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The Wordsmiths 3

mathematics

A corporation seven times its annual bonus to 5 of its employees. What percent of the employees’ new bonus is the increase?

Let the annual bonus be X. A corporation triples its annual bonus. So new bonus = 7X. Increase = 7X-X =6X The increase is what percent of the employees’ new bonus = (6X/7X)*100 = 85.71% Hence B. The answer is: B

B

mathematics

A fair coin is to be tossed twice and an integer is to be selected at random from one of the integers 3, 8, and 10. What is the probability that at least one head is tossed and an even integer is selected?

1) Let us simply state the possibilities. This method works for this problem due to the limited number of possibilities Ways of getting at least a head and an even number =6 HT8 TH8 HT10 TH10 HH8 HH10 Ways of not getting at least one head and an even number=6 TT8 TT10 HT3 TH3 HH3 TT3 Total probability=6/12=1/2 Answer:D The answer is: D

D

mathematics

Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?

The price with 30% off 30 - 30% of 30 = 30 - (30 / 100) *30 = 30 - 9 = 21 The price with another 25% off 21 - 25% of 21 = 21 - (25/100)* 21 = 21 - (525 / 100) = 21 - 5.25 = $15.75 correct answer C The answer is: C

C

mathematics

Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries?

Probability of basket = 3/5 Probability of no basket = 2/5 Required probability=3* 3/5*2/5*2/5 =36/125 A is the answer . The answer is: A

A

mathematics

A cistern which could be filled in 7 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?

1/7 - 1/x = 1/10 => 70/3 hrs Answer: B The answer is: B

B

mathematics

The cost of 3 kg of sugar is $12. What will the cost of 8 kg of sugar be?

3 kg costs $12 1 kg costs $4 8 kg costs $32 The answer is A. The answer is: A

A

mathematics

Each of the three people individually can complete a certain job in 4, 5, and 8 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?

The two slowest people work at rates of 1/5 and 1/8 of the job per hour. The sum of these rates is 1/5 + 1/8 = 13/40 of the job per hour. The answer is D. The answer is: D

D

mathematics

Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 3. Which of the following operations would decrease the standard deviation of Set J?

CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e. 1) It depends on the separation between the successive terms of the set 2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant 3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number C The answer is: C

C

mathematics

In how many different ways can 4 identical blue pants and 4 identical red pants be shared among 8 children such that each child receives a pant?

BBB RRR Therefore total number of ways is 6! but there are two groups of 3 identical things. Therefore total number of "different" ways is 8!/ (4!) (4!) = 40320 ANS:C The answer is: C

C

mathematics

If athul rows 16 km upstream and 24 km down steam taking 4 hours each, then the speed of the stream

Speed upstream = 16/4 = 4 kmph Speed down stream = 24/4 = 6 kmph Speed of stream = ½ (6-4) = 1 kmph ANSWER:A The answer is: A

A

mathematics

On a sum of money, the simple interest for 2 years is Rs. 660,while the compound interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is

Explanation: Difference in C.I and S.I for 2 years = Rs(696.30-660) =Rs. 36.30. S.I for one years = Rs330. S.I on Rs.330 for 1 year =Rs. 36.30 Rate = (100x36.30/330x1)% = 11% Answer: B) 11% The answer is: B

B

mathematics

If (4x + 7)(x + 2) = 8x^2 + x, what is a possible value of x?

Rearranging the given expression: (4x + 7)(x + 2) = 8x^2 + x i.e. 8x^2 + 15x + 14 = 8x^2 + x i.e. 14x = -14 i.e. x = -14/14 = -1 Answer: Option D Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible The answer is: D

D

mathematics

In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 20, the dividend is:

Divisor = (5 * 20) = 100 = 10 * Quotient = Divisor => Quotient = 100/10 = 10 Dividend = (Divisor * Quotient) + Remainder Dividend = (100* 10) + 20 = 1020. C The answer is: C

C

mathematics

In a friendship gang Raja has 9 gang, in how many ways can he invite one or more of the gang to his house?

Raja can select one or more than one of his 8 gang. => Required number of ways = 2^9 – 1= 511. D The answer is: D

D

mathematics

How long does a vehicle 150 m long traveling at 50 kmph takes to cross a bridge of 150 m in length?

D = 150 + 150 = 300 m S = 50 * 5/18 = 125/9 T = 300 * 9/125 = 21.6 sec Answer:B The answer is: B

B

mathematics

In a garment industry, 12 men working 9 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 15 hours a day, the number of men required is:

Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 15 : 9 :: 12 : x => 12 x 15 x x = 10 x 8 x 12 => x = 10 x 9 x 12 / (12 x 15) => x = 7 Answer : D The answer is: D

D

mathematics

The equation x/y - 2/5 = 0 is equivalent to each of the following EXCEPT

x/y - 2/5 = 0 5x=2y x= 2/5 * y or y = 5/2 *x plug in x or y depending on the equation. all expressions are true except for B. (5x - 3y)/y = 21/5 where y=-21 B. (5x - 3y)/y = 21/5 ANSWER:B The answer is: B

B

mathematics

In an IT company 35% of employees are given Development Department and 40% of employees are given Testing Department and 20% are given both.What is the probability for an employee is given Development or testing department

(dUt)=d(n)+t(n)-dnt =35+40-20 ANSWER:C The answer is: C

C

mathematics

23, 29, 31, 37, 41, 43, 47, 53, 59, (...)

Explanation : All are prime numbers in their order, starting from 23 Hence, next number is 61 Answer : C The answer is: C

C

mathematics

Two cars start at the same time from opposite ends of a highway that is 500 miles long. One car is riding at 40 mph and the second car is riding at 60 mph. How long after they begin will they meet?

As cars are moving in opposite directions their speeds will be added. So their relative speeds: 60+40 = 100 mph Total distance to be covered = 500 miles. Time taken would be: 500 miles/100 mph = 5 hours E is the answer. The answer is: E

E

mathematics

8873 + x = 13200, then x is ?

Answer x = 13200 - 8873 = 4327 Option: B The answer is: B

B

mathematics

If c<0, which of the following represents a positive number?

Answer : C The answer is: C

C

mathematics

1804 x 1804 = ?

1804 x 1804 = (1804)2 = (1800 + 4)2 = (1800)2 + (4)2 + (2 x 1800 x 4) = 3240000 + 16 + 14400. = 3254416. A) The answer is: A

A

mathematics

From a group of 3 boys and 3 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?

The total number of ways to choose 2 children from 6 is 6C2 = 15 The number of ways to choose 1 boy and 1 girl is 3*3 = 9 P(1 boy and 1 girl) = 9/15 The answer is D. The answer is: D

D

mathematics

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 10% Vermouth by volume. How many ounces of Gin must he add?

4 ounces is vermouth 6 ounces of gin... Total volume 10. To make vermouth account for 10% of total volume the new volume must be.... x*0.1=4 x=40 ounces.... So now you see that he must add 30 ounces of gin... Plug in 15 for n in the answer choices and look for answer 30 E The answer is: E

E

mathematics

Dropbox charges $3.10 for first 1/5 of a month for 500 GB storage, plus $0.40 for each additional 1/5 of a month. What would Dropbox charge for a data storage of 500 GB for 8 months ?

first 1/5 month charge = $3.10 rest of the months = 8 - (1/5) = 39/5 charge for the rest of the months = 39 *0.4 = 15.6 total charge = 3.10+15.6 = 18.7 Answer is D. The answer is: D

D

mathematics

Find number which is 70% less than 60.

Explanation: 70% less is 30% of the given number Therefore, 30% of 60 is 18. ANSWER: A The answer is: A

A

mathematics

Find the perimeter and area of a square of side 11 cm.

We know that the perimeter of square = 4 × side Side= 11 cm Therefore, perimeter = 4 × 11 cm = 44 cm Now, area of the square = (side × side) sq. units = 11 × 11 cm² = 121 cm² ANSWER : OPTION E The answer is: E

E

mathematics

A man's speed with the current is 16km/hr and the speed of the current is 2km/hr. The man's speed against the current is:

Man's rate in still water = (16 - 2) km/hr = 14 km/hr. Man's rate against the current = (14 - 2) km/hr = 12 km/hr C The answer is: C

C

mathematics

The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?

one man can consume the same food in 30*40 = 1200 days. 10 more men join, the total number of men = 40 The number of days the food will last = 1200/40 = 30 days. ANSWER:C The answer is: C

C

mathematics

In a 100 m race, A runs at 8km per hour. If A gives B a start of 8 m and still him by 15 seconds, what is the speed of B ?

Time taken by A to cover 100 m =(60 X 60 / 8000) x 100 sec = 45 sec. B covers (100 - 8) m = 92 m in (45 + 15) sec = 60 sec. B's speed = (92 x 60 x 60)/(60 x 1000)km/hr = 5.52 km/hr. Answer is A The answer is: A

A

mathematics

By walking at 3/4th of his usual speed, a man reaches office 5 minutes later than usual. What is his usual time?

let T be the usual time. time spent=4T/3 therefore, 4T/3=T+5 4T=3T+15...therefor T=15min ANSWER:A The answer is: A

A

mathematics

A certain company reported that the revenue on sales increased 15 % from 2000 to 2003, and increased 30 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?

Assume the revenue in 2000 to be 100. Then in 2003 it would be 115 and and in 2005 130, so from 2003 to 2005 it increased by (130-115)/115=15/115=13%. Answer: E. The answer is: E

E

mathematics

A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?

Let the total distance be x km total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64 Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph. Answer:B The answer is: B

B

mathematics

Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?

The number of miles to drive to finish his journey is given by 1200 - 768 = 432 miles correct answer A The answer is: A

A

mathematics

Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes

total eastward distance= 25kmph*1/4hr=6.25 km total westward distance= 40kmph*1/4hr=10 km total distn betn them= 6.25+10=16.25km ans 16km ANSWER:B The answer is: B

B

mathematics

Present ages of X and Y are in the ratio 4:5 respectively. 6 years hence this ratio will become 5:6 respectively. What is X's present age in years?

Let the present ages of X and Y be 4x and 5x years respectively. Then, (4x + 6)/(5x + 6) = 5/6 6(4x + 6) = 5(5x + 6) => 24x+36 = 25x+30 => x=6 X's present age = 4x = 4*6 = 24 ANSWER: B The answer is: B

B

mathematics

A single discount equal to a discount series of 10% and 20% is

Equivalent discount = 10 + 20 - 10×20/100 = 30 – 2 = 28% Answer B The answer is: B

B

mathematics

In the junior basketball league there are 18 teams, 2/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad

total teams =18 bad teams=(2/3)*18=12 rich teams=9 so maximum value that the both rich and bad can take will be 9. so E= 10 can not be that value. ans D. The answer is: D

D

mathematics

After 6 games, team B had an average of 65 points per game. If it got only 47 points in game 7, how many more points does it need to score to get its total above 500?

(6*65) + 47 +x >500 390+47+x > 500 437+x >500 => x>63 Option D The answer is: D

D

mathematics

Calculate the time it will take for a full tank to become completely empty due to a leak given that the tank could be filled in 7 hours, but due to the leak in its bottom it takes 8 hours to be filled ?

Part filled without leak in 1 hour = 1/7 Part filled with leak in 1 hour = 1/8 Work done by leak in 1 hour =1/7−1/8=56 hours Answer:D The answer is: D

D

mathematics

Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?

D 70 km/hr Let their speed be x km/hr and y km/he respectively. Then, 120/(x + y) = 1 => x + y = 120 --- (i) Now, when they move in same direction: (Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km 6x - 6y = 120 => x - y = 20 --- (ii) Sloving (i) and (ii), we get x = 70, y = 50 P's speed = 70 km/hr. The answer is: D

D

mathematics

Which of the following functions does not intersect with R = 3x^2 + 2x + 1

Let’s find the actual intersecting point of given function and each choice R A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0 B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1 C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect. D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2 E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1. So only choice (C) has no intersecting point. The answer is (C). The answer is: C

C

mathematics

if the price of a book is first decreased by 20% and then increased by 20%, then the net change in the price will be :

Explanation: Let the original price be Rs. 100. Decreased by 20% = 80 Then increased 20% on Rs 80 = 80 + 16 = 96 Net change in price = 100 - 96 = 4 Answer : C The answer is: C

C

mathematics

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

The given words contain 8 letter MTHMTCS(AEAT), so 8!. Then the 4 vowels can be formed differently, 4!. But there are three words have repeated in the given words. So it should be divided by 2!*2!*2!. Hence the solution is (8! * 4!) / (2! * 2! * 2!) = 120960 ANSWER:C The answer is: C

C

mathematics

The speed of a car is 98 km in the first hour and 60 km in the second hour. What is the average speed of the car?

S = (98 + 60)/2 = 79 kmph Answer: D The answer is: D

D

mathematics

a dealer buys 4 varieties of rice costing rs. 40,rs.42,rs.54 and rs.50 per kg in the ratio 6:5:10:9 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of rice?

CP = 40*6+42*5+54*10+50*9=1440 SP = 1.5*1440=2160 Total no.of kgs=6+5+10+9=30 SP per kg=2160/30=72 ANSWER:C The answer is: C

C

mathematics

Three years ago the average age of a class of six members was 20 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?

6 * 23 = 138 7 * 20 = 140 `2 B The answer is: B

B

mathematics

If (n+2)!/n!=156, n=?

(n+2)!/n!= 156 Rewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132 Cancel out terms: (n+2)(n+1) = 156 From here, we might just TEST the answer choices. Since (13)(12) = 156, we can see that n = 11 D The answer is: D

D

mathematics

If Yury has been writing programming code for 13 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?

5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 13 HOURS = 900 X 13 = 117(10^2) ANSWER A The answer is: A

A

mathematics

Average between two sets of numbers is closer to the set withmore numbers?

If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86. Here, 90 has a weight of 3 => it occurs 3 times. Whereas 80 has a weight of 2 => it occurs 2 times. So the average is closer to 90 than to 80 as we have just calculated. B The answer is: B

B

mathematics

45 is the product of two negative numbers. If the greater number is doubled, it is 1 more than the lesser number. What is the greater number?

Test the options. (B) - 5 Double of -5 is -10 and 1 less is -9. -9 * -5 = 45 (Correct) Correct Answer (B) The answer is: B

B

mathematics

f, b, and c are positive integers. If f, b, and c are assembled into the six-digit number fbcfbc, which one of the following must be a factor of fbcfbc?

Plug in some values and check - fbcfbc = 123123 Not divisible by 16 and 5 let fbcfbc = 125125 Not divisible by 3 Only option (B) and (E) is left in both the cases... Check once more to marke (B) as correct answer let fbcfbc = 135135 Again divisible by 13 So, mark answer as (B) 13 The answer is: B

B

mathematics

The distance between 2 cities A and B is 1000km. A train starts from A at 12 p.m. and travels towards B at 100 km/hr. Another starts from B at 1 p.m. and travels towards A at 150 km/hr. At what time do they meet?

Suppose they meet x hrs after 12 p.m. Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000 100x + 150 (x-1) = 1000 x = 4.60 = 5 hrs They meet at 10+5 = 5 p.m. Answer is C The answer is: C

C

mathematics

There have 12 basket,7 red balls and 5 white balls,find the probability of getting at least 1 red ball and 1 blue ball, if 8 balls are to be drawn ?

(7c3*5c5)+(7c4*5c4)+(7c5*5c3)+(7c6)5c2)+(7c1*5c1)=495 ANSWER:B The answer is: B

B

mathematics

How many 2 digit number contain number 3 ?

total 2 digit no. = 9*10* = 90 not containing 3 = 8*9 = 72 total 2 digit number contain 3 = 90 - 72 = 18 ANSWER:A The answer is: A

A

mathematics

Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 4 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 4 minute mark.)

4 minutes is 240 seconds. Lamp A and Lamp B will flash together every 24 seconds. 240/24=10. In the time period, Lamp A and Lamp B will flash together 10 times. Lamp A and Lamp C will flash together every 30 seconds. 240/30=8. In the time period, Lamp A and Lamp C will flash together 8 times. Lamp B and Lamp C will flash together every 40 seconds. 240/40=6. In the time period, Lamp B and Lamp C will flash together 6 times. All three lights will flash together every 2*2*2*3*5=120 seconds. 240/120=2. We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together. The number of times that exactly two lights flash together is 10+8+6-6=18 times. The answer is C. The answer is: C

C

mathematics

A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.1 per sq m?

Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 => 675 675 * 1 = Rs. 675 ANSWER:B The answer is: B

B

mathematics

There are 5 boys and 3 girls. In how many ways can they be seated in a row so that all the three girls do not sit together?

Total number of persons = 5+3 = 8 they can be seated in a row in 8! ways Treat 3 girls as 1 so we have 6 people can be arranged in 6! ways Three girls can be arranged among themselves in 3! ways Required number of ways = 8!-6!*3! = 36000 Answer is B The answer is: B

B

mathematics

The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 23 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken under 10 minutes ?

a must be an integer as it is the number shoots at a rate of 23sec/shoot 3*60 + 23a = 10*60 23a = 420 a = 18 The total number of shoots -->1 +18 = 19 and 20th shoot will be taken at 617 seconds which is above 10 minutes ANSWER: E The answer is: E

E

mathematics

Nicky and Cristina are running a 100 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?

The distance traveled by both of them is the same at the time of overtaking. 3(t+12) = 5t t=18. Cristina will catch up Nicky in 18 seconds. So in 18 seconds Cristina would cover = 18*5 = 90 meter. Now Time taken my Nicky to cover 90 meter = 90/3 = 30 Seconds. A The answer is: A

A

mathematics

A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 4 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?

The cost price of a mango = 1/5 dollars. The selling price of a mango from the first stack = 1/4 dollars --> the profit from one mango = 1/4 - 1/5 = 1/20 dollars. The selling price of a mango from the second stack = 1/6 dollars --> the loss from one mango = 1/5 - 1/6 = 1/30 dollars. The profit from one mango from the first stack is 4 times the loss from one mango from the second stack. the ratio is 1/20*30/1= 3:2 D The answer is: D

D

mathematics

Sachin is younger than Rahul by 18 years. If the ratio of their ages is 7:9, find the age of Sachin

Explanation: If Rahul age is x, then Sachin age is x - 18, so, 9x - 162 = 7x 2x = 162 x = 81 So Sachin age is 81 - 18 = 63 Answer: B) 63 The answer is: B

B

mathematics

A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning.

Sol. Let the average after 17th inning = x. Then, average after 16th inning = (x - 3). 16 (x - 3) + 87 = 17x or x = (87 - 48) = 39. Ans: C The answer is: C

C

mathematics

Two pipes A and B fill at a certain rate.B is filled at 10,20,40,80(10 in 1 hour,20 in 2 hours,40 in 3 hrs and so on). if 1/16 of B is filled in 17 hrs,what time it will take to get completely filled?

1/16 in 17 hrs so 1/8 in 18 hrs 1/4 in 19 hrs 1/2 in 20 hrs and complete tank in 21 hrs ANSWER:B The answer is: B

B

mathematics

A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?

Favorable outcomes will be obtained by making Password using {0, 2, 3, 5, 7} i.e. 5 digits Total Such Passwords = 5*5*5*5*5 = 5^5 Total Possible Password = 10*10*10*10*10 = 10^5 Probability = (5^5) / (10^5) = 1/2^5 = 1/32 Answer: option A The answer is: A

A

mathematics

Ramesh can finish a piece of work in 10 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?

Ramesh can finish a piece of work in 10 days. Rohan is twice as efficient as Ramesh. So Rohan can finish a piece of work in 5 days. days needed to finish the same amount of work = 1/(1/5+1/10)=10/3 days ANSWER:C The answer is: C

C

mathematics

How many perfect squares less than 1000 end with the digit 6?

4:16 6:36 14:196 16:256 24:576 26:676 ANSWER:D The answer is: D

D

mathematics

A 6% stock yields 9%. The market value of the stock is:

Explanation: For an income of Rs. 9, investment = Rs. 100. For an income of Rs 6, investment =Rs.100/9 X6 =Rs 66.66 Market value of Rs. 100 stock = Rs. 66.66 Answer is E The answer is: E

E

mathematics

Tom planted vegetables in a rectangular garden that was 25 feet long and 15 feet wide. He used 1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?

area of garden is 25 x 15 = 375 sq. ft. 1/3 x 375 = 125 sq. ft. for corn 1/5 x 375 = 75 sq. ft. for peas 125 + 75 = 200 sq. ft. used 375 - 200 = 175 sq. ft. left over correct answer A The answer is: A

A

mathematics

It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

Explanation: Let 2^32 = x. Then, (2^32 + 1) = (x + 1). Let (x + 1) be completely divisible by the natural number N. Then, (296 + 1) = [(2^32)3 + 1] = (x^3 + 1) = (x + 1)(x^2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N. C The answer is: C

C

mathematics

If a and b are different positive integers and a + b = a(a + b), then which of the following must be true? I. a = 1 II. b = 1 III. a < b

a+b=a(a+b)a+b=a(a+b) --> a(a+b)−(a+b)=0a(a+b)−(a+b)=0 --> (a+b)(a−1)=0(a+b)(a−1)=0 --> as aa and bb are positive the a+b≠0a+b≠0, so a−1=0a−1=0 --> a=1a=1. Also as aa and bb are different positive integers then bb must be more than a=1a=1 --> a<ba<b (bb can not be equal to aa as they are different and bb can not be less than aa as bb is positive integer and thus can not be less than 1). So we have that: a=1a=1 and a<ba<b. I. a = 1 --> true; II. b = 1 --> not true; III. a < b --> true. Answer: E (I and II only). The answer is: E

E

mathematics

Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n =

Given 10m=n.2210m=n.22 ⇒⇒ 2m×5m=n.22⇒2m−2×5m=n2m×5m=n.22⇒2m−2×5m=n For m = 2 we get least value of n = 25, and for m > 2 we get infinite values are possible for n. Answer:D The answer is: D

D

mathematics

In a shop 90% of the articles are sold at a profit of 20% and the remaining at a loss of 40%.what is the overall profit/loss?

90*1.05+10*0.6/100=1.14 ANSWER:A The answer is: A

A

mathematics

When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?

Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40 Answer:A The answer is: A

A

mathematics

A boy was asked to find 7/9 of a number. But he divided the number by 7/9, Thus he got 32 more than the correct answer. Find the number.

Explanation: Let the number be x. x/7/9 = 9x/7 = 32 + y Actualy he should do 7x/9 = y y = (9x/7) - 32 y = (9x - 224)/7 (9x - 224)/7 = 7x/9 81x - 2016 = 49x 81x - 49x = 2016 32x = 2016 x = 63 Answer: Option B The answer is: B

B

mathematics

A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of D feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1) Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2) Revolutions = distance/circumference So, from equation (1) 100 = D/(x*pi) D = 100 * x * pi ---------- (3) From equation (2) Revolutions = D/(y*pi) = (100 * x * pi) / (y*pi) = 100x/y Answer (C) The answer is: C

C

mathematics

If 24 men can do a piece of work in 25 hours, in how many hours will 15 men do it ?

Let the required number of hours be x. Then, Less men, More hours (Indirect Proportion) 15 : 24 : : 25 : x<=>(15 x x) =(24 x 25)<=>(24 x 25)/15 = 40 Hence, 15 men can do it in 60 hours Answer is A. The answer is: A

A

mathematics

In one hour, a boat goes 11 km along the stream and 5 km against the stream. the sped of the boat in still water (in km/hr) is :

Solution Speed in still water= 1/2(11+5) km/hr= 8kmph. Answer C The answer is: C

C

mathematics

Which of the following is the highest fraction?

Note : If the difference between the numerator and the denominator is constant, then the fraction which has larger value in the numerator is the larger fraction. Using the above, among the options (a), (c), (d) and (e), (e) has the larger value. Now, compared to option(a), (e) has the larger value. Answer E The answer is: E

E

mathematics

Pointing to an old man, Kailash said, "His son is my son's uncle." How is the old man related to Kailash ?

Explanation: Kailash's son's uncle — Kailash's brother. So. the old man's son is Kailash's brother i.e., the old man is Kailash's father. Answer: C The answer is: C

C

mathematics

A train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds. Its length is :

Sol. Let the length of the train be x metres and its speed be y m/sec. Then, x / y = 20 ⇒ y = x / 20 ∴ (x + 500) / 40 = x / 20 ⇔ x = 500 m. Answer C The answer is: C

C

mathematics

Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?

Explanation: x + y = 15 2x – 3y = 5 x = 10 y = 5 ANSWER IS B The answer is: B

B

mathematics

The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:

Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets. In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992: $100 + 4x$100 = $100 + $400 =$500 In 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 200% of 1993: $500 + 2x$500 = $500 + $1000 =$1500 This is 15 times the 1992 number, so the correct answer is 15N. D The answer is: D

D

mathematics

If four coins are tossed, the probability of getting two heads and two tails i

Since four coins are tossed, sample space = 24 Getting two heads and two tails can happen in six ways. n(E) = six ways p(E) = 6/24 = 3/8 Answer:A The answer is: A

A

mathematics

Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?

S:E = 1:3 E:M = 3:5 ------------ S:E:M = 3:9:15 3/27 * 162 = 18 Answer:A The answer is: A

A

mathematics

Some persons can do a piece of work in 16 days. Two times the number of these people will do half of that work in?

16/ (2 * 2) = 4 days Answer:B The answer is: B

B

mathematics

If 50! × 50!/50^n is an integer, what is the largest possible value of n?

50! × 50!/50^n is an integer. Or 50! × 50!/(5^2n*5^n) This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator. Largest power of 5 in 50! = [50/5] + [50/25] = 12 Since there are 2 20!'s, power of 12 in the numerator = 2*12 = 24 Hence the largest value of b for which 50! × 50!/50^n is integer = 24 Correct Option : B The answer is: B

B

mathematics

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 10 and 100?

numbers are 11,13,15-------,97,99 Average of the set: (largest+smallest)/2=(99+11)/2=55; # of terms: (largest-smallest)/2+1=(99-11)/2+1=45 The sum = 45*55= 2475 Answer: C The answer is: C

C

mathematics

There are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?

The number of ways to choose two teams is 17C2 = 17*16/2 = 136 The total number of games in the season is 10*136 = 1360. The answer is C. The answer is: C

C

mathematics

Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?

Let the rate of interest be R% p.a. 17400[1 + R/100]2 = 17400 + 1783.50 [1 + R/100]2 = (17400 + 1783.50)/17400 = 1 + 1025/10000 = 1 + 41/400 = 441/400 = [21/20]2 [1 + R/100] = 21/20 R/100 = 1/20 Therefore R = 5.Answer: D The answer is: D

D

mathematics

If x and y are positive integers, and x^3*y^4 = 648, which of the following is the value of xy?

648 = 2*324 = 2^2*162 = 2^3*81 = 2^3*3^4 xy = 2*3 = 6 The answer is A. The answer is: A

A

mathematics

The least number which should be added to 3218 so that the sum is exactly divisible by 5, 6, 4 and 3 is?

L.C.M. of 5, 6, 4 and 3 = 60. On dividing 3220 by 60, the remainder is 40. Number to be added = (60 - 40) = 20 B) The answer is: B

B

mathematics

Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed?

Solution Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4) 8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224 Number of group,each having 3 consonants and 1 vowels = 224 . Each group contains 4 letter. Number of ways of arranging 5 letters among themselves = 4 ! = (4 × 3 × 2 × 1) = 24 . So, Required number of words = (24 × 224) = 5376 .Answer D The answer is: D

D

mathematics

A 60 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?

Explanation: 1: 2/5 = 5: 2 2/7 * 60 = 20 Answer: Option D The answer is: D

D

mathematics

How many positive integers r less than 30 have no common prime factor with 30?

r=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5. This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers. Answer: D. The answer is: D

D

mathematics

Mirun travels the first 3 hours of her journey at 20 mph speed and the remaining 2 hours at 40 mph speed. What is the average speed of Mirun 's travel in mph?

Explanation : Average speed=Total Distance/Time. Total distance travelled by Mirun = Distance covered in the first 3 hours + Distance covered in the next 2 hours. Distance covered in the first 3 hours = 3×20=60 miles Distance covered in the next 2 hours= 2×40=80 miles Therefore, total distance travelled = 60+80=140 miles. The total time taken = 3+2=5hours. Hence, the average speed =140/5= 28mph. Answer : D The answer is: D

D

mathematics

A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 30 times, A has killed:

Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 30 or x =(30 x 16)/3= 160. Birds killed by A =(5x/24) =(5/24*160)= 33. Answer is C. The answer is: C

C

mathematics

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?

Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer: A The answer is: A

A

mathematics

X starts a business with Rs.45000. Y joins in the business after 7 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?

Explanation: Ratio in which they should share the profit = Ratio of the investments multiplied by the time period =45000×12:30000×5 =45×12:30×5 =3×12:2×5 =18:5 Answer: Option B The answer is: B

B