mathewhe/aqua_rat huggingface dataset:
Question: Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
(A) 30 miles.
(B) 35 miles.
(C) 45 miles.
(D) 60 miles.
(E) 65 miles.
Rationale: In 1st hour: Relative speed of the two will be 10+5 = 15 miles / hour. As they move towards each other, The distance between them reduces by 15 miles. Distance left between them: 90 - 15 = 75 miles.
In 2nd hour: Speed of Tim: 20Mph, That of Elan: 10 Mph. Relative speed of the two will be 20+ 10 = 30 miles / hour. As they move towards each other, The distance between them reduces by 30 miles. Distance left between them: 75 - 30 = 45 miles.
In 3rd hour: Speed of Tim: 40 Mph, That of Elan: 20 Mph. Relative speed of the two will be 40+ 20 = 60 miles / hour.
Now in order to cover the remaining distance of 45 miles. They will take: (45/ 60) hrs. = (3/4) hour.
Distance travelled by Tim?
In first hour: 1 hour * (10 miles per hour) = 10 miles
In second hour: 1 hour * (20 miles per hour) = 20 miles
In third hour: (3/4) hour * (40 miles per hour) = 30 miles
Total distance travelled: 10+20+30 = 60 miles.
D is the answer
Answer: (D) 60 miles.
Question: Peeta asks Katniss, 'It is 10 am as per my watch right now.Do you know what will be the time 23, 999, 999 hours later?'
Katniss knows the answer. Do you ?
(A) 5pm
(B) 6pm
(C) 4am
(D) 7am
(E) 8pm
Rationale: D
7pm
The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer: (D) 7am
Question: A certain country is divided into 6 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/18 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?
(A) 1/5
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: Let P be the number of Progressives in the country as a whole.
In each province, the number of traditionalists is P/18
The total number of traditionalists is 6P/18 = P/3.
The total population is P + P/3 = 4P/3
P / (4P/3) = 3/4
The answer is E.
Answer: (E) 3/4
Question: There was a cycle race going on. 1/5th of the those in front of a person and 5/6th of those behind him gives the total number of participants. How many people took part in the race?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: let total =x
1/5*(x-1)+5/6(x-1)=x by solving this we will get 31
ANSWER:B
Answer: (B) 31
Question: A retailer sold two articles at a profit percentage of 10% each. The cost price of one article is three – fourth that of the other. Find the ratio of the selling price of the dearer article to that of the cheaper one
(A) 4:3
(B) 3:4
(C) 41:31
(D) 51:41
(E) 61:41
Rationale: Let C.P of one of the article be X, Then C.P of the other = ¾X,
S.P 1 = 11X/10, S.P2 =3/4*11/10X,
S.P1/S.P2 = 11X/10 *40/33X = 4/3
S.P1: S.P2 = 4 : 3
ANSWER:A
Answer: (A) 4:3
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 56%
(B) 44%
(C) 78%
(D) 55%
(E) 33%
Rationale: B
g% = 20 + 20 + (20*20)/100
= 44%
Answer: (B) 44%
Question: A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 400 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: The distance between the nest and the ditch is 400 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 400 = 12000.
D = ST
12000/1.5 = T , I think we can take 12000 meters as 12km, then only we get T = 8.( 1000 meters = 1 km)
D)
Answer: (D) 8
Question: Fifteen identical machines, running continuously at the same constant rate, take 10 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by five days?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 9
Rationale: From the question you know that 15R = 1/10. The question asks you (partially) to make the rate from 1/10 to 1/5 (drop from 10 day to 5). So the only thing that you need to do is to find the magic number than can convert 1/10 to 1/5.
So 1/10 * x = 1/5 (1 equation with one unknown). So by solving this you get x = 10/5 or 2/1. Thats it then! Take the magic number 4/3 and multiply BOTH sides of the original equation and you have:
12*(2/1)*R = (2/1) * 1/10
12 * 2 * R = 1/5, Hence 24R = 1/5, therefore 9 more machines!
E
Answer: (E) 9
Question: If the least common multiple of two prime numbers x and y is 10, where x > y, then the value of 2x + y is
(A) 7
(B) 9
(C) 11
(D) 12
(E) 21
Rationale: LCM of two prime numbers will basically be multiple of those numbers. LCM = 10 = 2*5, both of which are prime.
Now we know x>y, so x=5 and y =2.
2x+y = 2*5 + 2 = 10 + 2 = 12.
ANSWER:D
Answer: (D) 12
Question: When a is divided by b, the quotient is c with remainder 5. What is a in terms of 5, b, and c?
(A) bc-5
(B) 5bc
(C) 5b/c
(D) b/c
(E) bc+5
Rationale: a/b =c with remainder 5
i.e, a-5 = bc
a= bc+5
Answer : E
Answer: (E) bc+5
Question: In a board game, a stack of 46 cards, 8 of which have pictures of fruit, are shuffled and then placed face down. If the first 2 cards selected do not have pictures of fruit, what is the probability that the third card selected will have a picture of fruit?
(A) 2/11
(B) 1/6
(C) 1/8
(D) 3/7
(E) 4/23
Rationale: After 2 cards have been selected, there are 44 cards remaining.
P(third card has a picture of fruit) = 8/44 = 2/11
The answer is A.
Answer: (A) 2/11
Question: Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 37% ryegrass, what percent of the weight of the mixture is from mixture X?
(A) 20%
(B) 40%
(C) 50%
(D) 60%
(E) 80%
Rationale: 37% is 12%-points above 25% and 3%-points below 40%.
Thus the ratio of mixture Y to mixture X is 1:4.
The percent of mixture X is 4/5 = 80%.
The answer is E.
Answer: (E) 80%
Question: Jacob is now 13 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
(A)  8
(B)  7
(C)  15
(D)  21
(E)  25
Rationale: Jacob=x years, Michael=x+13 years
9 years from now,
2(x+9)=x+22
2x+18=x+22
x=4
x+4=8 years
Answer A
Answer: (A)  8
Question: Lakshmi invested some money in 25% stock at 500.If Usha wants to invest in an equally good 50% stock ,he must purchase a stock worth of :
(A) Rs. 1000
(B) Rs. 1200
(C) Rs. 1300
(D) Rs. 1400
(E) Rs. 1500
Rationale: Solution
For an income of Rs. 25, investment = Rs. 500
For an income of Rs. 50, investment = Rs.(500/25x50) = Rs. 1000
Answer A
Answer: (A) Rs. 1000
Question: The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 24-inch flat-screen television than a square 17-inch flat-screen television?
(A) 143.5
(B) 154
(C) 160
(D) 148.75
(E) 142.25
Rationale: If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 24-inch flat-screen television
The diagonal (hypotenuse) = 24
So, we can apply the Pythagorean Theorem to get x² + x² = 24²
Simplify: 2x² = 24²
Divide both sides by 2 to get: x² = 24²/2
Since the area of the square = x², we can see that the area of this square is 24²/2
square 17-inch flat-screen television
The diagonal (hypotenuse) = 17
So, we can apply the Pythagorean Theorem to get x² + x² = 17²
Simplify: 2x² = 17²
Divide both sides by 2 to get: x² = 17²/2
Since the area of the square = x², we can see that the area of this square is 17²/2
DIFFERENCE IN AREAS =24²/2-17²/2
= 288 -144.5 i.e = 143.5
A
Answer: (A) 143.5
Question: A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?
(A) 25.7 years
(B) 28 years
(C) 29.3 years
(D) 28.8 years
(E) 28.9 years
Rationale: Present age of the son be P, he was born P years ago.
The age of the man was: (48 - P).
His age when the son was born should be equal to 2/3 of P.
(48 - P) = 2/3 P
5P = 144 => P = 28.8
ANSWER:D
Answer: (D) 28.8 years
Question: what is the sum of the first 25 odd natural numbers
(A) 300
(B) 400
(C) 625
(D) 600
(E) 700
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 25 odd natural numbers=(25)^2=625
ans 625
ANSWER:C
Answer: (C) 625
Question: Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5.
(A) 187
(B) 197
(C) 207
(D) 219
(E) 227
Rationale: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5.
Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197.
ANSWER:B
Answer: (B) 197
Question: Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 140% of Charlie's weight. Charlie weighs 180% of Mary's weight. Which of these 5 people weighs the highest?
(A) Mary
(B) Mike
(C) Michelle
(D) Alan
(E) Charlie
Rationale: Mary < Michelle < Mike
Charlie < Alan
Let x be Mary's weight.
Mike's weight is 2x and Alan's weight is 1.4*1.8x = 2.52x.
The answer is D.
Answer: (D) Alan
Question: A train 210 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 18 sec
(B) 16 sec
(C) 76 sec
(D) 12 sec
(E) 17 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 210 * 2/35 = 12 sec
Answer:D
Answer: (D) 12 sec
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
(A) 2211
(B) 2721
(C) 227
(D) 176
(E) 167
Rationale: 25x + 46 = 26(x – 5)
x = 176
Answer:D
Answer: (D) 176
Question: There are 4 periods in each working day of a school. In how many ways can one organize 3 subjects such that each subject is allowed at least one period?
(A) 32
(B) 36
(C) 24
(D) 34
(E) None of these
Rationale: 3 subjects can be arranged in 4 periods in 4P3 ways.
Remaining 1 period can be arranged in 3P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (4p3 x 3P1)/2! = 36
ANSWER:B
Answer: (B) 36
Question: Which one of the following is not a prime number?
(A) 2
(B) 3
(C) 5
(D) 9
(E) 7
Rationale: 9 is divisible by 3. So, it is not a prime number.
Answer:D
Answer: (D) 9
Question: At a company, the average wage of male employees is $5 per hour, and the average wage of female employees is $8 per hour. If the average wage of all employees is $7.5 per hour, what is the ratio of the number of male employees to the number of female employees?
(A) 1 to 5
(B) 2 to 3
(C) 3 to 2
(D) 5 to 3
(E) 2 to 1
Rationale: Average hourly wage of male employees = 5 $
Average hourly wage of female employees = 8 $
Average hourly wage of all employees = 7.5 $
Let number of male employees = m
number of female employees = f
7.5 = (5m + 8f ) / m+f
=>7.5m + 7.5f = 5m + 8f
=> 2.5m = .5f
=> m/f = 2.5/.5 = 1/5
Answer A
Answer: (A) 1 to 5
Question: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
(A) 21/46
(B) 25/117
(C) 1/50
(D) 3/25
(E) 2/13
Rationale: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S)	= Number ways of selecting 3 students out of 25
= 25C3 `
=(25 x 24 x 23)/(3 x 2 x 1)
= 2300.
n(E)	= (10C1 x 15C2)
=10 x((15 x 14)	/(2 x 1))
= 1050.
P(E) =	n(E)/n(S)	=1050/2300=21/46
Option A
Answer: (A) 21/46
Question: Find the probability that a leap year selected at random will have 53 Mondays
(A) 6/7
(B) 5/7
(C) 4/7
(D) 3/7
(E) 2/7
Rationale: There are 366 days in a leap year: 52 weeks and 2 more days. So, 52 Mondays and 2 days.
These 2 days can be: {Mon, Tue}, {Tue, Wed}, {Wed, Thu}, {Thu, Fri}, {Fri, Sat}, {Sat,Sun} and {Sun, Mon} (7 cases). In order to have 53 Mondays we should have either {Mon,Tuesday} or {Sun, Mon} case.
The probability of that is 2/7.
Answer: E.
Answer: (E) 2/7
Question: A person X working alone can complete a work in 6 days. A person Y completes the same amount of work in 15 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: The fraction of work completed in two days is 2/6 + 2/15 + 2/30 = 16/30
The fraction of work remaining is 1 - 16/30 = 14/30
The number of days required for Z is 14 days.
The answer is C.
Answer: (C) 14
Question: A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:
(A) Rs. 330
(B) Rs. 360
(C) Rs. 380
(D) Rs. 430
(E) Rs. 450
Rationale: If earlier their investmwnts were 4x and 5x for 3 months
and then
3x and 4x for next 7 months,
Then profit will be divided in ratio of (4x*3 + 3x*7) :( 5x*3+4x*7) or 33:43
Hence A's share in profit of Rs 760 = 760*33/76 = Rs 330.
ANSWER:A
Answer: (A) Rs. 330
Question: A student committee on academic integrity has 30 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 11
Rationale: xC1 * (x-1)C1=30
x^2 -x -30 =0
(X-6) (X+5) = 0
X= 6 , -5
-5 can't possible.
D
Answer: (D) 6
Question: Three table runners have a combined area of 212 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?
(A)  18 square inches
(B)  20 square inches
(C)  24 square inches
(D)  28 square inches
(E)  30 square inches
Rationale: Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither
80%*175 = 212 - 24 - 2*(all three) + 0
2*(all three) = 212 - 24 - 140
all three = 24
Answer: C
Answer: (C)  24 square inches
Question: In how many different ways can the letters of the word ‘PREPTY’ be arranged?
(A) 250
(B) 280
(C) 300
(D) 310
(E) 360
Rationale: Number of ways = 61/21 6X5X4X3X2X1 - 360
E
Answer: (E) 360
Question: The traffic lights at 3 different roads change after every 9 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.
(A) 9:18:36
(B) 9:42:15
(C) 10:15:24
(D) 9:54:12
(E) 10:01:20
Rationale: LCM of 9,72,108 = 216 = 3mnts 36sec
The lines will change every 3m 36sec
The light will change again after 9:15 AM is = 9:15+0:03:36 = 9:18:36
Answer is A
Answer: (A) 9:18:36
Question: If 15% of 30% of 50% of a number is 108, then what is the number?
(A) 4000
(B) 3050
(C) 4400
(D) 4800
(E) None of these
Rationale: Let the number be a
Given, 15/100 * 30/100 * 50/100 * a = 108
=> 3/20 * 3/10 * 1/2 * a = 108
=> a = 10 * 20 * 10 * 2 = 4800.
ANSWER:D
Answer: (D) 4800
Question: A bike covers a certain distance at the speed of 64km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
(A) 85 km/h
(B) 85.34 km/h
(C) 87.67 km/h
(D) 90.25 km/h
(E) 90.64 km/h
Rationale: Ans.(B)
Sol. Total distance = 64 × 8 = 512 km
Now speed = 512/6 = 85.34 km/h
Answer: (B) 85.34 km/h
Question: Two female friendstwo male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with menwomen alternating. How many possible arrangements may she chose?
(A) 40320
(B) 1680
(C) 1152
(D) 576
(E) 8
Rationale: now any of the alternate 2 places can be filled by 2 male or female in 2!
similarily,
other 2 alternate places can be filled in 2!
hence required probability= 2*2!*2!=8
hence E
Answer: (E) 8
Question: If P(A)=0.4, P(B)=0.6 and P(A ∪ B)=0.8. What is the value of P(A∩B')=?
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
(E) None
Rationale: Solution:
P(A∪B) = P(A) + P(B) - P(A∩B') =>
0.8=0.4 - P(A∩B) =>P(A∩B)=0.2
P(A∩B') = P(A) - P(A∩B) = 0.4 - 0.2 = 0.2
Answer B
Answer: (B) 0.2
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 13
(C) 14
(D) 15
(E) 12
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30	:	39 :: 12 : x
Working hours/day	6	:	5
Therefore 30 x 6 x x = 39 x 5 x 12
=> x =(39 x 5 x 12)/(30 x 6)
=> x = 13.
Correct answer is B
Answer: (B) 13
Question: When the positive integer z is divided by 9, the remainder is 5. What is the remainder when 3z is divided by 9?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 6
Rationale: Lets take the number as z
when x is divided by 9 the remainder is 5 hence z can be written as
z=9k +5
Multiplying by 3 will give
3z = 27k + 15
we can also write
3z = 27k + 9 + 6
Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
Answer: (E) 6
Question: How many three-digit integers between 310 and 400, exclusive, are divisible by 3 when the tens digit and the ones digit are switched?
(A) 3
(B) 19
(C) 30
(D) 22
(E) 90
Rationale: Answer is 30
No of digits between 310 and 400 (exclusive) = 400-310-1 = 89
No Intergers divisble by 3 =~ 89/3 ~ 30
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if ones digit and tens digits are switched.
e.g 372 is divisble by 3 (becae 3+7+2= 12 (divisble by 3))
switch digits 732 also divisble by 3 (becae 7+3+2= 12 (divisble by 3))
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if ones digit and tens digits are switched.
You have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1 =30.
Answer : C
Answer: (C) 30
Question: A beats B by 20metres ,B beats C by20 metres in a 100 m race .By how much A beats C
(A) 35metres
(B) 36metres
(C) 37metres
(D) 38metres
(E) 39metres
Rationale: A : B = 100 : 80
B : C = 100 : 80
A : C = (A/B * B/C)
= (100/80 * 100/80)
= (100/64)
Therefore A beats C by = (100-64) = 36metres.
ANSWER:B
Answer: (B) 36metres
Question: 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
(A) 2267
(B) 287
(C) 268
(D) 228
(E) 225
Rationale: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/6
15 women's 1 day work = (1/6 - 10/100) = 1/15
1 woman's 1 day work = 1/225
1 woman alone can complete the work in 225 days.
Answer: E
Answer: (E) 225
Question: A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
(A) 54 minutes
(B) 34 minutes
(C) 32 minutes
(D) 21 minutes
(E) 16 minutes
Rationale: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?
675 * 150 = 4.5 = 4 and 1/2
For each of these groups 8 minutes are needed. For 4 groups and 1/2
8* 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time)
We can also find the final answer as follows
4.5 x 8 = 32 minutes correct answer C
Answer: (C) 32 minutes
Question: The average of runs of a cricket player of 10 innings was 37. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
(A) 76
(B) 81
(C) 85
(D) 87
(E) 89
Rationale: Explanation:
Average = total runs / no.of innings = 37
So, total = Average x no.of innings = 37 x 10 = 370.
Now increase in avg = 4runs. So, new avg = 37+4 = 41runs
Total runs = new avg x new no. of innings = 41 x 11 = 451
Runs made in the 11th inning = 451 - 370 = 81 Answer: B
Answer: (B) 81
Question: How long does a train 145 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
(A) 52.66
(B) 53.66
(C) 54.66
(D) 58.66
(E) 59.66
Rationale: T = (660 + 145)/54 * 18/5
T = 53.66
ANSWER:B
Answer: (B) 53.66
Question: A train 100 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 19 Kmph
(B) 18 Kmph
(C) 72 Kmph
(D) 17 Kmph
(E) 91 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 100/20
S = 5 M/Sec
Speed= 5*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 18 Kmph
Answer: B
Answer: (B) 18 Kmph
Question: A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is?
(A) 100
(B) 220
(C) 120
(D) 130
(E) 240
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 12 = 240 m.
Answer: Option E
Answer: (E) 240
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 128798
(B) 134768
(C) 153600
(D) 168799
(E) 156789
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ?
(A) 7/19
(B) 7/15
(C) 7/16
(D) 7/12
(E) 7/11
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 7C2/15C2 + 8C2/15C2 = 7/15
Answer: B
Answer: (B) 7/15
Question: A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 4% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
(A)  0.25
(B)  .05^10
(C)  1-0.95^10
(D)  1-0.05^10
(E)  1-0.96^10
Rationale: Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.96^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.96^10.
Answer: E.
Answer: (E)  1-0.96^10
Question: The sale price sarees listed for Rs.600 after successive discount is 20% and 5% is?
(A) 227
(B) 358
(C) 456
(D) 787
(E) 191
Rationale: 600*(80/100)*(95/100)
= 456
Answer: C
Answer: (C) 456
Question: A group of medical interns at Bohemus Medical School want to go on dates. There are 6 girls and 6 guys. Assuming girls go on dates with guys, how many possible ways can these 12 medical interns date each other?
(A) A)320
(B) B)420
(C) C)520
(D) D)620
(E) E)720
Rationale: 1st girl can go with 6 guys
2nd girl can go with remaining 5
3rd girl can go with remaining 4 and so on
so the total ways are 6!= 720
E should be the answer
Answer: (E) E)720
Question: A grocer has a sales of Euro 520, Euro 320 , Euro 480, Euro 600 and Euro 800 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Euro 620?
(A) uro 4691
(B) uro 4591
(C) uro 2000
(D) uro 7791
(E) uro 1000
Rationale: E
Euro 1000
Total sale for 5 months = Euro (520 + 320 + 480 + 600 + 800) = Euro 2720.
Required sale = Euro [ (620 x 6) - 2720]
= Euro (3720- 2720)
= Euro 1000.
Answer: (E) uro 1000