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The Wordsmiths 3

mathematics

If w is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?

Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey w=4n, if it really wanted to convey so. From other questions that I have seen, proper wordings could be: If w is three times as large as n OR simply, If w is three times n.C The answer is: C

C

mathematics

A survey was sent to 60 customers, 7 of whom responded. Then the survey was redesigned and sent to another 72 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?

Rate of first survey = 7/60 Rate of second survey = 9/72 % Response rate increase (9/72-7/60)/(7/60) = 7% Answer is B = 7% The answer is: B

B

mathematics

Divide Rs.32000 in the ratio 1:9?

1/10 * 32000 = 3200 9/10 * 32000 = 28800 Answer: D The answer is: D

D

mathematics

If {g} denote the remainder when 3g is divided by 2 then which of the following is equal to 1 for all positive integers g? I. {2g+1} II. {2g}+1 III. 2{g+1}

C - I and II 3g/2 = 0 or 1 I just substituted 1 in the equations and solved. The answer is: C

C

mathematics

The function f is defined for all positive integers n by the following rule. f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime, number then f(p)=

p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p). For example: if p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6. Answer: A. The answer is: A

A

mathematics

What would be the local minimum for the function represented as f(x,y) = x2 +ay+y2 -3x ?

f(x,y) = x2 + ay + y2 - 3x = 4 - a + 1 - 6 = -a-1 So the above value will be the minimum if u check for all other options also. therefore, the answer is (2,-1) ANSWER:B The answer is: B

B

mathematics

There are 3 bags, in 1st there are 9 Mangoes, in 2nd 8 apples & in 3rd 6 bananas. There are how many ways you can buy one fruit if all the mangoes are identical, all the apples are identical, & also all the Bananas are identical?

Since bags are different so it should be 9+8+6=23 ANSWER:C The answer is: C

C

mathematics

New town is straight to the north of New york. A high way M runs from newtown making an angle of 61 degree south east. from newyork there is also an high way N which runs Northeast 61 degrees. If high ways M and N are straight then findout the acute angle made at their intersection point.

the acute angle must be 58 degree . taking north-south as reference axis . from center M is at an angle of 61degree near south and N is at an angle of 61degree from north .therefore, 180-61-61 gives 58degree ANSWER:C The answer is: C

C

mathematics

Which of the following is a prime number ?

Clearly, 97 is a prime number The answer is: C

C

mathematics

What number should replace the question mark? 100, 93, 79, 53, ?.

A 30 The sequence progresses –7, –14, –21, –28. The answer is: A

A

mathematics

1 Decade ago, Karthik’s mother was quadrice older than her son. After one decade, the mother will be two times older than her son. The current age of Karthik is? [Decade = 10 Years; quadrice= 4 times]

A 20 years Let Karthikh’s age 10 years ago be A year His mother’s age 1 decade ago = 4A (4A + 10) + 10 = 2 (A + 10 +10) 2A = 20 or A =10 Current age of Karthikh = (A + 10) = 20 years The answer is: A

A

mathematics

Tanks A and E are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank E has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank E?

B. For A, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi For E, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi A/E = 160pi/200pi = 0.8=B. The answer is: B

B

mathematics

Today John is 3 times older than Mark. If in 13 years, John will be one year younger than twice the age of Mark on that day, how old is Mark today?

today +13yrs J =3M 3M+13 M M+13 Given after 13yrs john will be 1 year younger than twice mark's age i.e 3M+13 = 2(M+13)-1 M=12 Answer is A. The answer is: A

A

mathematics

If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?

Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. The answer is: E

E

mathematics

Evaluate: 6502.5 + 650.25 + 65.025 + 6.5025 + 0.65025

6502.5 650.25 65.025 6.5025 + 0.65025 --------------- 7224.92775 Answer is C. The answer is: C

C

mathematics

Java House charges $4.25 for a cup of coffee that costs a total of $3.85 to make. Cup'O'Joe charges $4.80 for a cup that costs $4.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

Java: Profit/Cup = 4.25-3.85 = 0.4 : No of Cups = 55,000 : Gross Profit = 55,000*0.4 = 22,000 Joe: Profit/Cup = 0.15 : Gross Profit = 22,000 : No of Cups = 22,000/0.15 = 220,000/1.5 (only closes is 146,667) Answer E The answer is: E

E

mathematics

The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 120 metres?

Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 120/5 = 24 seconds. Answer:C The answer is: C

C

mathematics

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?

S.I. for 1 year = (854 - 815) = Rs. 39 S.I. for 3 years = 39 * 3 = Rs. 117 Principal = (815 - 117) = Rs. 698.Answer:C The answer is: C

C

mathematics

A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 3500. The difference between the profit shares of A and C is?

Explanation: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6 And also given that, profit share of B is Rs. 3500 => 5 parts out of 15 parts is Rs. 3500 Now, required difference is 6 - 4 = 2 parts Required difference = 2/5 (3500) = Rs. 1400 Answer:B The answer is: B

B

mathematics

150 is increased by 40%. Find the final number.

Final number = Initial number + 40%(original number) = 150 + 40%(150) = 150 + 60 = 210. Answer B The answer is: B

B

mathematics

Tom, who has 50 math questions, will get 7 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 3 points per question. Then, which of the following can be the score if he solves all the 50 questions?

Let x be the correctly answered questions. y be the wrongly answered/ skipped ones. We have x + y = 50; Score = 7x-3y 3x+3y = 150; 7x-3y = Score; ==> 10x = 150+Score; check for answer choices where 150+Score is divisible by 10 Choice (A) 190 fits the equation ! The answer is: A

A

mathematics

The first three terms of a proportion are 4, 12 and 16. The fourth term is?

(12*16)/4 = 48 Answer:E The answer is: E

E

mathematics

If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?

Explanation: 100 150 ------ 150-------50 100-------? => 331/3% A) The answer is: A

A

mathematics

A jeep takes 9 hours to cover a distance of 480 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?

Time = 9 Distance = 480 3/2 of 9 hours = 9 * 3/2 = 13.5 Hours Required speed = 480/13.5 = 35 Kmph C) The answer is: C

C

mathematics

The area of a parallelogram is 288sq m and its altitude is twice the corresponding base. Then the length of the base is?

2x * x = 288 => x = 12 Answer: E The answer is: E

E

mathematics

If a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%?

96% ---- 72 144% ---- ? 96/144 * 72 = 48 Answer: B The answer is: B

B

mathematics

Cuboid volume and Base area are 144 m^3 and 18m^3 respectively.Find the height of a cuboid?

Height of the cuboid=Volume* Base area =144/18 =8 metre Answer is option D The answer is: D

D

mathematics

A, B and C enter into a partnership by investing Rs. 15000, Rs.21000 and Rs.27000 respectively. At the end of 8 months, B receives Rs.1260 as his share. Find the share of A.

Explanation: Ratio of capital of A, B and C = 15000 : 21000 : 27000 = 5 : 7 : 9 Let the total profit be Rs. x. Then, B's share = Rs. 7x/21 = Rs. x/3 But x/3 = 1260 => x = 3780 Hence, the total profit = Rs. 3780 A's share = Rs.[(5/21) × 3780] = Rs. 900 Answer: Option D The answer is: D

D

mathematics

What is the sum of all possible solutions to |x + 3|^2 + |x + 3| = 20 ?

Denote |x + 3| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x + 3|, so it's an absolute value and thus cannot be negative. y = |x + 3| = 4 --> x = 7 . The sum = 7. Answer: C. The answer is: C

C

mathematics

The average (arithmetic mean) of 8 numbers is Z, and one of the numbers is 14. If 14 is replaced with 28, then what is the new average (arithmetic mean) in terms of Z?

(8z−14+28)/8 Or, (8z+14)/8 Or, (4z+7)/4 Or, z+7/4 So, correct answer will be (B) z+7/4 The answer is: B

B

mathematics

In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 20 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 50 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?

I will go with option B According to question 50 percent of total votes (N) cas were cast by independent voters. This implies 50 percent of N are voters that belong to political party. And she received 7000 votes from independent voters and 20 percent from registered voters (i.e 0.2 * 0.5 * N = 0.1N). Hence total votes = 7000 + 0.1N ....option B The answer is: B

B

mathematics

The sum of first five prime numbers is:

Explanation: Required sum = (2 + 3 + 5 + 7 + 11) = 28. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. ANSWER IS D The answer is: D

D

mathematics

If x > 0.3, which of the following could be the value of x?

Answer : C The answer is: C

C

mathematics

Which one of the following is the common factor of (47^43 + 43^43) and (47^47 + 43^47) ?

Explanation: When n is odd, (x^ + a^n) is always divisible by (x + a). Each one of (47^43 + 43^43) and (47^47 + 43^47) is divisible by (47 + 43). B The answer is: B

B

mathematics

A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?

Explanation: Let the number be x. Therefore, 3(2x + 5) = 105 6x + 15 = 105 6x = 90 x = 15 ANSWER:D The answer is: D

D

mathematics

A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 210, then how much amount should C pay as his share of rent?

A : B : C =10×7:12×5:15×3 =2×7:12×1:3×3 =14:12:9 Amount that C should pay =210×9/35=6×9=54 Answer is A The answer is: A

A

mathematics

A reduction of 30% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?

800*(25/100) = 240 ---- 5 ? ---- 1 => Rs.48 Answer: C The answer is: C

C

mathematics

When a number is divided by 13, the remainder is 6. When the same number is divided by 7, then remainder is 1. What is the number ?

Explanation: Take 243 243 ÷ 7 = 34, remainder = 5 Hence this is not the answer Take 312 312 ÷ 7 = 44, remainder = 4 Hence this is not the answer Take 253 253 ÷ 7 = 36, remainder = 1. 253 ÷ 13 = 19, remainder = 6 This satisfies both the conditions given in the question. Hence it is the answer. Answer: B The answer is: B

B

mathematics

Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 50 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?

7:00 am so 6 hours later is 1:00 pm In six hours, Robert will have driven 6*30 = 180 miles In six hours, Alive will have driven 6*50 = 300 miles So Robert needs 300-180 = 120 miles do catch Alice up. So at 30 mph, he will need 2 hours 1:00 pm + 6 hours = 7:00 pm ANS : D The answer is: D

D

mathematics

How many ways are there to award a gold, silver and bronze medal to 15 contending teams?

we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 15 ways if gold medal is given to 1 of the teams then only possible 14 teams can be considered for silver medal. we can do selection in 14 ways similarly if gold and silver medals are awarded then only remaining 13 teams can be considered for a bronze medal. we can do the selection in 13 ways Total number of ways to select the 3 possible medal winners = 15 * 14 * 13 Correct answer - A The answer is: A

A

mathematics

MANO,INC recently conducted a survey and found that 100,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of MANO,INC customers live in urban areas ?

Let's say that we have a starting value of X... 100% of X = X 100% MORE than X = X + X = 2X 200% MORE than X = X + 2X = 3X 300% MORE than X = X + 3X = 4X Etc. Here, we're told that 100,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas... 3(100,000) = 300,000 Final Answer:D The answer is: D

D

mathematics

A sells a bicycle to B at a profit of 50% and B sells it to C at a loss of 40%. Find the resultant profit or loss.

The resultant profit or loss = 50 - 40 - (50*40)/100 = -10% loss = 10% Answer is E The answer is: E

E

mathematics

The sum of money at compound interest amounts to thrice itself in 5 years. In how many years will it be 15 times itself?

100 ---- 300 --- 5 600 --- 5 900 ---5 1200 ---5 1500--- 5 25 years Answer: D The answer is: D

D

mathematics

The number of the members of a club is more than 50 and less than 80. When 5 people sit at a table, other people exactly divided to 8-people groups (8 people sit at a table) or 7-people groups (7 people sit at a table). If the members are divided to 9-people groups, how many people will be left?

The number of members is 7k+5 = 8j+5 The only number in this range which satisfies this is 61. 61/9 = 6(9) + 7 The answer is D. The answer is: D

D

mathematics

The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 8 months, find for how much time did Q invest the money?

7*5: 8*x = 7:10 x = 16 Answer:D The answer is: D

D

mathematics

Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points?

A 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. The answer is: A

A

mathematics

In the xy-coordinate system, if (m,n) and (m+2, n+k) are two points on the line perpendicular to x=2y+5, then k=?

the slope= k/2 the line perpendicular to x=2y+5 or y=1/2x-5/2 has a slope= -1/ (1/2) =-2 --->k/2=-2 --> k=-4 Answer is D The answer is: D

D

mathematics

What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?

160 = (180*4*R)/100 R = 5% Answer: A The answer is: A

A

mathematics

Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 15 books, how many shelves does the bookcase have?

Let x be the number of shelves. 12x - 21 = 8(x-1) + 15 4x = 28 x= 7 The answer is C. The answer is: C

C

mathematics

What is the total number of prime numbers less than 60?

Solution Prime numbers less than 60 are =17. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59 Their number is 17. Answer A The answer is: A

A

mathematics

If x/|y| = -2 which of the following must be true?

x/|y| = -2 x= -2 |y| Squaring both sides x^2= (-2 |y|) ^2= 4*y^2 D is the answer The answer is: D

D

mathematics

HCF of two numbers is 11 and the product of these numbers is 363, what is the the greater number?

The numbers be 11a and 11b 11a × 11b = 363 ab = 3 co-primes with product 3 are (1, 3) Hence the numbers with HCF 11 and product 363 = (11 × 1, 11 × 3) = (11, 33) Numbers are 11 and 33 The greater number = 33 The answer is: C

C

mathematics

What is the difference between the place value of 2 in the numeral 7889?

Answer: Option 'E' 800 - 80 = 720 The answer is: E

E

mathematics

In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 6, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?

Sugar:Flour = 5:6 = 25:30; Flour:Soda = 10:1 = 30:3; Thus we have that Sugar:Flour:Soda = 25x:30x:3x. Also given that 30x/(3x+60) = 8/1 --> x=80 --> Sugar = 25x = 2,000. Answer: E. The answer is: E

E

mathematics

A child has 36 blue marbles and 10 red marbles, and he kept they into a bag. If he asks you to pick up 3 marbles, what is the probability that all the 3 marbles will be red?

There are 10 red marbles in a group of 36 + 10 that is 46. Thus the probability of picking all 3 red marbles is: (10/46)(9/45)(8/44) = 2/253. The correct answer is B. The answer is: B

B

mathematics

To be undaunted is to be impervious, undisturbed and ‘fearless’.

Answer:D The answer is: D

D

mathematics

In the set of positive integers from 1 to 60, what is the sum of all the odd multiples of 5?

1 - 60 5 - 15 - 25 - 35 - 45 are valid multiples of 5. Add them 5+15+25+35+45+55 =180 A The answer is: A

A

mathematics

There are 24 students in Chad’s class. He brought 26 cookies to pass out for his birthday. How many cookies will each student get? Will there be any cookies left over?

26/24 = 1 R 2 Chad will give each student 1 cookie and there will be 2 cookies left over correct answer D The answer is: D

D

mathematics

23 people are there, they are shaking hands together, How many hand shakes possible, if they are in pair of cyclic sequence ?

Answer:A The answer is: A

A

mathematics

The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is?

Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x)= 750 => x = 225 m. Answer: C The answer is: C

C

mathematics

What is the sum of natural numbers between 20 and 100

a = first number l = last number Sn = n/2[a + l] between 20 and 100 numbers = 81 => 100 - 20 = 80 + 1 = 81 Sn = 81/2 × 120 = 81 × 60 = 4860 B) The answer is: B

B

mathematics

The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?

39x = 5 + 12 + 15 + 19 + (x – 4)44 x = 25 ANSWER B The answer is: B

B

mathematics

A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?

Explanation: A : B : C =20000×24:15000×24:20000×18=20×4:15×4:20×3=4×4:3×4:4×3=4:3:3=20000×24:15000×24:20000×18=20×4:15×4:20×3=4×4:3×4:4×3=4:3:3 B's share = 25000×310=7500 ANSWER IS A The answer is: A

A

mathematics

In a class ,there are 15 boys and 10 girls .one student is selected at random. The probability that one girl is selected,is:

Total number of students = 10+15= 25 no.of girls in a class = 10 probability of one girl is selected = 10/25= 2/5 Answer is B The answer is: B

B

mathematics

A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

CATEGORY Formulae Examples DIRECTIONS : Problems based on Trains. 11. A train 280 m long, running with a speed of 63 km/hr will pass a tree in A. 15 sec. B. 16 sec. C. 18 sec. D. 20 sec. Solution Speed = (63 x 5/18) m/sec = 35/2 msec Time taken = (280 x 2 /35)m/sec = 16 sec. 12. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is ihe length of the train? A. 120 metres B. 180 metres C. 324 metres D. None of these Solution 13. A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? A. 3.6 sec B. 18 sec C. 36 sec D. 72 sec Solution Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr = (36 x 5/18) m/sec = 10 m/sec Distance covered = (240+120) m = 360 m Time taken = (360 / 10)sec = 36 sec. Answer C The answer is: C

C

mathematics

A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 50% while buying and by 10% while selling. What is his percentage profit?

The owner buys 100kg but actually gets 150kg; The owner sells 100kg but actually gives 90kg; Profit: (150-90)/90*100=50% Answer: D. The answer is: D

D

mathematics

I. x2 - x - 42 = 0, II. y2 - 17y + 72 = 0 to solve both the equations to find the values of x and y?

I. x2 - 7x + 6x - 42 = 0 => (x - 7)(x + 6) = 0 => x = 7, -6 II. y2 - 8y - 9y + 72 = 0 => (y - 8)(y - 9) = 0 => y = 8, 9 => x < y ANSWER:A The answer is: A

A

mathematics

225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees

26 trees have 25 gaps between them, Required distance (225/25) = 10 A The answer is: A

A

mathematics

Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?

A:B:C = 3:4:5 Total parts = 12 A's share is = 3 parts 12 -----> Rs.600/- 3 -----> Rs.150/- A's total = 150 + 10 = Rs.160/- A) The answer is: A

A

mathematics

The length of a rectangle is reduced by 15%. By what % would the width have to be increased to maintain the original area?

Sol. Required change = (15*100)/(100-15)=17.6% C The answer is: C

C

mathematics

Use distributive property to solve the problem below: Maria bought 10 notebooks and 5 pens costing 3 dollars each.How much did Maria pay?

Solution 3 × (10 + 5) = 3 × 10 + 3 × 5 = 30 + 15 = 45 dollars Answer C The answer is: C

C

mathematics

Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was ?

Let the average expenditure be Rs. x Then, Total money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50 Answer: A The answer is: A

A

mathematics

Jancy decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Jancy s savings by the end of the year from these monthly savings were five times the amount she spent per month, what should be the fraction of her salary that she spent each month?

Let Jancy's monthly savings = S Jancy's monthly pay = P Jancy's monthly expenditure = P-S Jancy's savings by the end of the year from these monthly savings were Five times the amount she spent per month 12S = 5*(P-S) =>12/5 S = P-S => P = 17/5 S Jancy's monthly expenditure = P-S = 17/5S-S = 12/5S fraction of her salary that Jancy spent each month = 12/5S / 17/5S=P-S/P = 12/17. Answer is E The answer is: E

E

mathematics

A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?

Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 6 = 100 m Answer: D The answer is: D

D

mathematics

A box contains 5 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?

Each ball has an equal chance (1/11) of being selected fourth. The probability that a black ball is selected fourth is 6/11. The answer is E. The answer is: E

E

mathematics

Josh spends a total of $6.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?

Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=6.5 ---> x+10y=130 ...(1) Also, x+y=N ...(2) Solving 1 and 2 , we get, N = 130-9y ---> only value satisfied is when y = 1---> N = 130-9=121. C is the correct answer. Other options are not equal to multiples of 9 removed from 130. The answer is: C

C

mathematics

A sum of money is to be distributed among A, B, C, D in the proportion of 6 : 2 : 4 : 3. If C gets $500 more than D, what is D's share?

Let the shares of A, B, C and D be 6x, 2x, 4x and 3x respectively. Then, 4x - 3x = 500 x = $500 A's share = 6x = 6*$500 = $3000 The answer is C. The answer is: C

C

mathematics

If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 3m + n?

k^4=5400∗mn k^4=3^3.2^3.5^2.mn In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2 mn=3.2.5^2 mn = 150 = 10 * 15 (Least possible) Answer = 3*10 + 15 = 45 ANSWER:D The answer is: D

D

mathematics

If a,b ,and c are positive real numbers such that a(b+c) = 152, b(c+a) =162 , and c(a+b) = 170, then abc is

ab+bc = 152 --------------------------------------1) bc+ba = 162---------------------------------------2) ac+ab = 170---------------------------------------3) Re-writing equation 3 as follows: ac+cb = 162 + 8 ac+cb = bc+ba + 8 ac = ba + 8 ............... (4) Adding (1)(4) 2ac = 160 ac= 80 abc has to be multiple of 80, only 720 fits in Answer = D The answer is: D

D

mathematics

What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?

d2 = 122 + 42 + 32 = 13 Answer: D The answer is: D

D

mathematics

19 5 17 = x 65 8 10 = y What will be the value of x + y?

according to options units digit is 9 7+1+1=9 10 's place +10's place+ unit place=1+1+7=9 according to this 5+1+6=12 so over all answer =129 ANSWER:B The answer is: B

B

mathematics

A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?

A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B The answer is: B

B

mathematics

3 friends A,B,C went for week end party to McDonald's restaurant and there they measure there weights in some order in 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 155 kg, then find the average weight of all the 7 rounds?

Its finally a easy one..haha (A+B+C+AB+BC+CA+ABC)/7 ...as given ABC=155 so A+B+C also equal to 155 and AB+BC+CA=2ABC=(2*155) finally..(155+2*155+155)/7=88.57 ANSWER:D The answer is: D

D

mathematics

Which of the following will divide evenly into 347,406,520?

Rule: 4: Last two digits should be divisible by 4 the last two digits are 00, which are divisible by 4 Answer: A The answer is: A

A

mathematics

A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 300 that is both a prime and a palindrome. What is the sum of the digits of p?

Given that p is smallest integer greater than 300 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313 D The answer is: D

D

mathematics

A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 1,043,504,000 pounds, how many widgets have been unloaded?

We need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number. When we divide 1,043,504,000 by 1000, we get 1,043,504,000 = 1,043,504 * 5^3 *2^3. 1,043,504 is not divisible by 5, thus there are 3 widgets. The answer is B. The answer is: B

B

mathematics

There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day while the average expenditure per head diminishes by Re 1. Find the original expenditure of the mess.

Let d be the average daily expenditure Original expenditure = 35 × d New expenditure = 35 × d + 42 New average expenditure will be : (35 × d + 42)/42 = d - 1 On solving, we get d = 12 Therefore original expenditure = 35 × 12 = 420 Answer: C The answer is: C

C

mathematics

A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?

Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs. 24000 Answer:B The answer is: B

B

mathematics

Seven years ago the average age of a family of 2 members was 21 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?

Explanation: Average of the family of two numbers 7 years ago = 21 = (21+ 7) * 2 = 56 years Average age of the family of three members at present = 23 years = 23 * 3 = 69 YEARS Age of child = 69 - 56 = 13 years Answer: Option B The answer is: B

B

mathematics

Calculate the circumference of a circular field whose radius is 5 centimeters.

Circumference C is given by C = 2πr = 2π*5 = 10 π cm correct answer E The answer is: E

E

mathematics

Ajay marked the price of his goods 30% more than his C.P. He then sells 1/4th of his stock at a discount of 15%, and half of the stock at the marked price, and the rest at a discount of 30%. Find his gain percentage.

If C.P = 100, M.P = 130 S.P = (1/4) x 110.5 + (1/2) x 130 + (1/4) x 91 S.P = 27.625 + 65 + 22.75 = 115.375 Hence , Profit = 15.375% ANSWER:B The answer is: B

B

mathematics

In how many ways letters of the word CORPORATION be arranged?

CORPORATION has 11 letters, out of which O repeated 3 times, R repeated 2 times. Hence total ways = 11! / (3!*2!) = 3326400 ways B The answer is: B

B

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 80 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 = 80*5 = 400 Student's average = (600+400)/11 = 90.91 Answer D The answer is: D

D

mathematics

According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 15 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 15 oz can = 300 oz/15 oz = 20 Answer A, 20 cans The answer is: A

A

mathematics

If 20 men can build a wall 66 metres long in 4 days, what length of a similar can be built by 86 men in 8 days?

If 20 men can build a wall 66 metres long in 4 days, length of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(4*20) = 567.6 mtrs ANSWER:E The answer is: E

E

mathematics

A number is increased by 20% and then decreased by 20%, the final value of the number is ?

Here, x = 20 and y = - 20 Therefore, the net % change in value = ( x + y + xy/100)% = [20 - 20 + (20x - 20)/100]% or - 4% Since the sign is negative, there is a decrease in value by 4%. ANSWER:D The answer is: D

D

mathematics

How many keyboards do you need if you have to place 1024 keys into keyboards that each hold 32 keys?

Sol. 1024 keys of 32 each = 1024 / 32 = 32 Answer : C The answer is: C

C

mathematics

In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets T can be created from this process?

T=7C4 * 3C2 = 105 Answer B. 7C4 ways to choose 4 numbers for Box 1 3C2 ways to choose 2 numbers for Box2 1 way for Box 3 . every combination will give a different product and can be arranged least to highest only in one way .B The answer is: B

B

mathematics

A car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for the rest of the trip. If the average speed for the entire trip is 34 miles per hour, how many hours long is the trip?

Let T be the total time of the trip. 30*5 + 42(T-5) = 34T 8T = 210-150 T = 7.5 The answer is B. The answer is: B

B

mathematics

Calculate 469158 x 9999 = ?

Answer 469158 x 9999 = 469157 x (10000-1) = 4691580000 - 469158 = 4691110842. Option: E The answer is: E

E