mathewhe/aqua_rat huggingface dataset:
Question: 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?
(A) 57%
(B) 22.2%
(C) 20%
(D) 12.5%
(E) 11.1%
Rationale: 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 (A) 57%
Answer: (A) 57%
Question: What is the probability of getting at least one six in a single throw of three unbiased dice ?
(A) 31/216
(B) 91/216
(C) 125/216
(D) 81/216
(E) 81/359
Rationale: 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 : B
Answer: (B) 91/216
Question: 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?
(A) 56
(B) 70
(C) 90
(D) 98
(E) 80
Rationale: Total=180
Television=115
Radio=110
Magazine=130
All the three =180-115-110-130+85+75+95=80
ANSWER E
Answer: (E) 80
Question: 30 is subtracted from 40% of a number, the result is 50. Find the number?
(A) 200
(B) 997
(C) 266
(D) 288
(E) 271
Rationale: (40/100) * X – 30 = 50
4X = 800
X = 200
Answer:A
Answer: (A) 200
Question: 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.
(A) 125/127
(B) 127/125
(C) 125/126
(D) 126/125
(E) 126/127
Rationale: Required probability = 1 - 1/126 = 125/126
Answer: C
Answer: (C) 125/126
Question: 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?
(A) 81
(B) 100
(C) 120
(D) 132
(E) 160
Rationale: 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:D
Answer: (D) 132
Question: 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)
(A) 8/3
(B) 3/8
(C) 8/5
(D) 12/5
(E) 5/3
Rationale: Distance traveled by Eddy = 540 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 540/3 = 180 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 180/75 = 12/5
Answer D
Answer: (D) 12/5
Question: 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?
(A) 16C₅ * 10
(B) 16C₇ * 10
(C) 16C11 * ¹⁰C₅
(D) 12 * ¹⁰C₅
(E) None of these
Rationale: 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 = 16C₅ * ¹⁰C₅ = 16C11 * ¹⁰C₅
since 16C₅ = 16C11
ANSWER:C
Answer: (C) 16C11 * ¹⁰C₅
Question: 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?
(A) 3:4:6
(B) 3:4:7
(C) 3:4:0
(D) 3:4:2
(E) 3:4:1
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7.
Answer: B
Answer: (B) 3:4:7
Question: The difference between the place value and the face value of 6 in the numerical 856973 is
(A) 973
(B) 6973
(C) 5994
(D) 9554
(E) None of them
Rationale: =(place value of 6)-(Face value of 6)
=(6000-6)
=5994
Answer is C
Answer: (C) 5994
Question: 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?
(A) 24
(B) 48
(C) 56
(D) 72 ways
(E) 96
Rationale: 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:D
Answer: (D) 72 ways
Question: A car is running at a speed of 90kmph. What distance will it cover in 10sec?
(A) 100m
(B) 150m
(C) 180m
(D) 200m
(E) 250m
Rationale: Speed = 90kmph = 90*5/18 = 25 m/s
Distance covered in 10sec = 25*10 = 250m
Answer is E
Answer: (E) 250m
Question: The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers.
(A) 28 and 17
(B) 27 and 18
(C) 25 and 15
(D) 27 and 15
(E) 25 and 18
Rationale: 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.
Answer is A.
Answer: (A) 28 and 17
Question: 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?
(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
Rationale: 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. E
Answer: (E) 5x = y - 3
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 year?
(A) 306.06
(B) 306.02
(C) 306.04
(D) 306.09
(E) 306.12
Rationale: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer: C
Answer: (C) 306.04
Question: The angles of a triangle are in the ratio 1 : 2 :3 . Find the measurement of the 3angles of triangle.
(A) 100°
(B) 110°
(C) 60°
(D) 180°
(E) 190°
Rationale: 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°
C
Answer: (C) 60°
Question: 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?
(A) 210
(B) 240
(C) 270
(D) 290
(E) 360
Rationale: 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 BDA = 360 - 70 = 290 degrees
Answer =(D)
Answer: (D) 290
Question: 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?
(A) $148,000
(B) $167,000
(C) $156,000
(D) $175,000
(E) $144,000
Rationale: 6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x.
correct answer A
Answer: (A) $148,000
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
(A) 258
(B) 124
(C) 525
(D) 343
(E) 729
Rationale: 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: E
Answer: (E) 729
Question: 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?
(A) 1200km
(B) 1500km
(C) 2000km
(D) 2400km
(E) 3600km
Rationale: 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 D
Answer: (D) 2400km
Question: What is the value of x^2yz − xyz^2, if x = -1, y = 1, and z = 3?
(A)  20
(B)  24
(C)  30
(D)  12
(E)  48
Rationale: 1*1*3 -(- 1*1*9)
=3+9 = 12
Ans: D
Answer: (D)  12
Question: 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?
(A) 97.1 kgs
(B) 88.5 kgs
(C) 86.5 kgs
(D) 67.5 kgs
(E) 88.2 kgs
Rationale: Average 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
Answer:A
Answer: (A) 97.1 kgs
Question: 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?
(A) 395
(B) 275
(C) 355
(D) 415
(E) 398.2
Rationale: 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:E.
Answer: (E) 398.2
Question: 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?
(A) 20ltr
(B) 21ltr
(C) 23ltr
(D) 24ltr
(E) 25ltr
Rationale: 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 = 140x + 147
112x = 336
x = 3.
So, the can contained 21ltr of M
B
Answer: (B) 21ltr
Question: 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?
(A)  24
(B)  30
(C)  48
(D)  54
(E)  75
Rationale: Speed = Distance/Time
Distance for Tom = Speed * Time = 40 * 1/2 = 20 miles
Distance for Beth = Distance for Tom +5 = 20+5 = 25 miles
Time taken by Beth = Time taken by Tom + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour
Hence, B is the answer.
Answer: (B)  30
Question: 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
(A) 12 kg
(B) 60 kg
(C) 72 kg
(D) 96 kg
(E) None
Rationale: 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 B
Answer: (B) 60 kg
Question: 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?
(A) 1:2
(B) 1:3
(C) 2:3
(D) 5:7
(E) 4:9
Rationale: 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 C
Answer: (C) 2:3
Question: 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?
(A) 30
(B) 20
(C) 58
(D) 48
(E) 68
Rationale: 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.
ANSWER:A
Answer: (A) 30
Question: 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?
(A) 10
(B) 12
(C) 15
(D) 11
(E) 18
Rationale: 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 =6.
And,
=> c + d = 3+5 =8
Putting these values in (i), we get :-
=> 6 + 1.5 * 8 = x.
=> x = 18 .
Answer : E
Answer: (E) 18
Question: 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?
(A)  x/6
(B)  x/12
(C)  x/15
(D)  3x/40
(E)  3x/80
Rationale: 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 C.
Answer: (C)  x/15
Question: 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?
(A) 24/576
(B) 125/864
(C) 1/25
(D) 1/64
(E) 1/5
Rationale: 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: D.
Answer: (D) 1/64
Question: 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?
(A) 15/25
(B) 4/20
(C) 3/4
(D) 15/20
(E) 9/10
Rationale: 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 = 5
Remaining = 20-5 = 15
Required = 15/25
Answer (A).
Answer: (A) 15/25
Question: 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 :
(A) 334
(B) 378
(C) 377
(D) 400
(E) 288
Rationale: 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 = 400.
Answer: D) 400
Answer: (D) 400
Question: 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?
(A) 1/4.
(B) 4/17.
(C) 5/29
(D) 4/13
(E) 1/3
Rationale: P(10) = (4+12) / (52+12)
= 16/64
= 1/4.
Answer:A
Answer: (A) 1/4.
Question: 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?
(A) 477
(B) 396
(C) 279
(D) 276
(E) 291
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 12 + 21 = 33
T = 12
D = 33 * 12 = 396.Answer: B
Answer: (B) 396
Question: Look at this series: 0.6, 0.3, ____, 0.075, 0.0375, ... What number should fill the blank?
(A) 0.015
(B) 1.15
(C) 0.15
(D) 0.25
(E) 0.35
Rationale: This is a simple multiplication series. Each number is multiple by 1/2.
Answer: C
Answer: (C) 0.15
Question: 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?
(A) 1 hr 20 min
(B) 2 hr
(C) 3 hr
(D) 4 hr
(E) 5 hr 50 min
Rationale: 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 hour = 2 hours.
Therefore
3 taps can fill half tank in 2/2 hour =60 minutes = 1hour.
Total time taken=4 hours
Answer: Option D
Answer: (D) 4 hr
Question: Find out the C.I on Rs.2000 at 4% p.a. compound half-yearly for 1 1/2 years.
(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
Rationale: A = 2000(51/50)3
= 2122.41
2000
-----------
122.41
ANSWER:C
Answer: (C) C)Rs.306.04
Question: 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?
(A) 18.6
(B) 27
(C) 12
(D) 121
(E) 28
Rationale: Explanation:
T = 14/45 * 60 = 18.6
Answer: Option A
Answer: (A) 18.6
Question: 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?
(A) 7/10
(B) 11/20
(C) 13/30
(D) 17/30
(E) 19/30
Rationale: 1/2 of the small beaker is 1/10 of the large beaker.
1/10 + 1/3 = 13/30
The answer is C.
Answer: (C) 13/30
Question: 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?
(A) 2 4/2 hours
(B) 2 hours
(C) 2 1/6 hours
(D) 2 1/1 hours
(E) 2 1/2 hours
Rationale: Required time
= (5 1/4)/4 + (5 1/4)/7
= 2 hours.
Answer:B
Answer: (B) 2 hours
Question: 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)
(A) 1/4
(B) 1/5
(C) 1/7
(D) 2/5
(E) 2/9
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1
P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4.
A
Answer: (A) 1/4
Question: 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?
(A) 1110
(B) 1120
(C) 1130
(D) 1140
(E) 1150
Rationale: 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=1120
ANSWER:B
Answer: (B) 1120
Question: A certain no. when divided by 80 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 2
(B) 4
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
80 + 25 = 105/15 = 7(Remainder)
C
Answer: (C) 7
Question: 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?
(A) 18 : 15 : 20
(B) 6 : 7 : 8
(C) 6 : 8 : 9
(D) Cannot be determined
(E) None of these
Rationale: 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
Answer A
Answer: (A) 18 : 15 : 20
Question: 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?
(A) 1/5
(B) 3/7
(C) 2/5
(D) 5/14
(E) 2/7
Rationale: 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
D
Answer: (D) 5/14
Question: John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.
(A) 24
(B) 12
(C) 7
(D) 6
(E) 5
Rationale: 5 different colours = 5 single colours = 5 different clients
There are 7 clients to go
The use of the factorial is the easiest way to solve this kind of problem for me.
A B C D E (different colour)
C C N N N (2 colour coding + 3 colour non chosen)
5!/2!3!= 10
15 codings can be done with 5 different colours
Ans E
Answer: (E) 5
Question: A wolf eats 5 Kg of meat in 2 days. A baby tiger eats 3 Kg of meat in 4 days. How much meat can the two combined eat in three days?
(A) 10.5
(B) 9.75
(C) 8.25
(D) 7.15
(E) 6.0
Rationale: 3/2*5+3/4*3=9.75 kg
B
Answer: (B) 9.75
Question: In how many ways can a team of 5 be chosen out of a batch of 8 players?
(A) 45
(B) 56
(C) 32
(D) 50
(E) 61
Rationale: required number of ways = 8C5 = 56
Answer is B
Answer: (B) 56
Question: All factors of a positive integer X are multiplied and the product obtained is X^3. If X is greater than 1, how many factors does X have?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The question can be done in seconds if you understand the properties of factors of a number. Note that every distinct factor of a number which is not a perfect square has a complementary factor.
For example,
Factors of 6: 1, 2, 3, 6
1 has a complementary factor 6 such that 1*6 = 6 (the original number)
2 has a complementary factor 3 such that 2*3 = 6 (the original number)
So if you have a number, n, which is not a perfect square, and start multiplying its factors, you will get n to a certain power. the power will half of the number of factors. For example, 6 has 4 factors and when you multiply all 4 factors, you get 6^2 (2 is half of 4).
So if you know that the product of all factors is X^3, it means there must have been twice the number of factors i.e. 3*2 = 6 factors.
E)
Answer: (E) 6
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 277
(C) 269
(D) 2656
(E) 290
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: A
Answer: (A) 432