16 D)20:21 E)It cannot be determined from the information given SOLUTION:The ratio cannot be straight way added any quantity... 1:2means 1X:2X... So when you add a quantity, it becomes 1x + 15 : 2x +15.. So value of x is must.. Ans E #### E QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.) options: A)25 pounds B)46 pounds C)92 pounds D)100 pounds E)146 pounds SOLUTION:Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*10 --> x = 100. Answer: D. #### D QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)48 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E QUESTION:The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 422 C)Rs. 419 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2560 TD = Rs. 360 PW = F - TD = 2560 - 360 = Rs. 2200 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2200 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2160 for unexpired time =360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C #### C QUESTION:Two wheels are connected via a conveyor belt. The larger wheel has a 48cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r? options: A)90r B)75r C)48r D)24r E)(64π)/3 SOLUTION:Interesting to note that the larger wheel has a diameter of 48 (8*6) while the smaller one has a diameter of 32 (8*4)... If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 48pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.5 = 15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.5 = 900 revolutions per hour. If r = 10, then the answer choice must be b. A. 90r #### A QUESTION:Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 50 paisa and Z gets 40 paisa. If the share of X is RS. 30, what is the total amount? options: A)67 B)55 C)62 D)47 E)57 SOLUTION:x:y:z = 100:50:40 10:5:4 10 --- 30 19 --- ? => 57 Answer: E #### E QUESTION:in how many possible ways you can write 3240 as product of 3 positive integers a, b, c . options: A)450 B)420 C)350 D)320 E)300 SOLUTION:3240 => 2^3 * 3^4 * 5^1 a => 2^x1 * 3^y1 * 5^z1 b => 2^x2 * 3^y2 * 5^z2 c => 2^x3 * 3^y3 * 5^z3 a * b * c = 3240 x1 + x2 + x3 = 3 => 5C2 y1 + y2 + y3 = 4 => 6C2 z1 + z2 + z3 = 1 => 3C2 5C2 * 6C2 * 3C2 = 10 * 15 * 3 = 450 ANSWER:A #### A QUESTION:In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 7 women? options: A)A)84 B)B)15 C)C)20 D)D)18 E)E)21 SOLUTION:Required number of ways = 4C3*7C2 = 4*21 = 84 Answer is A #### A QUESTION:If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)? options: A)9. B)12. C)15. D)16 E)18. SOLUTION:Expand this to get: (2X + Y)(2Z + W) = 4XZ + 2XW + 2YZ + YW = 4 XZ + YW + 2XW + 2YZ [I rearranged the terms] = 3 + 2XW + 2YZ [replaced 4XZ + YW with 3] = 3 + 2(XW + YZ) factored out a 2 = 3 + 2(6) = 3 + 12 = 15 ANSWER:C #### C QUESTION:In order to fulfill a local school’s request for x cakes, B parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled? options: A)px/B B)px/(B(B - P)) C)x/(B - P) D)p/(B - Px) E)p/(B(B - p)) SOLUTION:No of cakes each parent has to bake : x/B No of parents did not bake cake = p No of cakes that were not baked by p parents = p*x/B No of parents has to bake additional cakes = B-p additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(B(B - P)) Answer B #### B QUESTION:A furniture dealer purchased a desk for $100 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? options: A)40% B)45% C)50% D)55% E)60% SOLUTION:Anyway, in this question, there is no discount but the mark up is given as 40% of the selling price. So it is not 40% of $100 but instead, 40% of Selling price which is obtained by adding mark up to $100. So if selling price is S, 100 + 40% of S = S or 100 = 0.6S therefore S = 100/0.6 = S = Profit = 100/0.6- 100 which is calculated on cost price in % terms. So 40/100 * 100 = 40% is profit. A #### A QUESTION:Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water? options: A)3:2 B)1:4 C)3:1 D)5:2 E)4:3 SOLUTION:G = 10W C = 5W Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy 1gm gold + x gm copper = x+1 gm of alloy 10W+5Wx = x+1 * 6W 10+5x = 6(x+1) x = 4 Ratio of gold with copper = 1:4 = 1:4 Answer is B #### B QUESTION:If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil? options: A)9 B)5 C)7 D)8 E)4 SOLUTION:Let the total length be xm Then black part =x/8cm The remaining part=(x-x/8)cm=7x/8cm White part=(1/2 *7x/8)=7x/16 cm Remaining part=(7x/8-7x/16)=7x/16cm 7x/16=7/2 x=8cm Answer is D. #### D QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:Pavan travelled for 15 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:How long will it take for a sum of money to grow from Rs.1000 to Rs.5,000, if it is invested at 20% p.a simple interest? options: A)8 years B)20 years C)72 years D)56 years E)None SOLUTION:In this case, Rs. 1000 has become Rs.5000. Therefore, the interest earned = 5000 – 1000 =4000 Interest for Rs 1000 @ 20% for 1 year = 200 200 - 1 4000 - ? => 20 years Answer : B #### B QUESTION:Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations X of project assignments are possible? options: A)252 B)1,680 C)2,340 D)362,880 E)592,704 SOLUTION:The ways to select three employees out of 9 for first project = 9C3 The ways to select three employees out of Remaining 6 for Second project = 6C3 Third Project already has the group of three to be assigned to it so need to select that So total ways to assign 3 employees to each of 3 projects X= 9C3 * 6C3 * 1 = 1,680 Answer: Option B #### B QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5 SOLUTION:We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10. # of different approximations are possible. Approach #1: 2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200); 2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107 Answer: C. Approach #2: 2*5=10 3*17=~50 (actually more than 50); 7*13=~100 (actually less than 100); 11*19=~200 (actually more than 200) 2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107. Answer: C. #### C QUESTION:The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 * 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:A disease has infected an ant colony that consists of "workers" and "soldiers": 30% of the soldiers and 14% of the "workers" were infected. If that colony is inhabited by 7000 ants, out of which 1700 are infected, how many "workers" inhabit the colony? options: A)1500 B)2500 C)2750 D)3000 E)3250 SOLUTION:From two question we get wo equations: (1) 0,3s + 0,14w = 1700 (2) s + w = 7000 From (2) we get w=7000-s In (1) 0,3s + 980-0,14s= 1700 0,16s=720 72000:16= 4500 =s In (2) 4500 + w = 7000 w= 2500 ANSWER:B #### B QUESTION:At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? options: A)20 greater B)17 fewer C)28 fewer D)36 fewer E)44 fewer SOLUTION:Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/10 * 480 =48 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 48-68 =20>>> therfore answer is 20 greater A #### A QUESTION:A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water? options: A)32 kmph B)34 kmph C)30 kmph D)50 kmph E)65 kmph SOLUTION:US = 45 DS = 55 M = (45 + 55)/2 = 50 Answer:D #### D QUESTION:If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is? options: A)22 B)65 C)78 D)33 E)25 SOLUTION:Given that, cost price of 50 article is equal to selling price of 40 articles. Let cost price of one article = Rs. 1 Selling price of 40 articles = Rs. 50 But Cost price of 40 articles = Rs. 40 Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25% Answer:E #### E QUESTION:Which of the following is satisfied with |x-4|+|x-3|<6? options: A)1<x<5 B)2<x<5 C)0.5<x<6.5 D)0.5<x<4 E)3<x<4 SOLUTION:--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5 Therefore, the answer is C. #### C QUESTION:What approximate value should come in place of question mark (?) in the following equation? 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ? options: A)230 B)225 C)232 D)220 E)240 SOLUTION:? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12 = 256.3 + 40.3 – 66.12 ≈ 232 Answer C #### C QUESTION:There are 9 books on a shelf that consist of 3 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)95 B)103 C)111 D)119 E)127 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 6C4 = 15 The number of combinations with at least one paperback is 126-15 = 111 The answer is C. #### C QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)Rs.7288 B)Rs.2542 C)Rs.2522 D)Rs.2625 E)Rs.6271 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)13.9 sec B)12.1 sec C)17.9 sec D)61.9 sec E)47.98 sec SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec. Answer:B #### B QUESTION:Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day A on which the buses leave at the same time. options: A)A=Tuesday B)Wednesday C)Thursday D)Sunday E)A=The busses will never leave at the same time SOLUTION:The answer is E. I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide. Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E #### E QUESTION:If -2/(a - 6) = 4/(a + 4), then a = ? options: A)2/3 B)1/2 C)5/3 D)8/3 E)7/3 SOLUTION:Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve (a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ] - 2 (a + 4) = 4 (a - 6) a = 8/3 correct answer D #### D QUESTION:It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn options: A)16 B)45 C)36 D)20 E)90 SOLUTION:1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min.. only A and B are left.. if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins.. ans 20 D #### D QUESTION:How many three letter words are formed using the letters of the word TIME? options: A)28 B)21 C)26 D)24 E)29 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24. Answer: D #### D QUESTION:Solve x^2 – 7x = 0 options: A)(0,7) B)(0,3) C)(0,2) D)(0,5) E)(0,6) SOLUTION:This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved x^2 – 7x = 0 x(x – 7) = 0 x = 0 or x – 7 = 0 x = 0 or x = 7 The solution is x = 0, 7 Ans: A #### A QUESTION:The ratio Q , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio Q, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is? options: A)8118 B)8127 C)8618 D)8436 E)8128 SOLUTION:A = 7500(26/25)3 = 8436 Answer: D #### D QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)45 B)20 C)25 D)27 E)22 SOLUTION:Average = (10 + 15 + 20 + 25 + 30)/5 = 100/5 = 20. Answer:B #### B QUESTION:A bicyclist's wheel has a circumference of 6 meters. if the bicyclist covers 180 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour. To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.=180/6*5 =6 Answer (E) #### E QUESTION:In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is. options: A)7 B)8 ½ C)7 ½ D)7 ¾ E)9 ½ SOLUTION:Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T = 5/2 T=15/2 = 7 ½ Answer is C. #### C QUESTION:By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1 SOLUTION:Explanation: Let the cost of the brand be Rs. X per kg. C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x) S.P of 5 kg = Rs. (5 * 177) = Rs. 885 [885 - (400 + 3x)]/(400 + 3x) * 100 = 18 24250 - 150x = 3600 + 27x 177x = 20650 => x = 116 2/3 So, cost of the other brand = Rs. 116.66. Answer: D #### D QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 8 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score? options: A)24 B)30 C)40 D)50 E)60 SOLUTION:One way to do this would be weighted average method.. 1) let the average of 5 mocks be x... so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67... By alligation/weighted average.. the difference in 760 and 726.67 is 5/6 of difference of 760 and x.. 760-726.67 = 5/6 * (760-x) 760-x= 33.33*6/5=40... so x = 720.. the last of mock test will be 720+8+8=736... so ans = 760-736=24 A #### A QUESTION:A train 200 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)15 sec E)18 sec SOLUTION:Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec Time taken by the train to cross the man = Time taken by It to cover 200 m at 50/3 m / sec = 200 *3/ 50 sec = 12sec Answer : C #### C QUESTION:If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A) 6x B) 4x C) 5x/3 D) 3x/2 E) 3x/5 SOLUTION:Note that we have 5positivetemperatures. Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<D<5x --> only option B fits. Answer: B. #### B QUESTION:If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available. options: A)35 7/8 B)36 C)21 3/7 D)34 5/7 E)34 6/7 SOLUTION:Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts. If we use 8 tons of cement, then we'll get 5/7*30 = 21 3/7 tons of mixture. Answer: C. #### C QUESTION:Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? options: A)5/5 B)5/9 C)3/4 D)5/7 E)5/2 SOLUTION:In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27 The probability = 27/36 = 3/4. Answer: C #### C QUESTION:3 pig’s and 10 hens are brought for Rs.1200. If the average price of a hen be Rs.30. What is the average price of a pig. options: A)300 B)350 C)400 D)425 E)275 SOLUTION:Explanation: Average price of a hen = Rs.30 total price of 10 hens = 10*30 = Rs.300 But total price of 3 pigs and 10 hens = Rs. 1200 Total price of 3 pigs is = 1200 - 300 = 900 Average price of a pig = 900/3 = Rs. 300 Answer: A #### A QUESTION:If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ? options: A)4x + 6y B)x + y + 4 C)4x - 9y D)9x + 4y E)x + y - 4 SOLUTION:By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11. (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11; (x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11; (9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11; (4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11. correct answer C #### C QUESTION:Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in six hours, what fraction of the room can Joseph paint in 20 minutes? options: A)1/6x B)x/(x-3) C)(x-6)/18x D)x/(x-6) E)(x-6)/x SOLUTION:Let J be Joseph's rate per hour. 1/x + J = 1/6 of a room per hour J = 1/6 - 1/x, of a room per hour In 20 minutes, Joseph can paint 1/3*(1/6-1/x) = 1/18-1/3x = (x-6)/18x The answer is C. #### C QUESTION:If after 700 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used? options: A)180 grams B)220 grams C)250 grams D)350 grams E)1400 grams SOLUTION:I too think 1400 grams should be the answer. My reasoning is The h20 content in 700 gms of water is 1 h20 content in 24% solution is 0.76 Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84 Let amount of solution be X Then the equation can be set up 700*1 + 0.76X = 0.84 (X+700) 0.08X = 112 8X = 11200 X = 1400 (ANS E) #### E QUESTION:Sum of the numbers from 1 to 35 is options: A)630 B)660 C)670 D)450 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 35. So S20=35×36/2=630 Correct Option: A #### A QUESTION:A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck? options: A)2:1 B)3:4 C)4:3 D)1:4 E)5:6 SOLUTION:Given; 4 duck = 3 hen; Or, duck/hen = 3/4; Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter. Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''Answer: 2:1; #### A QUESTION:In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg? options: A)16 : 30 B)30 : 14 C)16 : 31 D)31 : 15 E)15 : 31 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (31.50 - 23.75) / (23.75 - 20) = 31/15 ANSWER:D #### D QUESTION:power windows: 60% anti-lock brakes: 25% CD player: 45% The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? options: A)25 B)8 C)11 D)3 E)0 SOLUTION:Answer: B Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for. If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation: 45=15+22+x x=8, choice B. #### B QUESTION:If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 5. II. x is an integer multiple of 3 III. x is an integer multiple of 6 options: A)a) I only B)b) II only C)c) I and II only D)d) I and III only E)e)II and III only SOLUTION:The answer should be D i.e. X will be an integer and multiple of 3 and 6. Let us take example n, n+1, n+2 as 3 three consecutive positive integers. In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12 Hence in a product of 3 consecutive integers, the product is always divisible by 3. Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also. Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even Answer E #### E QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)19% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer: C #### C QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)8 years B)10 years C)12 years D)14 years E)15 years SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = | (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:What is the SI on Rs.8000 from August 6th to Dec 30th at 5% per annum rate of interest? options: A)Rs 100 B)Rs 120 C)Rs 140 D)Rs 160 E)Rs 200 SOLUTION:Number of days from August 6th to December 30th = 146 days ( we don’t count the given day) Simple Interest= PTR 100 = 8000 x 146 365 x 5 100 = Rs 160 D #### D QUESTION:210 school students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers? options: A)25 B)40 C)50 D)60 E)75 SOLUTION:We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20. So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40. #### B QUESTION:A three digit number divisible by 7 becomes divisible by 3 when 7 is added to it. The largest such number is : options: A)891 B)896 C)882 D)867 E)864 SOLUTION:Out of all the 5 options, only 896 is NOT divisible by 3. All others are divisible So Answer = B(No further calculation required) Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3 7 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3 Applying the above rule,It means that the number which we are going to add should be non-divisible by 3 So comes the answer = 896 Answer : B #### B QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places? options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5 SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset. Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300 Number CA possible = 1C1 = 1 Number FL possible = 1C1 = 1 Number HI possible = 1C1 = 1 Number other possible = 47C1 = 47 Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes) P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900 Answer: D #### D QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is options: A)360 B)240 C)2520 D)480 E)None of these SOLUTION:Solution Order of vowels of fixed ∴ required number of ways are 7!/2!. Answer C #### C QUESTION:If 15% of 40 is greater than 25% of a number by 2, the number is options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Explanation: 15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16 Option B #### B QUESTION:If eight machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job? options: A)45 B)60 C)75 D)96 E)100 SOLUTION:using the std formula m1d1h1/w1=m2d2h2/w2 substituting the values we have 8*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2) 16/3=10/3*x x=8/5 hour so 96 minutes ANSWER:D #### D QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:The area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is? options: A)7 B)7.67 C)8.75 D)8.98 E)8.28 SOLUTION:(4 * 3.5)/2 = 7 Answer:A #### A QUESTION:Pencils, Pens and Exercise books in a shop are in the ratio of 14: 4 : 3. If there are 140 pencils, the number of exercise books in the shop is: options: A)30 B)27 C)35 D)33 E)37 SOLUTION:Explanation : Let Pencils = 14x, Pens = 4x & Exercise books = 3x. Now, 14x = 140 hence x = 10 Number of exercise books = 3x = 30 Answer : A #### A QUESTION:A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train? options: A)230 m B)250m C)643m D)832m E)270m SOLUTION:Speed = (72 x 5/18)m/sec = 20 m/sec. Time = 26 sec. Let the length of the train be x metres. Then, x + 270/26 = 20 x + 270 = 520 x = 250. Answer:B #### B QUESTION:A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$333.33 C)$100.25 D)$277.78 E)$377.00 SOLUTION:Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 ) $25000 is 60% of total amount. So total amount = 25000 * 100/60 Remaining amount is 40% of total amount. 40% of total amount = 25000 * (100/60) * (40/100) = 50000/3 This amount has to be divided by 50( remaining people are 50 ) So per head amount is 50000/3 / 50 = 32000/180 = 333.33; ANSWER:B #### B QUESTION:A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? options: A)66 2/3 % B)33 7/3 % C)33 1/3 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer: A #### A QUESTION:By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article? options: A)72.0 B)75.0 C)70.00 D)68.00 E)None of these SOLUTION:Let the cost price of the article be x. Then,2(84 –x) = 96 – x l68 – 2x= 96 – x \ x = 72 Answer A #### A QUESTION:Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756 options: A)16 B)33 C)105 D)424 E)2124 SOLUTION:2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16. 3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34 4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105 5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424 6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125 3th term should 34 instead of 33. B #### B QUESTION:A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water: options: A)1.8h B)3h C)4h D)5h E)None of these SOLUTION:Explanation: Upstream speed = B-S Downstream speed = B + s B - S = 15/5 = 3 km/h Again B = 4S Therefore B - S = 3 = 3S => S = 1 and B = 4 km/h Therefore B + S = 5km/h Therefore, Time during downstream = 15/5 = 3h Answer: B #### B QUESTION:The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages. options: A)30% B)32.50% C)33 1/3% D)40% E)50% SOLUTION:Explanation: The gain is 4 out of 12 articles. Therefore, gain percentage = 4x100/12 = 100/3 = 33 1/3% Answer: Option C #### C <<<Examples ends QUESTION:The two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z? options: A)16 B)3/√2 C)8 D)2√2 E)(√2)/3 SOLUTION:800score Official Solution: The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(3 × 3) = 9/2; so z = 9/2. The next step requires us to find the length of a side of a cube that has a face area equal to 9/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 9/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 9/2. Clearly s = √9/2 = 3/√2 , oranswer choice (B). #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.6*J)=0.8*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. #### B QUESTION:David works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 600 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 4,800. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.? options: A)2400 B)3600 C)3000 D)2800 E)2500 SOLUTION:let the rate be x, then population of the bacteria after each hour can be given as 600,600x, 600(x^2), 600(x^3) now population at 4pm =4800 thus we have 600(x^3) = 4800 =8 thus x=2 therefore population at 3pm = 600(4) = 2400 Answer : A #### A QUESTION:The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child? options: A)7 years B)9 years C)6 years D)4 years E)5 years SOLUTION:28 * 2 = 56 20 * 3 = 60 ----------- 4 years Answer: D #### D QUESTION:Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in. options: A)40 min B)25 min C)54 min D)65 min E)58 min SOLUTION:Distance = Speed * time 3*20/3= 20km New Speed = 18 kmph Therefore time = 20/18 = 10/9= 54min Answer : C. #### C QUESTION:If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king? options: A)6/13 B)7/10 C)4/11 D)7/13 E)5/26 SOLUTION:There are 26 black cards and 2 red kings. P(black card or king) = 28/52 = 7/13 The answer is D. #### D QUESTION:The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is? options: A)288 B)267 C)200 D)4096 E)2771 SOLUTION:Principal = [4913 / (1 + 25/(4 * 100))3] = 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096. Answer: D #### D QUESTION:If the probability W of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period? options: A)8/125 B)2/25 C)5/16 D)8/25 E)3/4 SOLUTION:5C3 (1/2)^3(1/2)^2 = (5 * 4 * 3!)/2!3! * 1/32 W= 5/16 Answer - C #### C QUESTION:In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun? options: A)67 kg. B)68 kg. C)69 kg. D)Data inadequate E)None of these SOLUTION:EXPLANATION Let Arun’s weight by X kg. According to Arun, 65 < X < 72 According to Arun’s brother, 60 < X < 70. According to Arun’s mother, X <= 68 The values satisfying all the above conditions are 66, 67 and 68. Required Average =( 66 + 67 + 68 /3 )= (201/3) = 67 kg Answer A #### A QUESTION:A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? options: A)2.0 B)4.0 C)5.0 D)6.0 E)8.0 SOLUTION:For the total revenue to remain the same when the price is one fourth, the number of products sold must four times. Therefore increase in the number of products sold is 100% => The required ratio = 100%/25% = 4.0 Answer : B #### B QUESTION:How many four letter words are formed using the letters of the word POLICE? options: A)280 B)321 C)330 D)360 E)370 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is 6P4 = 6 * 5 * 4 * 3 = 360. Answer: D #### D QUESTION:The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation? options: A)1 B)5 C)7 D)8 E)11 SOLUTION:Let me define terms: in g(p) = R p is argument, R is result, g() is function, in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1:1 Even g2: 1*(Even,Odd ) =1 Even 1 Odd g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8 Ans D it is! #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10 SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others C #### C QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is options: A)22 B)30 C)99 D)28 E)17 SOLUTION:Explanation: Total age increased = (8 * 2) years = 16 years. Sum of ages of two new men = (21 + 23 + 16) years = 60 years Average age of two new men = (60/2) years = 30 years Answer: B #### B QUESTION:A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number? options: A)297 B)187 C)278 D)200 E)267 SOLUTION:25 + 25 = 50 25% ------ 50 100% ----- ? => 200 Answer:D #### D QUESTION:Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10? options: A)2140 B)2520 C)2980 D)3260 E)3680 SOLUTION:The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5. The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520 The answer is B. #### B QUESTION:If P represents the product of the first 13 positive integers, which of the following must be true? I. P is an odd number II. P is a multiple of 24 III. P is a multiple of 23 options: A)I only B)II only C)III only D)None of the above E)All of the above SOLUTION:The correct answer is B. #### B QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)12% C)22% D)24% E)21 SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer:A #### A QUESTION:An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 1/2M + 15, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold? options: A)a. A - 10 B)b. B - 15 C)c. C – 22.5 D)d. D – 30 E)e. E – 67.5 SOLUTION:A --- 10/2 + 15 = 20 --- CORRECT B --- 15/2 + 15 = not an integer --- wrong C --- 22.5(1/2) + 15 = not an integer --- wrong D --- 30/2+15 =30 --- wrong This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method. A #### A QUESTION:An bus covers a certain distance at a speed of 100 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? options: A)500 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (100 x 5) = 500 km. Required speed = 500 km/hr. A #### A QUESTION:Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.90? options: A)426 B)430 C)443 D)480 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones. Having 7.9$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.9 $ left. so we buy 1 pack of 50 for 1$. We now have 0.9$ left, so we buy 30 individual envelopes. If we add up the numbers, we get 400+50+30=480 envelopes. Answer D #### D QUESTION:In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is- options: A)42 B)32 C)48 D)28 E)38 SOLUTION:X/63 = 24. X = 24 *63. So correct answer would be, (24 *63) /36 = 42. ANSWER : A #### A QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? options: A)176 m B)198 m C)197 m D)150 m E)168 m SOLUTION:Let the length of the train be x meters and its speed be y m/sec. They, x / y = 15 => y = x/15 x + 100 / 25 = x / 15 x = 150 m. Answer:D #### D QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)767 m B)467 m C)245 m D)567 m E)544 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer:C #### C QUESTION:If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is options: A)40 B)44 C)80 D)86 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 24 and x2 + y2 = 404. Now, 2xy = (x+y)2 - (x2 + y2) = (24)2 - 404 = 576- 404 = 172 xy = 86. Answer D #### D QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 25 per kg, then his gain percent is options: A)12% B)33% C)14% D)15% E)16% SOLUTION:Explanation: Suppose he bought 5 kg and 3 kg of tea. Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150. Selling price = Rs. (8 x 25) = Rs. 200. Profit = 200 - 150 = 50 So, Profit % = (50/150) * 100 = 33% Option B #### B QUESTION:Simplify: 256 x 256 - 144 x 144 options: A)761200 B)44800 C)761800 D)761500 E)None of them SOLUTION:(256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800 Answer is B #### B QUESTION:Kira's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ? options: A)7cdx/100 B)d + 7cx/100 C)7d + xc/100 D)7d + 7xc/100 E)7cdx SOLUTION:Answer is D. #### D QUESTION:Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: options: A)175.5 B)170 C)169.5 D)180 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. average price = 126+135/2 = 130.50 o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x - 153 = 22.50 x = 175.50 ANSWER A #### A QUESTION:John bought a total of 20 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 20 mangoes and oranges that John originally purchased was 69 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Let number of mangoes be x, number of oranges be 12-x 0.80x +(20-x)0.60/20 = 0.69 solving for x, we get x = 9 --> Mangoes 9, Oranges 11 Now, number of oranges to be returned be y 0.80*9 + (11-y)*0.60/20-y = 0.72 solving for y, y = 5 Ans: B #### B QUESTION:If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD? options: A) 62 B) 55 C) 48 D) 31 E) 25 SOLUTION:I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square. 25 is a perfect square. Ans:E #### E QUESTION:Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes. How much time will it take Roy to consume all the five tablets? options: A)60 min B)50 min C)70 min D)65 min E)80 min SOLUTION:A 60 min Roy will be able to consume all the five tablets in an hour. Tablet 1 will be taken in 0 min. Tablet 2 will be taken in 15 min. Tablet 3 will be taken in 30 min. Tablet 4 will be taken in 45 min. Tablet 5 will be taken in 60 min. #### A QUESTION:Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81? options: A)1020600 B)1020593 C)56693 D)28343 E)18900 SOLUTION:14 = 2 * 7 25 = 5 * 5 36 = 2 * 2 * 3 * 3 81 = 3 * 3 * 3 * 3 So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C. #### C QUESTION:The average of first four prime numbers greater than 50 is? options: A)50 B)57 C)89 D)56 E)60 SOLUTION:53 + 59 + 61 + 67 = 240/4 = 60 Answer: E #### E QUESTION:In how many ways can 6 boys and 3 girls be arranged at a table if 3 girls are never together? options: A)47520 B)45620 C)47888 D)42156 E)43210 SOLUTION:Total ways of arranging 10 person in a circle = 9! = 51840 ways If we consider three women as one, then we have 6+1=7 persons. Arranging these seven persons in circle will take = 6! = 720 ways And three women can arrange themselves in 3! ways Total ways in which three women sit together in circle = 6!*3! = 4320 ways Total ways in which three women doesn’t sit together in circle = 9! - 6!*3! = 51840 - 4320 = 47520 ways A #### A QUESTION:Find value of x (11^2 + 12^2 + 13^2 + ... + 20^2) = x options: A)1200 B)1340 C)1234 D)1203 E)2485 SOLUTION:(11^2 + 12^2 + 13^2 + ... + 20^2) = (1^2 + 2^2 + 3^2 + ... + 20^2) - (1^2 + 2^2 + 3^2 + ... + 10^2) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = (2870 - 385) = 2485 E #### E QUESTION:Marge has C candies, where C is an integer such that 20 <C< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children? options: A) 0 B) 1 C) 2 D) 3 E) 4 SOLUTION:If Marge divides the candies equally among 5 children, she will have 2 candies remaining. This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47 If she divides the candies among 6 children, she will have 1 candy remaining. this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49 ONLY 37 is common, so candies are 37 in number.. if 37 is divided in 7 kids, remainder C= 2 C #### C QUESTION:In an encryption code 'PLAYS' is written as '{:SUD' when encoded and 'SLEEP' is written as 'D:RR{' when encoded. How is ''SLAPPY" written in that encryption code? options: A)D:S{{U B)SLAPPY C){RUDD: D){:SUU{ E)U{{S:D SOLUTION:D = S : = L S = A P = { P = { Y = U Correct Answer: A #### A QUESTION:How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)52 sec B)50 sec C)51 sec D)55 sec E)58 sec SOLUTION:B 50 sec The distance to be covered = Sum of their lengths = 200 + 300 = 500 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 500/10 = 50 sec. #### B QUESTION:Helen went to the stationers and bought things worth Euro 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)Euro 15 B)Euro 15.7 C)Euro 19.7 D)Euro 20 E)None SOLUTION:Explanation: Let the amount taxable purchases be Euro x. Then, 6% of x = 30/100 x = (30/100 x 100/6) = 5. Cost of tax free items = Euro [25 - (5 + 0.30)] = Euro 19.70 Answer: Option C #### C QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)? options: A)0 B)20 C)75 D)5 E)10 SOLUTION:Explanation : Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0 Answer : A #### A QUESTION:Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is? options: A)10 B)30 C)40 D)50 E)60 SOLUTION:Let the numbers be 3x,4x and 5x their L.C.M. = 60x 60x =600 x = 10 The numbers are 3*10 , 4*10 , 5*10 Hence required H.C.F. = 10 Answer is A #### A QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall? options: A)120 B)350 C)1470 D)2,520 E)5,040 SOLUTION:Number of ways to choose 2 colors among 7 - 7c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 7c2 * 2* 7c4 = 1470 C #### C QUESTION:Solve for x if (log2)(1-x/2)=x-2. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(log2)(1-x/2)=x-2 or,log2-(x/2)log2=x-2 or,2log2-xlog2=2x-4 or,log4+4=2x+xlog2 or,4.60=2.3x i.e.x=2. ANSWER:B #### B QUESTION:Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4. So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes. If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1. The number of 10 pound boxes remains the same so we still have 4 of them. To get a ratio of 1:1, the number of 20-pound boxes must be 4. We need to remove 12 of the 20-pound boxes. The answer is B. #### B QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 18 hours and pipe C in 36 hours. If all the pipes are open, in how many hours will the tank be filled ? options: A)2.5 hours B)2 hours C)4 hours D)3 hours E)None of these SOLUTION:Explanation: Part filled by A in 1 hour = 1/6 Part filled by B in 1 hour = 1/18 Part filled by C in 1 hour = 1/36 Part filled by (A+B+C) in 1 hour = 1/6+1/18+1/36=9/36 So all pipes will fill the tank in 4 hours. Option C #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)26 B)22 C)12 D)24 E)20 SOLUTION:Explanation: Let the required number of days be x More men, less days (indirect proportion) Hence we can write as (men) 36 : 27 :: x : 18 ⇒36×18=27 × x ⇒12×18=9 × x ⇒12×2=x ⇒x=24 Answer: Option D #### D QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)376 C)1267 D)198 E)621 SOLUTION:624/6 = 104 kmph Answer: A #### A QUESTION:If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is options: A)48 km B)50 km C)40 km D)22 km E)70 km SOLUTION:B 50 km. Let the actual distance travelled be x km. Then x/10=(x+20)/14 --> 14x = 10x + 200 --> 4x = 200 --> x = 50 km. #### B QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 36. options: A)5 B)4 C)12 D)32 E)35 SOLUTION:First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7. Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc and n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above) Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form n = 5a + 1 and n = 7b + 3 Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10. Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4) Now this question is exactly like the question above. So when you divide n by 36, remainder will be -4 i.e. n will be 4 less than a multiple of 36. So you must add 5 to n to make it a multiple of 36 A #### A QUESTION:Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Six years ago Jim was 7 times as old as Sam. How old is Jim now? options: A)8 B)12 C)16 D)20 E)24 SOLUTION:We're asked how old Jim is NOW. We're given three facts to work with: 1) Today, Jim is TWICE as old as Fred 2) Today, Sam is 2 years younger than Fred 3) Six years ago, Jim was 7 times as old as Sam. let's TEST Answer D: 20 IF....Jim is currently 20 years old.... Fred is 10 years old Sam is 8 years old 6 years ago, Jim was 14 and Sam was 2, so Jim WAS 7 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer. D #### D QUESTION:Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = options: A)18 B)15 C)-13 D)-21 E)-24 SOLUTION:f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = f(4) = 0= 16+4b+c--- Taking 16 to the other side -> 4b+c= -16 f(-3) = 0= 9-3b+c --- taking -3b+c to the other side -> 3b-c=9 When we add these 2 equations, we get 7b= -7---> b= -1 And while substituting b= -1 we get c= -12. b+c= -13--- Answer C #### C QUESTION:What is the maximum number of points that 10 circles of different radii intersect? options: A)24 B)26 C)33 D)90 E)100 SOLUTION:the maximum number of points that two circles intersect is two. therefore, each of these 10 circles intersect two point with each of the other 9 circles. as a consequence, the number of these points is equal to two times the number of combination of the 10 circles. 2∗(10!)/(2!∗10!)=90 Answer: D #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 7 sec. What is the length of the train? options: A)112.21 B)27.21 C)117.66 D)277 E)116.66 SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 7 = 116.66 Answer: E #### E QUESTION:The cost of 3 kg of sugar is $30. What will the cost of 8 kg of sugar be? options: A)20 B)40 C)80 D)160 E)180 SOLUTION:3 kg costs $30 1 kg costs $10 8 kg costs $80 The answer is C. #### C QUESTION:What is the smallest positive integer that can be multiplied by 605 to make it a perfect square? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:605 is multiplied by 5 gives 3025 Its a square root of 55 Answer is 5 -Option C #### C QUESTION:If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ? options: A)141 B)200 C)618 D)391 E)412 SOLUTION:The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work). We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as... A + (A+2) + (A+4) = 3A + 6 We know that 3A + 6 COULD equal one of those five answers; we just have to find it... Could 3A + 6 = 141 3A = 135 A = 45 This is NOT an EVEN INTEGER, so 141 is NOT the answer Could 3A + 6 = 200 3A = 194 A = 64.6666 This is NOT an EVEN INTEGER, so 200 is NOT the answer Could 3A + 6 = 618 3A = 612 A = 204 This IS an EVEN INTEGER! The numbers would be 204, 206 and 208. This IS the answer Final Answer: C #### C QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:Denise is trying to open a safe whose combination she does not know. IF the safe has 3000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one correct combination. options: A)1 B)159/160 C)157/160 D)0.875 E)0.975 SOLUTION:If Denise does not pick the correct combination in first 75 try, then the correct combination is one of remaining 2925. So Probability = 2925/3000 = 0.975. answer is E #### E QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 300*1 = revenue (eq -1) if he reduced his price by 20% then , 240*(customer) = 125/100*revenue customer = 1.25*300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/12 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 2*x Hence, a1+a2+..+a20+n = 22x So, the fraction asked = 2x/22x = 1/12 B #### B QUESTION:If it takes a machine 1⁄3 minute to produce one item, how many items will it produce in 2 hours? options: A)1⁄3 B)4⁄3 C)80 D)120 E)360 SOLUTION:1 item takes 1/3 min so it takes 120 min to produce x x/3=120 the x=360 Answer:E #### E QUESTION:John throws a coin until a series of four consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fifth throw? options: A)1/16 B)2/16 C)3/16 D)7/16 E)9/16 SOLUTION:Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are H-T-T-T-T ----> P = (1/2)^5 = 1/32 T-H-H-H-H ----> P = (1/2)^5 = 1/32 Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability. 1/32 + 1/32 = 2/32 = 1/16 Answer(A). #### A QUESTION:John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him? options: A)10 B)67 C)32 D)44 E)55 SOLUTION:75-20=55. Answer is E #### E QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent? options: A)705 B)655 C)656 D)657 E)658 SOLUTION:total cost 940 940*25/100=235 so the cut in amount is 235 the less amount to be spend is 940-235=705 ANSWER:A #### A QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)15 bukets B)17 bukets C)18 bukets D)19 bukets E)None of these SOLUTION:Explanation: Capacity of the tank = (12*13.5) litres = 162 litres Capacity of each bucket = 9 litres. So we can get answer by dividing total capacity of tank by total capacity of bucket. Number of buckets needed = (162/9) = 18 buckets Option C #### C QUESTION:Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/8 gallon of paint. How many statues can she paint? options: A)7 B)20 C)28 D)14 E)19 SOLUTION:number of statues=all the paint÷amount used per statue =7/8 ÷ 1/8 =7/8*8/1 =7/1 =7 Answer is A. #### A QUESTION:Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:In the xy-coordinate system, line k passes through points (-8m, 0) and (0, 2m). Which of the following is a possible equation of line k? options: A)y = -4x + 2m B)y = 1/4*x - 8m C)y = 4x + 2m D)y = 1/4*x + 2m E)y = -1/4*x - 8m SOLUTION:The slope of the line is 2m/8m=1/4. The y-intercept is 2m. the equation of the line is: y = 1/4*x +2m The answer is D. #### D QUESTION:Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years. options: A)306.05 B)306.00 C)306.04 D)306.05 E)306.01 SOLUTION:A = 5000(51/50)3 = 5306.04 5000 ----------- 306.04 Answer: A #### A QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? options: A)13680 B)13885 C)14005 D)14280 E)14680 SOLUTION:dana borrows 6000 and returns 2% per month. so returns 120 per month. and 1440 per year. so dana owes 6000-1440=4560 per year. after 3 years she will owe 13680. Ans (A) #### A QUESTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ? options: A) None B) Two C) Four D) Five E) Seven SOLUTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain? R=2,4,6,8,10,12... S=4,16,36,64... Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets. Solution: Five Answer: D #### D QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)18 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :D #### D QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)95 SOLUTION:number of handshakes = 10C2= 10*9/2 = 45 ANSWER:B #### B QUESTION:A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails? options: A)1/8 B)1/4 C)3/8 D)1/2 E)9/16 SOLUTION:We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin. Using the binary formula and defining a head as a success, P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2 t= 6/16 = 3/8 The answer is therefore (C) #### C QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute? options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 68 kilometers per hour = 68 km/hr = (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute correct answer is B)1133.33m/min #### B QUESTION:The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is: options: A)60 kg B)59 kg C)62 kg D)63 kg E)61 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (75 x 3) = 225 …. (i) A + B = (88 x 2) = 176 …. (ii) B + C = (72 x 2) = 144 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 288 …. (iv) Subtracting (i) from (iv), we get : B = 63. B’s weight = 63 kg. Answer D #### D QUESTION:Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern? options: A)90 min B)100 min C)110 min D)120 min E)None SOLUTION:Solution Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75) = (1/50 - 3/100) = -1/100. Therefore, the third pipe alone can empty the cistern in 100 min. Answer C #### C QUESTION:Which of the following is equal to the value of 2^7 + 2^7 + 3^7 + 3^7 + 3^7 ? options: A)2^8 + 3^8 B)2^6 + 3^8 C)2^8 + 3^6 D)2^9 + 3^9 E)2^5 + 3^5 SOLUTION:2^7 + 2^7 + 3^7 + 3^7 + 3^7 = 2 (2^7) + 3 (3^7) = 2^1 (2^7) + 3^1 (3^7) = 2^(1+7) + 3^(1+7) = 2^8 + 3^8 Ans: A #### A QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? options: A)5 B)6 C)9 D)7 E)3 SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 Answer: D #### D QUESTION:How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)4 C)20 D)25 E)30 SOLUTION:Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. Required number of numbers = (1 x 5 x 4) = 20. ANSWER C #### C QUESTION:Which of the following is a prime number ? options: A)33 B)81 C)97 D)93 E)none SOLUTION:Clearly, 97 is a prime number #### C QUESTION:A meal cost $ 32.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-39 E)36-37 SOLUTION:10%(32.5) = 3.25 15%(32.5) =4.875 total amount could have been 32.5+3.25 and 32.5+4.875 => could have been between 35.75 and 37.375 => approximately between 36 and 37 Answer is E. #### E QUESTION:Find the average of first 20 natural numbers? options: A)5.5 B)7.2 C)10.5 D)12.3 E)15.5 SOLUTION:Sum of first n natural numbers = n(n+1)/2 sum of first 20 natural numbers = 20*21/2 =210 average = 210/20 = 10.5 Answer is C #### C QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)22.4% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/53000 * 100 = 22.4% Answer: B #### B QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 130*4=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 8 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? options: A) 400 B) 625 C) 1,250 D) 2,500 E) 312 SOLUTION:total fish = x percentage of second catch = (8/50)*100 = 16% so, x * 16% = 50 x = 312 ans.E #### E QUESTION:Evaluate 30!/28! options: A)720 B)600 C)870 D)910 E)650 SOLUTION:we have 30!/28! = 30*29*28!/28! = 30*29 = 870 Answer is C #### C QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)2 C)3 D)4 E)6 SOLUTION:The distance between the nest and the ditch is 200 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 200 = 6000. D = ST 6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km) D) #### D QUESTION:12.5 * 6.2 * 8.8 = ? options: A)352 B)435 C)224 D)682 E)742 SOLUTION:D 682 ? = 12.5 * 6.2 * 8.8 = 682 #### D QUESTION:Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern? options: A)20 hours 30 min B)25 hours 30 min C)30 hours 30 min D)40 hours 30 min E)50 hours 30 min SOLUTION:A 20 hours 30 min 1/18 + 1/24 = 7/72 72/7 = 10 2/7 7/72 * 10 = 35/36 ----- 20 hours WR = 1 – 35/36 = 1/36 1 h ----- 1/18 ? ----- 1/36 = 1/2 hours => 20 1/2 hours #### A QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his original salary? options: A)25% B)50% C)75% D)85% E)95% SOLUTION:Salary he get after reduced 20% = 100-20% = 80% So,percentage should be added to get back his salary = (20/80)*100 = 25% ANSWER:A #### A QUESTION:Of the 50 researchers in a workgroup, 30 percent will be assigned to Team A and the remaining 80 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? options: A) 15 B) 17 C) 20 D) 25 E) 30 SOLUTION:I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case 30 will be in team A 70 will be in team B The larger diff is 70 want team A so diff is 70-30=40. At least 40 people will NOT get their wish, so for 50 researchers the same number is 20. Answer choice C #### C QUESTION:In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments? options: A)50% B)40% C)20% D)30% E)10% SOLUTION:Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9 Let total number of Apartments be X No. of 2 Bedroom Apartment = (1 / 10) * X percentage of apartments in the building are two-bedroom apartments ----> (1/10) * 100 ---> 10% Answer : E #### E QUESTION:What is the number of integers from 1 to 100 (inclusive) that are divisible by neither 5 nor by 6? options: A)35 B)47 C)58 D)26 E)34 SOLUTION:In 100 consecutive numbers, number of multiples of 5 = 100/5 = 20 (Ignore decimals) In 100 consecutive numbers, number of multiples of 6 = 100/6 = 16 Number of multiples of 5*6 i.e. 30 = 100/30 = 3 Number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - (29 + 16 - 3) {Using the concept of sets here) = 58 Answer is C #### C QUESTION:A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is? options: A)72 kmph B)88 kmph C)54 kmph D)18 kmph E)19 kmph SOLUTION:S = 120/6 * 18/5 = 72 kmph Answer: A #### A QUESTION:Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time W will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did? options: A)2 minute and 12 seconds. B)two minutes. C)44 seconds. D)20 seconds. E)12 seconds. SOLUTION:Tom is running alone for 20 seconds. So he will cover a distance of 20*2.5 = 50 m in 20 seconds=W Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side D is the answer #### D QUESTION:What percentage of numbers from 1 to 20 have squares that end in the digit 9? options: A)1 B)14 C)20 D)21 E)22 SOLUTION:Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 18 are 3,7,13,17. Number of such numbers = 4. Required percentage = (4/18 * 100) = 22% ANSWER:E #### E QUESTION:If x is negative and y is positive, which of the following cannot be positive? options: A)x/y B)-x*y C)-x/y D)x^2+y E)x^6+y SOLUTION:- /+ = - x/y is negative. Answer : A #### A QUESTION:A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 8.30 a.m. ? options: A)7 B)2 C)9 D)2 E)8 SOLUTION:B 2 Relative speed = 2 + 3 = 5 rounds per hour. So, they cross each other 5 times in an hour and 2 times in half an hour. Hence, they cross each other 2 times before 8.30 a.m. #### B QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:What is the principal sum? I. The sum amounts to Rs. 720 in 4 years at S.I. II. The sum amounts to Rs. 810 in 7 years at S.I. III. The rate of interest is 10% p.a. options: A)I and III only B)II and III only C)I and II only D)Any one of the three E)Any two of the above SOLUTION:Explanation: Clearly, any of the three will give us the answer Answer: E #### E QUESTION:A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse. options: A)2200 B)1800 C)1200 D)1000 E)1500 SOLUTION:Let the C.P of the horse be Rs. X, Then, C.P of the carriage = Rs.(3000- x). 20% of x - 10% of ( 3000-x ) =2% of 3000 = 60, x/5 - ( 3000-x )/10 = 60, 3x - 3000 = 600, 3x =3600, x = 1200. Hence, C.P of the horse = Rs. 1200 ANSWER:C #### C QUESTION:A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 4 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank? options: A)1.6 B)1 C)0.4 D)0.16 E)0.016 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi*16*10 = pi*h*100*100 (h is distance that the oil level dropped) h = 160/10,000 = 16/1000 = 0.016 ft The answer is E. #### E QUESTION:Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 14 years? options: A)30 B)34 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 14 years = (20 + 14) years =34 years. Answer : B #### B QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents. Answer: C. #### C QUESTION:If (A+B) = 5, (B+C) = 6 and (C+D) = 3, what is the value of (A+D)? options: A)16. B)8. C)7. D)2. E)-2. SOLUTION:Given A+B = 5 B+C = 6 C+D = 3 (A+B)-(B+C)+(C+D)=(A+D) => 5 - 6+3 = 2. Option D... #### D QUESTION:How many Books each of Volume 100 meter cube can be packed into a crate of volume 3000 meter cube? options: A)50 B)cannot be determined C)150 D)300 E)350 SOLUTION:Gud question with a simple concept. In geo if we want to insert one shape into another we need to know the dimensions of the two shapes. In above with volume given , we can come up with different shapes, so we cant know the answer For ex :3000 m3 can be 300*10 or 30*100 or just 3000*1 we don't know , so we cant calculate Answer : B #### B QUESTION:Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is? options: A)26 km/hr B)17 km/hr C)60 km/hr D)42 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/5 = 3x => x = 20/3. So, speed of the faster train = 40/3 = 40/3 * 18/5 = 42 km/hr. Answer:D #### D QUESTION:If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: options: A)0 B)1 C)2 D)3 E)None of these SOLUTION:(5+1+7+A+3+2+4)=(22+A)MUST BE DIVISIBLE BY 3. HENCE THE SMALLEST WHOLE No. must be 2 ANSWER:B #### B QUESTION:A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)18 seconds C)40 seconds D)19 seconds E)44 seconds SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 410+140 = 550 meter Time = Distance/speed = 550 * (2/25) = 44 seconds Answer: E #### E QUESTION:The average weight of 16 children in a class is 50.25 kg and that of the remaining 8 children is 45.15 kg. Find the average weights of all the children in the class. options: A)A)48.55 B)B)49 C)C)51 D)D)61 E)E)62 SOLUTION:Required average = (50.25 x 16 + 45.15 x 8)/(16 + 8) = (804 + 361.20)/24 = 1165.20/24 = 48.55kg Answer is A #### A QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d? options: A) 5/6*d B) 7/3*d C) 10/3*d D) 7/2*d E) 9/2*d SOLUTION:Favid has d books; Jeff has d/3 books; Paula has 2d books; Total = d+d/3+2d=10d/3. Answer: C. #### C QUESTION:A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? options: A)1/7 B)2/9 C)1/12 D)4/17 E)2/3 SOLUTION:Total number of balls = 7+2 = 9 n(S) = 9C3 = 9*8*7 / 3*2 = 84 n(E) = 2C2* 7C1 = 7 Probability = 7/84 = 1/12 Answer is C #### C QUESTION:Rectangular tile each of size 60cm by 56cm must be laid horizontally on a rectangular floor of size 560cm by 240cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: options: A)50 B)54 C)47 D)40 E)45 SOLUTION:Area of tile = 60*56 = 3360 Area of floor = 560*240 = 134400 No of tiles = 134400/3360 = 40 So, the no of tile = 40 ANSWER:D #### D QUESTION:In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 6 metres then what will be the area of the square so formed? options: A)Cannot be determined B)2600 cm2 C)5184 cm2 D)3025 cm2 E)None of these SOLUTION:Let the side of the square be x m. ∴ Perimeter of the square = 48 × 6 = 4x ∴ x = 72 m ∴ Area = (72)2 = 5184 m2 Answer C #### C QUESTION:If 5% more is gained by selling an book for $ 350 than by selling it for $ 340, the cost of the book is: options: A)160 B)210 C)200 D)227 E)220 SOLUTION:C 200 Let C.P. be $ x. Then, 5% of x = 350 - 340 = 10 x/20 = 10 => x = 200 #### C QUESTION:In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race? options: A)2min 10 sec B)2min 30 sec C)2min 40 sec D)2min 50 sec E)2min 20 sec SOLUTION:100 m = 15 sec 1 m = 15/100 sec 1000 m = 15/100*1000 =150 sec =2min 30 sec ANSWER:B #### B QUESTION:On flipping 3 coins together what is the outcomes for exactly one head and one tail? options: A){HHH, HTH, THH, TTH, THT, HTT} B){HHT, HTH, THH, TTH, THT, TTT} C){HHT, HTH, THH, TTH, THT, HTT} D){HHT, HTH, THH, TTH, THT, TTT} E)None SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for one head and one tail and favorable outcomes for more than one head and one tail. = {HHT, HTH, THH, TTH, THT, HTT} C #### C QUESTION:The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of B. options: A)250 B)450 C)750 D)800 E)None of them SOLUTION:C's 1 day's work = 1/3-(1/6+1/8)=24 A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1. A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450 C's share = Rs. [1200 - (300 + 225») = Rs. 150. Answer is B #### B <<<Examples ends QUESTION:what is the least number. which should be added to 221 to make it a perfect square? options: A)5 B)8 C)4 D)6 E)7 SOLUTION:221+4=225 15^2 ANSWER:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green? options: A)23/35 B)23/38 C)23/18 D)53/18 E)23/22 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂ = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7 = 46/70 = 23/35 Answer:A #### A QUESTION:The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? options: A)6535 B)6532 C)6725 D)6874 E)6972 SOLUTION:C 6725 CP = SP * (100/(100 + profit%)) = 8339(100/124) = Rs. 6725 #### C QUESTION:The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle? options: A)1 : 96 B)1 : 48 C)1 : 84 D)1 : 68 E)None of these SOLUTION:Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96. ANSWER:A #### A QUESTION:If it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed? options: A)400 B)420 C)480 D)500 E)600 SOLUTION:Minimum no of mail to be sent for getting 300 responses at 50% = 300/0.5 = 600 Option E #### E QUESTION:The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =12- pi*12/4 =12- pi*3 ANSWER:B #### B QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 3*20000/5=12000 ANSWER:E #### E QUESTION:Jen has a jar of jam, and she ate 1/3 of the jam for lunch. If Jen ate 1/7 of the remaining jam for dinner, what fraction of the jam was left after dinner? options: A)2/7 B)3/7 C)4/7 D)9/14 E)11/14 SOLUTION:Let x be the amount of jam at the beginning. After lunch, the remaining jam was (2/3)x. After dinner, the remaining jam was (6/7)(2/3)x = (4/7)x. The answer is C. #### C QUESTION:If mn > 0, which of the following must be negative? options: A)mn B)mn^2 C)m/-n D)m/n E)m+n SOLUTION:Given mn> 0 So both will be the positive integers. If both are positive, then A,B,D,E also positive. Answer :C #### C QUESTION:In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made? options: A)1:4 B)1:3 C)2:3 D)3:4 E)None of these SOLUTION:Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B #### B QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary? options: A)2888 B)1266 C)1000 D)2779 E)2661 SOLUTION:X * (110/100) * (95/100) = 1045 X * (11/10) * (1/100) = 11 X = 1000 Answer: C #### C QUESTION:Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2. options: A)29 B)27 C)28 D)24 E)21 SOLUTION:(4)^11x (7)^5 x (11)^2 = (2 x 2)^11 x (7)^5 x (11)^2 = 2^11 x 2^11 x7^5x 11^2 = 2^22 x 7^5 x11^2 Total number of prime factors = (22 + 5 + 2) = 29. Answer is A. #### A QUESTION:A sum of money becomes 7/6 of itself in 6 years at a certain rate of simple interest. The rate per annum is? options: A)50/9 B)50/13 C)50/17 D)25/9 E)5 5/1 SOLUTION:Let sum = x. Then, amount = 7x/6 S.I. = 7x/6 - x = x/6; Time = 6 years. Rate = (100 * x) / (x * 6 * 6) = 25/9 %. Answer:D #### D QUESTION:If r and t are positive integers, rt + r + t cannot be options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let rt + t + r = x Add 1 on both sides: rt + t + r + 1 = x + 1 t(r + 1) + r + 1 = x + 1 (r + 1)(t + 1) = x + 1 Minimum value of (r + 1) = 2 Minimum value of (t + 1) = 2 Hence x + 1 cannot be prime Substitute x from the given options: 6 + 1 = 7 --> prime --> rt + t + r cannot be 6 Answer: B #### B QUESTION:A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 5,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 11.11% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-5,500=4,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/4,500*100=~11.11% of the remaining solution of 4,500 gallons. Answer: E. #### E QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 140 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)49 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 140 / 20 = 7 sandwiches in one part For bologna we have 7 parts so: 7 * 7 = 49 Answer is E #### E QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number T of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:T=7 is the correct answer. Good solution Buneul.B #### B QUESTION:A parking garage rents parking spaces for $10 per week or $42 per month. How much does a person save in a year by renting by the month rather than by the week? options: A) $14 B) $16 C) $22 D) $24 E) $26 SOLUTION:10$ per week! An year has 52 weeks. Annual charges per year = 52* 10 = 520$ 30$ per month! An year has 12 months. Annual charges per year = 12 * 42 = 504$ 520 - 504 = 16 Ans B #### B QUESTION:Jill works as a waitress at the local diner where she earns an hourly wage of $7.00 per hour and a standard tip rate of 5% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week? options: A)280 B)300 C)320 D)432 E)400 SOLUTION:Jill earns 7 dollars/hour and the hourly tip is (1/20)*40. Jill thus earns 7*12+12*2 per day(or 7(12)+2(12)=9(12)=108). Jill has worked for 4 days -> 108*4=432. This matches answer choice D. #### D QUESTION:Claire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have? options: A)39 B)50 C)66 D)57 E)60 SOLUTION:G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300 G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66 C #### C QUESTION:The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E? options: A)60 B)80 C)40 D)120 E)160 SOLUTION:(1 + 1/8)x - (1 - 1/4)x = 30 (9/8)x - (3/4)x = 30 x = 80=E Answer: B #### B QUESTION:In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively? options: A)10,16 B)8,14 C)16,22 D)14,20 E)12, 18 SOLUTION:Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10. Given (x + 4) + (x + 10) = 30 => 2x + 14 = 30 => x = 8 The third number = x + 4 = 8 + 4 = 12. The sixth number = x + 10 = 8 + 10 = 18. Answer: E #### E QUESTION:A train 100 m long pass a telegraph pole in 5 seconds. Find the speed of the train options: A)66 km/hr B)68.4 km/hr C)72 km/hr D)79.2 km/hr E)None SOLUTION:Sol. Speed = [100/5] m/sec = [20 * 18/5] km/hr = 72 km/hr. Answer C #### C QUESTION:The function f is defined by subtracting 25 from the square of a number and the function v is defined as the square root of one-half of a number. If v(f(x))=10, then which of the following is a possible value of x? options: A)-15 B)-5 C)0 D)5 E)25 SOLUTION:f(x) = x^2-25 v(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number). v(f(x)) = 10 v(x^2-25) =10 sqrt((x^2-25)/2) = 10 => (x^2-25)/2 = 100 =>x^2 = 225 => x = 15 or -15 Answer is A. #### A QUESTION:A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 230 per month. What is his monthly salary? options: A)5000 B)5750 C)2878 D)2990 E)2771 SOLUTION:Income = Rs. 100 Expenditure = Rs. 80 Savings = Rs. 20 Present Expenditure 80*(20/100) = Rs. 96 Present Savings = 100 – 96 =Rs. 4 100 ------ 4 ? --------- 230 => 5750 Answer: B #### B QUESTION:Select the non termination decimal among the following. options: A)5/3 B)3/4 C)4/5 D)7/8 E)9/10 SOLUTION:A. Non terminating decimal means that 5/3 = 1.66666 and so on. #### A QUESTION:A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:In a suite there are men and cats. In all, there are 15 heads and 40 feet. How many men and how many cats are in the suite? options: A)8 men and 7 cats. B)7 men and 8 cats. C)6 men and 9 cats. D)10 men and 5 cats. E)11 men and 4 cats. SOLUTION:10 men and 5 cats. Let M = men and C = cats. We can come up with 2 equations. M + C = 15 2M + 4C= 40 Solving the 2 equations will give 10 men and 5 cats. Answer D #### D QUESTION:There are three departments having students 64,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required? options: A)73 B)74 C)75 D)76 E)77 SOLUTION:WE NEED TO TAKE GCD WHICH IS 2 THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT 1) 64/2 = 32 2) 58/2 = 29 3) 24/2 = 12 TOTAL NO. OF MIN ROOMS REQD = 32+12+29 = 73 ANSWER:A #### A QUESTION:The arithmetic mean of the set S = {8, K, 7, 13, M, 8} is 9. If K and M are integers, and K ≠ M, what is the median of the numbers in the set? options: A)7 B)7.5 C)8 D)8.5 E)9 SOLUTION:The sum of the numbers is 6*9 = 54 K+M = 54 - 13 - 8 - 8 - 7 = 18 Since K ≠ M, K and M do not equal 9. Thus one of the two numbers is 8 or less and one is 10 or more. Then middle two numbers in the set are 8 and 8. The median is 8. The answer is C. #### C QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6 options: A)4/7 B)5/3 C)4/5 D)5/8 E)7/18 SOLUTION:Clearly n(S)=6*6=36 Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2), (6,6)} n(E)=14. Hence p(e)=n(e)/n(s)=14/36=7/18 ANS: E #### E QUESTION:A dragon has 100 heads. A soldier can cut off 15, 17, 20 or 5 heads, respectively with one blow of his sword. In each of these cases, 24, 2, 14, 17 new heads grow on its shoulders. If all heads are cut off, the dragon dies. Can the dragon ever die? options: A)61 B)3 C)5 D)6 E)1 SOLUTION:Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die. Answer:B #### B QUESTION:Sakshi can do a piece of work in 10 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work : options: A)8 B)16 C)18 D)25 E)10 SOLUTION:Solution Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 . Suppose Tanya taken x days to do the work. 5 : 4 : : 10 : x ⇒ x = (10x4/5) ⇒ x = 8 days. Hence,Tanya takes 8 days is complete the work. Answer A #### A QUESTION:Which of the following is equal to 10^-(-2)^3? options: A)1/(10^8) B)1/(10^9) C)1/(10^5) D)1/(10^4) E)1/(10^3) SOLUTION:10^-(-2)^3 => 10^-(-2^3) => 10^-(8) = 1/(10^8) Answer : A #### A QUESTION:A car covers a distance of 630 km in 6 ½ hours. Find its speed? options: A)105 kmph B)176 kmph C)298 kmph D)186 kmph E)268 kmph SOLUTION:630/6 = 105 kmph Answer:A #### A QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination. options: A)15 B)21 C)17 D)19 E)21 SOLUTION:Total Money = Rs. 10350. Let 50 rupees note was X. Then 500 rupees note = 36 - X Now, 50*X + 500 * (36 - X) = 10350 50X + 18000 - 500X = 10350 - 450X = - 7650 X = 17. No. of 50 rupees note = 17. Answer: Option C #### C QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)63 B)30 C)36 D)45 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 14) = (x + 7) or x = 21. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63. Answer: A #### A QUESTION:A cylinder of height h is 7/8 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h? options: A)25% B)50% C)69% D)80% E)100% SOLUTION:Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder. This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5. Original cylinder 7/8 New cylinder 3/5 So 3/5/7/8 = 3/5*8/7 = 0.69 or 69%. Answer C #### C QUESTION:If (x + 1) times (2x + 1) is an odd integer, then x must be options: A)an odd integer B)an even integer C)a prime number D)a composite number E)a negative integer SOLUTION:(x + 1) times (2x + 1) means (x + 1) * (2x + 1).. (x + 1)*(2x + 1)= 2x^2+3x+1... for 2x^2+3x+1 to be odd, 3x+1 should be odd.. hence 3x should be even, which further leads to x as even.. so x is even integer.. ANSWER:B #### B QUESTION:The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? options: A)69 B)78 C)96 D)56 E)48 SOLUTION:let the digits be x,y x + y = 15 x - y = 3 2x = 18, x = 9 so y = 6 hence the number is 96 so the correct answer is option C) 96. #### C QUESTION:The sum of two consecutive number is 109. Which is the larger number? options: A)42 B)43 C)44 D)45 E)55 SOLUTION:Let consecutive number be x, x+1 Therefore sum of the consecutive number is x + x+1=109 2x+1=109 2x=108 x=54 Therefore larger number is x+1=55 ANSWER:E #### E QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 10 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)20 litres E)8 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+10)=4/5 20x=4(3x+10) 8x=40 x=5 Quantity of alcohol = (4 x 5) litres = 20 litres. Answer is D. #### D QUESTION:What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9? options: A)397 B)401 C)403 D)405 E)399 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=405. Answer: D. #### D QUESTION:If the President and Vice President must sit next to each other in a row with 2 other members of the Board, how many different seating arrangements are possible? options: A)10 B)16 C)18 D)12 E)18 SOLUTION:We need to take President and VP as one unit. Therefore we have 3 people to arrange=3! ways Also, we both President and VP can be arranged in 2 ! ways. Reqd no of ways=3!*2!=12 ways Answer D #### D QUESTION:A train ,135 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)270 m B)245 m C)235 m D)220 m E)240 m SOLUTION:Explanation: Assume the length of the bridge = x meter Total distance covered = 135+x meter total time taken = 30s speed = Total distance covered /total time taken = (135+x)/30 m/s => 45 × (10/36) = (135+x)/30 => 45 × 10 × 30 /36 = 135+x => 45 × 10 × 10 / 12 = 135+x => 15 × 10 × 10 / 4 = 135+x => 15 × 25 = 135+x = 375 => x = 375-135 =240 Answer: Option E #### E QUESTION:A person crosses a 1800 m long street in 12 minutes. What is his speed in km per hour? options: A)4.1 B)4.5 C)4.8 D)5.4 E)9 SOLUTION:Speed = 1800/(12x60) m/sec = 2.5 m/sec. Converting m/sec to km/hr =2.5 x(18/5) km/hr = 9 km/hr. ANSWER :E #### E QUESTION:In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 200 more than the correct answer. Find the number. options: A)384 B)76 C)26 D)28 E)11 SOLUTION:Explanation: Let the number be x. 5*x/6 = 5*x/16 + 200 25*x/48 = 200 x = 384 ANSWER: A #### A QUESTION:If 75 percent of 600 is 50 percent of x, then x=? options: A)800 B)900 C)1000 D)1100 E)1200 SOLUTION:0.75 * 600 = 0.5 * x x = 7.5/5 * 600 = 900 #### B QUESTION:Machine Z takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Z to make 40 widgets? options: A) 5 B) 6 C) 8 D) 10 E) 12 SOLUTION:i approached this one by plugging in numbers...started with C. if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Z is 4, and time of B is 2. rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and A reduces the time - the total # of widgets made will be even higher. now between D and E -> try only one ..if it doesn't work, then the other one is the answer. i picked E: 12h to make 40 widgets, and 6 hours to make 20. this is the time of Z. time of B=4 hours. 20/6 + 20/4 = 10/3 + 20/4 find LCM of 3 and 4 = 12. multiply first by 4, and second by 3: 40+60/12 = 100/12 divide by 4: 25/3 so this is the rate given. E is the correct answer #### E QUESTION:How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)24 sec B)30 sec C)27 sec D)28 sec E)29 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 400 * 3/50 = 24 sec. Answer:A #### A QUESTION:The value of (34.31*0.473*1.5)/(0.0673*23.25*7.57) is close to options: A)2 B)1.15 C)2.01 D)2.06 E)2.35 SOLUTION:(34.31*0.473*1.5)/(0.0673*23.25*7.57) = 24.343/11.845 = 2.06 ANSWER:D #### D QUESTION:If x is 20 percent greater than 98, then x = options: A)68 B)70.4 C)86 D)105.6 E)117.6 SOLUTION:x=98*1.2=117.6 So the answer is E. #### E QUESTION:In the Land of Oz only one or two-letter words are used. The local language has 65 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition? options: A)65 B)66 C)67 D)131 E)130 SOLUTION:The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ... The number of 1 letter words (X) that can be made from 65 letters is 65; The number of 2 letter words (XX) that can be made from 65 letters is 65*65, since each X can take 65 values. Total: 65+65*65. Similarly: The number of 1 letter words (X) that can be made from 64 letters is 64; The number of 2 letter words (XX) that can be made from 64 letters is 64*64, since each X can take 64 values. Total: 64+64*64. The difference is (65+65*65)-(64+64*64)=130. Answer: E. #### E QUESTION:Out of 470 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ? options: A)80 B)150 C)100 D)180 E)220 SOLUTION:n(A)=325,n(B)=175,n(AuB)=470-50=420. Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80. Answer is A #### A QUESTION:A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? options: A)$330.00 B)$331.00 C)$332.30 D)$333.30 E)$334.60 SOLUTION:The maximum interest in one month is 10%*$300=$30. The combined payment (base plus interest) is $300 + $30 = $330. The greatest possible payment is: 1.01*$330=$333.30. The answer is D. #### D QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:When positive integer F is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when F is divided by B? options: A) 13 B) 14 C) 15 D) 16 E) 17 SOLUTION:the remainder will be obtained from the decimal part when F is divided by B i.e. 0.35 0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this PS: for B-14 F=174 and B=40 #### B QUESTION:A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300 B)320 C)350 D)345 E)568 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 39 = 50/3 3(x + 300) = 1950 è x = 350 Answer: Option C #### C QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 4 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.22 B) 0.44 C) 0.55 D) 22 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/12*33 = 22 cents. Answer: D. #### D QUESTION:Divide Rs. 1300 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? options: A)346 B)368 C)375 D)337 E)325 SOLUTION:A+B+C = 1300 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1300 => 325 Answer:E #### E QUESTION:10^(600) ÷ 10^(580) = ? options: A)10^10 B)10^20 C)10^22 D)10^23 E)10^24 SOLUTION:10^(600) ÷ 10^(580) = 10^ (600-580) = 10^20 Answer : B #### B QUESTION:In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)3.75 sec D)12.5 sec E)6 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 150/40 = 3.75 sec. ANSWER:C #### C QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 70% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ? options: A)1/7 m B)1/3 m C)1/4 m D)1/5 m E)1/6 m SOLUTION:After the final transaction: Angela received $(m-n) for t hours; Linda received $(m+n) for 1.5t hours; We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/7. Answer: A. #### A QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)*100}=4% Answer is A. #### A QUESTION:Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat? options: A)3! B)8! C)11! D)12! E)14! SOLUTION:Ans.(A) Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways #### A QUESTION:If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ? options: A)3653 B)3657 C)2977 D)3957 E)2711 SOLUTION:Explanation: Given : Letter : T I E R B A N Code : 7 1 9 3 2 4 5 Thus, the code for RENT is 3957. ANSWER:D #### D QUESTION:30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years? options: A)15% B)20% C)80% D)70% E)90% SOLUTION:Explanation : Let number of men = 100. Then, 80 men are less than or equal to 50 years old i.e 20 men are greater than 50 years of age. Now, the number of men above 50 years who play football = 20% of 20 = 4. 20% of all men play football i.e total no. of men who play football = 20, out of which 4 men are above 50 years old. So, 20 - 4 = 16 men are less than or equal to 50 years old. Therefore, percentage of football players less than or equal to 50 years = (16/20) x 100 = 80% . Answer : C #### C QUESTION:A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers? options: A)5hr B)6hr 30min C)8hr 10min D)7hr E)9hr SOLUTION:speed of man = 20km/hr number of rests = (120/30)-1 = 3 time taken for the man = (120/20)+3*(20/60) = 7 hr Answer is D #### D QUESTION:Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 35.1 kg of zinc has been consumed in it? options: A)78 kg B)60 kg C)64 kg D)70 kg E)None SOLUTION:Sol. For 9 kg Zinc, mixture melted = (9+11) kg. For 35.1 kg Zinc, mixture, melted = [20/9 x 35.1] kg = 78 kg. Answer A #### A QUESTION:What is value of (P + Q)/(P - Q) if P/Q = 7 ? options: A)1/3 B)2/3 C)4/3 D)5/3 E)None of these SOLUTION:Explanation: (P + Q)/(P - Q) = (P/Q+1)/(P/Q - 1) = (7 +1)/(7 - 1) = 4/3. Answer: C #### C QUESTION:While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? options: A)1/2 B)17/36 C)190/827 D)11/36 E)25/216 SOLUTION:Probability of winning game = 1- Probability of losing game Probability of losing game = (Probability of not getting sum 7 in any of the three attempts) Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways Total ways of getting outcome on two dice =6*6=36 Probability of getting sum as 10 in any attempt =3/36=1/12 Probability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12 Probability of losing game =(11/12)*(11/12)*(11/12)=637/827 I.e. Probability of wining game = 1-(637/827) = 190/827 Answer : Option C #### C QUESTION:Each of 435 bags contains at least one of the following three items: coconut, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only coconut and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item? options: A)256 B)260 C)316 D)320 E)350 SOLUTION:Fill the diagram step by step: coconut, almonds, and peanuts.PNGAlso given that there are total of 435 bags and 210 bags contain almonds. From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320. Answer: D. #### D QUESTION:Two cars start at the same time from opposite ends of a highway that is 333 miles long. One car is riding at 54 mph and the second car is riding at 57 mph. How long after they begin will they meet? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:As cars are moving in opposite directions their speeds will be added. So their relative speeds: 57+54 = 111 mph Total distance to be covered = 333 miles. Time taken would be: 333 miles/111 mph = 3 hours C is the answer. #### C QUESTION:Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 10x boxes? options: A)13 minutes B)14 minutes C)15 minutes D)16 minutes E)20 minutes SOLUTION:Rate = Work / Time Given Rate of Machine A = X / 10 min Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min . Rate of Machine B = 4x / 10 we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates let's first find the combined Rate of Machine A and B Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10 Now combine Time = combine work needs to be done / Combine Rate = 10x/5x * 10 = 6 Min Ans: E #### E QUESTION:Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is options: A)2 : 3 B)4 : 3 C)6 : 7 D)9 : 16 E)None SOLUTION:Sol. Let us name the trains as A and B. Then, (A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3. Answer B #### B QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? options: A)26 B)39 C)42 D)65 E)156 SOLUTION:Here 156 has three two's two three's and one 13 rest of them must be in w so w= 13*3*4 = 156 Answer: E #### E QUESTION:If f(a)=5b, what is the value of (f(a)-f(6b)) ? options: A)32b B)25b C)6a-6b D)3a+2b E)52a SOLUTION:f(a)=5b f(6b) = 30b (f(6b)-f(a)) = 30b-5b = 25b Answer is B #### B QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point? options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west SOLUTION:she is currently at 5km north east from the starting point ANSWER:A #### A QUESTION:100 identical coins each with probability 'pp' showing up heads & tossed. options: A)13/101 B)11/101 C)51/101 D)53/102 E)54/101 SOLUTION:Let aa be the number of coins showing heads Then, P(A=50)=P(A=51)P(A=50)=P(A=51) ⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101 C #### C QUESTION:A shop owner sells 56 apples and gains SP of 16 apples. Find the gain %? options: A)30% B)40% C)50% D)56% E)78% SOLUTION:Gain=16 apples Total 56 apples CP 56-16=40 (16/40)*100 =40% Ans B #### B QUESTION:1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now? options: A)76 days B)98 days C)32 days D)45 days E)24 days SOLUTION:1600 ---- 28 days 1600 ---- 24 1200 ---- ? 1600*24 = 1200*x x = 32 days Answer: C #### C QUESTION:In three annual examinations, of which the aggregate marks of each was 500, a student secured average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 70% average total marks, it is necessary for him in third yearly examination to secure marks : options: A)300 B)350 C)400 D)450 E)550 SOLUTION:total marks:1500 for three exams 70% of 1500=1050 first exam marks=45% of 500=225 second exam marks=55% of 500=275 let X be the third exam marks 225 + 275 + X =1050 X=550 ANSWER:E #### E QUESTION:Pavan travelled for 15 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:Amy has two decks of 54 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack? options: A)1/6 B)1/8 C)1/9 D)1/10 E)1/12 SOLUTION:Your solution is correct answer should be 1/12. E #### E QUESTION:If 125(5^y) = 1 then y= options: A)–2 B)–1 C)0 D)1 E)-3 SOLUTION:5^x = 1/125 5^x = 1/5^3 5^x= 5^-3 x = -3 E #### E QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A QUESTION:At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day? options: A) 100 B) 1,800 C) 1,090 D) 200 E) 1,000 SOLUTION:Let the total number of sunlasses produced be x % of high quality sunglasses = 70% % of low quality sunglasses = 25% % of sunglasses defective = 100% - 95% = 5% But this number is given as 50 so 5% of x = 50 and x = (50)(100/5)) x = 180 Therefore there a total of 1,000 sunglasses made per day. Correct answer - E #### E QUESTION:Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought? options: A)20 B)18 C)24 D)26 E)28 SOLUTION:Smallest gumballs = (19-16) + (19-14) +19= 27 Largest gumballs = (25-16) + (25-14) +25= 45 Difference = 45 - 27 = 18 B #### B QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it? options: A)12 days B)18 days C)15 days D)21 days E)22 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/10 work in 1 day B alone can do (1/6 -1/10) =1/15 work in 1 day => complete work can be done in 15 days by B Answer: Option C #### C QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job? options: A)6 B)13 1⁄2 C)17 D)Data inadequate E)None of these SOLUTION:12 M × 18 = 12 W × 18 × 3/1 \ w = 1/3 M 10M + 8W = 10M + 8 × 1/3M = 12 2/3 M \12 2/3 men can complete the same work in 12×18/12 2/3=17days Answer C #### C QUESTION:The following sets each have a mean of 10 and the standard deviations are given in variable form. Set I = {7, 8, 9, 11, 12, 13}, standard deviation = P Set II = {6, 6, 6, 14, 14, 14}, standard deviation = Q Set III = {10, 10, 10, 10, 10, 10}, standard deviation = R Rank these three standard deviations from least to greatest. options: A)P, Q, R B)P, R, Q C)Q, P, R D)Q, R, P E)R, P, Q SOLUTION:SD is minimum when the terms are closer to the mean. In set 3, we have all terms equal to mean. hence, its SD is 0.(The Lowest) Comparing Set 1 and Set 2, Set 1 has terms more closer to mean than set 3. hence, Set 3 Sd is the highest. So, Answer is E #### E QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)15 bukets B)17 bukets C)18 bukets D)19 bukets E)None of these SOLUTION:Explanation: Capacity of the tank = (12*13.5) litres = 162 litres Capacity of each bucket = 9 litres. So we can get answer by dividing total capacity of tank by total capacity of bucket. Number of buckets needed = (162/9) = 18 buckets Option C #### C QUESTION:Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)33/7 sec D)21/7 sec E)32/7 sec SOLUTION:B 20/7 sec They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps. The time required = d/s = 100/35 = 20/7 sec. #### B QUESTION:In how many different ways can the letters of the word ‘INDIGO’ be arranged ? options: A)420 B)520 C)620 D)720 E)820 SOLUTION:D 720 Required number of arrangements = 6! = 720 #### D QUESTION:. A car covers a distance of 390 km in 4 hours. Find its speed? options: A)104 B)55 C)66 D)98 E)100 SOLUTION:390/4 = 98 kmph Answer: D #### D QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is? options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5 SOLUTION:3:1 Answer:B #### B QUESTION:A man buys milk at 6 per litre and adds one third of water to it and sells mixture at 7.20 per litre. The gain is options: A)40% B)80% C)60% D)25% E)None of these SOLUTION:C.P. of one litre = 6 After adding water to it One has to pay 7.20 for 2⁄3 litre of milk. So S.P. of 2⁄3 litre of milk = 7.20 ⇒ S.P. of 1 litre of milk = 7.20×3/2=10.80 ∵ S.P. > C.P. Hence gain = 10.80−6/6×100=4.80/6×100 = 0.80 × 100 = 80% Answer B #### B QUESTION:A train is moving at a speed of 132 km/hr. If the length of the train is 200 meters, how long will it take to cross a railway platform 295 meters long options: A)6 ½ sec B)7 ½ sec C)8 sec D)13 ½ sec E)9 sec SOLUTION:Explanation: Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec. Distance covered in passing the platform = (200 + 295) m = 495 m. Time taken =495 ×(3/110) sec =27/2 sec = 13 ½ sec Answer: Option D #### D QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age? options: A)22 B)15 C)77 D)21 E)182 SOLUTION:Present age is 4x and 3x, => 4x + 6 = 34 => x = 7 So Deepak age is = 3(7) = 21 Answer: D #### D QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs.7500 B)Rs.7502 C)Rs.7529 D)Rs.7596 E)Rs.7506 SOLUTION:A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs.7500. Answer:A #### A QUESTION:A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 860 D)Rs. 1040 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 1300 = 80/100 * 1300 = 1040 Option D #### D QUESTION:Horse started to chase a dog as it relived stable two hours ago. And horse started to ran with average speed of 22kmph, horse crossed 10 meters road and two ponds with depth 3 meters and it crossed 2 small streets with 200 meters length. After travelling 6 hours, 2 hours after the sunset it got dog. Compute the speed of dog? options: A)16.5 kmph B)16.6 kmph C)16.4 kmph D)16.9 kmph E)16.2 kmph SOLUTION:In an average speed of 22 kmph horse got dog in 6 hours So distance=speed*time distance=22*6=132km Dog takes 8 hours to travel 132 km. So the speed if dog is speed=distance/time speed=132/8=16.5 kmph Answer: 16.5 kmph Answer A #### A QUESTION:If 4-X < (2+5X)/3, which of the following is correct? options: A)X < -5. B)X > -5. C)X > 5/4. D)-5 < X < 0. E)0 < X < 5. SOLUTION:4-X < (2+5X)/3 12-3X < 2+ 5X 10 < 8X 10/8<X 5/4<X C is the answer #### C QUESTION:What is the smallest positive integer x, such that 1944x is a perfect cube? options: A)4 B)3 C)8 D)12 E)18 SOLUTION:Take out the factors of 1944 that will come 2^3*3^3 *3^2. for perfect cube you need every no. raise to the power 3. for 1944 to be a perfect cube, need 1 3 that means =3 B is the answer. #### B QUESTION:A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? options: A)15 kmph B)10 kmph C)12 kmph D)12.5 kmph E)None of these SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. ANSWER:D #### D QUESTION:Magnabulk Corp sells boxes holding i magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate? options: A)100bi/m B)bi/(100m) C)100bi/m D)m/(bi) E)bi/m SOLUTION:We're given some facts to work with: 1) Magnabulk Corp sells boxes holding I magnets each. 2) The boxes are shipped in crates, each holding B boxes. 3) Magnabulk charges M DOLLARS for each crate We're asked for the price charged per magnet, in CENTS.... IF.... I = 2 B = 3 M = 12 (2 magnets per crate)(3 crates) = 6 magnets $12 for 6 magnets = $2 per magnet = 200 cents per magnet So we're looking for an answer that equals 200 when I=2, B=3 and M=12. There's only one answer that matches... Answer is C #### C QUESTION:If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)? options: A)85/365∗84/364 B)13/65∗13/64 C)1 - 85!/365! D)1 - {365!}/{280!(365^8^5)} E)1 - 85!/(365^8^5) SOLUTION:Probability(At Least 2 share a bday) = 1 - Probability(All 85 have distinct birthdays) total ways to pick 85 birthdays = 365^85 Ways to pick distinct 85 out of the 365 & distribute it to 85 people = C(365,85)*85! Hence Probability = 1−365!/280!36585 ANswer is D #### D QUESTION:A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work? options: A)20days B)15days C)30days D)45days E)50days SOLUTION:10days work of A = 10/40 = 1/4 remaining work = 1-1/4 = 3/4 B can finish 3/4 work = 60*3/4 = 45days Answer is D #### D QUESTION:Set R has a mean of 12 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? options: A){15, 16} B){3, 4} C){6, 7} D){5, 6} E){11, 13} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 12,the values (11,13) are closer than others. Hence Answer : E #### E QUESTION:A red ant is sitting on one side of a table (point X) and a black ant is sitting on the opposite side of the table (point Y). Now both of them decides to exchange their places and starts crawling. On the way, both of the ants meet and after that, it takes 20 seconds for the Red ant to move to point Y and it takes 5 seconds for the Black ant to reach point X. Find out the total time taken by the Red and the Black ant to make the journey. options: A)30 and 15 seconds B)10 and 15 seconds C)20 and 15 seconds D)25 and 15 seconds E)5 and 15 seconds SOLUTION:Solution: Let the speed of red ant be R. Speed of Black ant be B. Time at which they cross their paths be T. Now we will apply the basic formula of distance Distance = Speed * Time The Red ant travels R * T distance before meeting and R * 20 after meeting. The Black ant travels B * T distance before meeting and B * 5 after meeting. Now as per the question, The distance traveled by red ant before they both meet will be equal to the distance covered by black ant after they meet. We can say the same for the vice versa case as well. Thus R * T = B * 5 and B * T = R * 20 Using both the quations T = 10 Thus the red ant will require 10 + 20 = 30 seconds to travel the distance. And the black ant will take 10 + 5 = 15 seconds to travel the distance. Answer A #### A QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A QUESTION:A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.8% on their total annual charges made on the credit card, then what was the customer's annual charge? options: A)$40,000 B)$45,000 C)$50,000 D)$55,000 E)$60,000 SOLUTION:The customer receives $75 for the first $5000. The customer receives $125 for the next $5000. Let x be the total amount of the customer's annual charge. $200 + 0.03(x-10,000)=0.028x 0.002x=100 x=50,000 The answer is C. #### C QUESTION:The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy? options: A)7 B)9 C)11 D)13 E)14 SOLUTION:Explanation: 3x + 5x + 7x = 45 x =3 3x = 9 B) #### B QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:In order to obtain an income of Rs. 580 from 15% stock at Rs. 100, one must make an investment of options: A)5363 B)6240 C)8700 D)5600 E)2732 SOLUTION:To obtain Rs. 10, investment = Rs. 100. To obtain Rs. 580, investment = = Rs. 8700. Answer: C #### C QUESTION:In a dairy farm, 20 cows eat 20 bags of husk in 20 days. In how many days one cow will eat one bag of husk? options: A)1 B)40 C)20 D)26 E)30 SOLUTION:Explanation : One bag of husk = 20 cows per day ⇒ 20 × 1 × 20 = 1 × 20 × x For one cow = 20 days Answer : C #### C QUESTION:Which of the following can be expressed as a terminating decimal? options: A)1/25 + 1/35 B)1/225 + 1/1,250 C)1/11,000 + 1/13,000 D)1/75 + 1/35 E)1/125 + 1/8 SOLUTION:In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first. A. 1/25 + 1/35 = 12/175 = 12/25*1/7 1/7 does is not a terminating decimal. E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000 This is a terminating decimal and our answer. Correct Option: E #### E QUESTION:A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? options: A)10.18 p.m B)10.29 p.m C)10.30 p.m D)10.38 p.m E)10.32 p.m SOLUTION:D = 70 * 1 ½ = 105 km RS = 85 – 70 = 15 T = 105/15 = 7 h 3.30 + 7 h = 10.30 p.m. Answer:C #### C QUESTION:The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 13 percent, what was the annual interest rate last year? options: A)1% B)1.1% C)9.1% D)11.81% E)11.50% SOLUTION:13=1.1*x X=11.81% Answer D) #### D QUESTION:One of the following numbers can be marked out as the odd one out. can you find which one? 1) 680986879 2) 716089780 3) 820670987 4) 932967879 options: A)The odd number is 680986879 B)The odd number is 820670987 C)The odd number is 716089780 D)The odd number is 932967879 E)None SOLUTION:Correct Answer : B if you add up the first three digits of all the numbers, it adds up to 14 except for second option 820670987 #### B QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest? options: A)49% B)90% C)60% D)40% E)41% SOLUTION:8 = (1*20*R)/100 R = 40% Answer:D #### D QUESTION:if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no. options: A)24 B)25 C)26 D)27 E)28 SOLUTION:25 m^3 = (3+1)(3+1) = 16 then m^4 = (4+1)(4+1)=25 ANSWER:B #### B QUESTION:A fruit drink is made of orange, watermelon, and grape juice, where 25 percent of the drink is orange juice and 40 percent is watermelon juice. If the drink is made with 105 ounces of grape juice, how many ounces is the drink total? options: A)220 B)250 C)280 D)300 E)340 SOLUTION:Let the total number of ounces in the drink be x. % of orange = 25% % of watermelon = 40% % of grape = 100% - 65% = 35% 0.35x = 105 x = 300 Therefore there are a total of 300 ounces in the drink. The answer is D. #### D QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used? options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7 SOLUTION:Rate of machine R =1/50 Rate of machine S =1/20 since same no of machines used for R and S to do the same work in 5 hrs So collective rate needed to finish the work in 5 hrs= 1/5 Let the no of machine be x So, x/50 +x/20 =1/5 (2x+5x)/100=1/5 7x=20 x=20/7 So no of machine R is 20/7 Answer E #### E <<<Examples ends QUESTION:The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is? options: A)235 B)240 C)245 D)250 E)255 SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec. Time = 30 sec Let the length of bridge be x meters. Then, (130 + x)/30 = 25/2 x = 245 m. Answer: Option C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)277 B)277 C)120 D)882 E)272 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:What approximate value should come in place of the question mark (?). 36.0001 ÷ 5.9998 × √? = 108.0005 options: A)325 B)316 C)256 D)16 E)18 SOLUTION:Using approximation, we get 36⁄6 × √? = 108 or, √? = 108⁄6 or, √? = 18 or, ? = 324 ≈ 325 Answer E #### E QUESTION:Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? options: A)5 B)3 C)4 D)6 E)1 SOLUTION:Rate of one machine = 1 job / (20*4) days let X = number of machines needed to complete the job in 10 days 1/(4*20) * 10 * X = 1 job X = 8 8-4= 4 ANSWER: C #### C QUESTION:The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday? options: A)1,159 B)1,333 C)1,860 D)2,160 E)2,272 SOLUTION:The question states that all these 4,999 locations were measured twice, once on each day. It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W. Therefore, we can write two equations: For each of the first and second day count of locations, T + W = 4999 But, for the second day count, W = 1.20 T i.e. for Second day count, T + 1.20T = 4999 i.e. 2.20 T = 4999 i.e. T = 2272 E #### E QUESTION:The sum of three consecutive odd natural numbers, each divisible by 3 is 90. What is the largest among them? options: A)21 B)24 C)27 D)33 E)45 SOLUTION:Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6 Given, X + X+3 + X+6 = 90 3X = 81 X = 27 The numbers are 27, 30, 33 Therefore the largest number is 33 Answer D. #### D QUESTION:What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? options: A)s.2.04 B)s.2.08 C)s.3.67 D)s.2.83 E)s.2.42 SOLUTION:C.I. when interest is compounded yearly = [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100] = 9000 * 26/25 * 51/50 = Rs. 9547.2 C.I. when interest is compounded half-yearly = [9000 * (1 + 2/100)2] = (9000 * 51/50 * 51/50 * 51/50) = Rs. 9550.87 Difference = (9550.87 - 9547.2) = Rs.3.67. Answer: C #### C QUESTION:A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 m B)200 m C)240 m D)320 m E)450 m SOLUTION:Sol. Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x metres. Then, x + 300 / 50 = 15 ⇔ x + 300 = 750 ⇔ x = 450 m. Answer E #### E QUESTION:The sale price sarees listed for Rs.150 after successive discount is 20% and 10% is? options: A)187 B)120 C)108 D)178 E)175 SOLUTION:150*(80/100)*(90/100) = 108 Answer:C #### C QUESTION:A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass? options: A)6 B)8 C)10 D)12 E)16 SOLUTION:1)If the two sides are co-prime, SUM of sides -1.. 2)and if not co-prime , Sum of sides - HCF of sides.. the difference is related to the diagonal passing through a vertex of squares at some place.. here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12 ANSWER:D #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? options: A)150 meter B)299 meter C)666 meter D)155 meter E)144 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer: A #### A QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)2.5 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 + x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 Answer:E #### E QUESTION:As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found? options: A)14 B)18 C)15 D)10 E)20 SOLUTION:E 20 If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14. #### A QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.64.50 per Kg? options: A)3 : 1 B)3 : 2 C)4 : 3 D)5 : 3 E)None SOLUTION:Required ratio = 750 : 250 = 3 : 1 Answer A #### A QUESTION:1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus? options: A)98 B)99 C)97 D)96 E)95 SOLUTION:Let x be the no of initial passenger no of passengr left in 1st stop (2x/3)+30 no of passenger in the 2nd stop 3/4((2x/3)+30) + 12 which is equal to 84 (passngr on last stop) so final eqn....3/4((2x/3)+30) + 12 = 84 Ans x = 99 ANSWER:B #### B QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 16 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)128% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,16 = 16/100 x= 80*16/100 x= 12.8 12.8/10 = 1,28 = 128%, Answer E #### E QUESTION:The number 0.8 is how much greater than 1/2 ? options: A)½ B)3/10 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .8-1/2=x 8/10-1/2=x x= 3/10 ans B #### B QUESTION:On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price Q per glass on the second day? options: A) $015 B) $0.20 C) $0.30 D) $0.40 E) $0.45 SOLUTION:On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade; On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade; So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3. We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day. Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4. Answer: D. #### D QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l * l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:V and B are integers. The expression (V+1)(B+1) is even. What can be said about V and B? options: A)They are both even numbers. B)At least one of them is even. C)At least one of them is odd. D)They are both odd. E)Nothing can be said surly on V and B SOLUTION:Odd x Odd = Odd Odd x Even = Even Even x Even = Even To fulfill condition Either (V+1) or (B+1) needs to be Even So either V or B needs to be odd Or At least one of them is odd. At least one of them is odd=C #### C QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:A reduction of 5% in the price of sugar enables a lady to obtain 5kgs more for Rs.500, find the original price per kg? options: A)5.26 B)5.0 C)5.52 D)6.2 E)5.8 SOLUTION:Answer: 500*(5/100) = 25 --- 5 ? --- 1 => Rs.5 500 --- 475 ? --- 5 => Rs.5.26.Answer: A #### A QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4? options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1 SOLUTION:Solving for y/x gives, 1/17 (C) #### C QUESTION:If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are the W odds that x^2+y^2>1? options: A)1. pi/4 B)2. W=pi/16 C)3. W=1-pi/4 D)4. W=1-pi/16 E)5.4-pi SOLUTION:area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi. then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1) total outcomes = 4 therefore probability = (4-pi)/4 C #### C QUESTION:The value of Underrot 32pi/4 + Underrot 25 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question) options: A)6 B)35 C)41 D)30 E)23 SOLUTION:Under root (32pi/4) ~ 25 Under root (25) = 5 Hence, 25+5 = 30 is the approx answer. D is the correct answer. #### D QUESTION:Marie has 248 $ in her account of the bank. She has to buy presents for her 7 children and wants to distribute the money fairly. How much he will once have the money shared fairly? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(248$ / 7children) = 35.42 Took the lowest number = 35 * 7 children = $245 $248 - $245 = staying $3 Correct option: C) 3$ #### C QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20 SOLUTION:Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(30-10) = 10 kmph => Rate in still water = 1/2(30+10) = 20 kmph Option E #### E QUESTION:If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? options: A)26 B)39 C)42 D)65 E)156 SOLUTION:Here 156 has three two's two three's and one 13 rest of them must be in w so w= 13*3*4 = 156 Answer: E #### E QUESTION:a dealer buys 4 varieties of wheat costing rs. 20,rs.25,rs.30 and rs.35 per kg in the ratio 6:4:3:1 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of wheat? options: A)30.5 B)31.0 C)32.0 D)33.0 E)34.5 SOLUTION:CP = 20*6+25*4+30*3+35*1=345 SP = 1.4*345=483 Total no.of kgs=6+4+3+1=14 SP per kg=483/14 = 34.50 ANSWER:E #### E QUESTION:A man can row upstream at 29km/hr and down stream at 15km/hr find mans rate of the current ? options: A)9.8km/hr B)3.6km/hr C)8.9km/hr D)7km/hr E)5.9km/hr SOLUTION:given upstream(u) =29km/hr down stream (v)= 15km/hr rate of the current =1/2(u-v) =1/2(29-15)=7km/hr Answer is (D) #### D QUESTION:The fourth proportional to 14, 22 and 28 is? options: A)21 B)66 C)88 D)99 E)44 SOLUTION:(22*28)/14 = 44 Answer: E #### E QUESTION:If a certain number X is divided by 62, the reminder is 7. what is the reminder when X+11 is divided by 31? options: A)3 B)5 C)18 D)6 E)8 SOLUTION:X can be written as 62K + 7 or X = 7,69,131,etc. X + 11 = 62K + 7+11= 62K +18 or X + 11 = 18,80,142 etc. When divided by 31, we will get the remainder 18. C #### C QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? options: A)230 m B)210 m C)260 m D)320 m E)330 m SOLUTION:Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B #### B QUESTION:In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000 options: A)3336,1667 B)3339,1667 C)3333,1666 D)3333,1668 E)3333,1669 SOLUTION:they invested in the ratio 1:2 a's share =1/3*5000=1666 b's share=2/3*5000=3333 ANSWER:C #### C QUESTION:The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area? options: A)298 B)148 C)289 D)987 E)282 SOLUTION:2(4*5 + 5*6 + 4*6) = 148 Answer:B #### B QUESTION:In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase? options: A)16.67% B)25% C)20.45% D)31.56% E)40% SOLUTION:Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67% Answer is A #### A QUESTION:What is the leastvalue of x. So that 23x57 is divisible by 3? options: A)3 B)4 C)1 D)5 E)6 SOLUTION:The sum of the digits of the number is divisible by 3, then the number is divisible by3. 2 + 3 + x + 5 + 7 = 17 + x Least value of x may be 1 Therefore 17 + 1 = 18 is divisible by 3. C #### C QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘POWER’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word ‘POWER’ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 5*4*3*2*1 = 120 ANSWER:E #### E QUESTION:Josh spends a total of $5.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following? options: A)99 B)100 C)101 D)109 E)140 SOLUTION:Let x be the number of single bubblegums and y be the number of bubblegum pack. then 5x+50y=550 or x+10y=110 or x=110-10y Now, let y=0, then x= 110 and N=x+y or N=0+110 =110. let y=1, then x=100 and N=100+1= 101 (given in the options) let y=2, then x= 90 and N=92 the value will further decrease and hence we do not need to calculate anymore values. ANSWER:- C #### C QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? options: A)7/11 B)6/7 C)1/5 D)2/7 E)None of these SOLUTION:Explanation : Let, the vessel initially contains 8 litres of liquid. Let x litres of this liquid be replaced with water then quantity of water in new mixture =>3−(3x/8)+x litres. Quantity of syrup in new mixture =5−5x/8 litres. Therefore, =>3−(3x/8)+x=5−5x/8. =>5x+24=40−5x. =>x=8/5. So part of the mixture replaced, =>(8/5)×(1/8)=1/5. Answer : C #### C QUESTION:Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 7 hours? options: A)675 B)750 C)1,800 D)5,900 E)1,575 SOLUTION:8 machines/ 360 cans = 5 machines/ x cans 8x= 1800 x=225 (225)(7 hours)= 1575 cans. The answer is E. #### E QUESTION:Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit? options: A)1% B)2% C)3% D)4% E)5% SOLUTION:A dozen toys cost $360, so each toy cost $30. selling price / cost price = 30.60 / 30 = 1.02 The percentage profit is 2%. The answer is B. #### B QUESTION:One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ? options: A)Rs. 130,000 B)Rs. 150,000 C)Rs. 160,000 D)Rs. 140,000 E)None SOLUTION:EXPLANATION Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then, 1/3x=1/2(350000-x) => x/3 + x/2 = 175000 => 5x/6 = 175000 => x= 175000 x 6 /5= 210000 Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000 Answer D #### D QUESTION:The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers? options: A)1500 B)1600 C)1400 D)1200 E)1000 SOLUTION:Sum of first n even numbers = n(n+1) =1640 Sum of first n odd numbers = n^2 = 40*40 = 1600 (here n=40) Answer : B #### B QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1232? options: A)1000 B)2217 C)1100 D)2777 E)2991 SOLUTION:1232 = P [1 + (5*12/5)/100] P= 1100 Answer: C #### C QUESTION:A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 6 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A? options: A)45 B)65 C)75 D)78 E)90 SOLUTION:A + B + C = 3 *84 = 252 A + B + C + D = 4 * 80 = 320 ---- (i) So, D = 68& E = 68 + 6 = 74 B + C + D +E = 79 * 4 = 316 --- (ii) From Eq. (i) & (ii) A-E = 320 – 316 = 4 A = E +4 = 74 + 4 = 78 D #### D QUESTION:A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle? options: A)96 km B)100 km C)106 km D)116 km E)126 km SOLUTION:Distance covered in first two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in next two hours = 14 × 2 = 48 km Distance covered in first six hours 20 + 24 + 48 = 92 km Remaining distance = 8 km 92 + 8 = 100 km Answer B #### B QUESTION:Find the value of x which satisfies the relation Log10 3+log10 (4x+1)=log10 (x+1)+1 options: A)2.5 B)3.5 C)3.2 D)6.8 E)9.8 SOLUTION:[log10a + log10b = log10 ab] and also 1 can be written as log10 10, so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)), this can be solved to get 12x+3=10x+10, that gives x=7/2=3.5 ANSWER:B #### B QUESTION:The number which exceeds 16% of it by 63 is : options: A)75 B)52 C)58 D)60 E)62 SOLUTION:Solution Solution Let the number be x. x-16% of x =63 x-16/100x =63 x-4/25x=63 21/25x=63 x=(63x25/21)= 75 Answer A #### A QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 19.7%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)26% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 19.70 Let marked price be Rs. x. Then, 95/100 x = 119.70 x = 11970/95 = Rs. 126 Now, S.P. = Rs. 126, C.P. = Rs. 100 Profit % = 26%. Answer: B #### B QUESTION:9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day? options: A)18 B)9 C)10 D)8 E)11 SOLUTION:We have, M1D1H1 = M2D2H2 So, 9*12*4= 6*D2*8 D2 = 9*12*4/6*8 = 9 ANSWER:B #### B QUESTION:A train 200 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)15 sec E)18 sec SOLUTION:Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec Time taken by the train to cross the man = Time taken by It to cover 200 m at 50/3 m / sec = 200 *3/ 50 sec = 12sec Answer : C #### C QUESTION:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 45min will be. options: A)60 km/h B)53 km/h C)40 km/h D)70 km/h E)65 km/h SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=S*T=48*5/6=40km time=45/60hr=3/4hr New speed = 40* 4/3 kmph= 53kmph Answer : B #### B QUESTION:A card is randomly drawn from a deck of 52 cards. What is the probability getting either a King or a Diamond? options: A)5/43 B)8/32 C)6/26 D)4/13 E)2/31 SOLUTION:Total number of cards = 52 Total Number of King Cards = 4 P(King) = 4/52 P(Diamond) = 13/52 P(King and Diamond) = 1/52 P(King or a Diamond) = P(King) + P(Diamond) – P(King and Diamond) =4/52+13/52–1/52=16/52=4/13 Answer D #### D QUESTION:How many numbers between 300 and 500 begin or end with 3? options: A)20 B)60 C)100 D)110 E)120 SOLUTION:How many numbers between 300 and 500 begin or end with 3? Just think that those numbers are: i) The ones ending in 3: 303, 313, 323, ... , 493 --> 20 numbers ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers BUT 10 out of the first 20 numbers are repeated in the second set. THEREFORE, the solution is 110 numbers. Answer: D #### D QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? options: A) 4 B) 2 C) 2 D) 10 E) 12 SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. Answer A #### A QUESTION:Seven years ago the average age of a family of 2 members was 25 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child? options: A)7 years B)5 years C)3 years D)8 years E)10 years SOLUTION:Explanation: Average of the family of two numbers 7 years ago = 25 = (25+ 7) * 2 = 64 years Average age of the family of three members at present = 23 years = 23 * 3 = 69 YEARS Age of child = 69 - 64 = 5 years Answer: Option B #### B QUESTION:In how many different number of ways a Committee of 4person of can be selected from 4boys and 4girls such that at least 1 girl is included in the committe options: A)70 B)69 C)67 D)68 E)65 SOLUTION:1G 3B 2G 2B 3G 1B 4G =(4C1*4C3)+(4C2*4C2)+(4C3*4C1)+4C4 = (4*4)+(6*6)+(4*4)+1 = 16+36+16+1=69 Total 4M 4W 8C4=70 4C4=1 At least one girl = total - with out girl At least one girl =70-1=69 B) #### B QUESTION:The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 20 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute? options: A)230/(30+10A) B)230/(30+60A) C)230/38A D)220/(30+10A) E)220/40A SOLUTION:Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution. Substitute A with 3.meaning tommy would have travelled a distance of ((160-20) + (160-70)) in 60 minutes. 230 Kms in 60 minutes ==> 3.8km/hr. Substitute A with 3 in the answer options. Option A #### A QUESTION:One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met? options: A)38.07 B)40 C)42 D)39 E)40.07 SOLUTION:Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows 9t + 8(t + 1) = 80 9t + 8t + 8 = 80 17t = 72 T = 4.23 (hours) Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A. #### A QUESTION:X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600: options: A)200 B)250 C)300 D)350 E)400 SOLUTION:X = Rs.5000/- Y = Rs.15000/- X share 1 part & Y share 3 parts Total 4 parts -----> Rs.1600/- ----> 1 part -------> Rs.400/- X share = 1 part -----> Rs.400/- E #### E QUESTION:A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is: options: A)19m B)17m C)15m D)16m E)20m SOLUTION:rectangular area = l × b = 120 and perimeter = 2(l+b) = 46 l+b = 23 (l-b)power2 - 4lb = (23)power2 - 4 × 120 = (529-480) = 49 = l-b = 7 l+b = 23, l-b = 7, we get l = 15, b = 8 Diagonal = √152+82 √225+64 => √289 = 17m Answer is B. #### B QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? options: A)7 B)10 C)8 D)12 E)15 SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C QUESTION:If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$60.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10 Total spent 50.50 + 10.10 = $60.60 correct answer B #### B QUESTION:Tom read a book containing 1000 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 15 pages a day more, how many days did Tom spend reading the book? options: A)20 B)18 C)16 D)15 E)15.39 SOLUTION:Actually u can set up 2 equation P--stands for the pages D--stands for the days 1) P*D=480 (we want to find the Days, soP=480/D) 2) (P+15)(D-5)=1000=> PD-5P+15D-75=1000 as the 1) stated u can put 1) into 2) => 1000-5P+15D-75=1000 => 15D-5P=75 put the bold one into it => 15D-5(480/D)=75the we get the final equation 16D^2-2400=80D (divide 16) => D^2-5D-160=0 so D=15.39days. Ans: (E) #### E QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are? options: A)11 B)18 C)99 D)77 E)51 SOLUTION:A:B = 2:3 B:C = 2:5 A:B:C = 4:6:15 6/25 * 75 = 18 Answer: B #### B QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? options: A)1227 B)2088 C)26788 D)8112 E)1871 SOLUTION:A = 7500(26/25)2 = 8112 Answer: D #### D QUESTION:Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)50 B)88 C)77 D)55 E)23 SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 46 - 36 = 10 km/hr. = 10 * 5/18 = 25/9 m/sec. 2x/36 = 25/9 => x = 50. Answer: A #### A QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is options: A)35 B)37 C)38 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 8) years. (x+8+10)=2(x—10) hence x=38. Present age of B = 38 years Answer: Option C #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. ANSWER:D #### D QUESTION:The number 0.650 is how much greater than 1/8 ? options: A)½ B)21/40 C)1/50 D)1/500 E)2/500 SOLUTION:let x be the difference then .65-1/8=x 65/100-1/8=x x=21/40 ans B #### B QUESTION:1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. options: A)$140 B)$125 C)$145 D)$135 E)$155 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 145. So after completing the 1st week she will get $ (x+145). Similarly after completing the 2nd week she will get $ (x + 145) + $ 145. = $ (x + 145 + 145) = $ (x + 290) So in this way end of every week her salary will increase by $ 145. ANSWER : OPTION C =$145 #### C QUESTION:A shopping mall give 40% sale on T-shirts and increase 25% price of pants. The cost price of pants and T-shirts are 1500 and 400 respectively. Overall they makes a? options: A)200 B)250 C)300 D)215 E)180 SOLUTION:Let the SP of the pants and T-shirts be Rs. p and Rs. t respectively. p = 1500(1 + 25/100) = 1500 + 375 t = 400(1 - 40/100) = 400 - 160 Total SP - Total CP = p + t - (1500 + 400) = 375 - 160 = Rs. 215 As this is positive, an overall profit of Rs. 500 was made. Answer: D #### D QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:14 To be divisible by three the sum of the digits must be divisible by 3. Highest number made by these digits is 75 that is divisible. We count down the selections from there and see what is feasible. 75-yes 72 -yes 69 and 66 -no 63 - yes 60 -no 57, 54, and 51 -yes 48 - no 45 and 42 - yes 39 - no 36 - yes 33 and 30 - no 27, 24, and 21 - yes 18 -no 15 and 12 yes Correct answer is E. #### E QUESTION:A bag contains 6 green jacks and 24 white jacks. One jack is drawn at random. What is the probability that the jack is white? options: A)3/4 B)4/5 C)7/8 D)1 E)None of these SOLUTION:Explanation: Total cases = 6 + 24 = 30 Favourable cases = 24 So probability = 24/30 = 4/5 Answer: A #### A QUESTION:If x and y are integers, what is the least positive number of 24x+9y? options: A)1 B)3 C)4 D)6 E)9 SOLUTION:24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1. 8(-1) + 3(3) = 1 Then 3(8x+3y) can have a minimum positive value of 3. The answer is B. #### B QUESTION:The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer? options: A)5 B)3 C)4 D)2 E)1 SOLUTION:Let the second integer be x and the fourth be a. Then [3x + x + (x+2) + a]/4 = 9 => 5x + 2 + a = 36 => 5x + a = 34 => a = 34 - 5x From the above equation we can see that a is minimum when x is maximum, provided both are positive The maximum value that x can take in the above equation while still keeping a positive is x=6 This gives us a= 34 - 30 = 4 Therefore the minimum value that the fourth integer can have is 4. Answer:C #### C QUESTION:If w<0, which of the following must be true? options: A)–100 < w < 100 B)w ≤ –1 C)w ≤ 1 D)w^2 ≥ 1/4 E)–100 < w < 0 SOLUTION:w is a negative number. A. –100 < w < 100w can be a negative number less than -100 B. w ≤ –1w can be a fraction, in which case it would be greater than -1 C. w ≤ 1must be true since 1 is positive and w is negative D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5 E. –100 < w < 0w can be a negative number less than -100=C #### C QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)299 B)277 C)266 D)992 E)188 SOLUTION:(800*3*3)/100 = 72 920 + 72 = 992 Answer:D #### D QUESTION:Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race? options: A)450 m B)680 m C)700 m D)900 m E)1000 m SOLUTION:Explanation: When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race ANSWER C #### C QUESTION:The average of eleven ten prime numbers which are odd is? options: A)17.72 B)18.52 C)19.63 D)16.53 E)15.63 SOLUTION:Explanation: Sum of first 11 prime no. which are odd = 195 Average = 195/11 = 17.72 Answer:A #### A QUESTION:Find compound interest on $ 8000 at 15% per annum for 2 years 4 months, compounded annually. options: A)3109 B)3209 C)3108 D)3107 E)3100 SOLUTION:Time = 2 years 4 months = 2(4/12) years = 2(1/3) years. Amount = $ [8000 X (1+­(15/100))2 X (1+((1/3)*15)/100)] =$ [8000 * (23/20) * (23/20) * (21/20)] = $ 11109. . :. C.I. = Rs. (11109 - 8000) = $ 3109. Answer A. #### A QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value W of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer W is 342. The correct answer is E. #### E QUESTION:If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? options: A)30 B)33 1/3 C)35 D)25 E)20 SOLUTION:100---150 150----50 100-----? ==>33 1/3 ANSWER B #### B QUESTION:If a truck is traveling at a constant rate of 54 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters) options: A)18 B)24 C)30 D)36 E)40 SOLUTION:Speed = 54 Km/hr => 54,000 m/hr In one minute => 54000/60 = 900 meters In one sec => 900/60 = 15 meters Time = Total distance need to be covered / Avg. speed => 600/ 15 =40 and hence the Answer : E #### E QUESTION:Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ? options: A)30 B)32 C)34 D)36 E)38 SOLUTION:First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 1*2*2*2*2*2 = 32 ANSWER:B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)200 B)220 C)240 D)250 E)260 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer: Option C #### C QUESTION:A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 18 km/hr. What is the length of the platform? options: A)80 B)240 C)288 D)277 E)221 SOLUTION:Speed = 18 * 5/18 = 5 m/sec. Length of the train =5 * 20 = 100 m. Let the length of the platform be x m . Then, (x + 100)/36 = 5 => x = 80 m. Answer: A #### A QUESTION:There are 9 people in the room. There are two pairs of siblings within that group. If we choose two people, what is the probability that they will not be siblings? options: A)12/18 B)17/18 C)2/9 D)1/18 E)4/18 SOLUTION:we have XXXXXBBCC We have to take into the account when we have XX, XB, XC So 5/9*4/8 5/9*2/8 and 5/9*2/8 note we need to multiply these by 2 (except the first) b/c we can have BX and CX. 20+20+20 --> 60/72 --> 30/36 --> 15/18 then next is BC 2/9*2/8 --> 4/72 2/36 1/18 --> multiply this by 2 b/c of CB so 2/18+15/18 --> 17/18 ANSWER:B #### B QUESTION:16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work? options: A)26.7 days B)77 days C)20 days D)88 days E)44 days SOLUTION:16 * 25 = 15 * x => x = 26.7 days Answer: A #### A QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:If x^2 + 1/x^2 = 9, what is the value of x^4 + 1/x^4 ? options: A)10 B)72 C)79 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 9 andSQUAREboth sides: (x² + 1/x²)²= 81 So, (x² + 1/x²)(x² + 1/x²) = 81 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 81 Simplify: x⁴ + 1/x⁴ = 79 Answer: C #### C QUESTION:The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n? options: A)w– 2n B)w–n + 1 C)w– 2(n– 1) D)n– 6 + w E)w – n/2 SOLUTION:Another method would be to use the concept of Arithmetic Progressions. Consecutive even integers form an AP where the common difference is 2. In an AP, Last term = First term + (n-1)*common difference w = First term + (n-1)*2 First term = w - 2(n-1) ANSWER:C #### C QUESTION:Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s amount. At the end of the year 10% profit was earned which was equal to 98,000. What was the amount invested by R? options: A)2,10,000 B)1,05,000 C)1,75,000 D)2,00,000 E)None of these SOLUTION:Ratio for amount invested by P, Q & R = 5x × 12 : 6x × 12 : 6x × 6 = 60x : 72x : 36x = 5x : 6x : 3x Profit = 98000 = 10% of T where, T = Total amount T = 980000 Amount received by R = 3x /3x+6x+5x(980000) = 210000 Answer A #### A QUESTION:A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B? options: A)1/3 B)2/9 C)9/46 D)7/19 E)1/6 SOLUTION:The first thing to notice is that A is faster than B and B is faster than C. Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work. If A works for 2 days, B works for 1 day and C works for only 2/3 of the day. Therefore total work done = (2*2) + (1*1) + (1/3*1/3) = 46/9 Proportion of work done by B = (1*1) / (46/9) = 9/46 Hence Answer C. #### C QUESTION:There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)315 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 7C2 Number of ways of selecting 2 non fiction books = 6C2 7C2 * 6C2 = 21 * 15 = 315 Answer: C #### C QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0 options: A)-1 B)1 C)2 D)3 E)4 SOLUTION:a = 3, b = 5, c = 2 x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6 x1 = (-5 + 1)/6 = -4/6 = -2/3 x2 = (-5 - 1)/6 = -6/6 = -1 A #### A QUESTION:calendar=52097083 november=538=8651 march=2*308 blue=7154 december=? options: A)9535&153 B)9585&153 C)9525&153 D)9525&*53 E)9525&*54 SOLUTION:from above in formation d=9 e=5 c=2 e=5 m=3 b=1 e=5 r=8 95253158( Order doesnot matter i guess!) another thing is &=8 for mathcing above ans ANSWER:C #### C QUESTION:Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option? options: A)1/2 B)1/6 C)1/12 D)6/10 E)3/10 SOLUTION:as coin has only two faces then probability must be 1/2 ANSWER:A #### A QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 5*60/60 = 5*1/1 = 5 New time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 3/3% C)33 1/3% D)39 1/3% E)33 4/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C? options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480 SOLUTION:Explanation : Amount of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400 Answer : Option D #### D QUESTION:Six cards numbered from 1 to 6 are placed in a cardboard box . First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 5 ? options: A)1/2 B)1/4 C)1/5 D)1/6 E)1/3 SOLUTION:(6,4) (4,6) (5,5) – only 3 possible scenarios for sum to be 10. One from this 5 has already happened. From this three cases, only in one we have 5. So, the probability is 1 chances out of 3 that the one that occurred had 5: P=1/3. Answer: E. #### E QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $8,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$61,500 B)$54,000 C)$21,000 D)$ 5,400 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 8200 less between 3 people(x-(8200*3))/3 Set both eq. equal to each other. 61,500 Answer A) #### A QUESTION:Two pipes P and Q can fill a cistern in 12 and 13 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? options: A)1/8 B)1/4 C)2/4 D)1/4 E)3/4 SOLUTION:3/12 + x/13 = 1 x= 7 3/4 Answer: E #### E QUESTION:A rectangular-shaped carpet that measures x feet by y feet is priced at $27. What is the cost of the carpet, in dollars per square yard? (1 square yard = 6 square feet) options: A)xy/297 B)11xy/3 C)3xy/11 D)297/(xy) E)162/(xy) SOLUTION:The area of the carpet in feet is xy. The area in square yards is xy / 6. The price per square yard is 27 / (xy/6) = 162/(xy). The answer is E. #### E QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? options: A)2 cm B)7 cm C)1 cm D)4 cm E)9 cm SOLUTION:Explanation: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer: Option E #### E QUESTION:Find the odd man out 2, 5, 14, 41, 122, 365, 1125 options: A)2 B)14 C)41 D)365 E)1125 SOLUTION:1*3-1 = 2 2*3-1 = 5 5*3-1 = 14 14*3-1 = 41 41*3-1 = 122 122*3-1= 365 365*3-1= 1094 ANSWER:E #### E QUESTION:In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? options: A)160 B)175 C)180 D)195 E)172 SOLUTION:Explanation: Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 x 8 x 4) = 160. Therefore, 160 x 2.40 + x x 3.20 = 432 => 3.20x = 432 - 384 = 48 => x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER IS B #### B QUESTION:If A : B = 4 : 9 and B : C = 5 : 9 then A : B : C is : options: A)20 : 35 : 63 B)35 : 36 : 63 C)30 : 35 : 65 D)20 :45: 81 E)None of these SOLUTION:Expl : A : B = 4 : 9 B : C = 5 :9 = 5*9/5 : 9 *9/5 = 9 : 81/5 A : B : C = 4 : 9 : 81/5 = 20 : 45 : 81 Answer: D #### D QUESTION:If 4x = 8^y, which of the following expresses x in terms of y? options: A)2^(y-2) B)2^(y-1) C)2^(3y-2) D)2^(2y-3) E)2^y SOLUTION:By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: C #### C QUESTION:A train crosses a platform in 15 sec, same train crosses another platform of length 250 m in 20 sec. If the speed of the train is 15 m/sec then find the length of the platform? options: A)277m B)180m C)165m D)278m E)175m SOLUTION:Length of the train be ‘X’ (X + 250)/20 = 15 X = 50m Let the length of the platform be y (y + 50)/15 = (50 + 250)/20 4y + 200 = 900 X = 1750m Answer: E #### E QUESTION:What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.? options: A)Rs. 8908.42 B)Rs. 9720 C)Rs. 10123.20 D)Rs. 10483.20 E)None SOLUTION:Amount = [22000 * (1 + 12/100)3] = 22000 * 28/25 * 28/25 * 28/25 = Rs. 30908.42 C.I. = (30908.42 - 22000) = Rs. 8908.42 ANSWER:A #### A QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 2050*5=10250 10250-10000=250 Answer E #### E QUESTION:A milk man has 30 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is: options: A)20% B)25% C)33.33% D)35% E)None of these SOLUTION:Explanation: when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 30 liters of milk. Therefore, profit percentage = 35 %. Answer: D #### D QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)2/215 B)3/155 C)1/216 D)2/213 E)3/212 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 * 2600 = Rs.1200 Answer: A #### A QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)3630 B)3637 C)3630 D)3631 E)3635 SOLUTION:6300:4200:10500 3:2:5 3/10 * 12100 = 3630 Answer: A #### A QUESTION:Narendra started a business, investing 45000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)A)Rs.7000 B)B)Rs.8000 C)C)Rs.8571 D)D)Rs.8600 E)E)Rs.8700 SOLUTION:The ratio of their investments = 45000 × 12 : 15000 × 6 = 6 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 6/7 = Rs.8571. C) #### C QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159 SOLUTION:46 + 28 + 10 = 84% 100 – 84 = 16% 850 * 16/100 = 136 Answer:A #### A <<<Examples ends QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 37 kmph. Of how many minutes does the train stop per hour? options: A)73 B)83 C)12 D)83 E)11 SOLUTION:Explanation: T = 8/45 * 60 = 11 Answer: Option E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:There are 35 students in a hostel. If the no. of students increases by 4, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)s. 99.75 B)s. 89.75 C)s. 72.75 D)s. 58.75 E)s. 49.75 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 4) = x – 1 or, 35x + 42 = 39x – 39 or, x = 20.25 Thus the original expenditure of the mess = 35 x 20.25=708.75 Therefore x-1 = 19.25 hence 42 x 19.25 = 808.50 808.50 - 708.75 = Rs. 99.75 A #### A QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? options: A)7/17 B)7/22 C)7/18 D)7/19 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ⁸C₂ ways. P = 7C2/¹15C2 + 8C2/15C2 = 7/15 Answer: E #### E QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)*100]%=50% Answer A) 50. #### A QUESTION:Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h options: A)20 seconds B)3 C)4 D)1 E)5 SOLUTION:swim in still water at = 3 speed of river= 1.4 US = 3 - 1.4= 1.6 Distance = 8 T = 8/1.6 = 5 Answer: E #### E QUESTION:a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles? options: A)0.76 B)0.86 C)0.96 D)1.16 E)1.26 SOLUTION:let the radius of circle is 'r' area of the circle which is at corner = (22/7*r^2)/4 hence the area of all four circles are = 22/7*r^2 areaof circle which is made on center of suare is = 22/7*r^2 total area of all circles are = 2*22/7*r^2...........................(1) if we construct the diagram we get the relation 4r = 2sqrt2 r = 1/sqrt2 put the value of r in eqn 1 and we get 2*22/7*1/2 = 22/7 = 3.14 area of suare = 2^2 = 4 area of remaining part = 4-3.14 = 0.86 ANSWER:B #### B QUESTION:The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D QUESTION:If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream options: A)1.5kmph B)0.5kmph C)0.4kmph D)1.6kmph E)2.5kmph SOLUTION:Speed upstream = 32/4 = 8 kmph Speed down stream = 72/8 = 9 kmph Speed of stream = ½ (9-8) = 0.5kmph ANSWER:B #### B QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is options: A)100 B)250 C)260 D)416 E)None of these SOLUTION:Explanation: Let the number of boys and girls be 8x and 5x. Total number of students = 13x = 13 × 32 = 416. Answer: D #### D QUESTION:A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings? options: A)12 B)13 C)46 D)37 E)26 SOLUTION:16x + 85 = 17(x + 3) x = 34 + 3 = 37 Answer: D #### D QUESTION:How many different ways can you select a pilot and a co pilot if you have 30 people to choose from? options: A) 870 B) 920 C) 1398 D) 4950 E) 9900 SOLUTION:You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot. So the answer is in a sense (30C2) x 2 = 870. Ans A #### A QUESTION:Find the unit's digit in the product 2467 153 * 34172? options: A)1 B)3 C)2 D)5 E)7 SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172 Now 7 4 gives unit digit 1 7 152 gives unit digit 1 7 153 gives 1*7=7.Also 172 gives 1 Hence unit's digit in the product =7*1=7. Option A #### A QUESTION:Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work? options: A)13 B)14 C)18 D)11 E)10 SOLUTION:(5 + x)/20 + 5/25 = 1 => x = 11 days Answer:D #### D QUESTION:3+33+333+33.33=? options: A)362.33 B)372.33 C)402.33 D)702 E)None of them SOLUTION:3 33 333 33.33 ---------- 402.33 ---------- Answer is C #### C QUESTION:The inverse ratio of 4: 2: 1 is? options: A)2:4:8 B)2:3:9 C)2:3:2 D)2:3:6 E)2:3:1 SOLUTION:1/4: 1/2: 1/1 = 2:4:8 Answer:A #### A QUESTION:If C.P. of 28 books is equal to S.P of 30 books , then your gain or loss is ? options: A)23 1/3 gain % B)30 10/23 loss % C)6.67 loss % D)30 1/3 loss % E)40 1/3 loss % SOLUTION:Say the cost price of 28 books is $28 so $1 for a book. The cost of 30 books would be $30, and the selling price of 30 books would be 28$, hence the loss = ($30 - $28)/$30 = ~6.67%. Answer: C. #### C QUESTION:The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers? options: A)12/35 B)1/35 C)35/8 D)7/32 E)7/33 SOLUTION:Let the numbers be a and b. Then, a + b = 12 and ab = 35. (a + b)/ab = 12/35 = (1/b + 1/a) = 12/35 Sum of reciprocals of given numbers = 12/35. ANSWER:A #### A QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value R of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer R is 342. The correct answer is E. #### E QUESTION:Two trains of length 120 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other? options: A)100/7 sec B)80/7 sec C)57/7 sec D)120/7 sec E)104/7 sec SOLUTION:Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps. The time required = d/s = (120 + 100 + 300)/35 = 520/35 = 104/7 sec. ANSWER:E #### E QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory? options: A)80.5 B)82 C)81.5 D)85 E)81.25 SOLUTION:Weighted mix method is best here.... Ratio is 1:10 for 88:80.5... So the answer required = 80.5+ (88-80.5)*1/10=80.5+7.5*1/10 80.5+0.75=81.25 E #### E QUESTION:If 4a = 16b and 8b = 13c, Find a:b:c? options: A)52:13:8 B)13:7:52 C)7:13:52 D)7:13:54 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (8b = 13c ==> b/c = 13/8) ==> a:b = 16:4 and b:c = 13:8 a:b:c = 52:13:8 Answer: Option A #### A QUESTION:Find the average of all prime numbers between 1 and 5. options: A)30 B)3.6 C)5.6 D)6.6 E)None SOLUTION:Sol. There are five prime numbers between 1 and 5. They are 2, 3, 5, 7, 11 ∴ Required average = [2 + 3+ 5+ 7+ 11 / 5] = 28/ 5 = 5.6 Answer C #### C QUESTION:3 workers transfer a tool weighing 120kg in 12 seconds. How many men are required to transfer it in 9 seconds? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:We have, M1D1H1 = M2D2H2 3*120*12 = M2*120*9 M2 = 3*120*12/120*9 = 4 ANSWER:A #### A QUESTION:There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to? options: A)7!*1! B)7!*2! C)6!*2! D)8!*2! E)6!*2! SOLUTION:Total number of ways = 7!*2!. B #### B QUESTION:What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58? options: A)Rs.3944 B)Rs.3948 C)Rs.3988 D)Rs.3949 E)Rs.3923 SOLUTION:Let the side of the square plot be a ft. a2 = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 * 58 = Rs.3944. Answer: A #### A QUESTION:If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a? options: A)2 B)1 C)3 D)7 E)9 SOLUTION:(a5,608 + 584)/88 = a6,192/88 Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 192/8 = 24 => So, we want divisible by 11. Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11. a619-2 => a61-7 => a5-4 => a1 => 11/11. So a = 1. Answer: B #### B QUESTION:Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? options: A)66 B)74 C)78 D)80 E)None of these SOLUTION:Explanation: Number of subjects = 6 Average of marks in 6 subjects = 74 Therefore total marks in 6 subjects = 74 * 6 = 444 Now, No. of subjects = 5 Total marks in 5 subjects = 74 * 5 = 370 Therefore marks in 6th subject = 444 – 370 = 74 ANSWER B #### B QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in? options: A)3 days B)5 days C)7 days D)11 days E)12 days SOLUTION:That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. A) #### A QUESTION:(112 x 54) = ? options: A)70000 B)71000 C)72000 D)73000 E)74000 SOLUTION:(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 A) #### A QUESTION:A person starting with Rs.64 and making 6 bets, wins 3times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is? options: A)Rs.37 B)Rs.45 C)Rs.47 D)Rs.53 E)Rs.59 SOLUTION:As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order). The overall resultant will remain same. So final amount with the person will be (in all cases): =64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727 Hence the final result is: 64−27=3764−27=37: A loss of Rs.37 A #### A QUESTION:The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square? options: A)277 B)268 C)287 D)480 E)281 SOLUTION:Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer:D #### D QUESTION:Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm. options: A)221 cm2 B)211 cm2 C)231 cm2 D)236 cm2 E)241 cm2 SOLUTION:Given: length = 17 cm, breadth = 13 cm Perimeter of rectangle = 2 (length + breadth) = 2 (17 + 13) cm = 2 × 30 cm = 60 cm We know that the area of rectangle = length × breadth = (17 × 13) cm22 = 221 cm2 ANSWER :A #### A QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job? options: A)4 days B)6 days C)8 days D)2 days E)9 days SOLUTION:Sandy can do 1/6 of the job each day. Molly can do 1/12 of the job each day. The combined rate is 1/6 + 1/12 = 1/4 of the job each day. The job will take 4 days. The answer is A. #### A QUESTION:Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $4,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money? options: A) 11,500 B) 24,500 C) 25,500 D) 26,500 E) 27,500 SOLUTION:OFFICIAL SOLUTION: The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 4,000), and Isabella’s are 0.10x. Set up the equation and solve: 550 + (0.08)(x – 4,000) = 0.10x Distribute the 0.08: 550 + 0.08x – 320 = 0.10x Combine terms and subtract 0.08x from both sides: 230 = 0.02x Divide both sides by 0.02: 11,500 = x Your answer is A. #### A QUESTION:In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum? options: A)1 1/4 B)1 1/6 C)1 1/0 D)1 1/5 E)1 5/1 SOLUTION:Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10% Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.Answer: A #### A QUESTION:A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? options: A)288 B)266 C)120 D)287 E)212 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:Total price of 5 packet milk=5*20=100 Total price of 3 packet milk=3*12=36 Total price of 2 packet returned milk=100-36=64 Average price of 2 packet milk=64/2=32 Correct option Answer:C #### C QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive? options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000 SOLUTION:There are 5 people inheriting the money. We have to take the total of the inheritance and divide it by 5 for each person receiving money. $527,500 / 5 = $105,500. Therefore the correct answer is D. #### D QUESTION:If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is options: A)48 km B)50 km C)40 km D)22 km E)70 km SOLUTION:B 50 km. Let the actual distance travelled be x km. Then x/10=(x+20)/14 --> 14x = 10x + 200 --> 4x = 200 --> x = 50 km. #### B QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 B)1 C)8 D)6 E)9 SOLUTION:100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer:D #### D QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/3*60/55 = 40 min D #### D QUESTION:If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1? options: A)a. 8 B)b. 9 C)c. 12 D)d. 7 E)e. 27 SOLUTION:Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30 We can write 30 as product of two numbers in following ways 1*30 2*15 3*10 5*6 4 cases = 4*2 i.e. 8 factors (including 1) Factors greater than 1 = 7 Answer: Option D #### D QUESTION:If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d. The sum of A + B = (10c+d)+(10d+c)=11(c+d). The only answer that is a multiple of 11 is 44. The answer is D. #### D QUESTION:The number of livestock in a farm at the beginning of year 2000 was 110,000. During the year, the number increased by p%. During the next year 2001, there was a famine and the number decreased by q%. A census at the end of year 2001 revealed that the number of livestock in the farm was 110,000. Which of the following expressions is correct? options: A)q>p B)p > q C)p = q D)With the exception of 1 instance, p will be equal to q E)There is no relation between p and q SOLUTION:Number plugging in will be best strategy for this question. Let p = 5%, Per the question 100000(1.05)(1-q/100) = 100000 ---> q = 4.7%. Thus p > q and hence B is the correct answer. #### B QUESTION:12.5 * 6.2 * 8.8 = ? options: A)352 B)435 C)224 D)682 E)742 SOLUTION:D 682 ? = 12.5 * 6.2 * 8.8 = 682 #### D QUESTION:A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income? options: A)Rs. 2000 B)Rs. 2010 C)Rs. 2100 D)Rs. 2200 E)Rs. 2300 SOLUTION:Total expenditure for the first 3 months = 3 × 1600 = 4800 Total expenditure for 4 months = 4 × 1550 = 6200 Total expenditure for 5 months = 5 × 1800 = 9000 Total expenditure and saving (which is income for one year) = 4800 + 6200 + 9000 + 5200 = Rs. 25200 So, Average monthly income = 25200/12 = Rs. 2100 C #### C QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)22.4% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/53000 * 100 = 22.4% Answer: B #### B QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.21000. A's share is? options: A)2999 B)2778 C)7000 D)2889 E)6612 SOLUTION:x* 12 : 2x* 6: 3x* 4 1:1:1 1/3 * 21000 = 7000 Answer:C #### C QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/- SOLUTION:100 % ------> 200 (100 * 2 = 200) 120 % ------> 240 (120 * 2 = 240) Selling price = Rs.240/- Answer : D #### D QUESTION:The difference between a number and its two-fifth is 510. What is 10% of that number ? options: A)33 B)85 C)37 D)27 E)28 SOLUTION:Explanation: Let the number be x. Then, . 10 % 0f 850 = 85. Answer: B) 85 #### B QUESTION:In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ? options: A)8% B)5% C)7% D)12% E)19% SOLUTION:A 8% of student hate all four subjects. #### A QUESTION:Let X be the smallest positive integer such that 10 and 14 are factors of 250 + X, so the value of X is: options: A)0 B)10 C)20 D)30 E)40 SOLUTION:You can calculate the LCM (10,14) = 70. After that you should check which of the possible X values will result in a number divisible by 70. The only possibility for this is 30 ( because 250 + 30 = 280 = 70*4) Answer D #### D QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)81.6 B)81.9 C)81.2 D)81.3 E)81.1 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer: A #### A QUESTION:A man invests Rs. 4,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? options: A)Rs. 1200 B)Rs. 1300 C)Rs. 1500 D)Rs. 2000 E)None of these SOLUTION:Explanation : Interest on Rs.4000 at 5% per annum = ( 4000 × 5 × 1) / 100 = Rs. 200 Let his additional investment at 8% = x Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25. To earn 6% per annum for the total, interest = (4000 + x) × 6 × 1/100. => 200 + 2x/25 = (4000 + x) × 6 × 1/100. => 20000 + 8x = (4000 + x) × 6. => 20000 + 8x = 24000 + 6x. => 2x=4000. => x=2000. Answer : D #### D QUESTION:The 323rd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is options: A)u B)v C)w D)y E)z SOLUTION:a is one time, b,2 times so on... so 323=n(n+1)/2.. 0r n(n+1)= 646... now 25*26=650...24*25<646 so n= 25. and 25th alphabet is Y. ans D #### D QUESTION:The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A? options: A)81 B)65 C)75 D)89 E)90 SOLUTION:A + B + C = 3 *70 = 210 A + B + C + D = 4 * 70 = 280 ---- (i) So, D = 70& E = 70 + 3 = 73 B + C + D +E =68 * 4 = 272 --- (ii) From Eq. (i) & (ii) A-E = 280 –272 = 8 A = E +8 = 73 + 8 = 81 Answer : A #### A QUESTION:A is 16th position and 29th from down of the people who passed. 5 failed , 6 didn't give . how many boys are there in the class? options: A)52 B)53 C)54 D)55 E)56 SOLUTION:A is 16th position, means = 15 + A 29th from down, means = A + 28 Total passed = A + 15 + 28 = 44 Total failed = 5 Didn't give = 6 Therefore, total boys = 44 + 5 + 6 = 55 ANSWER:D #### D QUESTION:A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ? options: A)20 B)10 C)15 D)5 E)7 SOLUTION:Time taken by A to finish the work = XY/(Y-X) = 10 x 20 / (20-10) = 200/10 = 20 days Answer: A #### A QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)20/9 hours E)30/43 hours SOLUTION:Speed downstream = 20 + 7 = 27 kmph. Time required to cover 60 km downstream = d/s = 60/27 = 20/9 hours. Answer: D #### D QUESTION:An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 1/4 %, then the amount invested at 11% was? options: A)12500 B)37500 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 37/4 * 1/100) (9x + 1100000 - 11x) = 37000/4 = 925000 x = 87500 Sum invested at 9% = Rs. 87500 Sum invested at 11% = Rs. (100000 - 87500) = Rs. 12500. Answer: A #### A QUESTION:Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 23 years. Father's age when Ayesha's brother was born = (29 + 3) years = 32 years. Required difference = (32 - 23) years = 9 years. Answer: Option E #### E QUESTION:The measure of the side of a square is quadrupled. If x represents the perimeter of the original square, what is the value of the new perimeter? options: A)3x B)4x C)9x D)12x E)27x SOLUTION:Original perimeter = x Hence original side = x/4 New side = 4x/4 New perimeter = 4*4x/4 = 4x Correct Option: B #### B QUESTION:When a number is divided by 31, the remainder is 29. When the same number is divided by 16, what will be the remainder? options: A)11 B)13 C)15 D)Data inadequate E)None of these SOLUTION:Number= (31 * Q)+ 29. Given data is inadequate. Answer: D #### D QUESTION:By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage? options: A)33 1/3% B)68 1/3% C)28 1/3% D)18 1/3% E)11 1/3% SOLUTION:Explanation: Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 33 pens = Rs. 33 Profit% = 33/99 * 100 = 33 1/3% Answer: A #### A QUESTION:A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target? options: A)175/256 B)451/365 C)312/456 D)156/754 E)164/784 SOLUTION:The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes. So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes. The event of not hitting the target even once is the complement of the event of hitting the target at least once. The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾ Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256 The probability that he will hit the target at least in one of the four shots=1-81/256 =175/256 Ans:A #### A QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is options: A)35 B)37 C)38 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 8) years. (x+8+10)=2(x—10) hence x=38. Present age of B = 38 years Answer: Option C #### C QUESTION:How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? options: A)52 sec B)50 sec C)51 sec D)55 sec E)58 sec SOLUTION:B 50 sec The distance to be covered = Sum of their lengths = 200 + 300 = 500 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 500/10 = 50 sec. #### B QUESTION:In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? options: A)20% B)40% C)50% D)60% E)70% SOLUTION:70 + 55 + 35 = 160% The number is 60% above 100% because 60% of the counties were counted twice. The answer is D. #### D QUESTION:If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks. options: A)120 MILES B)130 MILES C)140 MILES D)150 MILES E)160 MILES SOLUTION:LET ORIGINAL SPEED BE V AND TIME TAKEN BE T... AS DISTANCE BETWEEN TWO POINTS IS CONSTANT, 30*(T-1)=20*(T+1)=V*T HENCE, V=24MILE/HR T=5 HRS DISTANCE BETWEEN TWO POINTS IS 120 MILES ANSWER:A #### A QUESTION:A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ? options: A)A.0.6 B)B.1 C)C.2.1 D)D.3 E)E.2.4 SOLUTION:30% of 6 = 1.8 50% of 6 = 3 shortage is 1.2 so we need to have 1.2/50% to get 50% alcohol content. = 2.4 E #### E QUESTION:Working, independently X takes 10 hours to finish a certain work. He works for 9 hours. The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finish his work? options: A)2hrs B)4hrs C)6hrs D)8hrs E)10hrs SOLUTION:machine X will do 9/10 in 9 hrs, so X does 9/10 of the work .. Therefore, Y will do the remaining 1/10 th work alone.. As the speed of Y is 1/10 rate of X, Y will do the 1/10 th work in same time that X takes to complete full job... ans 10 E #### E QUESTION:2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost? options: A)26 B)56 C)110 D)28 E)54 SOLUTION:Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D #### D QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)21% C)21.33% D)22.109% E)23% SOLUTION:Lets say the indicated weight is x for $10 but the trader actually get 1.1x for $10 now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1 so profit % = (12.1-10)/ 10 = 0.21 = 21% ANSWER:B #### B QUESTION:A family made a down payment of $20 and borrowed the balance on a set of encyclopedias that cost $120. The balance with interest was paid in 7 monthly payments of $15.2 each and a final payment of $7. The amount of interest paid was what percent of the amount borrowed? options: A) 6% B) 12% C) 13.4% D) 16% E) 20% SOLUTION:interest paid = 15.2*7+7 - 100 = 13.4 % off the balance = (13.4/100) * 100 = 13.4 % Answer is C. #### C QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities? options: A)48 B)72 C)96 D)120 E)192 SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again Rate x time = distance. For the initial trip lets the distance Q to the midpoint be represented by P. EQN1: R x 2 = P For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by: Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5 EQN2: R x 2.5 = P + 24 EQN2-EQN1 : 0.5R=24 R=48 So the distance is rate x time = 48 x 4 = 192. ANS = E #### E QUESTION:3, 5, 7, 11, 13, 17, 19, ____ options: A)25 B)36 C)23 D)49 E)27 SOLUTION:The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23.... Answer : C. #### C QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160 SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 8*12=96 five-minute intervals, thus total of 96*30 tickets were sold. Say x student and 3x regular tickets were sold, then x+3x=96*30 --> x=24*30 and 3x=3*(24*30)=24*90. Therefore, the total revenue from ticket sales that day was 24*30*6+24*90*10=$25,920. Answer: B. #### B QUESTION:How many C ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen? options: A)3 B)16 C)28 D)32 E)56 SOLUTION:Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56 Ways to select 1 twin + 1 people = 4C1*6C1 = 24 Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen C = 56 - 24 = 32 Ans: D #### D QUESTION:210 school students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers? options: A)25 B)40 C)50 D)60 E)75 SOLUTION:We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20. So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40. #### B QUESTION:A tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume. If 6,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 15% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-6,000=4,000 gallons and sodium chloride is 600 gallons (6% of initial solution of 10,000 gallons) then sodium chloride is 600/4,000*100=15% of the remaining solution of 4,000 gallons. Answer: E. #### E QUESTION:In a stack of cards, 11 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 5/6 . What is the number of cards in the stack? options: A)10 B)11 C)12 D)15 E)18 SOLUTION:This question can be solved by TESTing THE ANSWERS. Answer C: 12 total cards With 12 total cards, and 11 blue cards, the probability of pulling two blue cards is... (11/12)(10/11) = 110/132 ~= 5/6 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: C #### C QUESTION:If r and s are positive integers and r-s=6, which of the following has the greatest value M? options: A)2r B)2s C)r +s D)2r-s E)2s-r SOLUTION:You can answer this question by using Number Properties and logic or by TESTing VALUES. We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value. IF.... R = 8 S = 2 Answer A: 2R = 2(8) = 16 Answer B: 2S = 2(2) = 4 Answer C: R+S = 8+2 = 10 Answer D: 2R-S = 2(8) - 2 = 14 Answer E: 2S-R = 2(2) - 8 = -4 Final Answer: A #### A QUESTION:Convert the 11/36 m/s into kilometers per hour? options: A)2.9 kmph B)1.1 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:11/36 m/s = 11/36 * 18/5 = 11/10 = 1.1 kmph. Answer: B #### B QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)18 B)24 C)42 D)81 E)28 SOLUTION:Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 * 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. ANSWER:B #### B QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/9 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)11/30 B)29/60 C)17/30 D)13/18 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/2*1/3=x/6 Platinum card unspent limit is= x-1/9x=8/9x So if gold card balance is transferred then the rest unspent will be 8/9x-x/6=13/18x So the ans is D #### D QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120? options: A)1000 B)289 C)209 D)280 E)892 SOLUTION:1120 = P [1 + (5*12/5)/100] P= 1000 Answer: A #### A QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)8 B)twelve (12) C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:5216 x 51 = ? options: A)266016 B)212016 C)266436 D)216314 E)None of these SOLUTION:Explanation : Normal way of multiplication may take time. Here are one alternative. 5216 x 51 = (5216 x 50) + 5216 = (5216 x 100/2) + 5216 = 521600/2 + 5216 = 260800 + 5216 = 266016. Answer : Option A #### A QUESTION:The length of a rectangle is reduced by 10%. By what % would the width have to be increased to maintain the original area? options: A)10% B)11.1% C)25% D)30% E)35% SOLUTION:Sol. Required change = (10*100)/(100-10)=11.1% B #### B QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)60 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 105 ⇒ 1.75x = 105 ⇒ x = 60 coins Answer D #### D QUESTION:How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together? options: A)56 B)72 C)48 D)60 E)59 SOLUTION:The given word contains 5 different letters. Taking the vowels EA together, we treat them as one letter. Then, the letters to be arranged are XTR (EA). These letters can be arranged in 4! = 24 ways. The vowels EA may be arranged amongst themselves in 2! = 2 ways. Number of words, each having vowels together = (24x2) = 48 ways. Total number of words formed by using all the letters of the given words = 5! = (5x4x3x2x1) = 120. Number of words, each having vowels never together = (120-48) = 72. Ans: B #### B QUESTION:Express a speed of 90 kmph in meters per second? options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps SOLUTION:90 * 5/18 = 25 mps Answer:E #### E QUESTION:Bernice's income is 70 percent more than Cathy's income, and Cathy's income is 65 percent less than Camilla's income. What percent of Camilla's income is Bernice's income? options: A)54.5% B)52.5% C)59.5% D)51.5% E)55.5% SOLUTION:Camilla's income = 100 (assume); Cathy's income = 35 (65 percent less than Camilla's income); Bernice's income = 59.5 (70 percent more than Cathy's income). Thus, Bernice's income (59.5) is 59.5% of Camilla's income (100). Answer: C #### C QUESTION:If a : b = 5 : 9 and b : c = 4: 7, find a : b : c options: A)63:36:20 B)36:20:63 C)20:63:36 D)20:36:63 E)None of them SOLUTION:a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4 a:b:c = 5:9:63/4 =20:36:63. Answer is D. #### D QUESTION:Worker W produces n units in 5 hours. Workers V and W, workers independently but at thesame time, produce n units in 2 hours.how long would it take V alone to produce n units? options: A)1 hr 26 min B)1 hr 53 min C)2 hr 30 min D)3 hr 30 min E)3 hr 20 min SOLUTION:V and W produce n units in 2 hours. So they produce n/2 units in 1 hour. W produces n units in 5 hrs. So he alone produce n/5 units in 1 hr. So V produces in 1 hr. = n/2 - n/5 = 3 n/10 units. V produces n units in 10/3 hrs. which is 3 hrs 20 min. ANSWER:E #### E QUESTION:What should come in place of the question mark (‘?) in the following equation? 18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16 options: A)2764.44 B)2864.34 C)1864.44 D)2684.44 E)None of these SOLUTION:? = 8697.32 – 3058.16 – 92⁄5 × 150.8 = 5639.16 – 2774.72 = 2864.44 Answer E #### E QUESTION:What is the smallest positive integer that can be multiplied by 605 to make it a perfect square? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:605 is multiplied by 5 gives 3025 Its a square root of 55 Answer is 5 -Option C #### C QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean? I. 13.7 II. 12.3 III. 9.3 options: A)I only B)I and II only C)II only D)III only E)I and III only SOLUTION:Mean = 12 SD = 1.3 2 SD above mean = 12+2*1.3 = 14.6 2 SD below mean = 12-2*1.3 = 9.4 12.3 and 13.7 lies in the range of 2SD from mean Answer: Option D #### D QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:The total marks obtained by a student in Mathematics and Physics is 32 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)26 C)27 D)28 E)22 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 32 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (32 + 20) / 2 = 26.Answer:B #### B QUESTION:Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky's salary more than Ashu's? options: A)96% B)51.1% C)90% D)52.1% E)None of these SOLUTION:Solution: Let Ashu's salary = 100; Ashu's salary after rise = 125. Then Vicky's salary = 175. Vicky's salary after rise of 40% = 245. [As 10% of Vicky's salary is 17.5 then 40% = 17.5*4 = 70] . Difference between Vicky's salary and Ashu's salary = 245-125 = 120; . % more Vicky's salary than Ashu's = 120*100/125 = 96%. Answer: Option A #### A QUESTION:How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 15% solution? options: A)A)5.8 B)B)1.3 C)C)9.6 D)D)12.5 E)E)7.9 SOLUTION:Amount salt in 100kg solution = 10*100/100 = 10 kg Let x kg of pure salt be added then(10+x)/(100+x)=15/100 200+20x=300+3x 17x = 100 x = 5.8 Answer is A #### A QUESTION:Sakshi can do a piece of work in 10 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work : options: A)8 B)16 C)18 D)25 E)10 SOLUTION:Solution Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 . Suppose Tanya taken x days to do the work. 5 : 4 : : 10 : x ⇒ x = (10x4/5) ⇒ x = 8 days. Hence,Tanya takes 8 days is complete the work. Answer A #### A QUESTION:If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent? options: A)16 1⁄6% B)25% C)33 1⁄3% D)50% E)66 2⁄3% SOLUTION:This question can be dealt with conceptually or by TESTing VALUES. We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction. Let's TEST 2/1 If we triple the numerator and double the denominator, we end up with.... (2x3)/(1x2) = 6/2 = 3 Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50% D #### D QUESTION:The third proportional to 2 and 6 is? options: A)18 B)17 C)14 D)15 E)13 SOLUTION:(6*6)/2 = 18 Answer:A #### A QUESTION:In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100? options: A)22 B)88 C)25 D)99 E)01 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (100 - 75) = 25 points to C. Answer: C #### C QUESTION:A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday SOLUTION:This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B #### B QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/7) B)Rs. 2(1/9) C)Rs. 3(2/11) D)Rs. 2(2/13) E)Rs. 2(2/7) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B #### B QUESTION:From a number of mangoes, a man sells half the number of existing mangoes plus 1 to the first customer, then sells 1/3rd of the remaining number of mangoes plus 1 to the second customer, then 1/4th of the remaining number of mangoes plus 1 to the third customer and 1/5th of the remaining number of mangoes plus 1 to the fourth customer. He then finds that he does not have any mangoes left. How many mangoes did he have originally? options: A)12 B)14 C)15 D)13 E)16 SOLUTION:Let the No. of mangoes that the man had originally = X No. of mangoes sold balance 1st customer = (X/2) + 1 (X - 2)/2 2nd customer = (X - 2)/6 + 1 (X - 5)/3 3rd customer = (X - 5)/12 + 1 (X - 9)/4 4th customer = (X - 9)/20 + 1 0 (X - 9)/20 + 1= (X - 9)/4 => X = 14 ANSWER:B #### B QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)150 m B)200 m C)240 m D)400 m E)150 m SOLUTION:Answer: Option C Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. #### C QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:A man divides $8600 Among 5 Sons, 4 Daughters and 1 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive? options: A)A)$200 B)B)$1000 C)C)$819 D)D)$1200 E)E)$400 SOLUTION:Let the share of each nephews be $X. Then, share of each daughter=$4X, share of each son= $5X. So, 5*5X+4*4X+1*X=8600 25X+16X+X=8600 42X=8600, X=204.76. Daughter receives four times of nephew so 4 * 204.76= 819. So Each Daughter receives $800. answer is option C) $819. #### C QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer: A #### A QUESTION:Find the simple interest on Rs.300 for 9 months at 6 paisa per month? options: A)142 B)152 C)162 D)172 E)182 SOLUTION:I = (300*9*6)/100 = 162 ANSWER:C #### C QUESTION:The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides? options: A)0 sq m B)7 sq m C)5 sq m D)4 sq m E)3 sq m SOLUTION:S = (1 + 2 + 3)/2 = 3 => No triangle exists Answer:A #### A QUESTION:By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x =30 kmph. Answer: A #### A QUESTION:If S = {50, 72, 108, 120, 205}, how much less is the mean of the numbers in S than the median of the numbers in S? options: A)2 B)3 C)5 D)8 E)9 SOLUTION:Mean = (50 + 72 + 108 + 120 + 205)/5 = 111 Median = 108 Difference = 111-108 = 3 Option B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)12 B)72 C)48 D)99 E)11 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.75 + 1.25 = 3 km = 3000 m. Required time = 3000 * 3/125 = 72 sec. Answer: B #### B QUESTION:We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let x be the number of canoes. Then 2x/3 is the number of kayaks. 12x+(2x/3)*18=504 12x+12x=504 24x=504 x=21 (canoes) 2x/3=14 (kayaks) There were 21-14 = 7 more canoes rented out. The answer is C. #### C QUESTION:Three sets of 80, 50 and 90 students appeared for an examination and the pass percentage was 75, 90 and 100 respectively. the pass percentage of the whole set is options: A)87.63% B)88.53% C)88.93% D)88.63% E)89.63% SOLUTION:Explanation: total passed student =60+45+90=195 195 is 88.63% of 220 ANSWER:D #### D QUESTION:There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes? options: A)18 B)21 C)35 D)42 E)56 SOLUTION:Note that each handshake includes two people. The total number of handshakes is 14*3/2 = 21 The answer is B. #### B QUESTION:Which of the following is non-negative number? options: A)(a-0.9)(a-1) B)(a+1)(a-1) C)(a+0.9)(a+1) D)(a-0.6)(a-0.6) E)a(a+1) SOLUTION:5-sec approach: D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative. Answer: D. #### D QUESTION:When 2/3 of the garments in the shipment were inspected, 28 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 90 percent of the garments in the shipment pass? options: A)10 B)9 C)13 D)7 E)5 SOLUTION:B = 9 2/3x= 30 x=45 for 90% approval we need 41 garments approved. already approved = 28 we need 13 more. Answer : C #### C QUESTION:There are between 100 and 110 marbles in a collection of cards. If they are counted out 3 at a time, there are 1 left over, but if they are counted out 4 at a time, there is 4 left over. How many marbles are in the collection? options: A) 100 B) 103 C) 106 D) 108 E) 109 SOLUTION:Let number of cards = x If the cards are counted 3 at a time , there are 2 left over- x = 3p+1 x can take values 100 , 104 , 109 If the cards are counted 4 at a time , there is 1 left over x= 4q+4 x can take values 100 , 108 Therefore , x = 100 Answer A #### A <<<Examples ends QUESTION:Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year? options: A)32:21 B)12:17 C)17:12 D)21:32 E)15:19 SOLUTION:Here capital is not the same. Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =(20000×6+15000×6) Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio =(30000×4+50000×4) Suresh : Kiran =(20000×6+15000×6) :(30000×4+50000×4) =(20×6+15×6):(30×4+50×4) =(20×3+15×3):(30×2:50×2) =105:160 =21:32 Answer is D. #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Which of the following inequalities is equivalent to 11 - 11x > 133? options: A) x > -2 B) x > -1 C) x > -3 D) x > -11 E) x > -5 SOLUTION:You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc. The only important thing to note is the following: When you multiply/divide by a negative number, the sign of the inequality flips. To illustrate, 11 - 11x > 133 11x > -122 (Correct) x > -11 (Correct) the correct option is D #### D QUESTION:The smallest value of n, for which n+1 is not a prime number, is options: A)5 B)6 C)8 D)3 E)10 SOLUTION:(1 + 1) = 2. (2 + 1) = 3. (3 + 1) = 4. (4 + 1) = 5. which is not prime , n=3. ANSWER:D #### D QUESTION:The list price of a watch is 160. A retailer bought the same watch 122.40. He got two successive discounts one at 10% and the other at a rate which was not legible. What is the second discount rate? options: A)12% B)14% C)15% D)18% E)None of these SOLUTION:Retailer price = list price (1−d1/100)(1−d2/100) ⇒ 122.40 = 160(1−10/100)(1−d2/100) ⇒ 1−d2/100=122.40×100/160×90=0.85 ⇒ d2 = (1 - 0.85) × 100 = 15% Answer C #### C QUESTION:For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2? options: A)5 B)3 C)2 D)1 E)0 SOLUTION:4”2= 4 - 4=0 Answer: E #### E QUESTION:If SAVOURY is coded as OVUARSY then how will RADIATE be coded? options: A)AIDARET B)IDARATE C)ARIADTE D)IDAATRE E)None of these SOLUTION:Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :- letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..) Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get IDAATRE ANSWER:D #### D QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 3*20000/5=12000 ANSWER:E #### E QUESTION:If x=kc and y=kt,then 2y+x =? options: A)k(t-c) B)k(c-t) C)c(k-t) D)k(2t+c) E)k(1-t) SOLUTION:Just put in the given values of y and x 2y +x =2 kt +kc Now take k common 2y + x = k(2t +c) You get (D) as your answer. #### D QUESTION:The equation of line s is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line s? options: A)48 B)50 C)60 D)75 E)100 SOLUTION:This can be solve in two steps and without any complex calculation. Given : equation of line s as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.5*100*75=0.5*125* x => x=60; SO answer is 60=C #### C QUESTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ? options: A) None B) Two C) Four D) Five E) Seven SOLUTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain? R=2,4,6,8,10,12... S=4,16,36,64... Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets. Solution: Five Answer: D #### D QUESTION:The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? options: A)c is not changed. B)c is halved. C)c is doubled. D)c is multiplied by 4. E)c is multiplied by 16. SOLUTION:a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. E c is multiplied by 16. #### E QUESTION:Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)491 B)481 C)471 D)441 E)445 SOLUTION:Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 3*7/100*2100 = 441. D #### D QUESTION:When N is divided by T, the quotient is S and the remainder is M. Which of the following expressions is equal to N? options: A)ST B)S + V C)ST + M D)T(S+V) E)T(S – V) SOLUTION:Using the rule dividend = Quotient * divisor + remainder =>ST + M C is correct #### C QUESTION:The average age 15 girls of a class is 15 years. Out of these, the average age of 12 girls is 13 years and that of the other 3 girls is 14 years. The age of the 15th girl is? options: A)35 B)30 C)31 D)28 E)27 SOLUTION:Age of the 15th girl = 15*15 - (12*13+3*14) = 225-198 = 27 years Answer is E #### E QUESTION:A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 4, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit? options: A)23/24 B)31/36 C)55/64 D)65/81 E)75/121 SOLUTION:P(no even digits) = 2/3*2/3*2/3*2/3 = 16/81 P(at least one even digit) = 1 - 16/81 = 65/81 The answer is D. #### D QUESTION:If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b = options: A) −48 B) −2 C) 2 D) −7 E) 48 SOLUTION:a(a + 7) = 18 and b(b + 7) = 18 => a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively => a+b = -7 Ans: D #### D QUESTION:In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia? options: A)c/e B)e/c C)e/(c-e) D)c/(c-e) E)1- (e/c) SOLUTION:We're given a couple of facts to work with: 1) There were a total of c earthquakes 2) Of those earthquakes, e of them occurred in Asia We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia. Let's TEST VALUES c = 5 total earthquakes e = 2 occurred in Asia Thus, there were 3 earthquakes that DID NOT occur in Asia.... The answer to the question is 2:3 We just need to plug in the values for c and e and find the match... Answer A: c/e = 5/2 NOT a match Answer B: e/c = 2/5 NOT a match Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match C #### C QUESTION:The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is? options: A)38 B)27 C)75 D)28 E)21 SOLUTION:Explanation: The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75. Answer: C #### C QUESTION:In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 80 and a standard deviation of 14, which of the following is exactly 2.60 standard deviations more than the mean? options: A)a) 43.6 B)b) 60 C)c) 72 D)d) 77.5 E)e) 81 SOLUTION:Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it. Here, we're told two things about a group of numbers: 1) The average of the group is 80 2) The standard deviation of the group is 14 If you go 1 SDupfrom the average, you hit.....80+14 = 94 If you go 1 SDdownfrom the average, you hit.....80-14 = 66 If you go 2 SDsupfrom the average, you hit.....80+2(14) = 108 If you go 2 SDsdownfrom the average, you hit.....80-2(14) = 52 Etc. Here, we're asked for the number that is EXACTLY 2.60 SDs above the mean.... 2.60 SDsupwould be.....80 + 2.60(14) = 43.6 A #### A QUESTION:1!+2!+3!+4!+5!+..100! is divided by 24. Find the remainder? options: A)2 B)5 C)9 D)10 E)12 SOLUTION:By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24. So the remainder = 1 + 2 + 6 + 0 + 0....... = C #### C QUESTION:The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction? options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively. d = 2n - 1 (n + 1)/(d + 1) = 4/5 5n + 5 = 4d + 4 5n + 5 = 4(2n - 1) + 4 => n = 5/3 d = 2n - 1 => d = 3/7 Hence the fraction is : 5/7 ANSWER:B #### B QUESTION:The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.90 per metre. options: A)2399 B)3888 C)2999 D)5808 E)6468 SOLUTION:Explanation: Area = (13.86 x 10000) sq.m = 138600 sq.m Circumference = Cost of fencing = Rs. (1320 x 4.90) = Rs. 6468. Answer: E) 6468 #### E QUESTION:If the population of a certain country increases at the rate of 1 person every 60 seconds, by how many persons does the population increase in 2 Hours? options: A)120 B)80 C)100 D)150 E)140 SOLUTION:Answer = 1 * 120(2 hour = 120 minutes)= 120 Answer = A #### A QUESTION:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:For 1rs 4p interest wat will be for 5000rs? options: A)350Rs B)450Rs C)200Rs D)30Rs E)448Rs SOLUTION:For 1rs , 4p interest for 5000rs, x x= 5000/1 * 4p ==> 20000 paise To express in rs, 20000/100 = 200rs ANSWER:C #### C QUESTION:If an average hard drive had a capacity of 0.1 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)768 D)1024 E)1536 SOLUTION:0.1*2^10=0.1*1024=102.4 The answer is D. #### D QUESTION:You are filling up your car with gas. Your tank can hold 19 gallons. Your car started with x gallons in it. You paid $20 in gas. What was the cost of gas per gallon? options: A)19/20 B)x/20 C)(19-x)/20 D)x-19)/20 E)19+20/x SOLUTION:Amount of gas you added to your car: 19-x Price per gallon: (19-x)/20 Answer: C #### C QUESTION:o mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by 33×13%33×13%, and finished the work 1 day earlier than it was planned. A) What is the area of the grass field? B) How many days did it take to mow the whole field? C) How many days were scheduled initially for this job? options: A)387 B)39 C)37 D)20 E)28 SOLUTION:Hint: See problem 20 and solve by yourself. Answer: A) 120 hectares; B) 7 days; C) 8 days. Answer:D #### D QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream. options: A)7 kmph B)8 kmph C)9 kmph D)7 kmph E)6 kmph SOLUTION:Speed in still water = (10 + 4)1/2 kmph = 7 kmph. answer :A #### A QUESTION:If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals? options: A)4:3 B)4:0 C)4:5 D)4:7 E)4:2 SOLUTION:Explanation: a1:a2 = 4:3 d1:d2 = 4:3 Answer: Option A #### A QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow? options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10% So 8100+15100⋅x+10100⋅(8100−x)=9100 Therefore 8100+320x+110(8100−x)=9100 120x=190 x=3800 Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres correct answer is D)4370 lt #### D QUESTION:If 3^x = 2, then 3^(4x+3) = options: A)429 B)454 C)432 D)438 E)108 SOLUTION:3^x=2 3^4x=2^4 3^4x=16 3^(4x+3) =3^4x*3^3 =16*27 =432 Answer: C #### C QUESTION:The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of R is? options: A)A)Rs.4078 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.6400 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10100 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv) Subtracting (i) from (iv), we get, P = 6400. P's monthly income = Rs.6400. Answer: E #### E QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T? options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150 SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1. The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15. Hence, the probability that at least one light bulb fails is 1-0.94^15. Answer: A. Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A QUESTION:A man can row 7 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? options: A)3.3 B)3.4 C)3.5 D)3.6 E)3.7 SOLUTION:M = 7 S = 1.2 DS = 7 + 1.2 = 8.2 US = 7 - 1.2 = 5.8 x/8.2 + x/5.8 = 1 x = 3.40.Answer: B #### B QUESTION:If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $81, how much does one shirt cost? options: A)$10 B)$12 C)$13.20 D)$21 E)$16.80 SOLUTION:3J + 2S = 69 2J + 3S = 81 ---------------- 5J + 5S = 150 ----(divide by 5)---> J + S = 30 3J + 2S = J + 2(J + S) = J + 60 = 69 ---> J = 9 3*9 + 2S = 69 27 + 2S = 69 2S = 42 S = 21 Answer: D #### D QUESTION:4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days? options: A)25 B)19 C)39 D)61 E)64 SOLUTION:Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 16 :: 4 : x Days 4:16 4 * 4 * x = 16 * 16 * 4 x = (16 * 16 * 4)/(4 x 4) x = 64. Answer is E. #### E QUESTION:Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number? options: A)6 B)9 C)11 D)12 E)15 SOLUTION:Explanation: 3x/5 – x/5 = 6 => x =15 1 + 5 = 6 A) #### A QUESTION:Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm. options: A)456 B)234 C)285 D)342 E)213 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2 Answer: Option C #### C QUESTION:If the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers? options: A)4:9 B)4:3 C)3:7 D)2:5 E)1:6 SOLUTION:The ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9. The ratio of apples to bananas to cucumbers is 4 to 3 to 9. The answer is A. #### A QUESTION:20 balls are numbered 1 to 20. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers? options: A)7/30 B)3/14 C)9/38 D)4/21 E)5/26 SOLUTION:P(1st ball is even) = 10/20 P(2nd ball is also even) = 9/19 P(both balls are even) = 10/20 * 9/19 = 9/38 The answer is C. #### C QUESTION:Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? options: A)8 B)6 C)4 D)10 E)12 SOLUTION:Together they make 5/4 w widgets in 3 days. So they make w widgets in 3*4/5 = 12/5 days. 1/(t+2) + 1/t = 5/12 Now, calculating this is really cumbersome so try to plug in options to get to the answer. If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4. 1/6 + 1/4 = 5/12 It works so t = 4. Answer : A #### A QUESTION:There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is: options: A)9 B)13 C)15 D)12 E)19 SOLUTION:Explanation: abc/bcd=385/1001=>a/d=5/13 So d = 13 Option B #### B QUESTION:A boat running up stram takes 6 hours to cover a certain distance, while it takes 9 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively? options: A)2 : 3 B)5 : 1 C)4 : 5 D)7 : 1 E)8 : 1 SOLUTION:Explanation: Let speed of boat is x km/h and speed stream is y km/hr 6(x+y) = 9(x-y) 6x+6y = 9x-9y 15y = 3x 5y = x x/y = 5/1 5 : 1 Answer: Option B #### B QUESTION:What is the sum of odd integers from 35 to 55, inclusive? options: A)495 B)1,500 C)1,240 D)1,120 E)1,100 SOLUTION:Number of odd integers = (55-35)/2 + 1 = 20/2 + 1 = 11 Sum of odd integers = (35+55)/2 * 11 = 495 Answer A #### A QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)19% C)78% D)48% E)11% SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer: A #### A QUESTION:The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 75 terms of set X? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:75*4 + 74*40 + 73*400 = 300 + 2960 + 29200 = 32460 The hundreds digit is 4. The answer is C. #### C QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted? options: A)6 B)7 C)8 D)2 E)9 SOLUTION:Let xx be the number of roses. Then the number of birches is 24−x24−x, and the number of boys is 3×(24−x)3×(24−x). If each girl planted 3 roses, there are x3x3 girls in the class. We know that there are 24 students in the class. Therefore x3+3(24−x)=24x3+3(24−x)=24 x+9(24−x)=3⋅24x+9(24−x)=3⋅24 x+216−9x=72x+216−9x=72 216−72=8x216−72=8x 1448=x1448=x x=18x=18 So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches. Answer:A #### A QUESTION:A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream? options: A)6 hr B)2 hr C)4 hr D)1 hr E)None of these SOLUTION:Explanation : Speed downstream = 96⁄8 = 12 kmph Speed of current = 4 km/hr Speed of the boatman in still water = 12-4 = 8 kmph Speed upstream = 8-4 = 4 kmph Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B #### B QUESTION:How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once? options: A)21 B)42 C)120 D)600 E)200 SOLUTION:Vowel: E O Consonants: V R M N T First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel) Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant) Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter Second letter can be filled in 5 Ways Third letter can be filled in 4 Ways So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200 Answer E #### E QUESTION:Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? options: A)24/64 B)32/64 C)36/64 D)40/64 E)42/64 SOLUTION:Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5. Expected value of three dice is 3*3.5=10.5. Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2 = 32/64. That's because the probability distribution is symmetrical for this case: The probability of getting the sum of 3 (min possible sum) = the probability of getting the sum of 18 (max possible sum); The probability of getting the sum of 4 = the probability of getting the sum of 17; The probability of getting the sum of 5 = the probability of getting the sum of 16; ... The probability of getting the sum of 10 = the probability of getting the sum of 11; Thus the probability of getting the sum from 3 to 10 = the probability of getting the sum from 11 to 18 = 1/2. Answer: B. #### B QUESTION:|16 - 5| - |5 - 12| = ? options: A)3 B)2 C)1 D)0 E)4 SOLUTION:|16 - 5| - |5 - 12| = | 11 | - | -7 | =11 - 7 = 4 correct answer E #### E QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:The purchase price of an article is $48. In order to include 30% of cost for overhead and to provide $12 of net profit, the markup should be options: A)15% B)25% C)35% D)40% E)55% SOLUTION:Cost price of article = 48$ % of overhead cost = 30 Net profit = 12 $ We need to calculate % markup Net profit as % of cost price = (12/48)*100 = 25% Total markup should be = 25 + 30 = 55% Answer E #### E QUESTION:A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? options: A)2.4 km B)2.6 km C)2.9 km D)4.4 km E)5.6 km SOLUTION:Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour ⇒ x/7+x/5=1 ⇒5x+7x=35 ⇒12x=35 ⇒x=2.9 km Answer: Option C #### C QUESTION:There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns? options: A)A)10 B)B)12 C)C)24 D)D)60 E)E)100 SOLUTION:Using anagram method: 4_3_2_1 R_R_B_B so.. 4!/Number of repeated letters (2!)(2!) = 6 ANS:D #### D QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 160 six-ounce servings of orange juice? options: A)20 B)24 C)28 D)32 E)36 SOLUTION:1 X 12 ounce can of concentrate + 3 X 12 ounce cans of water = 48 ounces of the mixture. 48 ounces of mixture gives (48 / 6 ) = 8 servings. Thus 1 x 12 ounce can of concentrate is used to produce 8 servings of the mixture. To make 160 servings of the mixture, we need 160 / 8 = 20 cans of the concentrate. The answer is A. #### A QUESTION:What could be the range of a set consisting of odd multiples of 3? options: A)21 B)24 C)35 D)62 E)70 SOLUTION:Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 3*(2n+1) where n is any positive integer. Range = 3*(2m + 1) - 3*(2n + 1) = 3*2*(m-n) = 6 * (m-n). m, n - any positive integers The answer must be divisible by 6, which is only 24. The correct answer is B #### B QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3% SOLUTION:Let 100 is the enrollment in 1990. Enrollment in 1980= 83.3 % increase= (Increase from 1980 to 1990)/Enrollment in 1983 =>16.7*100/83.3 =20% ANSWER:C #### C QUESTION:The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)80,70 kmph B)80,40 kmph C)75,35 kmph D)80,80 kmph E)84,40 kmph SOLUTION:Speed downstream = 55 + 20 = 75 kmph Speed upstream = 55 - 20 = 35 kmph Answer: C #### C QUESTION:12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points? options: A)990 B)495 C)1980 D)none E)Cannot be determined SOLUTION:Explanation : For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals. Answer : B #### B QUESTION:There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men? options: A)1932 B)1933 C)1934 D)1935 E)1936 SOLUTION:(5c3*11c3)+(5c4*11c2)+(5c5*11c1) 1936 ANSWER:E #### E QUESTION:If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest? options: A)$ 4 B)$ 8 C)$ 12 D)$ 16 E)$ 432 SOLUTION:Solution Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.08/2)^2= 5408 Amount (SI) = P+PTR/100 = 5000+(5000*1*8/100)=5400 Difference = 5408-5400=8 $ ANSWER:B #### B QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? options: A)7:6 B)7:3 C)7:4 D)7:2 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer: B #### B QUESTION:8k8 + k88 -------- 1,6t6 If k and t represent non-zero digits within the integers above, what is t? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16t6 Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and t=6. Answer: A. #### A QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)30 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:In case O is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)P and Q E)T and U SOLUTION:P and Q should serve on A ANSWER:D #### D QUESTION:If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)9 E)18 SOLUTION:Let length of rectangle = L 6^2 = L*4 => L = 36/4 = 9 Answer D #### D QUESTION:A box contains ten bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that exactly two bulbs are good? options: A)7/21 B)10/21 C)9/21 D)8/21 E)5/21 SOLUTION:Required probability = (5C2 . 5C2)/10C4 = (10 * 10)/210 = 10/21 Answer:B #### B QUESTION:When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number? options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these SOLUTION:Let the first and the second numbers be x and y respect then y + 30% of x = 140% of y or, y + 0.3x = 1.4y or, 0.3x = 0.4y ∴ x : y = 0.4 : 0.3 = 4 : 3 Answer B #### B QUESTION:An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? options: A)4.04 B)4.02 C)4.01 D)4.05 E)4.06 SOLUTION:Formula for Calculation of Percentage error is: =(x−y−(xy)/100)% =(2+2+(2×2)/100)%=4.04% Answer is A. #### A QUESTION:The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool? options: A)1400 B)1600 C)1800 D)1500 E)2000 SOLUTION:volume of pool = 80*150*10 cu.ft ,100% full = 60*100*10*1 cu.ft water is available to drain. draining capacity =60 cu.ft /min therefore time taken = 80*150*10*1/ 60 min= 2000 min E #### E QUESTION:If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number? options: A)10 B)60 C)30 D)40 E)50 SOLUTION:Explanation: 6:7 6x + 10 : 7x + 10 = 7 : 8 8[6x + 10] = 7[7x + 10] 48x + 80 = 49x + 70 49x - 48x = 80 - 70 x = 10 Then smallest number is = 6 6x = 60 Answer: Option B #### B QUESTION:The fourth proportional to 5, 8, 15 is: options: A)15 B)5 C)24 D)8 E)28 SOLUTION:Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : 15 : x = 5x = (8 x 15) x = (8 x 15)/5= 24. Answer is C. #### C QUESTION:Y and Z start a business with Rs.3000 and Rs.6000 respectively. How should they share their profits at the end of one year? options: A)4:1 B)1:3 C)1:4 D)1:5 E)1:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by Y and Z = 3000 : 6000 => 1:2 . Answer:E #### E QUESTION:Jerry wrote down all the positive integers that have at most 7 digits and contain only the digits 0 and 1. How many times did he write down the digit 1 ? options: A)128 B)224 C)288 D)448 E)512 SOLUTION:Jerry wrote down a total of 27 − 1 = 127 numbers (0 is missing). Add 0 to the numbers Jerry wrote. We divide the resulting 128 numbers in pairs. If x is one of the numbers Jerry wrote then we put it in pair with 1111111 − x (whose digits are also 0s and 1s). For example 1100101 is paired with 11010. In this way, we divide the numbers into 64 distinct pairs so that each number appears exactly once. Note that there are exactly 7 digits 1 in each pair. So, Jerry wrote the digit 1 exactly 64 × 7 = 448 times. correct answer D #### D QUESTION:A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is? options: A)200 B)150 C)455 D)300 E)600 SOLUTION:Amount = (15000)* (1 + (3/4*100))^4 Amount = 15000 * (1+ 0.0075)^4 = 15455 ------(for investment in 1st month) Interest = 15455-15000 = 455.............. Ans -C #### C QUESTION:A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? options: A)$330.00 B)$331.00 C)$332.30 D)$333.30 E)$334.60 SOLUTION:The maximum interest in one month is 10%*$300=$30. The combined payment (base plus interest) is $300 + $30 = $330. The greatest possible payment is: 1.01*$330=$333.30. The answer is D. #### D QUESTION:A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 B)(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2 C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D)(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.1 Probability of Tail, P(T) = 0.9 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2*(0.1)^3*(0.9)^2 1 Tail and 4 Heads, Probability = 5C1*(0.1)^4*(0.9)^2 0 Tail and 5 Heads, Probability = (0.1)^5 Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 Answer: option A #### A QUESTION:Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = options: A)18 B)15 C)-13 D)-21 E)-24 SOLUTION:f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = f(4) = 0= 16+4b+c--- Taking 16 to the other side -> 4b+c= -16 f(-3) = 0= 9-3b+c --- taking -3b+c to the other side -> 3b-c=9 When we add these 2 equations, we get 7b= -7---> b= -1 And while substituting b= -1 we get c= -12. b+c= -13--- Answer C #### C QUESTION:For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game? options: A)1/9 B)4/9 C)5/9 D)2/3 E)1/3 SOLUTION:Paul picks A with the same probability as A’schances of winning So probability of picking a winner = prob picking of ghana * ghana winning + prob picking of bolivia * bollivia winning = 2/3 * 2/3 + 1/3 * 1/3 = 5/9 ANSWER:C #### C QUESTION:A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is? options: A)675 B)680 C)685 D)690 E)695 SOLUTION:Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec. Length of the train = 75 * 9 = 675 m. Answer: Option A #### A QUESTION:Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 450 or over 650. If the individual ranges of the three people's scores in those 4 practice tests were 30, 80 and 110, what is the difference between the maximum and minimum possible ranges of all their scores put together. options: A)90 B)120 C)50 D)70 E)100 SOLUTION:According to the information in the question the maximum range would be between 450 and 650(200). The minimum range would be the greatest range for any one individual, which is listed in the problem as 110. So the difference between these would be 200-110 or 90. Answer: A #### A QUESTION:According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 120 12-ounce smoothies? options: A) 120 B) 150 C) 180 D) 240 E) 600 SOLUTION:This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base? D #### D QUESTION:What is the value of x if (64^2)-(36^2)=20*x? options: A)120 B)100 C)140 D)130 E)115 SOLUTION:20*x=(64+36)(64-36) 20*x=100*28 x=(100*28)/20 x=5*28 x=140 Option C #### C QUESTION:3 of the 4 expressions (1), (2), (3) & (4) given below are exactly equal . Which of the expression is not equal to the other four expressions? options: A)(A + B)2 - 4AB B)(A – B)2 + 4AB C)A2 + B2 - 4AB + 2AB D)A2 – B2 + 2B(B – A) E)None of these SOLUTION:1) (A + B)2 – 4AB = A2 + 2AB + B2 - 4AB = A2 + B2 - 2AB 2) (A – B)2 + 4AB = A2 – 2AB + B2 + 4AB = A2+ B2 + 2AB 3) A2 +B2 – 4AB + 2AB = A2 + B2 - 2AB 4) A2 – B2 + 2B(B – A) = A2 – B2 + 2B2 – 2AB = A2 + B2 – 2AB Therefore, (1) = (3) = (4) ≠ (2) Therefore, expression (2) is wrong ANSWER IS B #### B QUESTION:If the product of 2 integers is negative, at most how many of the integers can be negative? options: A)1 B)3 C)4 D)5 E)6 SOLUTION:The product of 2 integers is negative Thus an odd number of integers need to be negative to have a negative product We are asked at most how many are required. So, the highest odd integer before 6,i.e. 1 Correct Option : A #### A QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is? options: A)Rs. 3900 B)Rs. 4900 C)Rs. 4980 D)Rs. 5000 E)Rs. 5900 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. A) #### A QUESTION:The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: options: A)Rs. 3500 B)Rs. 3750 C)Rs. 3840 D)Rs. 3900 E)None SOLUTION:EXPLANATION Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5b/2 x 15x + 2y = 4000 15x + 2 x 5/2 x= 4000 20x = 4000 x = 200. So, y = 172 = 500. Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. Answer D #### D QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,15 = 15/100 x= 80*15/100 x= 12 12/10 = 1,2 = 120%, Answer C #### C QUESTION:5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are? options: A)6 B)5 C)2 D)7 E)2 SOLUTION:5M = xW = 8B 5M + xW + 8B ----- 90 Rs. 5M + 5M + 5M ----- 90 Rs. 15M ------ 90 Rs. => 1M = 6Rs. Answer: A #### A QUESTION:A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? options: A)17 kmph B)45 kmph C)86 kmph D)197 kmph E)15 kmph SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph. Answer:B #### B QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)11 B)25 C)77 D)99 E)21 SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25%.Answer:B #### B QUESTION:In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun? options: A)67 kg. B)68 kg. C)69 kg. D)Data inadequate E)None of these SOLUTION:EXPLANATION Let Arun’s weight by X kg. According to Arun, 65 < X < 72 According to Arun’s brother, 60 < X < 70. According to Arun’s mother, X <= 68 The values satisfying all the above conditions are 66, 67 and 68. Required Average =( 66 + 67 + 68 /3 )= (201/3) = 67 kg Answer A #### A QUESTION:The average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher. options: A)40 yrs B)42 yrs C)45 yrs D)46 yrs E)47 yrs SOLUTION:The average age of 30 boys of a class is equal to 14 yrs: i.e Sum of all boys:30*14 include class teacher:31 candidates in a class & avg age is:15 yr i.e. sum of all:31*15(include class teacher)=465 so,the age of the class teacher:465-420=45yr answer will be 45 yrs ANSWER:C #### C QUESTION:In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together? options: A)120 B)360 C)1440 D)13440 E)4320 SOLUTION:The word 'SOFTWARE' contains 8 different letters. when the vowels OAE are always together, they can be supposed to form one letter. Thus, we have to arrange the letters SFTWR (OAE) Now, 5 letters can be arranged in 6!=720 ways. The vowels (OAE) can be arranged among themselves in 3!=6 ways. Required number of ways =(720*6)=4320. Answer is E #### E QUESTION:A division of a company consists of four men and eight women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)7/11 B)7/33 C)14/33 D)7/66 E)14/66 SOLUTION:The total number of ways to choose two representatives is 12C2=66. The number of ways to choose two females is 8C2=28. P(choosing two female representatives)=28/66=14/33 The answer is C. #### C QUESTION:Tough and Tricky questions: Combinations. Three students - 2 boys and 1 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another? options: A)2 B)4 C)72 D)240 E)720 SOLUTION:2!*1!*2 = 2*1*2 = 4 ways. Ans. B) 4 #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not green? options: A)15/28 B)1/4 C)9/16 D)1/32 E)1/16 SOLUTION:The question asks they will both be not green. Considering that these are draws without replacement there are following possibilities : draw 1, draw 2 ===== ===== 1) Not green, green; 2) green, Not green; 3) green, green; 4) Not green, not green; The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are green P(4) = 6/8*5/7=15/28 1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28 A #### A QUESTION:Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Tuesday, what was the expected day when both the brothers were to return home and when did Rohit Return? options: A)Wednesday, Sunday B)Thursday, Monday C)Friday, Tuesday D)Monday, Friday E)none SOLUTION:Rajat returned on Tuesday -i.e. 3 days earlier so actual day to return home is Friday. Rohit returned after days so Tuesday. ANSWER:C #### C QUESTION:The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $95 per day. What was his wage on the 8th day? options: A)$76 B)$90 C)$92 D)$97 E)$104 SOLUTION:Average daily wage of a worker for 15 consecutive working days = 90$ During the first 7 days , the daily average daily wage = 87$ During the last 7 days , the daily average daily wage = 95$ Wage on 8th day = 90*15 -( 87*7 + 95 *7) = 1350 - (609 + 665) =1350 - 1274 = 76 Answer A #### A QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:20000*2+8*x=15665*10 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth? options: A)80 B)28 C)90 D)26 E)11 SOLUTION:Explanation: SP of 1m of cloth = 8925/85 = Rs. 105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 105 - Rs. 25 = Rs. 80. Answer: A #### A QUESTION:1/3, 1/2, 1/4, 2 1/3, 3 1/2, 4 1/4, 4 1/3, 6 1/2, ? options: A)8 1/4 B)9 1/4 C)8 1/2 D)8 1/3 E)6 1/4 SOLUTION:there are 3 series--- 1/3,2 1/3,4 1/3. 1/2,3 1/2,6 1/2. 1/4,4 1/4,? ans 8 1/4 ANSWER:A #### A QUESTION:An article is bought for Rs.750 and sold for Rs.700, find the loss percent? options: A)6 2/5% B)6 2/9% C)6 5/3% D)6 3/3% E)6 2/3% SOLUTION:750 ---- 50 50 ---- ? => 6 2/3% Answer: E #### E QUESTION:Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 45 days. On which day of the week in February was the task completed? options: A)Tuesday B)Wednesday C)Saturday D)Sunday E)Monday SOLUTION:This type of story problem is essentially just about a repeating pattern and a 'remainder.' We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 45 DAYS. We're asked on what day of the week the task was actually completed on. Since the task was supposed to be completed on a Wednesday.... A 1 day postponement would be Thursday A 2 day postponement would be Friday A 3 day postponement would be Saturday A 4 day postponement would be Sunday A 5 day postponement would be Monday A 6 day postponement would be Tuesday A 7 day postponement would be Wednesday A 8 day postponement would be Thursday Etc. So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 45 days. 45/7 = 6 remainder 3 This means that there are 6 full weeks AND 3 extra days after a Wednesday....Thus, the task was completed on a Saturday. C #### C QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? options: A)21 B)36 C)39 D)60 E)65 SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96. Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room. Therefore there are 3/8*96=36 people in the room under the age of 21. Answer: B. #### B QUESTION:In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)32% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 38 are employed males,hence 26% are employed females. (employed females)/(total employed people)=26/64=40% Answer: D. #### D QUESTION:How many quarters are equal to 4 dollars? options: A)16 B)8 C)12 D)9 E)7 SOLUTION:4*4 = 16 quarters Answer : A #### A QUESTION:How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/6!? options: A)2 B)3 C)5 D)6 E)9 SOLUTION:7! = 720 1/1000 < 1/720< 1/100 0.001 < 1/720 < 0.01 So 1/720 has 2 leading zeros Answer: A #### A QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value R of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer R is 342. The correct answer is E. #### E QUESTION:An aeroplane covers a certain distance at a speed of 100 kmph in 2 hours. To cover the same distance in 1 hours, it must travel at a speed of? options: A)100km/hr B)150km/hr C)200km/hr D)250km/hr E)300km/hr SOLUTION:Distance = 100*2 = 200 km Required speed = 200 *1 = 200km/hr Answer is C #### C QUESTION:Find 283/1983×100 options: A)14.29 B)14.21 C)14.22 D)14.27 E)14.23 SOLUTION:Never start finding common factors. Adjust the denominator to 2000. So we are introducing an error of 17 which is 171983=1117171983=1117 th of the denominator. 283002000=14.15283002000=14.15 But this answer is slightly less than actual answer. Now 14.1511714.15117 = 0.12 approximately. Adding 0.12 to 14.25 gives 14.27. Option B is correct. #### B QUESTION:Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 12 machines produce in 6 minutes? options: A)1344 B)3360 C)8400 D)5040 E)67200 SOLUTION:8 machines produce 560 in 1 min 8 machines produce 560* 6 in 6 min 12 machine produce 560*6*(12/8) in 6 minutes 560*6*12/8=5040 answer is D. #### D QUESTION:From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 7, what is the probability that the 2 numbers included the number 5? options: A)1/5 B)2/5 C)3/10 D)3/5 E)1/3 SOLUTION:We know that the sum of two numbers picked was 7. So, there could be the following cases: (1, 6); (6, 1); (2, 5); (5, 2); (3, 4); (4, 3); Total of 6 cases out of which 2 have 5, thus the probability is 2/6=1/3. Ans E #### E QUESTION:Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 5, what is the probability that it is an even number? options: A)1/2 B)2/5 C)3/5 D)2/7 E)3/10 SOLUTION:There are 5 numbers higher than 5 and 3 of them are even. The probability is 3/5. The answer is C. #### C QUESTION:If n ≠ 0, which of the following must be greater than n? I. 2n II. 2 - n III. n^2 options: A)I only B)II only C)I and II only D)II and III only E)None SOLUTION:n ≠ 0 => n = negative or n = positive if n = negative: 2n < n (n = -1 then 2n = -2 => -2 < -1) n^2 > n (n =-1 then n^2 = 1 => n^2 > n) 2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n) but if n = positive: n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II 2 - n < n(n =2 then 2-2 = 0) => only III =>answer is E #### E QUESTION:The perimeter of a rectangular yard is completely surrounded by a fence that measures 36 meters. What is the length of the yard if the area of the yard is 40 meters squared? options: A)12 B)10 C)8 D)14 E)16 SOLUTION:Perimeter of rectangular yard = 2(l + b) = 36 --> l + b = 18 Area = l * b = 40 b = 18 - l l(18 - l) = 40 18l - l^2 = 40 l^2 - 18l + 40 = 0 Upon simplifying we get l = 5 or 8. Only 8 is there in the answer choice. Answer: C #### C QUESTION:Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they? options: A)350 B)400 C)500 D)550 E)590 SOLUTION:N * 50 = (325000 - 300000) = 25000 N = 25000 / 50 = 500 C #### C QUESTION:9.7 , 9.7 , 9.9 , 9.9 , 10.0 , 10.1 , 10.2 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.25 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90% B)85% C)80% D)75% E)70% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.25; 10+0.25} = {9.75; 10.25}. From the 8 listed numbers, 5 are within this range so 5/8=75%. Answer: D. #### D QUESTION:How many positive integers less than 100 are neither multiples of 2 or 3? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:1) multiples of 2 till 100 = 100/2 = 50 2) multiples of 3 till 100 = 100/3 = 33.33= 33 add the two 50+33=83 ; subtract common terms that are multiple of both 2 and 3.. LCM of 2 and 3 = 6 Multiples of 6 till 100 = 100/6 = 16.66 = 16 so total multiples of 2 and 3 = 83-16 = 67 100-67 = 33 Answer : D #### D QUESTION:2 identical circles intersect so that their centre and point at which they intersect form a square of 1 cm.the area of portion that is common two circles is 4 options: A)π2-1 B)4 C)√2-1 D)√5 E)π/2-1 SOLUTION:the area of the sector is pi*r^2*90/360 (as it is a square, so the angle is 90) =pi*r^2/4 =pi/4 (as the area of the square is 1cm^2, so the sides are 1 cm each. the sides of the square are the radii of the circle) now, the area of the triangle formed by two radii and a line which joins the point of intersection of the two circles = 0.5*1*1=0.5 So, half of the portion of our desired area= (pi/4 - 0.5) therefore, the area of our desired portion is 2* (pi/4 - 0.5) = pi/2 - 1 ANSWER:E #### E QUESTION:If a continuous cable 10 meters long was marked off at intervals of 1/5 meter and also 1/8 meter, and then if the cable were cut at each mark, how many different size length of cable would result? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:In this particular example length (10 meter) is just extraneous information. The location of the marks for 1/3 meter would be 8/40, 16/40, 24/40, 32/40, 40/40, etc... The location of the marks for 1/8 meter would be 5/40, 10/40, 15/40, 20/40, 25/40, 30/40, 35/40, 40/40, etc... The distances between marks are 5/40, 3/40, 2/40, 1/40, and 4/40. The answer is E. #### E QUESTION:Find the invalid no.from the following series 9, 16, 21, 28, 33, 37 options: A)13 B)18 C)40 D)37 E)25 SOLUTION:The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 37 is wrong. Answer : D #### D <<<Examples ends QUESTION:Nil and Ethan are brothers. They left their home at the same time and drove to the same beach. Nil drove at a speed of 80 miles per hour. Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach? options: A)70 miles B)80 miles C)90 miles D)100 miles E)110 miles SOLUTION:Every hour, Nil gets ahead of Ethan 80 - 20 = 60 miles. When Nil arrived at the beach, Ethan is only 20 × 0.5 = 10 miles behind. That tells us they only drove 1 hour when Nil arrived at the beach. The distance between their home and the beach is Nil’s speed × Nil’s time = 80 × 1 = 80 miles. correct answer B #### B