mathewhe/aqua_rat huggingface dataset:
Question: A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A?
(A) Rs.240
(B) Rs.340
(C) Rs.260
(D) Rs.280
(E) Rs.440
Rationale: LCM = 180
Share of A = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c
= (180/15)/(180/15 +180/20 + 180/45)
= (12/25) * 500
= Rs.240
ANSWER:A
Answer: (A) Rs.240
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 70 m long and 16 1/2 m board?
(A) 99
(B) 18
(C) 16
(D) 10
(E) 231
Rationale: 70 * 33/2 = 5/2 * 2 * x => x
= 231
Answer:E
Answer: (E) 231
Question: A train 300 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
(A) 6 sec.
(B) 7 sec.
(C) 9 sec.
(D) 18 sec.
(E) None
Rationale: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 300 m at (50 /3)m/sec
= (300 x 3/50)sec
= 18 sec.
Answer D
Answer: (D) 18 sec.
Question: 3,7,12,18,25..............10th terms
(A) 43
(B) 53
(C) 63
(D) 65
(E) 74
Rationale: 3+4=7
7+5=12
12+6=18
18+7=25
25+8=33
33+9=42
42+10=52
52+11=63
63+11=74
ANSWER:E
Answer: (E) 74
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
(A) 120
(B) 139
(C) 140
(D) 122
(E) 178
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2
Answer: Option A
Answer: (A) 120
Question: The grade point average of one third of the classroom is 54; the grade point average of the rest is 45. What is the grade point average of the whole class?
(A) 52
(B) 54
(C) 48
(D) 58
(E) 60
Rationale: Let n=total students in class
total points for 1/3 class=54n/3=18n
total points for 2/3 class=45*2n/3=30n
total points for whole class=18n+30n=48n
48n total class points/n total students=48 grade point average for total class
Answer : C
Answer: (C) 48
Question: Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
(A) broke even
(B) lost 10 cents
(C) lost 4 cents
(D) gained 10 cents
(E) gained 4 cents
Rationale: 20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer: (A) broke even
Question: The speed of a car is 98 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 76 kmph
(B) 75 kmph
(C) 87 kmph
(D) 79 kmph
(E) 86 kmph
Rationale: S = (98 + 60)/2
= 79 kmph
Answer: D
Answer: (D) 79 kmph
Question: A test has a mean of 220 and a standard deviation of 10, find the corresponding z score for: a) a test score of 232?
(A) A)1.2
(B) B)2.4
(C) C)5
(D) D)5.6
(E) E)7
Rationale: A test has a mean of 220 and a standard deviation of 10,
find the corresponding z score for:
a) a test score of 232,
z(232) = (232-220)/10 = 12/10 = 1.2
Option A
Answer: (A) A)1.2
Question: If x and y are integers and x + y = 7, which of the following must be true?
(A) x and y are consecutive integers.
(B) Both x and y are less than 5.
(C) If x > 0, then y < 0.
(D) Both x and y are even.
(E) If x < 0, then y > 0.
Rationale: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option E is right could you explain
Answer: (E) If x < 0, then y > 0.
Question: If x>0, y>0, and |x| > |y|, which of the following must be true?
(A) x > y
(B) y^2 > x^2
(C) x^3 > y^2
(D) –x < y
(E) x < –y
Rationale: Correct Answer: (E)
Let’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus x > y is the same statement as |x| > |y|, and (A) must be true.
Answer: (A) x > y
Question: The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 140 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire?
(A) 90
(B) 120
(C) 160
(D) 360
(E) 560
Rationale: If we exclude those cases and take the question at face value, then it seems straightforward.
Group #1 = (didn't like, didn't understand) = 120
Group #2 = (likeunderstood) = 3/4
(1/4)N = 560
N = 480
Answer =(E)
Answer: (E) 560
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 1/2 %, then the amount invested at 11% was?
(A) 23777
(B) 25000
(C) 29977
(D) 26777
(E) 19871
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 19/2 * 1/100)
(9x + 1100000 - 11x) = 950000
x =75000
Sum invested at 9% = Rs. 75000
Sum invested at 11% = Rs. (100000 - 75000) = Rs. 25000.
Answer: B
Answer: (B) 25000
Question: There are 100 fish in a pond. A fisherman put 20 more fish in the pond. How many fish are in the pond
(A) 0
(B) 19
(C) 178
(D) 140
(E) 120
Rationale: If there are 100 fish and you put 20 more fish in the pond, you will have 120 fish
100+20=120 E
Answer: (E) 120
Question: A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
(A) 2.15 p.m.
(B) 1.15 p.m.
(C) 4.15 p.m.
(D) 3.15 p.m.
(E) 12.15 p.m.
Rationale: Suppose they meet x hours after 10 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x =	17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Option A
Answer: (A) 2.15 p.m.
Question: Let a be a positive integer. If n is divisible by 2^a and n is also divisible by 3^(2a), then it is possible that n is NOT divisible by
(A) 6
(B) 3 × 2^a
(C) 2 × 3^(2a)
(D) 6^a
(E) 6^(2a)
Rationale: Easiest method is to assume a value of a = 1
Given n is divisible by 2^2 ---> n = 2^1*p ---> n =2p
Also, n is also divisible by 3^(2a) ---> n = 3^(2a) * q = 3^2*q = 9q
Lets look at a few numbers that are multiples of both 2 and 9 are 18,36,72....
Thus looking at the options , A-D divide the numbers 18,36,72.... while E (=6^(2) = 36 ) does not divide 18. Thus E is the correct answer.
Answer: (E) 6^(2a)
Question: A train running at the speed of 60 km/hr crosses a pole in 27 seconds. What is the length of the train?
(A) 186 m
(B) 176 m
(C) 450 m
(D) 150 m
(E) 765 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 27) m
= 450 m.
Answer: C
Answer: (C) 450 m
Question: An alloy weighing 48 ounces is 25% gold. How many ounces of pure gold must be added to create an alloy that is 40% gold?
(A) 15
(B) 20
(C) 12
(D) 14
(E) 7
Rationale: An alloy of 48oz which is 25% gold means there is 12 oz of gold. To get to an alloy that is 40% gold, let's use this expression: (12 + x)/(48 + x) = 0.40 with x representing the amount of pure gold that must be added to get to 40%. The expression we are using represents the new total weight of pure gold over the new total weight of the alloy and this fraction should represent 40% or 0.4. you will see that 12 is the correct answer, as 24/60=0.4
Choose C
Answer: (C) 12
Question: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction R of time taken by the two wide pipes working together to fill the tank?
(A)  1/2
(B)  2/3
(C)  3/4
(D)  3/7
(E)  4/7
Rationale: I always plug in for these questions.. I find them easier
Let 2 large pipes each work fill 10lts/hr
small ones = 1/2*10 = 5
total 5 = 10+10+5+5+5 = 35 lts/hrs
now assume the total capacity = 140 lts ( LCM of 20,35)
Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank
all working together will take 140/35 = 4 hrs
two large pipes working will take 140/20 = 7 hrs
hence ratio R= 4/7 = E
Answer: (E)  4/7
Question: Can you find the missing number in the sequence given below?
10 16 22 11 17 ? 12 18 24 13 19 25
(A) 25
(B) 23
(C) 20
(D) 18
(E) 19
Rationale: Let's break the given series as below:
10 16 22
11 17 ?
12 18 24
13 19 25
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 23
Answer : B
Answer: (B) 23
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be A's share of the earnings?
(A) $1100
(B) $520
(C) $1040
(D) $1170
(E) $630
Rationale: Explanatory Answer
A, B and C will share the amount of $2340 in the ratio of the amounts of work done by them.
As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.
Similarly, B will complete 1/8th and C will complete 1/12th of the work.
So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12
Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.
We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.
i.e., the ratio in which A : B : C will share $2340 will be 4 : 3 : 2.
Hence, A's share will be 4*2340/9 = 1040
correct choice is (C)
Answer: (C) $1040
Question: For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 4 to n, inclusive. If p is the smallest prime factor of h(100) +4, then p is?
(A) 4
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) 2
Rationale: h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 100. So h(100)+4 will have 4 in the units digit so smallest prime factor is 4.
Answer: A
Answer: (A) 4
Question: Two numbers differ by 5. If their product is 336, then sum of two number is
(A) 33
(B) 34
(C) 36
(D) 37
(E) 38
Rationale: Explanation:
Friends you remember,
=>(x+y)2=(x−y)2+4xy
=>(x+y)2=(5)2+4(336)
=>(x+y)=1369−−−−√=37
Option D
Answer: (D) 37
Question: Which of the following numbers is between 1⁄3 and 1⁄2?
(A) .45
(B) .32
(C) .29
(D) .22
(E) .20
Rationale: Isn't it A?
1/3 = .33
1/2 = .50
The only answer between that is A, .45.
Answer: (A) .45
Question: A customer went to a shop and paid a total of $30, out of which 90 cents was for sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) $12.70
(B) $13.20
(C) $14.10
(D) $15.60
(E) $16.80
Rationale: The total cost was $30.
The tax was $0.90
Let the original price of the taxable items = x
Given that tax rate = 6%
0.06x = 0.90
x = $15
The cost of the tax free items was $30 - $15 - $0.90 = $14.10
The answer is C.
Answer: (C) $14.10
Question: Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?
(A) 20%
(B) 17%
(C) 4.0%
(D) 3.3%
(E) 2.8%
Rationale: 20/6 =3.33
Answer : D
Answer: (D) 3.3%
Question: Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?
(A) 87 km/hr
(B) 70 km/hr
(C) 76 km/hr
(D) 97 km/hr
(E) 57 km/hr
Rationale: Let their speed be x km/hr and y km/he respectively.
Then, 120/(x + y) = 1 => x + y = 120 --- (i)
Now, when they move in same direction:
(Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km
6x - 6y = 120 => x - y = 20 --- (ii)
Sloving (i) and (ii), we get x = 70, y = 50
P's speed = 70 km/hr.
Answer: B
Answer: (B) 70 km/hr
Question: How many prime numbers are between 28/3 and 86/6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 28/3 = 9.xxx
86/6 = 14.xxx
So we need to find Prime numbers between 9 (Exclusive) - 13 (Inclusive)
There are 2 Prime numbers 1113
Hence answer will be (B) 2
B
Answer: (B) 2
Question: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.1 , what is the value of n?
(A) 9
(B) 20
(C) 55
(D) 70
(E) 81
Rationale: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:
We're told that K and N are both INTEGERS.
Since K/N = 81.2, we can say that K = 81.2(N)
N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.
With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)
Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH
Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.
Final Answer:
E
Answer: (E) 81
Question: A test of 10 questions is chosen from 10 hard questions and 20 easy questions. The salad must have at least 4 hard questions at least 3 easy questions. How many ways can this test be created?
(A) 13500611
(B) 13200688
(C) 13200858
(D) 895
(E) 7289
Rationale: Solution: We have four possibilities 4H 6E , 5H 5E, 6H 4E, 7H 3E
(10C4)(20C6)+(10C5)(20C5)+(10C6)(20C4)+(10C7)(20C3)=13200858
C) 13200858
Answer: (C) 13200858
Question: On day one, a store sold 90 books. On each of the next d days, the company sold 62 books. If the average daily sales of books over this time period (including day one) is 66 books, what is the value of d?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 90 + 62d = 66(d+1).
4d = 24.
d = 6.
The answer is B.
Answer: (B) 6
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: You need to primarily find the primes of 990:
2,3,3,5,11
The integer must contain all these primes
By knowing 11 is an prime, we know the answer can be B,C,D or E as these all contain 11.
11=1,2,3,4,5,6,7,8,9,10,11
11 contains the 2,3,5 and 11 explicitly and the second 3 comes from the 6 (2*3), therefore the answer is 11.
This is because we know a number that contains all the primes of 990 will be a multiple of 990.
ANSWER:B
Answer: (B) 11
Question: A invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join?
(A) 2 months
(B) 3 months
(C) 5 months
(D) 4 months
(E) 1 months
Rationale: Suppose B was there in the business for x months. Then
A : B =76000×12:57000×x
Therefore,
76000×12:57000×x=2:1
76×12:57x=2:1
76×12×1=57x×2
76×4=19x×2
4×4=(x)×2
x=8
Hence B was there in the business for 8 months, or joined after 12-8 = 4 months
Answer is D.
Answer: (D) 4 months
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
(A) 16 2/3%
(B) 15 2/3%
(C) 18 2/3%
(D) 11 2/3%
(E) 22 2/3%
Rationale: A
16 2/3%
600 ---- 100
100 ---- ? => 16 2/3%
Answer: (A) 16 2/3%
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 2777
(C) 289
(D) 2779
(E) 27871
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000.Answer: A
Answer: (A) 1000
Question: How much time will take for an amount of Rs. 200 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 7
(B) 4
(C) 5
(D) 3
(E) 9
Rationale: Time = (100 * 81) / (200 * 4.5) = 4 years'
Answer:E
Answer: (E) 9
Question: P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
(A) 9(3/5) days
(B) 9(1/5) days
(C) 9(2/5) days
(D) 10 days
(E) 15 days
Rationale: Explanation :
Amount of work P can do in 1 day = 1/16
Amount of work Q can do in 1 day = 1/12
Amount of work P, Q and R can together do in 1 day = 1/4
Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 â€“ 1/12 = 5/48
=> Hence R can do the job on 48/5 days = 9 (3/5) days
ANSWER IS A
Answer: (A) 9(3/5) days
Question: A contractor undertook to do a piece of work in 6 days. He employed certain number of laboures but 7 of them were absent from the very first day and the rest could finish the work in only 10 days. Find the number of men originally employed ?
(A) 17.2
(B) 16.5
(C) 17.5
(D) 17.9
(E) 17.3
Rationale: Let the number of men originally employed be x.
6x = 10(x â€“ 7)
or x = 17.5
Answer C
Answer: (C) 17.5
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors Q?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have Q=2*3*5*7 = 840
Thus, answer B.
Answer: (B) 3
Question: Today David, who is 40 years old, and his daughter, who is 12 years old, celebrate their birthdays. How many years will pass before David’s age is twice his daughter’s age?
(A) 22
(B) 20
(C) 16
(D) 18
(E) 14
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
After x years passes David’s age will be (40+x) years old, and his daughter’s age will be (12+x) years old. Since the David’s age is twice his daughter’s age (40+x)= 2 * (12+x) --->
40+x=24+2x ---> x= 16
The answer is (C).
Answer: (C) 16
Question: 9000 + 16 2/3 % of ? = 10500
(A) 1500
(B) 1750
(C) 9000
(D) 7500
(E) None of these
Rationale: Explanation:
9000 + 16 2/3 % of ? = 10500 => 9000 + 50/3 % of ? = 10500
50/(3 * 100) of ? = 1500 => ? = 1500 * 6
? = 9000
ANSWER IS C
Answer: (C) 9000
Question: In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 7⁄19
(B) 2⁄3
(C) 3⁄4
(D) 9⁄21
(E) None of these
Rationale: If the drawn ball is neither red nor green, then it must be blue, which can be picked in 7C1 = 7 ways. One ball can be picked from the total(8 + 7 + 6 = 21) in 21C1 = 21 ways.
∴ Reqd probability = 7⁄21 = 1⁄3
Answer E
Answer: (E) None of these
Question: A tank is filled by 3 pipes with uniform flow. The first two pipes operating simultaneously fill the tan in the same time during which the tank is filled by the third pipe alone. The 2nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe. The time required by first pipe is
(A) 13 hours
(B) 45 hours
(C) 15 hours
(D) 12 hours
(E) 11 hours
Rationale: If first pipe fills tank in x hrs, then second pipe fills tank in x-5 hrs and 3rd pipe fills tank in x-9 hrs, then
as per given condition
1/x +1/(x-5) = 1/(x-9)
solving it, we get x= 15 hrs
ANSWER:C
Answer: (C) 15 hours
Question: A and B can finish a work in 16 days while A alone can do the same work in 32 days. In how many days B alone will complete the work?
(A) 76 days
(B) 48 days
(C) 98 days
(D) 32 days
(E) 22 days
Rationale: B = 1/16 – 1/32 = 1/32 => 32 days
Answer: D
Answer: (D) 32 days
Question: Convert 2/5 to a decimal
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
(E) 0.5
Rationale: Divide 2 by 5: 2 / 5 = 0.4
Answer: 2/5 = 0.4 (D)
Answer: (D) 0.4
Question: Last year 28 members of a certain club traveled to England, 28 members traveled to France, and 30 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
(A) 52
(B) 69
(C) 71
(D) 73
(E) 79
Rationale: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)
n(E or F or I) = 28+ 28 + 30 - 0 - 11 - 6 + 0
Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.
n(E or F or I) = 69
Answer (B)
Answer: (B) 69
Question: The batting average of a particular batsman is 62 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
(A) 179
(B) 208
(C) 210
(D) 225
(E) 229
Rationale: Explanation:
Total runs scored by the batsman = 62*46 = 2852 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2852 – 2552 = 300 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 300
2x = 450
x = 225 runs
ANSWER D
Answer: (D) 225
Question: A person bought 118 glass bowls at a rate of Rs. 12 per bowl. He sold 102 of them at Rs. 15 and the remaining broke. What is the percentage gain for A?
(A) 40
(B) 300/11
(C) 243/7
(D) 475/59
(E) 279/8
Rationale: CP=118*12=1416 and SP=102*15=1530
Gain %= 100*(1530-1416)/1100= 11400/1416=475/59
ANSWER:D
Answer: (D) 475/59
Question: There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability T that all three secretary are assigned at least one report?
(A) 8/9
(B) 64/81
(C) 4/9
(D) 16/81
(E) 5/9
Rationale: I got the same answer: Here's my reasoning
First Report you have 3 choices
Second Report you have 2 choices
Third Report you have 1 choice
Fourth report 3 choices again
Then total number of ways is: 3*2*1*3=3^2*2
This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.
The number of ways of ensuring at least one report goes to each secretary is 4C2 (select 2 reports out of 4 which go to the same person)*3C1 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36
Required probability T= 36/81.C
Answer: (C) 4/9
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) 80.56 km/h
(B) 85.34 km/h
(C) 95.05 km/h
(D) 98 km/h
(E) 99.56 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