MU-NLPC/Calc-aqua_rat huggingface dataset:
The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?  Choices.
A) 4	B) 8	C) 5	D) 2	E) 9

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35   So 30x + 35 + 31(x + 1) = > x = 4.   4nswer: 4
Answer: A
In a 1000 m race, A beats B by 50 m and B beats C by 20 m. In the same race, by how many meters does A beat C?	Choose the correct choice from the following choices.
A) A)69m B) B)829m C) C)822m D) D)929m E) E)132mj

Solution: By the time A covers 1000 m, B covers  (1000 - 50)= 
 (1000 - 50) = 950
950 m.   By the time B covers 1000 m, C covers  (1000 - 20)= 
 (1000 - 20) = 980
980 m.   So, the ratio of speeds of A and C=   1000/950 * 1000/980 = 1000/931 So, by the time A covers 1000 m, C covers 931 m.   So in 1000 m race A beats C by 1000 - 931= 
1000 - 931 = 69
69 m.   69mnswer:69m
Answer: A
A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze?  Choose the correct choice.
A) 154 cm2	B) 113 m2	C) 123 m2	D) 115 m2	E) None of these

Solution: Area of the shaded portion   = 1⁄4 × π × (12)2 = 113 m2   Answer 113 m2
Answer: B
If x and y are positive integers and 12x=21y what is the least possible value of xy?	Choose one: A) 9 B) 28 C) 63 D) 84 E) 252

Solution: 12x=21y   => x/y = 7/4   => 4x=7y   4(3)=7(3) => x*y=9   9
Answer: A
Average of five numbers is 9, and the sum of three of the numbers is 30, what is the average of the other 2 numbers?
Options:  A) 17  B) 15.5  C) 8.5  D) 7.5  E) 3.5

Solution: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e)/5=9a+b+c=30(30+d+e)/5=930+d+e=45d+e=15average=15/2= 
15/2 = 15/2 = around 7.5
7.5Ans 7.5
Answer: D
In a survey of 340 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured? Choose the correct choice from the following choices:	A) 7/12	B) 8/41	C) 39/68	D) 1/8	E) 41/91

Solution: ---------UI----------------NUI-------Total   PT ----(12.5/100)*104= 
 ----(12.5/100)*104 = 13
13----------- --54   NPT---104-13-------------- x--------286   Total--104----------------------------340   we have to find not part time and not uninsured . in other words not part time and insured= x/340 = (286-104+13)/340   = 39/68   Answer is 39/68.
Answer: C
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?	Choose the correct choice from the following answers.
A) 1/26 B) 1/25 C) 1/87 D) 1/17 E) 1/12

Solution: Let E1 be the event of drawing a red card.   Let E2 be the event of drawing a king .   P(E1 ∩ E2) = P(E1) . P(E2)   (1/26s E1 and E2 are independent)   = 1/2 * 1/13 = 1/26   1/26nswer:1/26
Answer: A
A table is bought for Rs.600/- and sold at a loss of 8% find its selling price	Pick.
A) s.500/-
B) s.552/-
C) s.540/-
D) s.600/-
E) s.700/-

Solution: 100 % ------> 600 (100 * 6 = 600)   92 % ------> 552 (92 * 6 = 552)   Selling price = Rs.552/-   s.552/-
Answer: B
19 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?  Choose one
A) 32
B) 87
C) 38
D) 99
E) 77

Solution: 3W = 2M   19M ------ 21 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   19 * 21 * 8 = 14 * x * 6   x = 38   Answer: 38
Answer: C
If 40 honey bees make 40 grams of honey in 40 days, then 1 honey bee will make 1 gram of honey in how many days?	Choose the correct option:  A) 1  B) 3.5  C) 40  D) 49  E) 30

Solution: Explanation :   Let the required number days be x.   Less honey bees, More days (Indirect Proportion)   Less honey, Less days (Direct Proportion)   Honey bees 1 : 40 :: 40 : x   Honey 40 : 1   => 1 x 40 x x = 40 x 1 x 40   => x = 40.   Answer : 40
Answer: C
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is? Choose the correct choice from the following: A) 4:6 B) 4:3 C) 4:9 D) 4:4 E) 4:2

Solution: Let us name the trains A and B.   Then, (A's speed) : (4:3's speed)   = √b : √a = √16 : √9 = 4:3.Answer: 4:3
Answer: B
If s is the product of the integers from 50 to 60 inclusive, and if t is the product of the integers from 50 to 61 inclusive, what is 1/s + 1/t in terms of t? Select the correct option: A) 32/t B) 42/t C) 52/t D) 62/t E) 72/t

Solution: Similarly in the actual problem   s =t/61. 1/s = 1/(t/61) or 1/s = 61/t   1/s + 1/t = 61/t + 1/t = 62/t   62/t
Answer: D
By selling 20 pencils for a rupee a man loses 35%. How many for a rupee should he sell in order to gain 30%?
Choices:
A) 8 B) 9 C) 6 D) 14 E) 10

Solution: 65% --- 20130% --- ?65/130 * 20= 
65/130 * 20 = 10
10Answer: 10
Answer: E
A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? Choose the correct choice from the following choices.
A) 30/83 hours B) 80/13 hours C) 30/13 hours D) 30/19 hours E) 32/13 hours

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 60 km downstream= d/s = 60/26   = 30/13 hours.   Answer:30/13 hours
Answer: C
If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?	Choose the correct option.
A) 33
B) 21
C) 92
D) 12
E) 25

Solution: Explanation:   Given that, cost price of 50 article is equal to selling price of 40 articles.   Let cost price of one article = Rs. 1   Selling price of 40 articles = Rs. 50   But Cost price of 40 articles = Rs. 40   Therefore, the trader made profit.\Percentage of profit = 10/40 * 100= 
10/40 * 100 = 25
25%   Answer:25
Answer: E
The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle? Choose the correct option
A) 432 B) 456 C) 546 D) 258 E) 277

Solution: 2(3x + x)   = 96   l = 36   b = 12   lb = 36 * 12= 
36 * 12 = 432
432   432nswer: 432
Answer: A
I bought two books; for Rs.360. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? Choose the correct choice from the following answers.
A) 197  B) 210  C) 189  D) 278  E) 268

Solution: x*(85/100)   = (360 - x)119/100   x = 210   Answer: 210
Answer: B
10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
Pick
A) 1/0 B) 1/3 C) 1/5 D) 1/2 E) 1/1

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability = 1/5   Answer: 1/5
Answer: C
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:	Choose the most appropriate option:
A) 39,30	B) 41,32	C) 42,33	D) 43,34	E) 35,36

Solution: Let their marks be (x + 9) and x.   then x+9 = 56/100(x+9+x)   3x=99   x=33   their marks 42 and 33   ANSWER 42,33
Answer: C
Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
Choose the correct choice from the following answers.
A) 2400 m^2 B) 2420 m^2 C) 2520 m^2 D) 2640 m^2 E) 2750 m^2

Solution: Solving the two equations, we get: l = 63 and b = 40.   Area = (l x b) = (63 x 40) m2 = 2520 m^2   2520 m^2
Answer: C
What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
Choose the correct choice from the following answers
A) 3:6 B) 3:4 C) 3:2 D) 3:1 E) 3:7

Solution: d = 3d d = d   a√2 = 3d a√2 = d   a = 3d/√2 a = d/√2   => 3:1   Answer: 3:1
Answer: D
If x is an integer, then x(x - 1)(x - n) must be evenly divisible by three when n is any of the following values EXCEPT  Select the correct option:
A) -4
B) -2
C) -1
D) 2
E) 5

Solution: here's another approach   x(x - 1)(x - n)   all three are consecutive, so the product MUST be a multiple of 3   we don't know the value of n just yet ... so let's extend the series ... the extension itself reveals the answers   ..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..   we can see the possible values of n too from the series   n = 2 OR 2+3n [25]   n = -1 OR -1+3n [-1-4]   B i.e. -2 does not fit in any value of n   so -2 it is
Answer: B
The parameter of a square is equal to the perimeter of a rectangle of length 7.5cm and breadth 6.5 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?  Choose the correct choice from the following answers:	A) 10.2	B) 10.27	C) 10.23	D) 10.21	E) 10.25

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(7.5+ 5.5) = 26 cm Parameter of the square = 26 cm   i.e. 4a = 26   a = 6.5   10.21iameter of the semicircle = 6.5 cm   Circimference of the semicircle   = 1/2(âˆ)(6.5)   = 1/2(22/7)(6.5) = 143/14 = 10.21 cm to two decimal places   Answer: 10.21
Answer: D
A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 3 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x?  Choose one:  A) x/70  B) x/35  C) 3x/70  D) 3x/10  E) 3x/7

Solution: cost of boat per day = x   cost per person =x/7   if three more persons afre there, cost =x/10   difference = x/7-x/10   =3x/70   ANSWER:3x/70
Answer: C
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ?
Choose the correct choice from the following options.
A) 7/19	B) 7/14	C) 7/98	D) 7/18	E) 7/15

Solution: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂   = 7/15   Answer: 7/15
Answer: E
At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 4 years?
Choose the correct option:
A) 4 %	B) 3.57 %	C) 2 6/7 %	D) 5 %	E) 6 %

Solution: Explanation:   250 = (1750x4xR)/100   R = 3.57 %   Answer: Option 3.57 %
Answer: B
The largest 4 digit number exactly divisible by 55 is?  Answers:
A) 9935
B) 9939
C) 9944
D) 9955
E) 9960

Solution: Largest 4-digit number = 9999   55) 9999 (181   9955   Answer : 9955
Answer: D
x is the product of each integer from 1 to 50, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?  Choose the correct answer.
A) 0
B) 5
C) 6
D) 10
E) 12

Solution: x = 1*2*3*4*5*......*49*50 = 50!   y = 100^k   100 = 10^2 = 2^2 * 5^2   On prime factorization of x, power of 5 will always be greater than power of 2   CONCEPT: In every Factorial value (x!), On prime factorization, the power of Bigger Prime number > the power of Smaller Prime number   Also, Power of any Prime Number in any factorial can be calculated by following understanding   Power of prime x in n! = [n/x] + [n/x^2] + [n/x^3] + [n/x^4] + ... and so on   Where,   [x] = Greatest Integer less than or equal to x and the explanation of terms is as follows   [n/x] = No. of Integers that are multiple of x from 1 to n   [n/x^2] = No. of Integers that are multiple of x^2 from 1 to n whose first power has been counted in previous step and second is being counted at this step   [n/x^3] = No. of Integers that are multiple of x^3 from 1 to n whose first two powers have been counted in previous two step and third power is counted at this step   And so on.....   Where [n/x] is greatest Integer value of (n/x) less than or equal to (n/x)   i.e. [100/3] = [33.33] = 33   i.e. [100/9] = [11.11] = 11 etc.   Power of 5 in x = [50/5] + [50/5^2] + [50/5^3]... = 10 + 2 + 0= 
10 + 2 + 0 = 12
12   Power of 2 in x= [50/2] + [50/2^2] + [50/2^3]... = 25 + 12 + 6 + 3 + 1= 
25 + 12 + 6 + 3 + 1 = 47
47   i.e. x= 50! = 2^47 * 5^12 * ... = 10^12 * ... = 100^6 * ...   i.e. x is divisible by a 6th power of 100 at the most   i.e. y = 100^k = 100^6   i.e. k = 6   Answer: option 6
Answer: C
The least number which should be added to 3218 so that the sum is exactly divisible by 5, 6, 4 and 3 is?  Choose the correct choice from the following answers:	A) 10	B) 20	C) 30	D) 40	E) 50

Solution: 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)= 
(60 - 40) = 20
20   20)
Answer: B
A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $120,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?	Select the correct option
A) $16,800  B) $50,000  C) $82,500  D) $92,000  E) $100,000

Solution: Team K's contract = $100,000 + $100,000*1.2 + $100,000*1.2*1.2 + $50,000 = $414,000   Team L's contract = $120,000 + $120,000*1.1 + $120,000*1.1*1.1 = $397,200   The difference = $16,800.   $16,800nswer: $16,800.
Answer: A
Three coworkers P , H , R meet for Dinner. P had 5 sandwiches, H had 3 and R had none. Both PH share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PH, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split. Choose the most appropriate option.
A) a) 5$	B) b) 3 $	C) c) 7 $	D) d) 4 $	E) e) 5.5 $

Solution: we got total 8 sandwiches ....we are dividing equally in 3 people.   per person: 8/3   initially   p:8   H:3   r:0   now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.   now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r   ok we have 8 dollars for 8/3 sandwich   therefore for 7/3 sandwich we will get 7 dollars.   hence p should get 7 dollars.   hence c) 7 $
Answer: C
A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 30 pints of Perfect Pink paint? Choose the correct option.
A) 9 B) 16 C) 15 D) 25 1/3 E) 28 1/2

Solution: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink   so 17/12 pint requires 3/4 pint of red..   1 pint will require 3/4 * 12/17=9/17..   30 pints will require 9/17 * 30= 15 pints..   15
Answer: C
Awordis defined as a sequence of Four dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?
Choose the most appropriate option:
A) 13
B) 15
C) 16
D) 18
E) 19

Solution: Each dot can be either yellow or blue, so 2 options for each dot:   2*2*2*2= 
  2*2*2*2 = 16
16.   Answer: 16
Answer: C
During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?  Choose the correct option
A) 80%
B) 107%
C) 116.7%
D) 120%
E) 140%

Solution: Kim purchased 20 gallons of gas. She paid for   5 + 0.9*15= 
  5 + 0.9*15 = 18.5
18.5 gallons, so the overall discount she got was 1.5/20= 7.5%.   Isabella purchased 25 gallons of gas. She paid for   5 + 0.9*20= 
  5 + 0.9*20 = 23
23 gallons, so the overall discount she got was .5/25= 8%.   8 is 8/7.5*100 = 107% of 7.5.   Answer: 107%.
Answer: B
One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 2,50,000 as total savings, how much has he saved in Public Provident Fund ?  Options:
A) Rs. 30,000	B) Rs. 50,000	C) Rs. 60,000	D) Rs. 100,000	E) None

Solution: EXPLANATION   Let savings in N.S.C and P.P.F. be Rs. x and Rs. (250000 – x) respectively. Then,   1/3x=1/2(250000-x)   => x/3 + x/2 = 125000   => 5x/6 = 125000   => x= 125000 x 6 /5= 150000   Savings in Public Provident Fund = Rs. (250000 – 150000) = Rs. 100000   Answer Rs. 100,000
Answer: D
A shopkeeper sold an article at $1050 and gained a 20% profit. What was the cost price?	Pick one.
A) $835  B) $845  C) $855  D) $865  E) $875

Solution: Let x be the cost price.   1.2x = 1050   x = 1050/1.2= 
1050/1.2 = 875
875   The answer is $875.
Answer: E
In how many different number of ways 6 men and 2 women can sit on a shopa which can accommodate persons?	Pick one:
A) 200
B) 1680
C) 240
D) 250
E) 260

Solution: 8p4 = 8 X 7 Ã— 6 Ã— 5 = 1680   1680
Answer: B
One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?	Choose the correct choice from the following options:
A) 90000  B) 85000  C) 50000  D) 75000  E) 60000

Solution: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,   =1/3 x = 1/2 (150000 - x)   =x/3 + x/2 = 75000   =5x/6 = 75000   =x = 75000 x 6 /5	= 90000   Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000   Answer is 60000.
Answer: E
5 cats can catch 5 mice in 5 minutes. How many cats does it take to catch 100 mice in 100 minutes?  Pick.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: let x be no. of cat   5 cat catch 5 mice in 5 min   5 cat catch 1 mice in (5/5=1 min)   1 cat catch 1 mice in 1*5= 
1*5 = 5
5 min   1 cat catch 100 mice in 5*100 min   x cat catch 100 mice in (5*100)/x min   A/Q (5*100)/x= 100   => 5*100=x*100   => x=5   ANSW5R:5
Answer: E
Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? Select:  A) 3  B) 9  C) 5  D) 6  E) 7

Solution: Suppose Anoop joined after 3 months.   Then, 20000 * 12 = 80000 * (12 – x)   => x = 9.   ANSWER:9
Answer: B
If n ≠ 0, which of the following could be less than n?
I. 2n
II. n^2
III. 2 - n  Options
A) I only  B) II only  C) I and II only  D) I and III only  E) None

Solution: n ≠ 0 => n = negative or n = positive   if n = negative:   2n < n (n = -1 then 2n = -2 => -2 < -1)   n^2 > n (n =-1 then n^2 = 1 => n^2 > n)   2 - n > n (n = -1 then 2--1 = 2+1= 
2+1 = 3
3=> 2-n > n)   but if n = positive:   n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II   2 - n < n(n =2 then 2-2= 
2-2 = 0
0)=>answer is I and III only
Answer: D
Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.40 at the candy store. What is this student’s weekly allowance? Choose the correct answer.
A) $1.20  B) $1.50  C) $1.80  D) $2.00  E) $2.50

Solution: Let x be the value of the weekly allowance.   (2/3)(2/5)x = 40 cents   (4/15)x = 40   x = $1.50   The answer is $1.50.
Answer: B
Due to construction, the speed limit along an 15-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?  Choose the correct choice from the following answers.
A) 5	B) 8	C) 9.36	D) 15	E) 24

Solution: Old time in minutes to cross 15 miles stretch = 15*60/55 = 15*12/11 = 16.36   New time in minutes to cross 15 miles stretch = 15*60/35 = 15*12/7 = 25.71   Time difference = 9.36   Answer 9.36)
Answer: C
A certain function f satisfies the equation f(x)+2*f(6-x)=x for all real numbers x. The value of f(1) is
Choose the correct choice from the following choices:	A) 3	B) 1	C) 2	D) 5	E) 6

Solution: Put x =1 ⇒ f(1)+2*f(6-1) = 1 ⇒ f(1) + 2*f(5) = 1   Put x = 5 ⇒ f(5)+2*f(6-5) = 5 ⇒ f(5) + 2*f(1) = 5   Put f(5) = 5 - 2*f(1) in the first equation   ⇒ f(1) + 2*(5 - 2*f(1)) = 1   ⇒ f(1) + 10 - 4f(1) = 1   ⇒ f(1) = 3   3nswer: 3
Answer: A
In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is
Choose the correct choice from the following options
A) 22 B) 7 C) 8 D) 6 E) 51

Solution: Let the number of cows be x and the number of hens be y. Then, 4x + 2y = 2 (x + y) + 14 4x + 2y = 2x + 2y + 14 2x = 14 x = 7.   Answer: 7
Answer: B
If 4 men working 10 hours a day earn Rs. 800 per week, then 9 men working 6 hours a day will earn how much per week?  Choose the correct choice.
A) Rs 840
B) Rs 1320
C) Rs 1080
D) Rs 1680
E) None of these

Solution: Explanation :   (Men 4:9) : (Hrs/Day 10:6) :: 800 : x   hence 4 * 10 *x = 9 * 6 * 800   or x = 9*6*800/ 4*10 = 1080   Answer : Rs 1080
Answer: C
Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in?
Choose the most appropriate option:  A) 6  B) 12  C) 28  D) 42  E) 21

Solution: The part of the tank filled by three pipes in one hour   = 1/14   => The part of the tank filled by two pipes in 1 hour   = 2/3 * 1/14= 1/21.   The tank can be filled in 21 hours.   Answer:21
Answer: E
In one hour, a boat goes 4 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Choose the correct option:
A) 3 km/hr
B) 4 km/hr
C) 5 km/hr
D) 6 km/hr
E) 8 km/hr

Solution: Upstream relative speed is u + v=4km/hr   Downstream speed is u-v = 2   Where u = speed of boat in still water and v is speed of stream   Then adding two equations u+v + u-v =4+2   2u=6   Finally, u=3.   3 km/hrNSWER : 3 km/hr
Answer: A
It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 220 cubic metres in 10 minutes. The inner radius of the pipe should be :
Select
A) √2 m  B) 2 m  C) 1 m  D) 1⁄√2 m  E) None of these

Solution: Let inner radius of the pipe be r.   Then, 220 = 22⁄7 × r2 × 7 × 10   or r2=220/22×10=1   or r = √1=1 m   Answer 1 m
Answer: C
A = {2, 3, 5, 7, 15}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained? Choose the correct choice from the following options:
A) 15
B) 16
C) 19
D) 20
E) 36

Solution: Step 1: Find out the number of products you get.   5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4= 
5*4 = 20
20   Step 2: Remove the products that appear more than once.   Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.   2, 3   2, 4, 6   The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.   Answer= 20 - 1 = 16   Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.   16
Answer: B
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Choose the most appropriate option:
A) 276
B) 280
C) 287
D) 267
E) 270

Solution: x*(85/100)   = (480 - x)119/100   x = 280   Answer:280
Answer: B
n what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?  Select:
A) 2  B) 7  C) 8  D) 6  E) 9

Solution: T = 60/36 * 18/5= 
60/36 * 18/5 = 6
6 sec   Answer: 6
Answer: D