MU-NLPC/Calc-aqua_rat huggingface dataset:
Cara and Dan drive at constant speeds toward each other on a highway. Cara drives at a constant speed of 32 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Cara is 110 km away from Dan at 7 am, and also 110 km away from Dan at 11 am, then how fast is Dan driving (in kilometers per hour)?  Choose the correct choice from the following answers:
A) 20  B) 23  C) 26  D) 29  E) 32

Solution: Cara and Dan complete 220 km / 4 hours = 55 km/hour   Dan's speed is  55-32= 
 55-32 = 23
23 km/hour   The answer is 23.
Answer: B
Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose? Select the correct option: A) 3/140 B) 1/28 C) 3/56 D) 3/35 E) 7/40

Solution: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.   Answer: 7/40.
Answer: E
Of the 3,600 employees of Company X, 16/25 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
Choose the correct answer.
A) 57% B) 22.2% C) 20% D) 12.5% E) 11.1%

Solution: Let's see, the way I did it was   16/25 are clerical out of 3600 so 2304 are clerical   2304 reduced by 1/4 is 2304*1/4   so it reduced 576 people , so there is 1728 clerical people left   but since 576 people left, it also reduced from the total of 3600 so there are 3024 people total   since 1728 clerical left / 3024 people total   you get (57%) 57%
Answer: A
What is the probability of getting at least one six in a single throw of three unbiased dice ?  Select.
A) 31/216	B) 91/216	C) 125/216	D) 81/216	E) 81/359

Solution: Explanation :   Three cases arise:   Case 1: When only one dice shows up a six   This dice can be any of the 1st, 2nd or 3rd dice. Find the probability for these three independent events and add them up to get the total probability   Probability that only 1st dice shows up a six: (probability that first dice shows up a 6) and (probability that second dice shows up other than 6) and (probability that third dice shows up other than 6)   =(1/6)*(5/6)*(5/6)   =25/216   similarly probability that 2nd dice shows up a six: (5/6)*(1/6)*(5/6) = 25/216   And, probability that 3rd dice shows up a six: (5/6)*(5/6)*(1/6) = 25/216   So probability that only one dice shows up a six: (25/216)+(25/216) +(25/216) = 75/216   Case 2:When two dice show up a six   Total number of ways of selecting a pair of dice that show up a six from a set of 3 dice are: 3C2=3   Find the probability of getting six on a pair of dice and multiply it by total number of such possible pairs   Probability of getting a six on a pair of dice = (1/6)*(1/6)*(5/6) = 5/216   So, total probability = 3*(5/216) = 15/216   Case 3: When all dice show up a six   In this case total probability is just (1/6)*(1/6)*(1/6) = 1/216   So total probability of getting at least one six = (75/216) + (15/216) + (1/216) = 91/216   Answer : 91/216
Answer: B
An advertising agency finds that, of its 180 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three? Choose the correct choice:
A) 56 B) 70 C) 90 D) 98 E) 80

Solution: Total=180   Television=115   Radio=110   Magazine=130   All the three =180-115-110-130+85+75+95= 
180-115-110-130+85+75+95 = 80
80   ANSW80R 80
Answer: E
30 is subtracted from 40% of a number, the result is 50. Find the number?
Choose the correct choice from the following options:	A) 200	B) 997	C) 266	D) 288	E) 271

Solution: (40/100) * X – 30 = 50   4X = 800   X = 200   200nswer:200
Answer: A
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Choices.
A) 125/127	B) 127/125	C) 125/126	D) 126/125	E) 126/127

Solution: Required probability = 1 - 1/126 = 125/126   Answer: 125/126
Answer: C
A retailer bought a machine at a wholesale price of $99 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?  Choose the correct choice:	A) 81	B) 100	C) 120	D) 132	E) 160

Solution: My solution: Wholesale Price= 99   Retail Price, be = x   He provides 10 % discount on Retail price= x-10 x/100   This Retail price = 20 % profit on Wholesale price   x-10 x/100 = 99+ 1/5(99)   x=132;   ANSWER:132
Answer: D
Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)	Choose the correct choice:
A) 8/3  B) 3/8  C) 8/5  D) 12/5  E) 5/3

Solution: 12/5istance traveled by Eddy = 540 km   Time taken by Eddy = 3 hours   Average speed of Eddy = 540/3= 
540/3 = 180
180 km/hour   12/5istance traveled by Freddy= 300 km   Time taken by Freddy = 4 hours   Average speed of Freddy = 300/4= 
300/4 = 75
75 km/hour   Ratio of average speed of Eddy to Freddy= 180/75 = 12/5   Answer 12/5
Answer: D
A group of 10 representatives is to be selected out of 16 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?  Select:
A) 16C₅ * 10 B) 16C₇ * 10 C) 16C11 * ¹⁰C₅ D) 12 * ¹⁰C₅ E) None of these

Solution: Here, five seniors out of 16 seniors can be selected in 16C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 1616C11 * ¹⁰C₅₅ * ¹⁰16C11 * ¹⁰C₅₅ = 1616C11 * ¹⁰C₅11 * ¹⁰16C11 * ¹⁰C₅₅   since 1616C11 * ¹⁰C₅₅ = 1616C11 * ¹⁰C₅11   ANSWER:16C11 * ¹⁰C₅
Answer: C
A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?	Choose one:	A) 3:4:6	B) 3:4:7	C) 3:4:0	D) 3:4:2	E) 3:4:1

Solution: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)   = 144:192:336 = 3:4:7.   Answer: 3:4:7
Answer: B
The difference between the place value and the face value of 6 in the numerical 856973 is
Answers:
A) 973	B) 6973	C) 5994	D) 9554	E) None of them

Solution: =(place value of 6)-(Face value of 6)   =(6000-6)= 
(6000-6) = 5_994
5994   Answer is 5994
Answer: C
In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?
Choices.
A) 24 B) 48 C) 56 D) 72 ways E) 96

Solution: These 5 people can be arranged in 5! ways. These are the total number of ways you get.   Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.   Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72   ANSWER:72 ways
Answer: D
A car is running at a speed of 90kmph. What distance will it cover in 10sec?  Choose the correct choice from the following options:  A) 100m  B) 150m  C) 180m  D) 200m  E) 250m

Solution: Speed = 90kmph = 90*5/18= 
90*5/18 = 25
25 m/s   Distance covered in 10sec= 25*10= 
25*10 = 250
250m   Answer is 250m
Answer: E
The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers.  Answers
A) 28 and 17	B) 27 and 18	C) 25 and 15	D) 27 and 15	E) 25 and 18

Solution: Let the number be x and y. Then,   x – y = 11 ----(i) and 1/5 (x + y) = 9 => x + y = 45 ----(ii)   Adding (i) and (ii), we get: 2x = 56 or x = 28. Putting x = 28 in (i), we get: y = 17.   Hence, the numbers are 28 and 17.   28 and 17nswer is 28 and 17.
Answer: A
Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 9?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?	Choose the most appropriate option: A) 25x^2 + 4 = y^2 B) 75x^2 = 3y^2 - 12 C) 25x^2 = (y + 2)(y - 2) D) 5x = y - 2 E) 5x = y - 3

Solution: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers   2) Take each answer choice and see if you can manipulate it to make it into the original equation.   With Answer D, we have...   5X = Y - 3   If we square both sides, we end up with....   (5X)^2 = (Y-3)^2   (5X)(5X) = (Y-3)(Y-3)   25X^2 = Y^2 - 6Y + 9   This is NOT a match for the original equation, so it's the answer that is NOT equivalent. 5x = y - 3
Answer: E
Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 year?
Select:
A) 306.06
B) 306.02
C) 306.04
D) 306.09
E) 306.12

Solution: A = 5000(51/50)3   = 5306.04   5000   -----------   306.04   Answer: 306.04
Answer: C
The angles of a triangle are in the ratio 1 : 2 :3 . Find the measurement of the 3angles of triangle.	Choices:
A) 100° B) 110° C) 60° D) 180° E) 190°

Solution: If the ratio of the three angles is 1:2:3, then the measures of these angles can be written as x, 2x and 3x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence   x + 2x + 3x = 180   Solve for x   6x = 180   x = 30   The measures of the three angles are   x = 30°   2x = 2 × 30 = 60°   3x = 3 × 30 = 90°   60°
Answer: C
A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of arc BDA when angle A is 35 degrees?	Select the correct option:
A) 210 B) 240 C) 270 D) 290 E) 360

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 A = 35 degrees   Thus,   arc BCD = 70 degrees   A whole circle has 360 degrees of arc, so arc BDA should be the rest of the circle.   arc B290A = 360 - 70= 
360 - 70 = 290
290 degrees   Answer=(290)
Answer: D
A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?	Choose the correct choice from the following answers.
A) $148,000  B) $167,000  C) $156,000  D) $175,000  E) $144,000

Solution: 6% x = 8,880 : x = selling price of house.   x = $148,000 : solve for x.   correct answer $148,000
Answer: A
Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
Pick one: A) 258 B) 124 C) 525 D) 343 E) 729

Solution: The first ring can be worn in any of the 3 fingers (3 ways).   Similarly each of the remaining 5 rings also can be worn in 3 ways.   Hence total number of ways   =3×3×3×3×3×3=36=729   Ans: 729
Answer: E
A walks at 30 kmph and 30 hours after his start, B cycles after him at 48 kmph. How far from the start does B catch up with A?  Options: A) 1200km B) 1500km C) 2000km D) 2400km E) 3600km

Solution: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 30 hours.   x/30 - x/48 = 30   x = 2400 km   Answer is 2400km
Answer: D
What is the value of x^2yz − xyz^2, if x = -1, y = 1, and z = 3?	Choose the correct choice from the following
A) 20  B) 24  C) 30  D) 12  E) 48

Solution: 1*1*3 -(- 1*1*9)   =3+9= 
3+9 = 12
12   Ans: 12
Answer: D
3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 170kg then find the average weight of all the 7 rounds? Answers:	A) 97.1 kgs	B) 88.5 kgs	C) 86.5 kgs	D) 67.5 kgs	E) 88.2 kgs

Solution: 97.1 kgsverage weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 170/7 = 97.1kgs   97.1 kgsnswer:97.1 kgs
Answer: A
If the mean of numbers 12, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?
Choose the correct choice from the following answers:
A) 395  B) 275  C) 355  D) 415  E) 398.2

Solution: The mean of numbers 12, x, 42, 78 and 104 is 62: 12+x+42+78+104=62*5 --> x=74;   So, the mean of 128, 255, 511, 1023 and x is (128+255+511+1023+74)/5=398.2.   Answer:398.2.
Answer: E
A vessel contains a mixture of two milk M and N is the ratio 7 : 5. When 9 ltr of mixture are drawn off and the vessel is filled with B, the ratio of Mand N becomes 7 : 9. How many ltrof liquid M was contained by the can initially?  Options:
A) 20ltr B) 21ltr C) 23ltr D) 24ltr E) 25ltr

Solution: Suppose the can initially contains 7x and 5x of mixtures A and B respectively.   Quantity of M in mixture left = 7x -	7	x 9 ltr= 7x -	21 ltr.   12	4   Quantity of N in mixture left = 5x -	5	x 9 ltr = 5x -	15 ltr.   12	4   7x -	21   4   =	7   5x -	15 + 9   4   9   28x - 21	=	7   20x + 21	9   252x - 189 28  - 21= 
28  - 21 = 7
7   20x + 21	9   252x - 189= 140x + 147   112x = 336   x = 3.   So, the can contained 21ltr of M   21ltr
Answer: B
Tom and Beth each drove from Smallville to Crown City by different routes. Tom drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Tom to complete the trip. How many miles per hour was Beth's average speed on this trip? Choose the most appropriate option:	A) 24	B) 30	C) 48	D) 54	E) 75

Solution: Speed = Distance/Time   Distance for Tom = Speed * Time = 40 * 1/2= 
40 * 1/2 = 20
20 miles   Distance for 30eth= Distance for Tom +5 = 20+5= 
20+5 = 25
25 miles   Time taken by 30eth= Time taken by Tom + (1/3 hour) = 1/2+1/3 = 5/6   Speed of 30eth = D/T = 25/(5/6) = 25*6/5= 
25*6/5 = 30
30 miles per hour   Hence, 30 is the answer.
Answer: B
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is	Choose the correct choice from the following choices.
A) 12 kg
B) 60 kg
C) 72 kg
D) 96 kg
E) None

Solution: Solution   Volume of water displaced	= (3 x 2 x 0.01)m3   = 0.06m3.   Mass of man	=Volume of water displaced ×Density of water   = (0.06×1000) kg   = 60 kg.   Answer 60 kg
Answer: B
The ration between the present ages of P and Q is 1:2. If Q is 8 years older than P, what will be the ratio of the ages of P and Q after 8 years?
Choose the correct choice
A) 1:2
B) 1:3
C) 2:3
D) 5:7
E) 4:9

Solution: Let P's and Q's age be x and 2x   2x-x = 8   x = 8   Required ratio = (x+8):(2x+8) = 16:24 = 2:3   Answer is 2:3
Answer: C
The sum of three numbers is 98. If the ratio between first and second be 2 : 3 and that between second and third be 5 : 8, then the second number is?	Pick: A) 30 B) 20 C) 58 D) 48 E) 68

Solution: Let the numbers be X, Y and Z. Then,   X + Y + Z = 98, X/Y = 2/3 and Y/Z = 5/8   Therefore, X = 2Y/3 and Z = 8Y/5. So, 2Y/3 + Y + 8Y/5 = 98.   49Y/15 = 98   Y = 30.   30NSWER:30
Answer: A
The last time Parag bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.50, Rs.3.50, Rs.3.00 and Rs.5.00 each. As Rahul wanted 50 cards, he took ten each of two kinds and fifteen each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did paragl give?	Choose the correct choice from the following:
A) 10	B) 12	C) 15	D) 11	E) 18

Solution: Explanation :   Let the four cards be a, b ,c and d. 'x' be the number of notes.   Then, according to the question,   =>10a + 10b + 15c + 15d = 10*x.   => a +b + 1.5(c+d) = x . -----------------------------(i)   Since, a + b = 2.50+3.50= 
2.50+3.50 = 6
6.   And,=> c + d = 3+5= 
3+5 = 8
8   Putting these values in (i), we get :-=> 6 + 1.5 * 8 = x.   => x = 18 .   Answer : 18
Answer: E
The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 30, how many more dollars, in terms of x, will it cost per person?  Choose the correct option
A) x/6	B) x/12	C) x/15	D) 3x/40	E) 3x/80

Solution: Just plugging in values   X= 300   Cost per person if we consider 10 = 30   Cost per person if we consider 30 = 10   Difference between costs is 20 dollars.   Plugging in the value of x into the answer choices, let's see which one yields a result of 20. And that is x/15.
Answer: C
In a series of three football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 3 draws in the series?
Choose the correct choice.
A) 24/576
B) 125/864
C) 1/25
D) 1/64
E) 1/5

Solution: Since the probability of a draw is 1/4, then the probability of 3 draws in 3 matches is (1/4)^3=1/64.   Answer: 1/64.
Answer: D
A sales executive receives an annual bonus if he meets a certain target. This year, the salesman has so far sold 1/4 of last year's quota. If this year's quota is reduced by 20 percent from last year, how much target percentage of this year's target does he still need to complete to get bonus? Choose the correct choice from the following:
A) 15/25
B) 4/20
C) 3/4
D) 15/20
E) 9/10

Solution: We have 1/5 and 20% which is 1/5. Let's pick some smart numbers.   Assume last year's quota to be 25.   This year's quota = 20% reduction from 25 = 20   Sold so far = 1/5 * 25= 
1/5 * 25 = 5
5   Remaining= 20-5= 
20-5 = 15
15   Required= 15/25   15/25nswer (15/25).
Answer: A
The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is :	Choose the correct option:
A) 334 B) 378 C) 377 D) 400 E) 288

Solution: Explanation:   Let the numbers be x and y.   Then, xy = 9375 and x/y = 15.   =>   => y = 25   => x = 15y = 15 x 25 = 375.   Sum of the numbers = 375 + 25= 
375 + 25 = 400
400.   Answer: 400) 400
Answer: D
In a deck of cards there are 52 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?	Choose the correct choice from the following choices: A) 1/4. B) 4/17. C) 5/29 D) 4/13 E) 1/3

Solution: P(10) = (4+12) / (52+12)   = 16/64   = 1/4.   1/4.nswer:1/4.
Answer: A
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 12 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? Choose the correct choice from the following:
A) 477
B) 396
C) 279
D) 276
E) 291

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 12 + 21= 
12 + 21 = 33
33   T= 12   D = 33 * 12= 
33 * 12 = 396
396.Answer: 396
Answer: B
Look at this series: 0.6, 0.3, ____, 0.075, 0.0375, ... What number should fill the blank?	Select:
A) 0.015  B) 1.15  C) 0.15  D) 0.25  E) 0.35

Solution: This is a simple multiplication series. Each number is multiple by 1/2.   Answer: 0.15
Answer: C
A tap can fill a tank in 6 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely? Choose the correct choice:
A) 1 hr 20 min
B) 2 hr
C) 3 hr
D) 4 hr
E) 5 hr 50 min

Solution: Explanation:   1 tap can fill the tank in 6 hours.   Therefore   1 tap can fill half tank in 3 hours.   3 taps can fill the tank in 6/3= 
6/3 = 2
2 hours.   Therefore   3 taps can fill half tank in 2/2 hour=60 minutes = 1hour.   Total time taken=4 hours   Answer: Option 4 hr
Answer: D
Find out the C.I on Rs.2000 at 4% p.a. compound half-yearly for 1 1/2 years.  Pick
A) A)Rs.420.20
B) B)Rs.319.06
C) C)Rs.306.04
D) D)Rs.294.75
E) E)Rs.295.75

Solution: A = 2000(51/50)3   = 2122.41   2000   -----------   122.41   ANSWER:Rs.306.04
Answer: C
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 31 kmph. Of how many minutes does the train stop per hour?	Options
A) 18.6 B) 27 C) 12 D) 121 E) 28

Solution: Explanation:   T = 14/45 * 60 = 18.6   18.6nswer: Option 18.6
Answer: A
A small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 1/3 filled with fresh water. After dumping all of the salt water from the small beaker into the large beaker, to what fraction of its capacity will the large beaker be filled?	Choices.
A) 7/10
B) 11/20
C) 13/30
D) 17/30
E) 19/30

Solution: 1/2 of the small beaker is 1/10 of the large beaker.   1/10 + 1/3 = 13/30   The answer is 13/30.
Answer: C
A man walks at a speed of 4 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Answers:
A) 2 4/2 hours B) 2 hours C) 2 1/6 hours D) 2 1/1 hours E) 2 1/2 hours

Solution: Required time   = (5 1/4)/4 + (5 1/4)/7   = 2 hours.   Answer:2 hours
Answer: B
Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)  Choose the correct choice from the following answers
A) 1/4	B) 1/5	C) 1/7	D) 2/5	E) 2/9

Solution: Here, E and F are events   P(E|F) = P(EnF)/P(F) = 0.4/0.4= 
0.4/0.4 = 1
1   P(F|E)= P(EnF)/P(E) = 0.4/0.16 = 1/4.   1/4
Answer: A
A group of 6 members to be made from 8 boys and 6 girls. How many ways of forming group provided that there will be exactly 3 boys?  Choose the correct choice from the following answers.
A) 1110
B) 1120
C) 1130
D) 1140
E) 1150

Solution: 3 boys out of 8 boys & 3 girls out of 6 girls bcz total 6 member of a group where exactly 3 boys.   8C3*6C3= 8!/(5!3!) * 6!/(3!3!)= 56*20= 
56*20 = 1_120
1120   ANSWER:1120
Answer: B
A certain no. when divided by 80 leaves a remainder 25, what is the remainder if the same no.be divided by 15?  Choose the most appropriate option
A) 2	B) 4	C) 7	D) 8	E) 9

Solution: Explanation:   80 + 25= 
80 + 25 = 105
105/15= 
105/15 = 7
7(Remainder)   7
Answer: C
Seats for Maths, Physics and Biology are in the ratio of 9 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?  Choose the correct choice from the following
A) 18 : 15 : 20	B) 6 : 7 : 8	C) 6 : 8 : 9	D) Cannot be determined	E) None of these

Solution: Reqd ratio 9 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100   = 9 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 18 : 15 : 20   18 : 15 : 20nswer 18 : 15 : 20
Answer: A
An urn contains 5 black and 3 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?	Select the correct option:
A) 1/5 B) 3/7 C) 2/5 D) 5/14 E) 2/7

Solution: Let E and F denote respectively the events that first and second ball drawn   are black. We have to find P(E n F) or P (EF).   Now P(E) = P (black ball in first draw) = 5/8   Also given that the first ball drawn is black, i.e., event E has occurred, now there are 4 black balls and three white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.   That is P(F|E) = 4/7   By multiplication rule of probability, we have   P (E n F) = P(E) P(F|E)   = 5/8 × 4/7 = 5/14   5/14
Answer: D