MU-NLPC/Calc-aqua_rat huggingface dataset:
A dishonest dealer professes to sell his goods at Cost Price but still gets 30% profit by using a false weight. What weight does he substitute for a kilogram? Choose the correct choice:
A) 769 1/7 grams B) 769 3/13 grams C) 769 8/3 grams D) 769 1/3 grams E) 769 1/13 grams

Solution: If the cost price is Rs.100, then to get a profit of 30%, the selling price should be Rs.130.   If 130kg are to be sold, and the dealer gives only 100kg, to get a profit of 30%.   How many grams he has to give instead of one kilogram(1000 gm).   130 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/130 = 769 3/13 grams.   Answer:769 3/13 grams
Answer: B
A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 16 miles per hour." What was their average speed in the whole journey?  Select
A) 10 miles/hour	B) 12.3 miles/hour	C) 11 miles/hour	D) 13 miles/hour	E) 14 miles/hour

Solution: 2xy/x+y=12.3 miles/hour   ANSWER:12.3 miles/hour
Answer: B
If x > 0 and m is x percent of y, then, in terms of x, y is what percent of m?  Choose the correct choice from the following options
A) a) 100m  B) b) 1/100m  C) c) 1/m  D) d) 10/m  E) e) 10,000/x

Solution: m= x/100 * y   So y= 100/x *m   So y= (10000/x)/100 * m   e) 10,000/x
Answer: E
An amount of money was invested at 10% a year. Five times that amount was invested at 15%. How much was invested at 15% if the total annual return was $1,615?  Choose the most appropriate option: A) 9500 B) 1000 C) 10500 D) 11000 E) 11500

Solution: Let x and 5x be the amounts invested as 10% and 15% respectively.   Annual return for x = .1x   Annual return for 5x = .75x   Total return = .85x = 1615   x = 1900   So amount invested for 15% = 9500.   9500NSWER:9500
Answer: A
There are 24 students in Chadâ€™s class. He brought 27 cookies to pass out
for his birthday. How many cookies will each student get? Will there be
any cookies left over?
Select the correct option: A) 1-9 B) 1-7 C) 2-8 D) 1-3 E) 3-10

Solution: 27/24 = 1 R 3 Chad will give each student 1 cookie and there will be 3   cookies left over   correct answer 1-3
Answer: D
Mary can do a piece of work in 11 days. Rosy is 10% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?  Choose the correct choice:
A) 10  B) 15  C) 20  D) 25  E) 30

Solution: Ratio of times taken by Mary and Rosy = 110:100 =11:10   Suppose Rosy takes x days to do the work.   11:10 :: 11:x => x= 10 days.   Hence, Rosy takes 10 days to complete the work.   10nswer: 10
Answer: A
If the average (arithmetic mean) of 2x, 4x, and 8x is 140, what is the value of x? Choose the correct answer: A) 20 B) 30 C) 15 D) 33 E) 31

Solution: AM of 2x, 4x and 8x = 2x + 4x + 8x / 3 = 14x/3   Given that 14x/3 = 140   x = 30   Answer is 30
Answer: B
If y is a positive integer, which of the following could NOT be the square of y?
Choose the correct choice from the following answers:
A) 4432 B) 9426 C) 4966 D) 6415 E) 3155

Solution: A number ending in 2 cannot be a perfect square.   4432 ends in a number 2, making that the correct answer   (4432) 4432
Answer: A
Find the odd man out. 24,36,52,72,96	Choose the correct choice.
A) 72
B) 52
C) 36
D) 24
E) 96

Solution: Explanation :   All except 52 are multiples of 6   Answer : Option 52
Answer: B
After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 240 billion gallons, the reservoir was approximately what percentage full before the storm?
Choose one
A) 40%
B) 48%
C) 54%
D) 58%
E) 65%

Solution: When the storm deposited 120 billion gallons, volume of water in the reservoir = 240 + 120= 
240 + 120 = 360
360 billion gallons   If this is only 60% of the capacity of the reservoir, the total capacity of the reservoir= 360/0.6= 
360/0.6 = 600
600 billion gallons   Therefore percentage of reservoir that was full before the storm= (240/600)*100= 
(240/600)*100 = 40
40%   Option 54%
Answer: C
A prize of $800 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
Pick:
A) $200 B) $220 C) $280 D) $300 E) $340

Solution: Total value of the prize =$800   Number of people = 20   2/5 of 800 (=$320) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 800-320= 
800-320 = 480
$480. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20= 
7*20 = 140
140.   Thus the maximum award can be= 480-140= 
480-140 = 340
$340, hence $340 is the correct answer.
Answer: E
A professional basketball player just signed a contract that has a 10% raise in base salary from last year to this year. The contract also has provisions for a performance bonus of up to $10,000. If he earns the maximum performance bonus, his new effective salary will be a 10.5% raise over last year's total salary, when he received no performance bonus. Assuming he earns the full performance bonus, what will be his new salary? Choose the correct choice from the following choices.
A) 2,010,000 B) 2,110,000 C) 2,150,000 D) 2,200,000 E) 2,210,000

Solution: let x=old salary   then (1+.10)*x+10,000 = (1+.105)*x   i.e. new base salary +10,000 = effective new salary   thus 1.1*x + 10,000 = 1.105*x   10,000 = .005*x   2,000,000 = x   thus the new effective salary is 1.105*2,000,000 = 2,210,000   2,210,000
Answer: E
A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?	Choose the correct choice from the following answers.
A) 32 kmph  B) 76 kmph  C) 34 kmph  D) 43 kmph  E) 40 kmph

Solution: S = (100 + 300)/45   = 400/45 * 18/5= 
400/45 * 18/5 = 32
32   32 kmphnswer:32 kmph
Answer: A
Nine highschool girls gather at the gym for a game of mini-foot ball. Three teams of 3 people each will be created. How many ways are there to create these 3 teams?
Choose the correct answer:	A) 27	B) 51	C) 45	D) 175	E) 12

Solution: Arrange the 6 boys 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 (45)   You get 6!/(2! * 2! * 2!) * 2!   Answer : 45
Answer: C
The tax on a commodity is diminished by 20% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it? Choose the most appropriate option:
A) 12%
B) 14%
C) 16%
D) 20%
E) 8%

Solution: 8%xplanation:   100 * 100= 
100 * 100 = 10_000
10000   80 * 115= 
80 * 115 = 9_200
9200   10000------- 800   100 ------- ?= 8%   8%)
Answer: E
A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of y when angle B is 75 degrees?	Choose the correct choice from the following answers.
A) 75  B) 95  C) 105  D) 115  E) 135

Solution: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.   An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.   angle B = 75 degrees   Thus,   arc ADC = 150 degrees   A whole circle has 360 degrees of arc, so arc ABC should be the rest of the circle.   arc ABC = 360 - 150= 
360 - 150 = 210
210 degrees   The angle that intersects this arc, angle D, should have half this measure.   angle D= y = 210/2= 
210/2 = 105
105 degrees   Answer=(105)
Answer: C
Jane makes toy bears. When she works with an assistant, she makes 89 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? Choose the correct option:
A) 20%
B) 80%
C) 110%
D) 180%
E) 200%

Solution: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 75.6 bears per 36 hours a week or 2.1 bears/hr ([40 bears * 1.89] / [40 hrs * .90]).   [(2.1 - 1)/1] * 100% = 110%   ANSWER:110% (2.1 - 1)/1  * 100= 
 (2.1 - 1)/1  * 100 = 110
110%   ANSWER:110%
Answer: C
The least number by which 72 must be multiplied in order to produce a multiple of 112, is:	Pick one.
A) 6 B) 12 C) 14 D) 18 E) 20

Solution: Required number is divisible by 72 as well as by 112, if it is divisible by their LCM, which is 1008.   Now, 1008 when divided by 72, gives quotient= 14.   Therefore, required number= 14.   Answer: 14
Answer: C
Which of the following is closer to √0.1+√0.15?	Choose the correct option:	A) 0.5	B) 0.7	C) 0.9	D) 1.1	E) 1.2

Solution: √0.1+√0.15=approximately √0.09+√0.16=0.3+0.4= 
0.3+0.4 = 0.7
0.7 . Hence, the correct answer is 0.7.
Answer: B
As x increases from 165 to 163, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x) Options:	A) I only	B) III only	C) I and II	D) I and III	E) II and III

Solution: I. 2x - 5 --> x increases from 165 to 163 --> 2x increases --> 2x - 5 increases. Correct.   II. 1 - 1/x --> x increases from 165 to 163 --> 1/x decreases --> 1 -1/x increases. Correct.   III. 1/(x^2 - x) --> x increases from 165 to 163 --> x^2-x increases --> 1/(x^2 - x) decreases.   Answer: I and II.
Answer: C
What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 9), (x, 9)?  Choose one
A) 121	B) 132	C) 144	D) 156	E) 169

Solution: To find the area of a square, knowing the length of one side is sufficient.   From the coordinates given, we can see that one side equals 11.   The area is 11*11= 
11*11 = 121
121.   The answer is 121.
Answer: A
Thirty men can do a work in 24 days. In how many days can 20 men can do the work, given that the time spent per day is increased by one-third of the previous time? Choose the correct choice from the following choices.
A) 27 days  B) 77 days  C) 88 days  D) 66 days  E) 22 days

Solution: Let the number of hours working per day initially be x. we have M1 D1 H1   = M2 D2 H2   30 * 24 * x = 20 * d2 * (4x)/3   => d2 = (30 * 24 * 3)/(24 * 4)   = 27 days.   27 daysnswer:27 days
Answer: A
Ram's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Ram's average score on the 5 tests to be 80?	Pick:  A) 80  B) 82  C) 84  D) 86  E) 88

Solution: E. 88   Ram must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so  80+8= 
 80+8 = 88
88.
Answer: E
The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 4 type B widgets, and the weight of 3 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?  Choose the most appropriate option:
A) 5:4
B) 7:6
C) 9:8
D) 11:10
E) 13:12

Solution: 3B = 7C and so B = 7C/3   7A = 4B and so A = 4B/7 = 4C/3   A+B = 4C/3 + 7C/3 = 11C/3   B+C = 7C/3 + C = 10C/3   The ratio of A+B:B+C = 11:10   The answer is 11:10.
Answer: D
A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?	Choose the correct choice from the following options
A) 20	B) 99	C) 28	D) 18	E) 11

Solution: Explanation:   There are three ladies and five gentlemen and a committee of 5 members to be formed.   Number of ways such that two ladies are always included in the committee = â¶Câ‚ƒ = (6 * 5 * 4)/6= 
(6 * 5 * 4)/6 = 20
20.   20nswer:20
Answer: A
In how many ways the letters of the word LOOC be arranged? Choose the correct option.
A) 10	B) 11	C) 12	D) 16	E) 18

Solution: In this four letters means 4! = 24 ways   But 'O' is repeated two times.   And thus we divide the final ways by 2. I.e. there are only  24/2= 
 24/2 = 12
12 ways of arranging the letters of this word.   LOOK, LOKO, LKOO, KOOL, KOLO, KLOO, OOLK, OOKL, OLOK, OKOL, OLKO, OKLO= 12 Ways   12
Answer: C
A closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?	Pick one:
A) 0 feet	B) 1 feet	C) 2 feet	D) 3 feet	E) 4 feet

Solution: 36 pie cubic feet of water and its filled to half tank's capacity...   volume of tank = 72 Pie cubic feet   height of tank = 4*2= 
4*2 = 8
8 feet ( since tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet.)   72 pie= pie * r2*8   r2=9   r = 3 feet   ANSWER:3 feet
Answer: D
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 60 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.	Select:
A) 22	B) 27	C) 15	D) 99	E) 21

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 80 x.   Total marks of (x - 5) students = 90(x - 5)   80x - (5 * 60) = 90(x - 5)   150 = 10x => x = 15.Answer: 15
Answer: C
If the square root of p^2 is an integer, which of the following must be true?
I. p^2 has an odd number of factors
II. p^2 can be expressed as the product of an even number of prime factors
III. p has an even number of factors	Pick one:
A) I B) II C) III D) I and II E) II and III

Solution: I. p^2 is a perfect square and a perfect square has pairs of factors and '1' with it. The total number of factors is odd   II. If p = 3 then p^2 = 9. The prime factors will always remain even as the p is an integer and the pairs have to come out of square root to make p an integer.   III. This is not true always. Let us say p = 4, it has three factors: 1, 2 and 4. Hence it will not hold true always.   Hence I and II is the answer.
Answer: D
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? Choose the correct choice from the following options:	A) 22 sec	B) 88 sec	C) 48 sec	D) 18 sec	E) 9 sec

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec.   Answer:48 sec
Answer: C
Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 4 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?	Choose the correct choice from the following answers:
A) 7/15
B) 9/20
C) 11/25
D) 13/27
E) 15/31

Solution: Tom paints 1/6 of the room in the first hour.   Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.   The three people then paint the remaining 2/6 in a time of (2/6) / (3/4) = 4/9 hours   Peter worked for 13/9 hours so he painted 13/9 * 1/3 = 13/27 of the room.   The answer is 13/27.
Answer: D
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? Choose the correct choice from the following choices:
A) 7%
B) 4%
C) 9%
D) 42%
E) 2%

Solution: 65*(90/100)*((100-x)/100)   = 56.16   x = 4%   Answer:4%
Answer: B
What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, 3158, 9476, x	Choose one
A) 2643 B) 5464 C) 3456 D) 7554 E) 28430

Solution: 12   12 Ã— 3 + 2 = 38   38 Ã— 3 + 2 = 116   116 Ã— 3 + 2 = 350   350 Ã— 3 + 2 = 1052   1052 Ã— 3 + 2 = 3158   3158 Ã— 3 + 2 = 9476   9476 Ã— 3 + 2 = 28430   28430
Answer: E
Find the simple interest on Rs.500 for 9 months at 6 paisa per month?  Pick one
A) 287
B) 270
C) 276
D) 129
E) 211

Solution: I = (500*9*6)/100= 
(500*9*6)/100 = 270
270   Answer: 270
Answer: B
If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 45 miles ahead of Joe? Choose the correct option:
A) 15	B) 60	C) 75	D) 90	E) 210

Solution: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.   Teena covers 55 miles in 60 mins.   Joe covers 40 miles in 60 mins   So teena gains 15 miles every 60 mins   Teena need to cover 7.5 +45 miles.   Teena can cover 7.5 miles in 30 mins   Teena will cover 45 miles in 180 mins   So answer 30+180= 
30+180 = 210
210 mins.(ANSW210R 210)
Answer: E
If P(A) = 6/17, P(B) = 5/17, and P(A ∪ B) = 4/17 Find P(B|A)? Choose the most appropriate option:
A) 2/3 B) 3/5 C) 2/7 D) 3/7 E) 4/9

Solution: P(B|A) = P(A ∪ B)/P(A)   P(B|A) = (4/17)/(6/17) = 4/6 = 2/3.   2/3
Answer: A
A bag contains 2 red, 2 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball? Choose the correct choice from the following options:
A) 5/7  B) 11/14  C) 17/21  D) 19/28  E) 23/35

Solution: P(no red balls) = 5/7*4/6*3/5 = 2/7   P(at least one red ball) = 1 - 2/7 = 5/7   The answer is 5/7.
Answer: A
If A is to be chosen at random from the set {8,1} and B is to be chosen at random from the set {2,7,9,6}, what is the probability that AB will be even? Options:
A) 5/9
B) 5/4
C) 3/8
D) 9/7
E) 2/5

Solution: Method-1   A5/4 will be even when   1) A is even and 5/4 is odd, Probability of A even is (1/2) and Probability of 5/4 odd is (2/4), so Probability of Case(1) = (1/2)*(2/4) = (2/8)   2) A is Odd and 5/4 is Even, Probability of A Odd is (1/2) and Probability of 5/4 Even is (2/4), so Probability of Case(2) = (1/2)*(2/4) = (2/8)   3) A is even and 5/4 is Even, Probability of A even is (1/2) and Probability of 5/4 Even is (2/4), so Probability of Case(1) = (1/2)*(2/4) = (2/8)   Total Favorable Probability = (2/8)+(4/8)+(4/8) = (10/8) = 5/4   Answer: option 5/4
Answer: B
If a^3 is divisible by 240 what is the least possible value of integer a?	Answers
A) 12
B) 30
C) 60
D) 90
E) 120

Solution: 240 can be written as (2^4)*3*5.   For a^3 to be divisible by 240 it should contain atleast 2^4 and 3 and 5 in its factors. We can leave out option A because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^3 will have 3 as the maximum power of 2, so we can leave out this option too.   Option C is the right answer if we follow the same method as we followed for other two previous options.   60 = (2^2)*3*5; 60^3 = (2^6)*(3^3)*(5^3). So it shows that 60^3 is divisible by 240 and hence the answer.   Answer : 60
Answer: C
If the price of bananas goes down by 10%, find the percentage of increase that a family should effect in its consumption so as not to increase expenditure on this account? Choose the correct choice from the following answers:
A) 13(1/9)%
B) 15(1/9)%
C) 11(1/9)%
D) 12(1/9)%
E) none of these

Solution: Increase in consumption   = [(P/(100 - P)] X 100)%   = [(10/(100 - 10)] X 100)%   = 11(1/9)%   ANSWER:11(1/9)%
Answer: C
A man distributed Rs. 100 equally among his friends. If there had been 5 more friends, each would have received one rupee less. How many friends had he ?	Pick:
A) 20
B) 25
C) 30
D) 35
E) 40

Solution: firstly we have 20 friends and money wiill be distribute each of them 5 rupee   then 5 more friends   it means total no frnd=25 each recv 4 rupee   which means all recv 1 less rupee   ANSWER:25
Answer: B
If (x - 1)^2 = 361, which of the following could be the value of x - 4?
Select:
A) 17  B) 15  C) -22  D) -24  E) -26

Solution: (x - 1)^2 = 361   (x - 1) = 19 or -19   x = 20 or -18   x - 4 = 16 or -22   The answer is -22.
Answer: C
A car traveled 35% of the way from Town X to Town Y at an average speed of 35 mph. The car traveled at an average speed of v mph for the remaining part of the trip. The average speed for the entire trip was 50 mph. What is v in mph? Choose the correct choice from the following choices:	A) 45	B) 65	C) 55	D) 75	E) 85

Solution: Assume total distance = 100miles   Time taken for 35 miles = 35/35= 
35/35 = 1
1 hour   Time taken for the rest of the 65 miles= 65/v hours.   Average speed = 50   Therefore the total time needed = 2 hours.   2 = 1 + 65/v   Hence v = 65 mph   Answer : 65
Answer: B
If the average of 5 positive integers is 65 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers? Choose one
A) 50  B) 52  C) 59  D) 68  E) 73

Solution: Sum of 5 Integer (a, b, c, d, e) = 5*65= 
5*65 = 325
325   e - a= 10   i.e. e = a+10   For e to be maximum remaining 4 MUST be as small as possible   Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers   i.e. a+a+a+a+(a+10) = 325   i.e. 5a = 315   i.e. a = 63   i.e. Largest e = 63+10= 
63+10 = 73
73   Answer: option 73
Answer: E
A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $42,000 commission, how many machines did she sell?	Choose the correct choice from the following options.
A) 90  B) 103  C) 130  D) 115  E) 120

Solution: First 100 machines = 3% commission = 0.03*100*10000= 
0.03*100*10000 = 30_000
30000   Commission from sale of next machines= 42000 - 30000= 
42000 - 30000 = 12_000
12000   So 30 more machines..   Total= 130 machines   IMO 130...
Answer: C
In a class of 50 students, 20 play Basketball, 15 play Cricket and 11 play Football. 7 play both Basketball and Cricket, 4 play Cricket and Football and 5 play Basketball and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports? Choose one:
A) 67	B) 45	C) 10	D) 675	E) 688

Solution: Notice that7 play both Basketball and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Basketball/Football.   [color=#ffff00]{Total}={Basketball}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS   [/color]   50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;   Those who play ONLY Basketball and Cricket are 7-2= 
7-2 = 5
5;   Those who play ONLY Cricket and Football are  4-2= 
 4-2 = 2
2;   Those who play ONLY Basketball and Football are  5-2= 
 5-2 = 3
3;   Hence, 5+2+3=10 students play exactly two of these sports.   Answer: 10.
Answer: C