mathewhe/aqua_rat huggingface dataset:
Question: In the equation g = 36.12f, f and g are integers. If g/f leaves a remainder of r, which of the following must divide into r?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Rationale: 1) It says it is a equation, so g=36.12f should be 36.12 * f..
2) It says f is an integer, again it means 36.12 * f..
Otherwise f would be just a digit and it would be mentioned..
Although not clearly mentioned that 36.12f is actually 36.12 * f, BUT entire info points towards that..
and that is why I have taken g/f = 36.12
Answer: (B) 3
Question: How many positive integers between 100 and 500 are there such that they are multiples of 19?
(A) 10
(B) 15
(C) 21
(D) 18
(E) 19
Rationale: Multiples of 19 = 114,133,152,-----,494
Number of multiples of 19 => 494-114/19+1= 21
Answer is C
Answer: (C) 21
Question: How many of the factors of 120 are divisible by 2?
(A) 4
(B) 8
(C) 10
(D) 12
(E) 16
Rationale: 120 = 2^3*3*5
The total number of factors is (1+3)(1+1)(1+1) = 16
The odd factors are 1, 3, 5, and 15.
The number of even factors is 16-4 = 12
The answer is D.
Answer: (D) 12
Question: The length of each side of an equilateral triangle having an area of 4âˆš3 cm2 is?
(A) 4/3 cm
(B) 3/4 cm
(C) 3 cm
(D) 4 cm
(E) 5 cm
Rationale: Explanation:
âˆš3/4a2=4âˆš3->a=4
ANSWER IS D
Answer: (D) 4 cm
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
(A) 15/7
(B) 4/17
(C) 7/18
(D) 19/6
(E) 7/15
Rationale: Let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Option E
Answer: (E) 7/15
Question: A bag contains 24 purple jellybeans, 16 green jellybeans, and 10 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
(A) 15%
(B) 20%
(C) 25%
(D) 32%
(E) 35%
Rationale: Probability of green beans = 16 / (24 + 16 + 10) = 16/50 = 32%
Answer is D
Answer: (D) 32%
Question: A sum amounts to Rs.3087 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
(A) s.4000
(B) s.5000
(C) s.4500
(D) s.4800
(E) s.2800
Rationale: CI=3087,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
3087=P[21/20]^2
3087[20/21]^2
2800
ANSWER:E
Answer: (E) s.2800
Question: A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is :
(A) 8 cm
(B) 6 cm
(C) 4 cm
(D) 3 cm
(E) None
Rationale: Sol.
Let the height of the cone be h cm. Then,
1/3 ∏ * 6 * 6 * h = 4/3 ∏ * 3 * 3* 3 ⇒
h = [36 * 3 / 36] = 3 cm.
Answer D
Answer: (D) 3 cm
Question: If x and y are positive integers, and 3 is not a factor of y, then y may be which of the following?
(A) (x−1)·x·(x+1)
(B) (x−3)·(x−1)·(x+1)
(C) (x−2)·x·(x+2)
(D) (x−1)·x·(x+2)
(E) (x−3)·(x+1)·(x+2)
Rationale: Plugged in values :
let x=5
A. (x−1)·x·(x+1) --> divisible by 3
B. (x−3)·(x−1)·(x+1) --> divisible by 3
C. (x−2)·x·(x+2) --> divisible by 3
D. (x−1)·x·(x+2) --> not divisible. Hence the answer.
Answer: (D) (x−1)·x·(x+2)
Question: If y = x^2 + px + q, y is minimum when x is:
(A) p /q
(B) -p/q
(C) -p/2
(D) -q/2
(E) q/p
Rationale: We're given the equation Y = X^2 + pX + q.
IF.. we use a simple Classic Quadratic....
p = 2
q = 1
Y = X^2 + 2X + 1
We can then go about finding the answer that yields the MINIMUM result when X = ...
Answer A: p/q = 2/1 = 2 --> 4+4+1 = +9
Answer B: -p/q = -2/1 = -2 --> 4-4+1 = +1
Answer C: -p/2 = -2/2 = -1 --> 1-2+1 = 0
Answer D: -q/2 = -1/2 -->(1/4)-1+1 = +1/4
Answer E: q/p = 1/2 --> (1/4)+1+1 = +2 1/4
From these results, we can see the minimum result:
C
Answer: (C) -p/2
Question: (7.5×7.5+3.75+2.5×2.5) is equal to
(A) 30
(B) 60
(C) 80
(D) 100
(E) 90
Rationale: Solution
Given expression=	(7.5x7.5+2×7.5×2.5+2.5×2.5)²
= (a²+2ab+b²)
=(a+b)²
= (7.5+2.5)²
= 10²
= 100.
Answer D
Answer: (D) 100
Question: After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
(A) 8
(B) 0
(C) 9
(D) 72
(E) 4
Rationale: Ans: Tricky one but simple. How do you put exactly 1 letter in the wrong envelope? we need minimum two. So answer is 0.
Answer:B
Answer: (B) 0
Question: Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 300 envelopes
(A) 6 minutes
(B) 5 minutes
(C) 7 minutes
(D) 3 minutes
(E) 4 minutes
Rationale: earl takes 1 min. for 36 envelopes.
ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.
so both of them when work together can stuff 36+24=60 envelopes in 1 min.
for 300 envelopes they will take 300/60 mins. i.e., 5 mins.
ANSWER:B
Answer: (B) 5 minutes
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
(A) 17/28
(B) 17/25
(C) 17/26
(D) 17/76
(E) 17/22
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer: B
Answer: (B) 17/25
Question: In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 7a then which of the following is c equal to?
(A) a/12
(B) a/8
(C) 6a
(D) 10a
(E) 12a
Rationale: The sum of the roots is = -b/a = -7a/a = -7. Let the other root be x. Thus, x-2 = -7
x = -5. Again, the product of the roots is -2*-5 = 10. Thus, c/a = 10. c = 10a.
D.
Answer: (D) 10a
Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
(A) 30
(B) 35
(C) 37
(D) 41
(E) 43
Rationale: Explanation:
Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ lO) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years.
Answer: Option B
Answer: (B) 35
Question: You have three pills with you which you are required to take one after every thirty minutes.
How long can the pills run for you?
(A) 1 hour
(B) 2 hour
(C) 3 hour
(D) 4 hour
(E) None
Rationale: Solution:
The pills can run for an hour.
Explanation:
If you had ninety minutes in mind, then you are wrong. You took the first pill at the zero minute. Then you took the second pill after 30 minutes and the third pill after 30 + 30 i.e. 60 minutes or an hour
Answer A
Answer: (A) 1 hour
Question: Solve this logic number sequence puzzle by the correct digit
8080 = 6
1357 = 0
2022 = 1
1999 = 3
6666 = ?
(A) 5
(B) 3
(C) 7
(D) 2
(E) 4
Rationale: E
Answer: (E) 4
Question: When Sally went to the candy store, she bought 25 licorice sticks. As she was walking home, she ate 1 licorice stick for each block that she walked. She walked 5 blocks. How many licorice sticks did she have left when she arrived at home?
(A) 30
(B) 25
(C) 20
(D) 19
(E) 21
Rationale: To determine the number of licorice sticks that she ate, you have to multiply the number of blocks that she walked by the number that she ate per block (5*1=5)To determine the number of licorice sticks remaining when she arrived home, you have to subtract the number of licorice sticks that she ate from the total that she bought. (25-5=20)
The correct answer is C
Answer: (C) 20
Question: Kiran had 85 currency notes in all , some of which were of Rs.100 denomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?
(A) 1500
(B) 5500
(C) 3500
(D) 6500
(E) 2500
Rationale: Let the no of fifty rupee notes be x
Then, no of 100 rupee notes =(85-x)
50x+100(85-x)=5000
x+2(85-x)=100
x=70
so, required amount=Rs.(50*70)= Rs.3500
Answer is C
Answer: (C) 3500
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 48km/h, what is the circumference of the tire?
(A) 2
(B) 1
(C) 4
(D) 3
(E) 5
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 48,000 m : C is the circumference
C = 2 meters
correct answer A
Answer: (A) 2
Question: A committee of 6 is chosen from 7 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
(A) 455
(B) 700
(C) 1404
(D) 2620
(E) 3510
Rationale: The only cases possible are :
1. 2 men and 4 women : 7C2 * 5C4 = 105
2. 3 men and 3 women: 7C3*5C3 = 350
Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)
Total possible combinations = 105+350 = 455. Thus A is the correct answer.
Answer: (A) 455
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
(A) 33
(B) 77
(C) 26
(D) 12
(E) 99
Rationale: Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps	4	:	3 :: 8 : x
Days	1	:	2
4 x 1 x x = 3 x 2 x 8
x =	(3 x 2 x 8)
(4)
x = 12.
Answer:D
Answer: (D) 12
Question: Aarti can do a piece of work in 3 days. In how many days will she complete 10 time of work of same type?
(A) 6 days
(B) 18 days
(C) 21 days
(D) 30 days
(E) 13 days
Rationale: We have the important relation, More work, More time (days)
A piece of work can be done in 3 days.
10 times of work of same type can be done in 3 x 10
= 30 days
Answer D
Answer: (D) 30 days
Question: The least number which should be added to 2400 so that the sum is exactly divisible by 5,6,4 and 3 is :
(A) 3
(B) 13
(C) 20
(D) 33
(E) 43
Rationale: Solution
L.C.M. of 5,6,4 and 3 = 60. on dividing 2400 by 60, the remainder is 40.
∴ Number to be added = (60-40) = 20. Answer C
Answer: (C) 20
Question: In a series of six consecutive odd numbers, the third number is 31. What is the fifth number?
(A) 35
(B) 33
(C) 45
(D) 31
(E) 29
Rationale: Let the numbers be x, x + 1, x + 3, x + 5 and x + 7.
Given (x + 3) = 31
=> x = 28
The fifth number = x + 7 = 28 + 7 = 35.
Answer: A
Answer: (A) 35
Question: Sixteen machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.
So 3/2* 16 = 24
So we need 24-16 = 8 more machines.
Answer : E
Answer: (E) 8
Question: Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
(A) 887pages
(B) 656 pages
(C) 435 pages
(D) 451 pages
(E) 232pages
Rationale: Pages read in the first book in one week which is 7 days with 25 pages everyday.
25 *7 = 175 pages
Pages read in the second book in 12 days with 23 pages everyday.
23 *12 = 276 pages
Total number of pages read
175 + 276 = 451 pages
correct answer D
Answer: (D) 451 pages
Question: If 0.5 of a number is equal to 0.09 of another number, the ratio of the numbers i
(A) 2 : 3
(B) 3 : 4
(C) 3 : 20
(D) 3 : 7
(E) 9 : 50
Rationale: Sol.
0.5A = 0.09 B â‡” A / B = 0.09 / 0.50 = 9/50
âˆ´ A : B = 9 : 50.
Answer E
Answer: (E) 9 : 50
Question: Marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 10%. What percent of the projected revenue was the actual revenue ?
(A) 53%
(B) 58%
(C) 62.5%
(D) 64%
(E) 75%
Rationale: Last year revenue = 100 (assume);
This year revenue = 90;
Projected revenue = 120.
Actual/Projected*100=90/120*100 = 75%.
Answer: E.
Answer: (E) 75%
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 612 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
(A) 170
(B) 179
(C) 196
(D) 240
(E) 200
Rationale: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(612-9-90*2)/3=240
Answer : D
Answer: (D) 240
Question: Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 85. If Jerry wants to raise his average by 3 points, what score must he earn on the fourth test?
(A) 97
(B) 89
(C) 90
(D) 93
(E) 95
Rationale: Total score on 3 tests = 85*3 = 255
Jerry wants the average to be = 88
Hence total score on 4 tests should be = 88*4 = 352
Score required on the fourth test = 352 - 255 = 97
Option A
Answer: (A) 97
Question: Sum of ages of two friends is 32 while difference is 2 then their ages are
(A) 15 years, 17 years
(B) 17 years, 15 years
(C) 16 years, 18 years
(D) 18 years, 16 years
(E) None
Rationale: 17,15
ANSWER:B
Answer: (B) 17 years, 15 years
Question: There are three foam generators in the factory, each of the first two can generate 14 liters of foam in one hour and the third can generate 20 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
(A) 120.
(B) 132.
(C) 146.
(D) 161.
(E) 166.
Rationale: Let the foam generators capacity be -
A = 14 lit/hr
B = 14 lit/hr
C = 20 lit/hr
Total foam generation in 1 hour will be 48 lit ( 14 + 14 + 20 ) ; since in 1 and 1/2 hr they will generate 48 + 24 => 72 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 14 lit/hr
C = 20 lit/hr
Total foam generation in 2 hour will be 68 litres {2 (14+20)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 14 => 21 litres
So, total foam generated will be 161 Litres ( 72 + 68 + 21 ) ; hence answer will be (D)
Answer: (D) 161.
Question: For how many integers n is 1^n+4 = (n+4)^1?
(A) 1
(B) 2
(C) 3
(D) None of these
(E) 4
Rationale: If n=0
1^0+4= (0+4)^1
1^4 = 1 ; 4^1 =4 not ok
If n=1
1^1+4 =1 ; (1+4)^1=5^1=5 not OK
So, Answer : D
Answer: (D) None of these
Question: An investment of d dollars at k percent simple annual interest yields $400 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $1,600 over a 5 year period?
(A) (2d)/3
(B) (3d)/4
(C) (4d)/3
(D) (3d)/2
(E) (8d)/5
Rationale: 400 dollars in 2 years means 200 dollars in 1 year.
To get 1600 dollars' it will take 8 years.
To get 1600 in 5 years, we need 8/5 times money. Answer is E.
Answer: (E) (8d)/5
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
(A) 10 hours
(B) 17 hours
(C) 12 hours
(D) 50 hours
(E) 16 hours
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer:A
Answer: (A) 10 hours
Question: The arithmetic mean of the 5 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 2?
(A) 2 + s + a
(B) 22 + a
(C) 2s
(D) 2a + 2
(E) 4 + a
Rationale: Here for The series
s,s+1...s+4 => mean = median = s+2 =a
hence for the next 9 consecutives => a,a+1,a+2...
=> Mean = Median = a+a+8/2 = a+4
ANSWER:E
Answer: (E) 4 + a
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
(A) 337
(B) 299
(C) 277
(D) 646
(E) 271
Rationale: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Answer: (D) 646
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 45%. Staff are allowed a further 40% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
(A) 0.35D
(B) 0.76D
(C) 0.65D
(D) 0.77D
(E) 0.33D
Rationale: Effective discount = a + b + ab/100 = - 45 - 40 + (-45)(-40)/100 = -67
Sale price = D * ( 1 - 67/100)
Sale price = .33 * D
Answer (E)
Answer: (E) 0.33D
Question: June 25, 1982, fell on a Friday. On which day of the week did December 25, 1983, fall?
(A)  Sunday
(B)  Monday
(C)  Tuesday
(D)  Wednesday
(E)  Thursday
Rationale: 6/25/82 - 12/25/83
The date range contains one full year of 365 days plus a partial year. The number of days in the partial year is:
June - 5, July - 31, August - 31, September - 30, October - 31, November - 30, and December - 25.
5 + 31 + 31 + 30 + 31 + 30 + 25 = 183.
183 + 365 = 548 total days in the date range.
Divide by 7 to determine how much the day of the week advances: 548 / 7 = 78 remainder 2.
Since the first date was a Friday, advance the day of the week by 2; the second date fell on a Sunday. The answer is A.
Answer: (A)  Sunday
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 167m
(B) 180m
(C) 187m
(D) 287m
(E) 276m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: (B) 180m
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
(A) 387 m
(B) 287 m
(C) 175 m
(D) 187 m
(E) 167 m
Rationale: RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer: C
Answer: (C) 175 m
Question: One fourth of a solution that was 10 percent gram flour by weight was replaced by a second solution resulting in a solution that was 16 percent gram flour by weight. The second solution was what percent gram flour by weight ?
(A) 34%
(B) 24%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of gram flour in 2nd sol)=34%=A
Answer: (A) 34%
Question: How many numbers between 101 and 250, exclusive are divisible by three?
(A) 34
(B) 41
(C) 50
(D) 83
(E) 148
Rationale: Numbers upto 250 divisible by 3 is 250/3 = 83
Numbers upto 101 divisible by 3 is 101/3 = 33
Total number of numbers between 101 and 250 that are divisible by 3 is 83 - 33 = 50
ANSWER:C
Answer: (C) 50
Question: In a poll of 44,000 dentists, only 30 percent responded; of these, 20 percent claimed to prefer Toothpaste A. How many of the dentists who responded did not claim a preference for Toothpaste A?
(A) 2,200
(B) 2,640
(C) 6,160
(D) 8,800
(E) 10,560
Rationale: Find those who responded to the poll-
44000∗3/10=4400∗3=13200
Find those who responded who do not prefer toothpaste A-
13200∗8/10=1320∗8=10560
ANSWER:E
Answer: (E) 10,560
Question: Solve:-
111 x 111 x 111 + 555 x 555 x 555 = ?(111 x 111 - 111 x 555 + 555 x 555)
(A) 888
(B) 666
(C) 555
(D) 988
(E) 889
Rationale: Given Exp. = (a3 + b3) = (a + b) = (111 + 555) = 666 (a2 - ab + b2)
Answer B
Answer: (B) 666
Question: Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 28 have long fur, 17 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
(A) 26
(B) 19
(C) 11
(D) 8
(E) 6
Rationale: No of dogs=45
Long fur=28
Brown=17
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=28+17-Both
Both=8
Answer D
Answer: (D) 8
Question: If K is the sum of reciprocals of the consecutive integers from 3 to 8, inclusive, then K is closest in value to which of the following?
(A) 1.2
(B) 1/10
(C) 1/8
(D) 1/6
(E) 1/4
Rationale: 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8
=0.33+0.25+0.20+0.16+ 0.14+0.12=1.2
A
Answer: (A) 1.2
Question: A student got twice as many sums wrong as he got right. If he attempted 36 sums in all, how many did he solve correctly ?
(A) 12
(B) 16
(C) 18
(D) 24
(E) 26
Rationale: Explanation:
Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 36 3x = 36 x = 12.
Answer:A
Answer: (A) 12
Question: A gang of 8 boys goes on an tour in 2cars, of which 1can seat 5 & the other only 4. In how many ways can they travel?
(A) 100
(B) 121
(C) 126
(D) 128
(E) 130
Rationale: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
C
Answer: (C) 126
Question: If P is a prime number greater than 3, find the remainder when p^2 + 17 is divided by 12.
(A) 6
(B) 1
(C) 0
(D) 8
(E) 7
Rationale: Take any prime number greater than 3 and check -
Say p = 5
So, p^2 + 17 = 25+17 => 42
42/12 will have remainder as 6
Say p = 7
So, p^2 + 17 = 49+17 => 66
66/12 will have remainder as 6
So answer will be (A) 6
Answer: (A) 6
Question: If the numerator of a fraction be increased by 12% and its denominator decreased by 2% the value of the fraction becomes 6/7. Thus, the original fraction is:
(A) 1/4
(B) 2/4
(C) 3/4
(D) 2/3
(E) 1/3
Rationale: If original fraction is x/y , then
1.12x/0.98y = 6/7
(8/7)*(x/y)=6/7
x/y =6/8=3/4
ANSWER:C
Answer: (C) 3/4
Question: In a 100 m race, A runs at 8km per hour. If A gives B a start of 9 m and still him by 15 seconds, what is the speed of B ?
(A) 5.46 km/hr.
(B) 5.56 km/hr.
(C) 5.76 km/hr.
(D) 6.76 km/hr.
(E) 5.72 km/hr.
Rationale: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.
B covers (100 - 9) m = 91 m in (45 + 15) sec = 60 sec.
B's speed = (91 x 60 x 60)/(60 x 1000)km/hr = 5.46 km/hr.
Answer is A
Answer: (A) 5.46 km/hr.
Question: Difference between two numbers is 5, six times of the smaller lacks by 4 from the four times of the greater. Find the numbers?
(A) 5,3
(B) 7,5
(C) 9,7
(D) 11,9
(E) 13,8
Rationale: Explanation:
x – y = 5
4x – 6y = 4
x = 13 y = 8
E)
Answer: (E) 13,8
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets T did Irwin score?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored T=2 11-point baskets in my opinion.
Answer C
Answer: (C) 2
Question: X can do a piece of work in 8hours. Y and Z together can do it in 6 hours, while X and Z together can do it in 4 hours. How long will Y alone take to do it?
(A) 24 HOURS
(B) 20 HOURS
(C) 34 HOURS
(D) 12 HOURS
(E) 10 HOURS
Rationale: X's 1 hour work= 1/8
(Y+Z)'s 1 hour work= 1/6
(X+Z)'s 1 hour work= 1/4
(X+Y+Z)'s 1 hour work= (1/8+1/6)=7/24
Y's 1hour's work= (7/24-1/4)= 1/24
Y alone will take 24 hours to do the work.
correct option is A
Answer: (A) 24 HOURS
Question: What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x
(A) 250
(B) 203
(C) 200
(D) 195
(E) None of these
Rationale: Explanation:
Given: 139.25 + 223.94 / 4.002 = x
Approximate 139.25 as 140, 223.94 as 224, 4.002 as 4,
we get, x = 140 + 224 / 4 = 140 + 56 = 196 =>195
ANSWER: D
Answer: (D) 195