MU-NLPC/Calc-aqua_rat huggingface dataset:
Of the 5 distinguishable wires that lead into an apartment, 3 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television? Choose the correct choice
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: Given:   Total number of wires = 5   Number of cable wires = 2   Number of telephone wires = 3   To find:   Number of combination which has at least one cable wires   Solution:   No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2   Since it is a combination of wires, the arrangement is not important   Approach 1:   Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)   Selection 1   Number of ways of selecting one cable wire = 2C1 = 2   Number of ways of selecting 2 telephone wires = 3C2 = 3   Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)   Selection 2   Number of ways of selecting one cable wire = 2C2 = 1   Number of ways of selecting 2 telephone wires = 3C1 = 3   Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)   Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire   Approach 2   Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)   Total number of ways of selecting 3 wires out of 5 = 5C2 = 10   Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1   Selection X - Selection Y = 7   Answer is Option 7
Answer: B
If a fair 6-sided die is rolled three times, what is the probability that exactly one 1 is rolled?
Choose the correct choice from the following answers: A) 25/216 B) 50/216 C) 25/72 D) 25/36 E) 5/6

Solution: Total ways in which a 6-sided die can be rolled three times = 6*6*6= 
6*6*6 = 216
216   To get exactly one 1, there are three ways:   A 1 on the first roll and non 1 on other two rolls. This can be done in 1*5*5= 
1*5*5 = 25
25 ways.   The 1 could be on the second or third roll too. So total favorable cases= 25*3= 
25*3 = 75
75   Required Probability= 75/216 = 25/72   Answer (25/72)
Answer: C
Jane spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?  Select:
A) 10
B) 25
C) 14
D) 16
E) 28

Solution: Every word problem has an unknown number. In this problem, it is the price of the blouse. Always let x represent the unknown number. That is, let x answer the question.   Let x, then, be how much she spent for the blouse. The problem states that "This" -- that is, $42 -- was $14 less than two times x.   Here is the equation:   2x − 14= 42.   2x= 42 + 14= 
42 + 14 = 56
56   x= 56/2= 
56/2 = 28
28.   Ans is 28
Answer: E
Molly can do a task in 18 days while Sandy can do the task in 12 days. How many days will it take to complete the task if both work together?  Pick:
A) 6.2	B) 6.6	C) 7.2	D) 7.8	E) 8.4

Solution: Each day, Molly can do 1/18 of the task.   Each day, Sandy can do 1/12 of the task.   Each day, they can do 1/18 + 1/12 = 5/36 of the task.   The task will be completed in 36/5= 
36/5 = 36/5 = around 7.2
7.2 days.   The answer is 7.8.
Answer: D
There are 9 people and 9 chairs. In how many different ways people can occupy the chairs?
Choose the correct choice:
A) 362880 B) 340009 C) 250909 D) 345008 E) 1000

Solution: number of ways =9! = 362880   362880nswer is 362880
Answer: A
Two pipes A and B can fill a cistern in 10 and 15 minutes respectively. Both fill pipes are opened together,but at the end of 3 minutes, ‘B’ is turned off. How much time will the cistern take to fill ?
Choose the correct choice:
A) 6 min B) 8 min C) 10 min D) 12 min E) None of these

Solution: In one min, (A + B) fill the cistern = 1⁄10 + 1⁄15 = 1⁄6th   In 3 min, (A + B) fill the cistern = 3⁄6 = 1⁄2th   Remaining part = 1 - 1⁄2 = 1⁄2   ∵ 1⁄10th part filled by A in one min.   ∴ 1⁄2nd part filled by A in 10 × 1⁄2 = 5 min.   ∴ Total time = 3 + 5= 
3 + 5 = 8
8 min.   Answer 8 min
Answer: B
The average of 26,29,n,35 and 43 lies between 25 and 35. If n is always an integer and greater than the average of the given integers then the value of n is :	Choose the correct choice from the following answers:
A) 36  B) 29  C) 33  D) 28  E) 21

Solution: Explanation:   Average of 26,29,35 and 43 is 33.25 . Also the average of 26 , 29, n, 35 and 43 lies between 25 and 35 i.e,   Rightarrow 125 < 26+29+n+35+43 < 175   Rightarrow 125 < 133 + n < 175   Rightarrow n < 42   Since the value of n is an integer and greater than 33.25 then 33 < n < 42 for every integer n.   Answer: 33
Answer: C
For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $6 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as Choose the correct choice.
A) 1 : 4 : 400
B) 1 : 4 : 100
C) 20 : 4 : 1
D) 100 : 4 : 1
E) 400 : 4 : 1

Solution: millionaire 20 cents = 1/5 dollar ..therefore 1 dollar M = 100 dollar of 1 : 4 : 100   therefore 6 dollar M = 600 dollar of 1 : 4 : 100 also 1 dollar Y   Y:M:1 : 4 : 100 = 1:6:600   = 1:6:600   1 : 4 : 100
Answer: B
Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies? Choose the most appropriate option.
A) Rs.6152 B) Rs.6159 C) Rs.6156 D) Rs.6150 E) Rs.6196

Solution: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15   = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60   Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.   The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k   It is given that A paid Rs. 1125   45k 45  + 60  + 81  + 60= 
45  + 60  + 81  + 60 = 246
246k   It is given that A paid Rs. 1125   45k= 1125 => k = 25   246k = 246(25) = Rs. 6150   Thus the total rent paid by all the four agencies is Rs.6150.   Answer: Rs.6150
Answer: D
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?  Choose the correct choice from the following choices:
A) 1: 96 B) 1: 97 C) 1: 98 D) 1: 99 E) 1: 92

Solution: 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= 
2 * 12 = 24
24   Ratio of the breadth and the areas= 3x : 12x2 = 1 : 4x = 1: 96.   1: 96nswer: Option 1: 96
Answer: A
Given that 268x74= 19732, find the value of 2.68x.74. Choose the correct choice from the following choices:  A) 1.9732  B) 1.0025  C) 1.5693  D) 1.0266  E) None

Solution: Solution   Sum of decimals places	=(2+2)= 
(2+2) = 4
4.   Therefore,= 2.68×.74   = 1.9732   1.9732nswer 1.9732
Answer: A
A man can row his boat with the stream at 12 km/h and against the stream in 8 km/h. The man's rate is?
Select the correct option:
A) 2 kmph B) 6 kmph C) 7 kmph D) 4 kmph E) 9 kmph

Solution: Explanation:   DS = 12   US = 8   S = ?   S = (12- 8)/2= 
(12- 8)/2 = 2
2 kmph   2 kmphnswer: 2 kmph
Answer: A
A and B enter into a partnership. A contributed Rs.5000 for 8 months and B Rs.6000 for 5 months. Find A's share in a total profit of rs.8400. Choose the most appropriate option.
A) Rs. 4800
B) Rs. 2400
C) Rs. 3600
D) Rs. 5600
E) None of these

Solution: Explanation:   Ratio of capitals of A and B   = Ratio of their investments   = 5000 × 8 : 6000 × 5   = 40000 : 30000 = 4 : 3   .: A's share = Rs. [(4/7) × 8400] = Rs. 4800   Rs. 4800nswer: Option Rs. 4800
Answer: A
On a ferry, there are 22 cars and 10 trucks. The cars have an average mass of 1200 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 32 vehicles on the ferry? Pick one:
A) 1686.5
B) 1762.5
C) 1824.5
D) 1878.5
E) 1906.5

Solution: The total mass of the vehicles is 22*1200+10*3000= 
22*1200+10*3000 = 56_400
56400   The average mass is   56400/32= 
  56400/32 = 3_525/2 = around 1_762.5
1762.5   The answer is 1762.5.
Answer: B
factor: 3y (x-3)-2(x-3) Options: A) (x-3)-2(x-3) B) (x-3)power2 C) (x-3)(3y-2) D) 3y(x-3) E) x-3

Solution: 3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: ((x-3)(3y-2))
Answer: C
fill in the blank space.
1, 9, 25, 49, 81, ?
Select the correct option
A) 100
B) 121
C) 144
D) 169
E) 172

Solution: The series consists of squares of consecutive prime numbers.   Answer : 121.
Answer: B
The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 3, what is the value of H?  Choose the correct answer:
A) 2
B) 3
C) 5
D) 4
E) 9

Solution: Integer is divisible by 3 - Sum of digits is divisible by 3   Answer: 4
Answer: D
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and if the repetition is allowed? Choose the correct choice from the following
A) 20	B) 5	C) 10	D) 36	E) 25

Solution: Since, each desired number is divisible by 5, so we must have 5 at the unit place.   So , the tens place can now be filled by any of the remaining 6 digits (2, 3, 6, 7, 9, 5)   therefore the 3-digit no can be formed by   (6 * 6 * 1)= 
  (6 * 6 * 1) = 36
36 ways ------(since repetition is allowed)   Ans- 36
Answer: D
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?	Choose one
A) 70 min  B) 16 min  C) 20 min  D) 10 min  E) 40 min

Solution: D   10 min   Due to stoppages, it covers 9 km less.   Time taken to cover 9 km = (9/54 x 60) min = 10 min
Answer: D
If ‘POOJA’ is coded as ‘SRRMD’, then ‘PRIYA’ is coded as  Pick
A) THGFE
B) GVFED
C) FREDCV
D) SULBD
E) SUUNF

Solution: P= 16 = 16+3= 
16+3 = 19
19= S   O = 15 =15+3= 
15+3 = 18
18= R   SIMILARLY,   P = 16 = 16+3= 
16+3 = 19
19= S   R = 18 = 18+3= 
18+3 = 21
21= U   I = 9 = 9+3= 
9+3 = 12
12= L   Y = 25 = 25 +3= 
25 +3 = 28
28= B   A = 1 = 1+3= 
1+3 = 4
4= SULBD   SO ANS IS   SULBSULBD
Answer: D
In the sea there are 3 fishers in a boat and they take 4 hours to complete one third of a fish container. They went to rest and were supplanted by 8 fishers. If they continue to fish at the same rate, how many hours will take to all of the fishers complete all the container?  Choose the correct choice from the following answers
A) 16 hours  B) 12 hours  C) 8 hours  D) 7 hours  E) 5 hours

Solution: We have that: 3 fishers ----- 4 hours, 8F ----- xhr, that is: (Xhr/ 3F) = (4hr/8F), then: Xhr = (4hr/8F)3F = (3/2)hr. Is to say, they did the same work in 3/2 hours; it is only one third of the container. Then, all the container is: C = C1 + C2 + C3 = 4 hr + (3/2) hr + (3/2) hr = (4 + 3)= 
(4 + 3) = 7
7 hr. Answer 7 hours.
Answer: D
By using the numbers 0, 1, 3, 5 and 6 only once, how many five digit numbers can be made that are divisible by 15? Choose the correct choice from the following choices.
A) 12  B) 18  C) 24  D) 36  E) 42

Solution: A number to be divisible by 15 must end with 15, 30, 45,60,75 or 70.   So, there are the following cases possible:   035-15 --> the first three digits can be arranged in 3=6 ways.   156-30 --> the first three digits can be arranged in 3=6 ways.   135-60 --> the first three digits can be arranged in 3=6 ways.   Total = 6+6+6= 
6+6+6 = 18
18.   Answer:18.
Answer: B
How many three digit numbers E are divisible by 78 or 91?	Choose the correct choice.
A) 17 B) 19 C) 20 D) 21 E) 22

Solution: The answer will be 19.   Explanation:   78= 2*3*13 now multiples of 78, 156 ....780, now   1000-780= 
  1000-780 = 220
220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are   9+2= 
  9+2 = 11
11   91= 13*7--Total number of three digit multiples --9   No remember we have a common multiples as well-- 13*7*6=91*6= 
91*6 = 546
546   So total number of multiples E--11+9 -1= 
--11+9 -1 = 19
19.   Hence Answer is 19.19
Answer: B
Nine people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
Pick one
A) 1 / 9
B) 1 / 8
C) 1 / 7
D) 7 / 8
E) 8 / 7

Solution: Let P = total cost of the rental van.   The original share per person is P/9.   The new share per person is P/8.   P/8 = P/9 * 9/8 = (1 + 1/8)*original share   The answer is 1 / 8.
Answer: B
The G.C.D of 1.08, 0.36 and 0.9 is
Pick
A) 0.03  B) 0.9  C) 0.18  D) 0.108  E) None

Solution: Solution   Given numbers are 1.08 , 0.36 and 0.90.   H.C.F of 108 ,36 and 90 is 18.   ‹=› H.C.F of given numbers = 0.18.   Answer 0.18
Answer: C
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?	Choose the most appropriate option
A) 65 B) 86 C) 30 D) 78 E) 38

Solution: US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30   Answer: 30
Answer: C
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 25%?	Choose the correct option:	A) 600	B) 887	C) 625	D) 654	E) 712

Solution: 625ost price = Rs.500   profit = 25% of 500 = Rs.125   Selling price = 625ost price + Profit   = 500 + 125= 
500 + 125 = 625
625   Answer: 625
Answer: C
Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.  Choose one:
A) Rs 400
B) Rs 300
C) Rs 3109
D) Rs 250
E) Rs 400

Solution: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.   Amount = Rs'. [8000 X (1+¬(15/100))2 X (1+((1/3)*15)/100)]   =Rs. [8000 * (23/20) * (23/20) * (21/20)]   = Rs. 11109.	.   :. C.I. = Rs. (11109 - 8000) = Rs. 3109.   ANSWER Rs 3109 Rs 3109
Answer: C
How many ways could two people sit at a table with four seats in which two of the four seats will remain empty?	Choose the correct option.
A) 60
B) 12
C) 112
D) 118
E) 120

Solution: ways in which 2 seats out 4 can be selected = 4C2   ways in which 2 people can be arranged in 2 seats = 2!   Total ways of arrangement = 4C2*2!   =4*3= 
4*3 = 12
12   Ans= 12
Answer: B
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?  Choose the most appropriate option:  A) 21 (1/9)  B) 21 (1/3)  C) 21 (1/2)  D) 21 (5/3)  E) 21 (1/6)

Solution: 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: 21 (1/3)
Answer: B
A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price  Pick:	A) Rs.500/-	B) Rs.510/-	C) Rs.515/-	D) Rs.530/-	E) Rs.540/-

Solution: 100 % ------> 600 (100 * 6 = 600)   90 % ------> 540 (90 * 6 = 540)   Selling price = Rs.540/-   Rs.540/-
Answer: E
Real-estate salesman Z is selling a house at a 25 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 5 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 30 percent discount. Salesman Y's final price is what fraction of salesman X's final price?	Choose the correct choice from the following answers
A) 21/34  B) 55/71  C) 25/34  D) 26/34  E) 27/34

Solution: Let the retail price be = x   Selling price of Z = 0.75x   Selling price of X = 0.95*0.75x = 0.71x   Selling price of Y = ((0.75x + 0.71x)/2)*0.70 = 0.73x * 0.75 = 0.55x   0.55x = k * 0.71x   k = 0.55/0.71 = 55/71   Answer: 55/71
Answer: B
An eccentric casino owner decides that his casino should only use chips in $5 and $8 denominations. Which of the following amount cannot be paid out using these chips?
Choose one.
A) $34  B) $27  C) $31  D) $29  E) $24

Solution: Yes, the number of 5 or/and 8 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.   Each option but B can be represented as the sum of a multiple of 5 and a multiple of 8:   A. $34 = 8*3 + 5*2   B. $31 = 8*2 + 5*3   C. $29 = 8*3 + 5*1   E. $24 = 8*3   Answer: $27.
Answer: B
A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?  Answers:
A) 6
B) 5
C) 4
D) 3
E) 2

Solution: 40*(40/100)= 
40*(40/100) = 16
16 --- 64   ? --- 12=> Rs.3   Answer: 3
Answer: D
Mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 80 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?	Choose the most appropriate option
A) 35
B) 15
C) 20
D) 25
E) 30

Solution: d = rt   M: r = 50mph, t = t + 1/4hr   d = 50 (t + 1/4)   P: r = 80, t = t   d = 80t   since they went the same distance:   50t + 50/4 = 80t   30t = 50/4 = 50/120 *60= 
50/120 *60 = 25
25 min   t= 25 min   25
Answer: D
The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 900. What is the banker's discount?  Options.
A) 1240 B) 1120 C) 1190 D) 2150 E) None of these

Solution: Explanation :   TD = (BG ×100)/TR = (900×100)/(6×12) = Rs. 1250   BG = B2150 – T2150   => 900 = B2150 - 1250   => B2150 = 2150 Answer : Option 2150
Answer: D
At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $40,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?  Choose the correct choice: A) $14,000 B) $11,200 C) $12,000 D) $12,800 E) $13,200

Solution: 1 machine of type B will cost: 20% down payment of 40,000 = 8,000plusremaining sum (50,000-8,000=42,000) with 40% of finance charges 42,000*1.4=58,800 --> 8,000+58,800=66,800;   2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;   Difference = 66,800 - 52,800 = 14,000.   $14,000nswer: $14,000.
Answer: A
Running 3/4th of his usual rate, a man is 9min late. Find his usual time in hours ?	Choose the correct option:
A) 6/4 hrs B) 3/4 hrs C) 9/20 hrs D) 3/4 hrs E) 1/4 hrs

Solution: Explanation:   Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time   so 1/3rd of the usual time = 9min   or usual time = 3 x 9 = 27min = 27/60 hrs = 9/20 hrs.   Answer: 9/20 hrs
Answer: C
A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 90 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
Choose the correct choice
A) 160
B) 240
C) 360
D) 495
E) 560

Solution: The number of jumbo tiles = x.   The number of regular tiles = 2x.   Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.   The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.   The area of regular tiles = 2x*a^2 = 90.   The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*90= 
4.5*90 = 405
405.   Total area= 90 + 405= 
90 + 405 = 495
495   Answer: 495.
Answer: D
A man bought some mangoes at Rs12 per dozen and bought the same number of at Rs 10 per kg. He sold these mangoes at Rs 13 per dozen and gained Rs 160.The total number of mangos bought by him are	Choose the correct choice:
A) 40dozens	B) 60dozens	C) 70dozens	D) 80dozens	E) 90dozens

Solution: let total no of mangoes is 2x..   then we profit=sp-cp   160=13*2x-(12x+10x)   160=4x   x=40   hence 2x=80   so total no are 80dozens   ANSWER:80dozens
Answer: D
In how many ways can you line up 7 cars in a row if one of them cannot be in the middle or at the either end?	Select the correct option.
A) 82	B) 92	C) 1,750	D) 2,880	E) 982

Solution: Since the car cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.   Answer: 2,880.
Answer: D
The averge score of a cricketer for ten matches is 35 runs. If the average for the first six matches is 23. Then find the average for the last four matches?
Choose the most appropriate option
A) 58	B) 53	C) 64.25	D) 55	E) 57

Solution: sum of last 4 matches = (10 × 35) – (6 × 23)=212   Average = 212/4= 
212/4 = 53
53   ANSWER:53
Answer: B
In a village ,50% of the students play football, 60% of the student play basketball,40% of the student play cricket. 20% play both football and basketball ,20% play both football and cricket,25% play both cricket and baseketball.5% of the student play all the three games and 100 students play none of the games.How many students are there in the college?
Choose the most appropriate option.
A) 700  B) 800  C) 900  D) 1000  E) 1100

Solution: the student play all three games=5%   the student play only both football n bsketball=(20-5)= 
(20-5) = 15
15%   the student play only both football n cricket=(20-5)= 
(20-5) = 15
15%   the student play only both basketball n cricket=(25-5)= 
(25-5) = 20
20%   the student play only football=(50-15-15-5)= 
(50-15-15-5) = 15
15%   the student play only basketball=(60-15-20-5)= 
(60-15-20-5) = 20
20%   the student play only cricket=(40-15-20-5)= 
(40-15-20-5) = 0
0%   so sdtudent play games=(0+20+15+15+15+20+5)= 
(0+20+15+15+15+20+5) = 90
90%   so student does not play games=(100-90)= 
(100-90) = 10
10%   as 10%=100 student den 100%=1000 student   there are 1000 student in the college   ANSWER:1000
Answer: D
A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Q that out of the two, one is white and one is blue?
Pick one:
A) 15/56 B) 41/56 C) 13/28 D) 15/28 E) 5/14

Solution: The required probability Q= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.   Ways to select 6 out of total 8 = 8C6   Ways to select 4 out of 5 white balls = 5C4   Ways to select 2 out of 3 blue balls = 3C2   Thus the required probability = (5C4*3C2)/8C6 = 15/28.   15/28 is thus the correct answer.
Answer: D
What will come in place of the x in the following Number series? 25, 100, 400, 1600, 6400, X  Choose the correct answer
A) 64000
B) 69000
C) 25600
D) 75000
E) 79000

Solution: (25600)   25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400, 6400 x 4 = 25600
Answer: C