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mathematics

If sushi rows 27 km upstream and 81 km down steam taking 9 hours each, then the speed of the stream

Speed upstream = 27/9 = 3 kmph Speed down stream = 81/3 = 27 kmph Speed of stream = ½ (27-3) = 12 kmph ANSWER:A The answer is: A

A

mathematics

A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 60 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?

Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6 A1+A2+A3+A4+A5+A6 = 100*6 = 600 The year before , the 5 courses be B1, B2 , B3 , B4 , B5 B1+B2+B3+B4+B5 = 60*5 = 300 Student's average = (600+300)/11 = 81.81 Answer D The answer is: D

D

mathematics

A computer program generates a sequence of numbers a1, a2, a3,... such that a1=1, a2=2, and ak = a(k-1) + 3ak-2 for 2 < k < n for n=20. Find a5.

a1=1 a2=2 a3=3*2-2=4 a4=3*4-2=10 a5=3*10-2=28 28 The answer is: C

C

mathematics

3 boys and 7 girls can complete John work in 10 days . But 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?

Work done by 4 boys and 6 girls in 1 day = 1/8 Work done by 3 boys and 7 girls in 1 day = 1/10 Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as 4m + 6w = 1/8 ---(1) 3m + 7w = 1/10 ---(2) Solving equation (1) and (2) , we get m=11/400 and w=1/400 Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40 Ie, 10 girls can complete the work in 40 days C The answer is: C

C

mathematics

A tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume. If 6,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?

The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-6,000=4,000 gallons and sodium chloride is 600 gallons (6% of initial solution of 10,000 gallons) then sodium chloride is 600/4,000*100=15% of the remaining solution of 4,000 gallons. Answer: E. The answer is: E

E

mathematics

Which of the following is closest to (9!-8!)/(9!+8!)?

(9!-8!)/(9!+8!) 8! (9-1)/8! (9+1) 8/9 = 0.8 B is the answer The answer is: B

B

mathematics

A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?

π (232 – 122) = 1210 Answer:C The answer is: C

C

mathematics

In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.

This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds. For this particular question : Increase in the population every 2 seconds = 7-3 = 4 people. Total 2 second interval in a day = 24*60*60/2 = 43,200 Population increase = 43,200 * 4 = 172,800. Hence B. The answer is: B

B

mathematics

The investment of A, B, and C in a business are in the ratio 3:1:4. The total investment is Rs. 60,000. Find the investment made by each.

ratio of the investment is 3:1:4 Total investment =60000 so, 8x = 60000 ie)x =7500 so the investment of A, B,C are : A's investment 3x = 22500 B's investment x = 7500 C's investment 4x =30000 ANSWER:A The answer is: A

A

mathematics

10 books are placed at random in a shelf. The probability that a pair of books will always be together is?

10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Answer: C The answer is: C

C

mathematics

Katy worked for h hours each day for d consecutive days. If she earns $3.5 per hour, what is the total amount she earned?

H hours for d days. Income each day = 3.5*h Total income = 3.5*h*d Correct option: E The answer is: E

E

mathematics

Train X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other?

Explanation : Total time taken by B to cover 60 km 60/50 hr i.e 6/5 hr. It stops at station C for 1/4 hr Now , in (6/5 + 1/4) hr , train X travels 70 x (29/20) = 101.5 km. This means they do not cross each other by the time train Y finishes it stops at station C. Let they meet after t hour. Then, 70t + 50(t- 1/4) = 180. t = 192.5/120 hr. Distance from A will be 70 x 192.5/120 km i.e 112 km approximately. Answer : A The answer is: A

A

mathematics

Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

Explanation : Votes received by the winning candidate = 11628 Total votes = 1136 + 7636 + 11628 = 20400 Required percentage = (11628/20400) × 100 = 11628/204 = 2907/51 = 969/17 = 57% Answer : Option A The answer is: A

A

mathematics

What is the remainder of Q= 3^19 when divided by 10?

I looked for patterns: ^2 - units digit 9 ^3 - units digit 7 ^4 - units digit 1 ^5 - units digit 3 hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9 and we can then see: ^16 - units digit 1, or ^18 - units digit 9 and ^19 - units digit 7 therefore, Q=when divided by 10, the remainder must be 7.D The answer is: D

D

mathematics

A and B complete a job in 6 days. A alone can do the job in 8 days. If B works alone, how many days will it take to complete the job?

The rate of A and B is 1/6 A's rate is 1/8 B's rate is 1/6 - 1/8 = 1/24 B can complete the job in 24 days. The answer is D. The answer is: D

D

mathematics

Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?

1/2 * 20(9 + 6) = 150 cm2 Answer:B The answer is: B

B

mathematics

A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)?

Speed = 5 km/hr Time = 15 minutes = 1/4 hour Length of the bridge = Distance Travelled by the man = Speed × Time = 5×1/4 km=5×(1/4)×1000 metre=1250 metre Answer is B The answer is: B

B

mathematics

What is the place value of 7 in the numeral 51468?

place value of 1 = 1 * 1000 = 1000 Answer is D The answer is: D

D

mathematics

A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?

Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 18 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 28 => x = 14, y = 4. Answer: D The answer is: D

D

mathematics

If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ?

x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer The answer is: D

D

mathematics

There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?

Note that each handshake includes two people. The total number of handshakes is 14*3/2 = 21 The answer is B. The answer is: B

B

mathematics

If (x^2 + 1)y=8, which of the following is not a possible value for y?

Its simple equation is (x^2 +1)y = 8 ===> x^2 = (8/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (8/y) - 1>= 0 ===> y =< 8. Now only option E has greater value of 'y' than 8. Thus, correct ans is E The answer is: E

E

mathematics

How many seconds will a 700 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

Let length of tunnel is x meter Distance = 700+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time 700+x = (65/3) * 60 700+x = 20 * 65 = 1300 x = 1300 - 700 = 600 meters Answer: C The answer is: C

C

mathematics

The population of a bacteria colony doubles every day. If it was started 3 days ago with 3 bacteria and each bacteria lives for 12 days, how large is the colony today?

9 days ago- 2 8 days ago- 4 7 days ago- 8 6 days ago- 16 5 days ago- 32 4 days ago- 64 3 days ago- 128 2 days ago- 256 Yesterday- 512 Today- 1024 Answer:B The answer is: B

B

mathematics

7 men, 5 women and 8 children were given as assignment of distributing 2000 books to students in a school over a period of 3 days. All of them distributed books on the 1st day. One of the 2nd day 2 women and 3 children remained absent and on the 3rd day 3 men and 5 children remained absent. If the ratio of the no. of books distributed in a day by a man, a woman & a child was 5 : 4 : 2 respectively, a total of approximately how many books were distributed on the second day?

Sol. Let the books distributed by man, a woman and a child be 5x, 4x and 2x respectively. ∴ No. of books distributed in 1st day = 7×5x+5×4x+8×2x=71x No. of books distributed in 1Ind day =7×5x+3×4x+5×2x=57x And no. of books distributed in IIIrd day =4×5x+5×4x+3×2x=46x 71x + 57x + 46x = 2000, x = 2000/174 57x=2000/174×57=650 D The answer is: D

D

mathematics

Find the invalid no.from the following series 3, 7, 15, 31 , 63, 127, 257

Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 257 is wrong. C The answer is: C

C

mathematics

If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b + c ?

consectutive even , X , X + 2 , X + 4 where X = Even now subtract X + (X+2) + (X+4) doing this leaves us with 3X + 6 what even number can we substitute in X to yield an answer choice A works 18 (plug in 4 for X) The answer is: A

A

mathematics

An equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 8, in how many ways can she choose and rank her top 4 picks?

Number of ways of choosing 4 stocks = 8C4 Number of ways of ranking the chosen stocks = 4! Hence total ways of chosing and ranking = 8C4 * 4! = 1680 Correct Option: B The answer is: B

B

mathematics

Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 70kmph. When will Raghu overtake Anup?

Suppose bike is overtaken by car xhrs after 6am Distance covered by the bike in x hrs = distance covered by the car in x-1 hr 60x = 70(x-1) 10x = 70 x = 7 hrs Required time = 6+7 = 01:00Pm Answer is D The answer is: D

D

mathematics

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the remainders will be.

4 l X --l--- 5 l Y - 1 Therefore Y = (5 x 1 + 4) = 9 --l------ X = (4 x Y + 1) = (4 x 9 + 1) = 37 l 1 - 4 Now 37 divided successively by 5 and 4, we get 5 l 37 --l--- 4 l 7 - 2 Therefore Y = (5 x 1 + 4) = 9 --l------ X = (4 x Y + 1) = (4 x 9 + 1) = 37 l 1 - 3 so the respective remainders are 2 and 3. Answer B. The answer is: B

B

mathematics

Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $31.50. What was the percentage profit?

A dozen toys cost $360, so each toy cost $30. selling price / cost price = 31.50 / 30 = 1.05 The percentage profit is 5%. The answer is B. The answer is: B

B

mathematics

If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:

(0.2)x = 2. Taking log on both sides log (0.2)x = log 2. x log (0.2) = 0.3010, [since log 2 = 0.3010]. x log (2/10) = 0.3010. x [log 2 - log 10] = 0.3010. x [log 2 - 1] = 0.3010,[since log 10=1]. x [0.3010 -1] = 0.3010, [since log 2 = 0.3010]. x[-0.699] = 0.3010. x = 0.3010/-0.699. x = -0.4306…. x = -0.4 (nearest tenth) The answer is: C

C

mathematics

There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?

In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence 3x + 5x = 600 Solve for x 8x = 600 x = 75 Number of boys 3x = 3 × 75 = 225 Number of girls 5x = 5 × 75 = 375 C The answer is: C

C

mathematics

1/x+1/y=1/z where x=12 and y,z positive integer how many possible value of y and z ?

1/12 = 1/z - 1/y y = 12 * z / ( 12 - z ) 0 < z < 12 Only for z = 3 ,4 ,6 ,8 , 9 ,10 and 11 , y is intiger Hence seven solutions ANSWER:B The answer is: B

B

mathematics

Pipe A can fill a tank in 4 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?

The part filled by A + B + C in 1 hour = 1/4 + 1/8 + 1/24 = 10/24 All the three pipes together will fill the tank in 24/10 = 2.4 hours. The answer is A. The answer is: A

A

mathematics

What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!?

the number of 7s in 21!= 21/7=3.. ans B The answer is: B

B

mathematics

Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.143 per kg, the price of the third variety per kg will be

Solution Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x-143/22.50 = 1 =› x - 143 = 22.50 =› x=165.50. Hence, price of the third variety = Rs.165.50 per kg. Answer A The answer is: A

A

mathematics

Victor gets 80 % marks in examinations. If these are 240 marks, find the maximum marks.

Let the maximum marks be m Then 80 % of m = 240 ⇒ 80/100 × m = 240 ⇒ m = (240 × 100)/80 ⇒ m = 24000/80 ⇒ m = 300 Therefore, maximum marks in the examinations are 300 Answer:B The answer is: B

B

mathematics

The difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is 45. Then the original sum is?

For 2 years = (100(power 2)D)/R(power 2) = (100(power 2) × 45)/(5 × 5) = (10000 × 45)/25 = Rs.18000/- Answer is E. The answer is: E

E

mathematics

Three unbiased coins are tossed. What is the probability of getting 1 heads, 1 Tail?

Let, H --> Head , T --> Tail Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting 3 heads Then E = {THT, HTH} P(E) = n(E)/n(S) =2/8 Answer is E The answer is: E

E

mathematics

In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?

A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (100 - 75) = 25 points to C. Answer:C The answer is: C

C

mathematics

What is the difference between the place values of two sevens in the numeral 54179759 ?

Explanation: Required Difference = 70000 - 700 = 69300 Answer is D The answer is: D

D

mathematics

A boat moves upstream at the rate of 1 km in 25 minutes and down stream 1 km in 12 minutes. Then the speed of the current is :

Rate upstream = (1/25 *60) = 2.4 kmph Rate dowm stream = 1/12 * 60 = 5 kmph Rate of the current = ½ (5-2.4) = 1.3 kmph ANSWER:D The answer is: D

D

mathematics

The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)

Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer:A The answer is: A

A

mathematics

A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 50min will be.

Time=50/60 hr=5/6hr Speed=48mph distance=S*T=48*5/6=40km time=50/60hr=5/6hr New speed = 40* 6/5 kmph= 48kmph Answer : C The answer is: C

C

mathematics

A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in one hour?

Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600 :. Distance moves = (600 *20) cms = 12000 cms In metres = 120 metre Answer: C The answer is: C

C

mathematics

If all the sides of a right triangle increase in length by 8%, then by what percentage does the area of the triangle increase?

Let B be the base and H be the height of the original triangle. The original area is (1/2)BH. The area of the expanded triangle is (1/2)(1.08B)(1.08H) = (1.08)(1.08)(1/2)BH = 1.1664(1/2)BH The answer is B. The answer is: B

B

mathematics

A man spends 20% of his income in house rent, 10% of the rest on his children’s education, 15% of the rest miscellaneous causes. If he now posses Rs. 6352 then his income is?

X * (80/100) * (90/100) * (85/100) = 6352 X * 0.8 * 0.9 * 0.85=6352 X = 6352/0.612 X = 10379 ANSWER:A The answer is: A

A

mathematics

ramesh,ram,kareem and Mohan collected coins of different countries. they collected 100 together. none collected less than 10.each collected an even number. each collected a different number. based on these, we can say that the number of coins collected by the boy who collected the most could not have exceeded

as other three must have collected atleast 10+12+14=36 coins the number of coins collected by the boy who collected the most could not have exceeded 100-36=64 ANSWER:B The answer is: B

B

mathematics

If a and b are the roots of the equation x2 - 5x + 5 = 0, then the value of a2 + b2 is:

Sol.(b) The sum of roots = a+ b = 5 Product of roots = ab = 5 Now, a2 + b2 = (a + b)2 - 2ab = 25 - 10 = 15 Answer C The answer is: C

C

mathematics

A and B go around a circular track of length 300 m on a cycle at speeds of 34 kmph and 50 kmph. After how much time will they meet for the first time at the starting point?

Time taken to meet for the first time at the starting point = LCM { length of the track / speed of A , length of the track / speed of B} = LCM { 300/ (36 * 5/18) , 300/ (54 * 5 /18) } = LCM (30, 20) =60 sec. Answer:B The answer is: B

B

mathematics

21, 9, 21, 11, 21, 13, 21, ?

D 15 In this alternating repetition series, the number 21 is interpolated. If you exclude 21, the series increases by 2, beginning with the number 9. The answer is: D

D

mathematics

If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions W represents the final price of the item?

-A- z=Original Price x=MU y= MD New price with MU: z(x/100+1) New price with MD: z[(x/100+1)(-y/100+1)] Solving… =z[((x+100)/100)((-y+100)/100)] =z(x100-xy+10000-100y)/10000 =(zx100-xyz+10000z-100yz)/10000 --> similar to A The answer is: A

A

mathematics

Mr. Sam's car gets him 50 miles per gallons of gas. If Mr Sam get a full tank with 14 gallons of gas, How far can Mr Sam go?

Solution Number of miles per gallon = 50 miles Number of miles 14 gallons = x x = 50 × 14 = 700 miles. So, Number of miles Sam gets with 14 gallons = 700 miles. Option C The answer is: C

C

mathematics

A reduction of 12% in the price of oil enables a house wife to obtain 6kgs more for Rs.1200, what is the reduced price for kg?

1200*(12/100) = 144 ---- 6 ? ---- 1 => Rs.24 Answer:A The answer is: A

A

mathematics

The rate of spin of a certain gyroscope doubled every 15 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 400 meters per second, what was the speed, in meters per second, when the stopwatch was started?

Let x be the original speed when the stopwatch was started. In 90 seconds, the speed doubled 6 times. 2^6 * x = 400 x = (2^4 * 25) / 2^6 = 25/4 The answer is B. The answer is: B

B

mathematics

The ratio of the number of students appearing for examination in the year 1998 in the states A, Band C was 3 : 5 : 6. Next year if the number of students in these states increases by 20%, 10% and 20% respectively, the ratio in states A and C would be 1 : 2. What was the number of students who appeared for the examination in the state A in 1998?

Let the number of students appearing for examination in the year 1998 in the states A, B and C be 3x, 5x and 6x respectively. According to the question, 3x×120/100 /6x×120/100=12 Hence data inadequate. Answer D The answer is: D

D

mathematics

An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

1.04*1.04*6000 = $6489.60 The answer is B. The answer is: B

B

mathematics

Three printing presses, L, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take L, working alone at its constant rate, to do the same job?

=1/4-1/5=1/20 L can do 1/20 job in 1 hour L can do the whole job in 20 hours=E The answer is: E

E

mathematics

I forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialing the first four, then what is the chance of dialing the correct number?

Explanation: It is given that last three digits are randomly dialled. then each of the digit can be selected out of 10 digits in 10 ways. Hence required probability = = 1/1000 Answer: C) 1/1000 The answer is: C

C

mathematics

When positive integer N is divided by positive integer J, the remainder is 28. If N/J = 142.07, what is value of J?

When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder So, Dividend/Divisor = Quotient + Remainder/Divisor Given that N/J = 142.07 Here 142 is the quotient. Given that Remainder = 28 So, 142.07= 142 + 28/J So, J = 400 Answer- C The answer is: C

C

mathematics

Sam taken a loan Rs.15000/- from Co-operative Society with an interest @ 11.5% per month. At the same time he deposited Rs. 10000/- as Fixed Deposit with an interest @ 9.5% per month. After one week sam asked the manager to calculate the interest to be paid. What is the interest amount for 7 days?

Loan amount : Rs.15000/- @ 11.5% Interest per month = 15000/- * 11.5% =Rs.1725 Interest for one day = 1725/30=57.50 Interest for 7 days is = 57.50*7 =403 FD amount is = Rs.10000/- @ 9.5% Interest per month = 10000 * 9.5% = 950/- Interest for 7 days = 950/30*7 = 222 Interest amount to be paid by Sam = 403-222 =181/- for 7 days Answer is E The answer is: E

E

mathematics

(5!+6!+4!)/4!*0!*5*6=?

4!(5+30+1)/4!*1*5*6 36/30=6/5 answer B The answer is: B

B

mathematics

If each term in the sum Q=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?

Min value of 'n' can be 10 i.e 4*22+6*12 =Q=> 22+22+22+22+2+2+2+2+2+2 = 100 Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options (20-1) + 22/2 = 30 digits ( not in options) (30-1) + 22/2 = 40 digits Hence C. The answer is: C

C

mathematics

The avearge score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 45. Then find the average for the last four matches?

Solution Required average =(38.9 x 10)-(45 x 6)/ 4 = 119 / 4. = 29.75 Answer D The answer is: D

D

mathematics

A+B+C+D=D+E+F+G=G+H+I=17 given A=4. Find value of G and H?

A+B+C+D=17 4+2+6+5=17 D=5 D+E+F+G=17 5+3+8+1=17 G=1 G+H+I=17 1+9+7=17 G=1,H=9. ANSWER:C The answer is: C

C

mathematics

Find the mean proportional between 81 & 100?

Formula = √a×b A = 81 and B = 100 √81×100 = 9 × 10 = 90 E The answer is: E

E

mathematics

In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

Distance covered by B in 9 sec. = \inline \fn_jvn {\color{Black} \left ( \frac{100}{45}\times 9 \right )m} = 20m \fn_jvn {\color{Black} \therefore } A beats B by 20 metres. Answer: A) 20m The answer is: A

A

mathematics

There are 10 books on a shelf: 6 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?

Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome) Favourable Outcomes Case-1: One book is English (out of 6 English books) and one book is Spanish (out of 3 Spanish books) i.e. 6C1*3C1 Case-2: One book is Spanish (out of 3 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 3C1*2C1 Case-3: One book is English (out of 6 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 6C1*2C1 Total favourable Outcomes = 6C1*3C1+3C1*2C1+6C1*2C1 = 18+6+12 = 36 Total Possible Outcomes = 10C2 = 45 i.e. Probability = 36/45=4/5 C The answer is: C

C

mathematics

In a group containing 6 cows and 4 buffalos, 4 livestock are to be selected in such a way that at least 1 cow should always be present. How many way of doing that are possible?

ANSWER:A The answer is: A

A

mathematics

A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 33. Find the profit percentage?

L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 165 (33 * 5) Profit percentage = (165 - 100)/100 * 100 = 65% Answer: A The answer is: A

A

mathematics

In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?

T = 60/36 * 18/5 = 6 sec Answer:D The answer is: D

D

mathematics

2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other ata distance of 110km from one of the stations.what is the ratio of their speeds.

In same time ,they cover 110km & 90 km respectively so ratio of their speed =110:90 = 11:9 Answer is B. The answer is: B

B

mathematics

B completes a work in 3 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?

1/3 + 1/10 = 13/30 30/13 = 2.31 days ANSWER:A The answer is: A

A

mathematics

The sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?

Sale Price = (5/4)*(Cost Price) If the sale price is an integer, then the cost price must be divisible by 4. The answer is E. The answer is: E

E

mathematics

If –2 < x < 2 and x ≠ 0, which of the following inequalities must be true? I. x^3 < x II. x^2 < |x| III. x^4 – x^5 > x^3 – x^2

Answer is D. Let's look at the statements one by one Stmt I. x^3 < x if 0<x<1 then x^3< x but if -1<x<0 then x^3>x So this statement is not always true Stmt II. x^2 < |x| Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|. Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2 So Stmt II is always true Stmt III. x^4 – x^5 > x^3 – x^2 This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1). Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 which means that (1-x)>0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true. So Stmt III is always true C The answer is: C

C

mathematics

Volume of a hemisphere is 19404 cu. cm. Its radius is :

Sol. Let the radius be R cm. Then, 2/3 * 22/7 * R³ = 19404 ⇔ R³ = [19404 * 21/44] = (21)³ ⇔ R = 21 cm. Answer C The answer is: C

C

mathematics

A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.

Explanation: Distance covered in one revolution = = 88m. Answer: A) 14 The answer is: A

A

mathematics

lexus car agency has 162 cars.he sold some cars at 9% profit and rest at 36% profit thus he gains 17% on the sale of all his cars.the no. of cars sold at 36% profit is?

ratio of 36% profit cars to 9% profit cars = 8:19 so no. of cars sold at 36% profit = 162*8/27= 48 cars ANSWER:C The answer is: C

C

mathematics

The number of positive integer solutions for the equation x +y +z + t = 10 is

The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k (k-1)C(n-1)- where k is the number and n is number of variable in the equation. 10-1 C 4-1 = 9C3 = 84 Answer : C The answer is: C

C

mathematics

If a:b=2:8 and b:c=3:4 find a:b:c?

a:b = 2:8, b:c = 3:4 2:8 3:4 (a = a × b, b = b × b and c = b × c) a:b:c = 3:12:16 A The answer is: A

A

mathematics

What is the area of a triangle with the following vertices L(1, 3), M(5, 1), and N(2, 5) ?

There is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem. Though if you make a diagram minimum simple calculations will be needed: Answer: C. The answer is: C

C

mathematics

On a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 800 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?

Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 500(1.10)^2 = 500(1.21) = 605 and Lana would have 800(1.05)^2 = 800(1.1025) = 882 Thus, Tim earned 105 dollars, while Lana earned 82 dollars The difference is $23 and the answer is C. The answer is: C

C

mathematics

Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.

If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by: Sa/Sb = √(b/a) i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken. Sa/Sb = √(4/9) = 2/3 This gives us that the ratio of the speed of A : speed of B as 2:3. Since speed of A is 60 kmph, speed of B must be 60*(3/2) = 90 kmph Answer B The answer is: B

B

mathematics

If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+3 ?

let we put values. a=1, b=3, c=5 5-3-1=1 1+3 =4 Answer :A The answer is: A

A

mathematics

When you multiply a number by 4 and then subtract 8, the result is the same as if you first subtracted 4 from the same number and then multiplied by 12. What is the number?

Let x equal the number and then change the words into an equation and solve for x: 4x – 8 = 12(x – 4) 4x – 8 = 12x – 48 40 = 8x 5 = x correct answer A)5 The answer is: A

A

mathematics

Two trains 120 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?

T = (120 + 165)/ (80 + 65) * 18/5 T = 7.07 Answer: C The answer is: C

C

mathematics

A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?

12:9 = 4:3 Answer:C The answer is: C

C

mathematics

Pipe A can fill a tank in 6 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled?

The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. The answer is: B

B

mathematics

Mike needs 30% to pass. If he scored 212 marks and falls short by 28 marks, what was the maximum marks he could have got?

If Mike had scored 28 marks more, he could have scored 30% Therefore, Mike required 212 + 28 = 240 marks Let the maximum marks be m. Then 30 % of m = 240 (30/100) × m = 240 m = (240 × 100)/30 m = 24000/30 m = 800 Answer:C The answer is: C

C

mathematics

If the sum of n consecutive positive integers is 33, what of the following could be the value of n? I. 3 II. 6 III. 11

solved it the way bunuel explained, although took some time to arrive to the answer choice. 3 -> 10+11+12=33. 6 ->3+4+5+6+7+8=33. 11 -> since we are told that we have a set of n consecutive POSITIVE numbers, we can have the smallest possible numbers: 1+2+3+4+5+6+7+8+9+10+11 - the sum is way over 33, it is actually 11*12/2 = 11*6=66. thus, only I and II works. the answer is D The answer is: D

D

mathematics

The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average?

Sum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled. The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72. ANSWER:D The answer is: D

D

mathematics

Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 14,950, Deepak's share is:?

Ratio of their shares = 22500 : 35000 = 9:14 Deepak's share = 14950 * 14/23 = Rs.9100. Answer:B The answer is: B

B

mathematics

Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?

Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation larger number – smaller number = 7 which is equivalent to Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31. C The answer is: C

C

mathematics

A train 350 m long, running with a speed of 63 km/hr will pass a tree in?

Speed = 63 * 5/18 = 35/2 m/sec Time taken = 350 * 2/35 = 20 sec Answer:B The answer is: B

B

mathematics

When a metallic ball bearing is placed inside a cylindrical container, of radius 2 cm, the height of the water, inside the container, increases by 0.6 cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is

Solution When the ball was put in water, the volume of water increased by. pi*22*0.6 = 2.4 pi cubic cm The above volume is equal to the volume of the ball with radius r to find. Hence (4/3)*pi*r3 = 2.4 pi Solve the above for r r = 1.2 cm Answer B The answer is: B

B

mathematics

A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?

Explanation: Method : 1 If a car covers a certain distance atxkmph and an equal distance at y kmph, the average speed of the whole journey = 2xy/x+y kmph. By using the same formula, we can find out the average speed quickly Speed with which he travels from A to B = x = 40 km/hr Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr average speed = (2×40×60)/(40+60) = 48 km/hr Assume that distance from A to B = x km Speed with which he travels from A to B = x = 40 km/hr Time to travel from A to B = distance/speed = x/40 hr Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr Time to travel from B to A = distance/speed = x/60 Total distance traveled = x+x = 2x Total time taken = x/40 + x/60 Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60) = 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr Answer: Option A The answer is: A

A

mathematics

A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year

Explanation: 5% is the rate of interest. 20% of the interest amount is paid as tax. i.e 80% of the interest amount stays back. if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value. The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest. = 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32 The amount at the end of 3 years = 5000 + 624.32 = 5624.32 Answer: A) Rs.5624.32 The answer is: A

A

mathematics

a pizza which is thin is cut into 'x' pieces by 4 straight lines then the lowest possible value of x is?

4 parallel lines will give minimum number of pieces. 5 pieces. ANSWER:C The answer is: C

C

mathematics

A train is 360 meter long is running at a speed of 30 km/hour. In what time will it pass a bridge of 140 meter length?

Speed = 30 Km/hr = 30*(5/18) m/sec = 25/3 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 * (3/25) = 60 seconds Answer: C The answer is: C

C