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The Wordsmiths 3

mathematics

The football association pays $2000 out of $8000 it owes to refrees. Then it pays $6000 out of the $12000 owes for the year to players. How much did the ratio of payments made to monies owed increase?

Ratio in 1st case 2000:8000(1/4) Ratio in second case 6000/12000 (2/4) percentage increase is (difference/initial quantity)*100 (1/4)/(2/4 )* 100= 100% Correct option is B The answer is: B

B

mathematics

Approximately what percentage of the world’s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world’s 8.076 billion hectares of forested land.

Approximation is a strategy that helps us arrive at less than an exact number and the inclusion in this problem of the word “approximately” is an obvious clue. First, 8.076 billion is 8,076 million. Next, 8,076 million rounds to 8,000 million and 53.42 million rounds to 53 million. Dividing 53 million by 8,000 million we arrive at 0.0066 (53M/8,000M). We convert this decimal figure to a percentage by multiplying by 100 (or moving the decimal point two places to the right) and adding a percent sign in order to obtain our answer of 0.66%. Note that the shortcut method involves comparing 53 million to 1% of 8,000 million or 80 million. Since 53 million is approximately two-thirds of 80 million then the answer is some two-thirds of 1% or 0.66%. Answer: C. The answer is: C

C

mathematics

10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?

10 men’s 1 day’s work = 1⁄15 15 women’s 1 day’s work = 1⁄12 (10 men + 15 women)’s 1 day’s work = (1⁄15 + 1⁄12) = 9⁄60 = 3⁄20 ∴ 10 men and 15 women will complete the work in 20⁄3 = 62⁄3 days. Answer C The answer is: C

C

mathematics

In how many ways can the letters of the word FINISHED be arranged?

FINISHED has 8 words, but I is repeated two times. Thus ways = 8! / 2! = 20160 ways E The answer is: E

E

mathematics

The value of x + x(x^x) when x = 5 is

Solution: x + x(x^x) Put the value of x = 5 in the above expression we get, 5 + 5(5^5) = 5 + 5(5 × 5 x 5 x 5 x 5 ) = 5 + 2(3125) = 5 + 15625 = 15630 Answer: (a) The answer is: A

A

mathematics

A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is :

Explanation: Number of bricks =Courtyard area /1 brick area =(1800×1200 /12×6)=30000 Option D The answer is: D

D

mathematics

In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?

1. the total number of permutations: 5! = 120 2. Let's consider Maggie and Lisa as one object, then the total number of permutations with Maggie and Lisa together: 4! = 24. 3. Take into account that [Maggie, Lisa] and [Lisa, Maggie] are different. 4. Maggie and Lisa cannot stand next to each other in: 120 - 2*24 = 72 ways. ANS:D The answer is: D

D

mathematics

The triplicate ratio of 1:4 is?

13: 43 = 1:64 Answer: A The answer is: A

A

mathematics

If the perimeter of a rectangular garden is 500 m, its length when its breadth is 100 m is?

2(l + 100) = 500 => l = 150 m Answer:E The answer is: E

E

mathematics

A car runs 10,000 miles using 5 tyres interchangeably. to have equal worn out by all tyres,how many miles each tyre should have run?

for 5 tyres running interchangeably 10,000 miles the car runs for 1 tyre=10000/5=2000 as you all know i suppose the car has 4 tyre to have equal worn out by 4 tyres we need=2000*4=8000 ANSWER:B The answer is: B

B

mathematics

In a class, there are 21 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?

Explanation: Let the number of boys be x. Then, (3/4)x = 21 or x = 21 x(4/3) = 28. If total number of students is y, then (2/3) y = 28 or y = 28 x (3/2) = 42. Therefore Number of girls in the class = (42 - 28) = 14. Answer: B The answer is: B

B

mathematics

A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?

1/A + 1/B + 1/C = 1/8 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/8 => (1 + 2 + 4)/2B = 1/8 => 2B/7 = 8 => B = 28 hours. ANSWER A The answer is: A

A

mathematics

If f > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - f) =

Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have f-x=2t. So y-x=-t, y-f=-3t. ---> (y - x)/(y - f) = 1/3. The answer is (B). The answer is: B

B

mathematics

The sum of two consecutive number is 67. Which is the larger number?

Let consecutive number be x, x+1 Therefore sum of the consecutive number is x + x+1=67 2x+1=67 2x=66 x=33 Therefore larger number is x+1=34 ANSWER:A The answer is: A

A

mathematics

Nine pens are in the table.To create three pens in each group like as three group. How many ways are there to create these 3 teams?

Arrange the 6 pen in a straight line in 6! ways. The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!) Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!. You get 6!/(2! * 2! * 2!) * 2! = 45 Answer (B) You get 6!/(2! * 2! * 2!) * 2! Answer : B The answer is: B

B

mathematics

If 2 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?

Total Cost = Weight(in pounds) * Price/pound; To find Total cost/pound, Divide by total pounds. Cost of Dried apricots = 2x; Cost of prunes = 2y; Cost per pound = (2x + 2y)/5; Ans is (A). The answer is: A

A

mathematics

In a question on division with zero remainder, a candidate took 22 as divisor instead of 11. The quotient obtained by him was 35. The correct quotient is?

Number = (35 * 22) = 770 Correct quotient = 770/11 = 70 A) The answer is: A

A

mathematics

Three cubes of metal whose edges are 9, 12 and 24 cm respectively, are melted and one new cube is made. Find the edge of the new cube?

93 + 123 + 243 = a3 => a = 25.3 Answer: E The answer is: E

E

mathematics

Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 20% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?

Correct Answer: B Solution: B. We know that when Pam and Stanley were both working, the ratio was 1 boxes by Pam to 4 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 1 to 8. Answer B is correct. The answer is: B

B

mathematics

The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?

Let the price of a saree and a shirt be Rs. x and Rs. y respectively. Then, 2x + 4y = 1600 .... (i) and x + 6y = 1600 .... (ii) Divide equation (i) by 2, we get the below equation. = x + 2y = 800. --- (iii) Now subtract (iii) from (ii) x + 6y = 1600 (-) x + 2y = 800 ---------------- 4y = 800 ---------------- Therefore, y = 200. Now apply value of y in (iii) = x + 2 x 200 = 800 = x + 400 = 800 Therefore x = 400 Solving (i) and (ii) we get x = 400, y = 200. Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400. answer : D The answer is: D

D

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. 50000, then the share of B is?

Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 50000 Share of B = 6/13 (50000) = Rs. 23076.92~ 23077 Answer: A The answer is: A

A

mathematics

The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.35. The probability of Matt playing any match is 0.8. If it is known that the team has won the last match, what is the probability that Matt played the match?

Out of 100 matches: Matt is plays in 80 and not plays in 20. Out of 80 matches Matt plays in, team wins 0.75*80 = 60. Out of 20 matches Matt does not play in, team wins 0.35*20 = 7. So, out of 100 matches 60 + 7 = 67 are won. It is known that the team has won the last match. Out of 67 matches won, Matt is in 60: 60/67 = 0.895... Answer: C. The answer is: C

C

mathematics

A man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream.

Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph. So,2x=18 or x=9. Rate upstream=9 km/hr,rate downstream=27 km/hr. Hence,rate of stream=1/2(27-9)km/hr=9 km/hr. ANSWER D 9 km/hr The answer is: D

D

mathematics

A batsman makes a score of 92 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.

Let the average after 17th inning = x. Then, average after 16th inning = (x – 3). ∴ 16(x – 3) + 92 = 17x or x = (92 – 48) = 44. Answer D The answer is: D

D

mathematics

In how many ways can the letters of the word CREATION be arranged such that all the vowels always appear together?

The 8 letters can be grouped into 4 consonants and one set of 4 vowels. The number of ways to arrange 5 units is 5! Then, for each arrangement, the 4 vowels can be arranged in 4! ways. The total number of arrangements is 5!*4! The answer is A. The answer is: A

A

mathematics

list of salaries of 8 employees are listed below. What is the median salary? $40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $32,000

Ordering the data from least to greatest, we get: $27,000, $29,000, $30,000, $31,000, $32,000, $35,500, $40,000, $43,000 Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers. $31,000 + $32,000 = $63,000 The median salary is $31,500. E The answer is: E

E

mathematics

Can you find the missing number in the sequence given below 11 19 27 12 20 ? 13 21 29 14 22 30

Solution: 28 Explanation : The sequence is given in the puzzle is : 11 19 27 12 20 ? 13 21 29 14 22 30 Let's break the given series as below: 11 19 27 12 20 ? 13 21 29 14 22 30 Now read the number from left hand side from top to bottom as : So the number that will replace '?' is 28. Answer C The answer is: C

C

mathematics

At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?

150 = (750*5*R)/100 R = 4% Answer: A The answer is: A

A

mathematics

5357 x 51 = ?

5357 x 51 = 5357 x (50 + 1) = 5357 x 50 + 5357 x 1 = 267850 + 5357 = 273207 E) The answer is: E

E

mathematics

In how many ways Chief Minister and Minister be elected from a team of 6 members?

To do this, if captain is elected first, then we have 6 ways of doing this. For election of vice-captain, we have only 5 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.) So, the ans is 6*5 = 30 ways. D The answer is: D

D

mathematics

Express 25 mps in kmph?

25 * 18/5 = 90 kmph Answer: C The answer is: C

C

mathematics

According to a recent survey report issued by the Commerce Ministry, Government of India, 30% of the total FDI goes to Gujarat and 20% of this goes to rural areas. If the FDI in Gujarat, which goes to urban areas, is $72 m, then find the size of FDI in rural Andhra Pradesh, which attracts 50% of the FDI that comes to Andhra Pradesh, which accounts For 20% of the total FDI?

30% of total FDI given to Gujarat is $90m. so,100% is $300m. 20%of 300m=60m. 50%of 60m=30m. ANSWER:A The answer is: A

A

mathematics

A man swims downstream 65 km and upstream 35 km taking 5 hours each time; what is the speed of the current?

65 --- 5 DS = 13 ? ---- 1 35 ---- 5 US = 7 ? ---- 1 S = ? S = (13 - 7)/2 = 3 Answer: B The answer is: B

B

mathematics

5862 is to 714 and 3498 is to 1113 and 9516 is to 156 therefore 8257 is to ?

A 157 7 + 8 = 15, 2 + 5 = 7; The answer is: A

A

mathematics

Frank is 15 years younger then John. In 3 years John will be twice as old as Frank. How old will Frank be in four years?

Frank is 15 years younger then John --> F+15=J; In 5 years John will be twice as old as Frank (in 3 year John will be J+3 years old and Frank will be F+3 years old) --> J+3=2*(F+3) --> (F+15)+3=2*(F+3) --> F=12; In 4 years Frank will be 12+4=16 years old. Answer: E. The answer is: E

E

mathematics

The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is?

Total height = 150 * 50 = 7500 cm. New average = [7500 - 5 * 146 + 5 * 156 ] / 50 = 151 cm. Answer:B The answer is: B

B

mathematics

If x is a positive integer, and two sides of a certain triangle have lengths x+2 and x+2 respectively, which of the following could be the length of the third side of the triangle? I. x + 1 II. x + 5 III. 2x + 1

Let the third side of triangle be AB. Triangle rule states that: Difference of other 2 sides < any side < sum of other two sides So x+2 - (x+2) < AB < x+2 + (x+2) i.e. 0 < AB < 2x + 4 Let's take x =1 : So 0 < AB < 6 Check if any of the answers are between 0 and 4. I: x+1 = 2 ; could be a possible value. II: x+5 = 6 ; could not be a possible value. III: 2x+1 = 3; could be a possible value. I, II and III could not be a possible value. Answer: D The answer is: D

D

mathematics

Insert the missing number 2, 4, 8, 16, 32, ..., 128, 256

series is 2* Previous Number. ANSWER:C The answer is: C

C

mathematics

Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A The answer is: A

A

mathematics

A certain series is defined by the following recursive rule: Sm=K(Sm-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?

Ans...D No need for any GP formula here The rule is that mth term is K times the (m-1)th term. 1st = 64 2nd = k.64 3rd = k^2.64 . . . 9th term = k^8 *64 . . . so 25th = k^24*64 Using this solve for k and substitute k in the equation for the 9th term The answer is: D

D

mathematics

A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?

400 --- 31 400 --- 3 120 --- ? 400*3 = 120*x => x =10 days Answer: C The answer is: C

C

mathematics

In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.

The amount of chromium in the new 15+40=55 kg alloy is 0.12*15+0.08*40=5 kg, so the percentage is 5/55*100=9.1%. Answer: D. The answer is: D

D

mathematics

If A:B = 1/2: 1/5 B:C = 1/2:1/5 then A:B:C?

A:B = 1/2:1/5 = 5:2 B:C = 1/2:1/5 = 5:2 -------------------- A:B:C = 8:12 Answer: C The answer is: C

C

mathematics

The list price of an article is Rs.67. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?

67*(90/100)*((100-x)/100) = 56.16 x = 6.86% ANSWER:D The answer is: D

D

mathematics

Mane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?

Method I: the rates solution “Mane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Mane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Mane + Zane is R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time: T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36 BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Mane and Zane need 36 weeks to make 15 drums. Answer = B. The answer is: B

B

mathematics

A man sitting in a train which is traveling at 70 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?

Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph. Speed of goods train = (112 - 70) kmph = 42 kmph. Answer : E The answer is: E

E

mathematics

Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?

Explanation: Number of subjects = 6 Average of marks in 6 subjects = 74 Therefore total marks in 6 subjects = 74 * 6 = 444 Now, No. of subjects = 5 Total marks in 5 subjects = 74 * 5 = 370 Therefore marks in 6th subject = 444 – 370 = 74 ANSWER B The answer is: B

B

mathematics

In how many ways Chief Minister and Minister be elected from a team of 14 members?

To do this, if captain is elected first, then we have 14 ways of doing this. For election of vice-captain, we have only 13 ways left, Bcoz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.) So, the ans is 14*13= 182 ways. C The answer is: C

C

mathematics

A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?

DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A The answer is: A

A

mathematics

What is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 84?

When increased by 3, the number must include at least 2^2*3^2*5^2*7 = 6300 The answer is D. The answer is: D

D

mathematics

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

Solved it the prime factorization way 440= 2*2*2*5*11 Sum=22 512= 2^6 Sum=2*6=12 620=2*2*5*31 Sum=40>35 Hence correct. Ans is C The answer is: C

C

mathematics

When a whole no. n is divided by 4,we will get 3 as remainder. What will be the remainder if 2n is divided by 4?

Let n ÷ 4 = p , remainder = 3 => n = 4p + 3 2n = 2(4p + 3) = 8p + 6 = 8p + 4 + 2 = 4(2p + 1) + 2 Hence, if 2n is divided by 4, we will get 2 as remainder. C The answer is: C

C

mathematics

What number comes next in the following number series? 12, 50, 202, 810, 3242, _____

12 12 × 4 + 2 = 50 50 × 4 + 2 = 202 202 × 4 + 2 = 810 810 × 4 + 2 = 3242 3242 × 4 + 2 = 12970 C The answer is: C

C

mathematics

An examiner rejects 0.16% of the meters as defective. How many will be examine to reject 4?

Explanation : Solution: let the number of meters to be examined be x. then, 0.16% of x = 4 =>(16/100 * 1/100 * x) = 4 =>x = (4*100*100)/16 = 2500. Answer : C The answer is: C

C

mathematics

A team of eleven footballers has an average height of 170 cm. Four footballers whose average height is 140 cm, left the team and four new others whose average height is 124 cm, joined. Calculate the new average height of the footballers (in cm) is?

Total height = 170 * 11 = 1870 cm. Total height of those who left = 140 * 4 = 560 Total height of those who joined = 124 * 4 = 496 New average = [1870 - 560 + 496 ] / 11 = 1806/11 cm. = 164.2 cm Answer:E The answer is: E

E

mathematics

Two numbers are in the ratio of 5:7. If 33 is subtracted from each number, they are in the ratio of 1:2. What are the two numbers?

(5x-33):(7x-33) = 1y:2y 5x - 33 = y 7x - 33 = 2y 231-165 = 10y - 7y 66 = 3y y = 22 5x-33 = 22 x = 11 The two numbers are 5x and 7x which are 55 and 77. The answer is C. The answer is: C

C

mathematics

If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability T that this product will be a multiple of 45?

There are 3 single digit multiple of 3, that is, 3,6,9. There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19 Total outcome - 8*3 = 24 Favourable outcome = 1 (9*5) Hence required probability T= 1/24. Answer C. The answer is: C

C

mathematics

If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true? I. x + y is even II. (x+z)/y is an integer III. xz is even

x, y, and z are consecutive integers ⇒ Y = X+2 Z = X+4 1- x+y is even - Correct: sum of any 2 odd integers is even 2- (x+z)/y is an integer - Correct: x+z = x+x+4 = 2x+4 = 2(x+2) and x+z/y = 2(x+2)/x+2 = 2 ⇒ integer 3- xz is even - Not Correct: multiplication of any 2 odd integers is always odd Answer: D The answer is: D

D

mathematics

Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?

26^2+26^3 = 26^2(1+26)=27*26^2 The answer is C. The answer is: C

C

mathematics

Excluding stoppages, the average speed of a bus is 50 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?

In 1hr, the bus covers 50 km without stoppages and 40 km with stoppages. Stoppage time = time take to travel (50 - 40) km i.e 10 km at 50 km/hr. stoppage time = 10/50 hrs = 12 min Answer: A The answer is: A

A

mathematics

Two vertical poles 2 meter and 8 meter high stand apart on a horizontal plane. find the height in meters of the point of intersection of the lines joining the top of each pole to the bottom of the other pole.

Let A be the point of the top of the 2m pole. Let B be the point of the foot of the 2m pole. Let C be the point of the top of the 8m pole. Let D be the point of the foot of the 8m pole. Let E be the point of intersection of the line segments AD and BC. From E drop a perpendicular to the ground. Let F be the point on the ground where perpendicular from E meets the ground. Let X be the distance from E to F. Let P be the distance from B to F. Let Q be the distance from F to D. Triangles BEF and BCD are similar so we get Equation 1: X/P = 8/(P+Q) Triangles DEF and DAB are similar so we get: X/Q = 2/(P+Q) Multiplying both sides by 4 we get Equation 2: (4X)/Q = 8/(P+Q) Combining Equations 1 and 2 we get: X/P = (4X)/Q Simplifying this we get: 1/P = 4/Q And then we get: Q = 4P Substituting Q=4P into Equation 1 we get: X/P = 8/(P+4P) Simplifying this we get: X/P = 8/(5P) X = (8P)/(5P) X = 8/5 X = 1.6 Therefore, the desired height is 1.6 meters. ANSWER:C The answer is: C

C

mathematics

When throwing 2 dices, and looking at the sum of numbers on the dices - what is the probability to have a sum which is smaller than 5?

a dice is composed of 6 numbers - 1,2,3,4,5,6. When trowing 2 dices - there are 36 options (6X6=36). If we want the sum of two dices to be< 5 there are those options: (1,1), (1,2), (2,1), (1,3), (3,1), (2,2) - total of 6 options. Therefore - the probability to have a sum which is smaller than 5 is 6/36=1/6. Answer:B The answer is: B

B

mathematics

A train 110 meters long completely crosses a 280 meters long bridge in 38 seconds. What is the speed of the train is?

S = (110 + 280 /38 = 390/38 * 18/5 = 40 Answer: C The answer is: C

C

mathematics

The lengths of the legs of a right triangle are x and y, while the length of the hypotenuse is x + y- 4. What is the maximum radius of a circle inscribed in this triangle?

Length of hypotenuse: x + y-4 = a + b. Hence x + y = a + b + 4. Sum of lengths of legs: x + y = a + b + 2r. Therefore 2r = 4, so r = 2. correct answer B The answer is: B

B

mathematics

Express of the following as a fraction: 42%

42% = 42/100= 21/50. Answer is B. The answer is: B

B

mathematics

In 10 years,A will be twice as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :

Solution Let B's present age = x years.Then,A's present age =(x +9) years. ∴ (x + 9)+ 10 = 2 (x - 10) ⇔ x + 19 = 2x- 20 ⇔ x = 39.Answer C The answer is: C

C

mathematics

Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 766.

Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two x + (x + 2) twice the sum of the last two is written as 2 ((x + 4) + (x + 6)) = 4 x + 20 sum of the first two added to twice the sum of the last two is equal to 766 is written as x + (x + 2) + 4 x + 20 = 766 Solve for x and find all four numbers x = 124 , x + 2 = 126 , x + 4 = 128 , x + 6 = 130 Answer A The answer is: A

A

mathematics

The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?

Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1:96. Answer:A The answer is: A

A

mathematics

An error 2%in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?

Explanation: Error =2% while measuring the side of a square. Let correct value of the side of the square =100 Then, measured value =100+2=102 (∵ 2 is 2%of 100) Correct area of the square =100×100=10000 Calculated area of the square =102×102=10404 Error =10404−10000=404 Percentage error =error /actual value×100 =404/10000×100=4.04% Answer: Option A The answer is: A

A

mathematics

If f(a)=2a+6, what is the value of (f(2a)+f(a)) ?

f(a)=2a+6 f(2a)= 4a+6 (f(2a)+f(a)) = 4a+6+2a+6 = 6a+12 Answer is D The answer is: D

D

mathematics

1!+2!+3!+4!+5!+..100! is divided by 24. Find the remainder?

By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24. So the remainder = 1 + 2 + 6 + 0 + 0....... = C The answer is: C

C

mathematics

A man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack?

Explanation: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (L.C.M of 3, 4, 5, 6) x + 1 i.e., (60x + 1 ) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So the number is 301. Answer: B) 301 The answer is: B

B

mathematics

At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score A of team B?

A to B = 3 : 4 So, on doubling we get 6 : 4 A to C = 3 : 5 So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20 So final ratio = 6 : 4 : 20. If 20x = 40 4x = 8 Hence, answer is A The answer is: A

A

mathematics

The average age of a group of persons going for tour is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for tour is:

Explanation : Let the initial number of persons be x. Then, => 16x + 20 x 15 -15.5 (x + 20) => 0.5x = 10 => x = 20 Answer : C The answer is: C

C

mathematics

Which of the following could be the value of x, if |4x – 2| = 10?

|4x – 2| = 10 => 4x - 2 = 10 or 4x - 2 = -10 => 4x = 12 or 4x = -8 => x = 3 or x = -2 Answer B The answer is: B

B

mathematics

The product of all the prime numbers less than 12 is closest to which of the following powers of 10 ?

P = 2*3*5*7*11 ~ 10^ 3 Answer : B The answer is: B

B

mathematics

A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?

72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer:B The answer is: B

B

mathematics

Having scored 96 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?

Explanation : Let the average score of the first 18 innings be n 18n + 96 = 19(n+4)=> n = 20 So, Average score after 19th innings = x+4 =24. Answer : E The answer is: E

E

mathematics

The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?

Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12 Answer:C The answer is: C

C

mathematics

The edge of a cube is 4a cm. Find its surface?

6a2 = 6 * 4a * 4a = 96a2 Answer:C The answer is: C

C

mathematics

If the integer p is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when p is rounded to the nearest ten. which of the following is a possible value of p?

We have to check options 1 by 1. 64 rounded to nearest hundred = 100 64 rounded to nearest ten = 60 now difference = 40 the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. therefore 40/60)*100 = 66 2/3 ==>this is the answer. 99 rounded to nearest ten = 100 133 rounded to nearest ten = 130 133 rounded to nearest hundred p= 100=A The answer is: A

A

mathematics

Three unbiased coins are tossed. What is the probability of getting at most 2 heads?

Here S={TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E=event of getting at least two heads ={TTT, TTH, THT, HTT, THH, HTH, HHT} P(E) = n(E)/n(S) = 7/8. Answer A. The answer is: A

A

mathematics

Sahil purchased a machine at Rs 9000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.

Explanation: Question seems a bit tricky, but it is very simple. Just calculate all Cost price, then get 150% of CP. C.P. = 9000 + 5000 + 1000 = 15000 150% of 15000 = 150/100 * 15000 = 22500 Option A The answer is: A

A

mathematics

A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?

2*12 : 3*12 : 4*24 1: 3: 4 1/8 * 3200 = 400 Answer: D The answer is: D

D

mathematics

A sum is divided among P, Q and R in such a way that for each rupee P gets, Q gets 25 paisa and R gets 15 paisa. If the share of P is RS. 70, what is the total amount?

p:q:r = 100:25:15 20:5:3 20 --- 70 28 --- ? => 84 Answer:B The answer is: B

B

mathematics

The traffic lights at three different road crossings change after every 48 sec., 72 sec and 108 sec. respectively .If they all change simultaneously at 8:20:00 hours, then at what time they again change simultaneously .

Interval of change = (L.C.M of 48,72,108)sec.=432sec. So, the lights will agin change simultaneously after every 432 seconds i.e,7 min.12sec Hence , next simultaneous change will take place at 8:27:12 hrs. Answer is A. The answer is: A

A

mathematics

Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.

D 300 km Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11 => x = 300 km The answer is: D

D

mathematics

A train moves with a speed of 189 kmph. Its speed in metres per second is

Solution Speed = 189 Kmph = (189 x 5/18)m/sec = 52.5 m/sec. Answer D The answer is: D

D

mathematics

If cost of sugar increases by 12%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?

100 112 ----- 112 ----- 12 100 ------ ? => 10.7% Answer:C The answer is: C

C

mathematics

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the president or the member chosen to be the treasurer?

This question is much easier than it appears. Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the president is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the president or the the treasurer is 1/10+1/10=2/10. Answer: C The answer is: C

C

mathematics

Total of ages of A,B and C at present is 80 years. If ratio of this ages is 2 : 2 : 4 what will be the age of C after 3 years?

2+2+4=9 4*(80/8)=40yrs after 5yrs=43 ANSWER:A The answer is: A

A

mathematics

Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/5, what is the value of X/Y ?

Answer is B : 5 X - Y = (X + Y)/2 Solving for X/Y = 5 The answer is: B

B

mathematics

A bicycle wheel has a diameter of 0.81m. How many complete revolutions does it make in 1km?

1 revolution = 3.14 * diameter. Number of revolutions in 1km = 1000m / ( 3.14 * 0.81m ) = 393.2. Hence 393 complete revolutions. Answer C The answer is: C

C

mathematics

How many odd numbers are possible between 1 to 10000000? find out the number of odd number of digits?

There are always one odd and one even no. And the question is odd no. Between 1 to 10000000 So we have to find no. Between 1 to 10000 so we should not includes 1 10000000/2 -1=4999999 ANSWER:E The answer is: E

E

mathematics

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 4 hours, how many minutes did it take Cole to drive to work?

First round distance travelled (say) = d Speed = 75 k/h Time taken, T2 = d/75 hr Second round distance traveled = d (same distance) Speed = 105 k/h Time taken, T2 = d/105 hr Total time taken = 4 hrs Therefore , 4 = d/75 + d/105 LCM of 75 and 105 = 525 4= d/75 + d/105 => 4 = 7d/525 + 5d/525 => d = 525 / 3 Km Therefore, T1= d/75 => T1 = 525 / (3 x 75) => T1 = (7 x 60) / 3 -- in minutes => T1 = 140 minutes. E The answer is: E

E

mathematics

A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?

Length = Speed * time Speed = L/T S = 700/20 S = 35 M/Sec Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 126 Kmph Answer:D The answer is: D

D

mathematics

P software has coding line 5% more than N, N software has coding line 1/3 more than M. M software has 90 lines of coding. find P lines.

M s/w has 90 line of code N s/w has = 90+90*1/3= 120 line of code P s/w 5% more N' code 120+6=126 ANSWER:C The answer is: C

C

mathematics

What is the average (arithmetic mean) of all multiples of 10 from 10 to 100 inclusive?

This question can be solved with the Average Formula and 'bunching.' We're asked for the average of all of the multiples of 10 from 10 to 100, inclusive. To start, we can figure out the total number of terms rather easily: 1(10) = 10 2(10) = 20 ... 10(10) = 100 So we know that there are 10 total numbers. We can now figure out the SUM of those numbers with 'bunching': 10 + 100 = 110 20 + 90 = 110 30 + 80 = 110 Etc. Since there are 10 total terms, this pattern will create 5 'pairs' of 110. Thus, since the average = (Sum of terms)/(Number of terms), we have... (5)(110)/(10) =55 Answer : E The answer is: E

E

mathematics

If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is

Since q is an integer so q cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making q^2 as a multiple of 12)) q^2 is divisible by 12 (12 = 2*2*3), So, q should have at least one 2 and one 3 so that q^2 has a 2^2 and two 3 So, q will have a 2 and a 3. Or q will be a multiple of 6 So, largest possible integer than should divide q^3 is 6^3 So, Answer will be D The answer is: D

D

mathematics

In how many different ways can the letters of the word RUMOUR be arranged?

Reqd. number of ways 6!/2!×2!=6×5×4×3/1×2=180 Answer A The answer is: A

A