mathewhe/aqua_rat huggingface dataset:
Question: If the sum of the interior angles of a regular polygon measures up to 1260 degrees, then how many sides does the polygon have?
(A) 10
(B) 9
(C) 12
(D) 11
(E) 14
Rationale: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1260
180n - 360 = 1260
180n = 1620
n = 1620/180 = 9
ANSWER:B
Answer: (B) 9
Question: The probability of pulling a black ball out of a glass jar is 1/Q. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
(A) 1/(XY)
(B) Q/Y
(C) Y/X
(D) 1/(X+Y)
(E) 1/(X-Y)
Rationale: P of pulling a black ball out of a glass jar AND breaking the jar = 1/Y
P of pulling a black ball out of a glass jar is 1/Q
Lets say P of breaking the jar = n
That means 1/Q*n=1/Y
n= Q/Y
B is the answer
Answer: (B) Q/Y
Question: A cistern can be filled by 3 pipes in 30, 40 and 60 min and emptied by an escape pipe in half an hour the 3 taps are turned on at noon but the escape pipe is at the same time accidentally left open and not closed for a quarter of an hour at what time will the cistern be full?
(A) 60 min
(B) 90 min
(C) 120 min
(D) 150 min
(E) 170 min
Rationale: Explanation:
Let the total time be x min
x/30 + x/40 + x/60 – x/15 = 1
=> x = 120 min
Answer: Option C
Answer: (C) 120 min
Question: The factorial expression 13!/7! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: 13!/7!
= (13*12 * 11 *10 * 9 * 8 * 7!)/7!
= 13*12 * 11 * 10 * 9*8
The given factorial expression is not divisible by 7
Answer D
Answer: (D) 7
Question: Rahul travels from A to B a distance of 200 miles in 5 hours. He returns to A in 4 hours. Find his average speed?
(A) 52.2mph
(B) 61.9mph
(C) 44.4mph
(D) 35.7mph
(E) 65.6mph
Rationale: Speed from A to B = 200/5 = 40 mph
Speed from B to A = 200/4 = 50 mph
Average speed = 2*40*50 / 90 = 44.4mph
Answer is C
Answer: (C) 44.4mph
Question: Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L
(A) 1/3.
(B) 1/2.
(C) 3.
(D) 2.
(E) 6.
Rationale: Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2
C
Answer: (C) 3.
Question: The function f is defined for all the positive integers h by the following rule: f(h) is the number of positive integers each of which is less than h and has no positive factor in common with h other than 1 . if p is a prime number then f(p)?
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: The moment you put a prime number in the function f(h), notice that all the numbers lesser than h have no divisor clashing with divisor of h since h is prime!!.
For instance f(7)= {6, 5, 4, 3, 2, 1}
Thus for f(p) number of integers falling under this set will be p-1
Answer :- A
Answer: (A) p-1
Question: In 24 minutes, the hour hand of a clock moves through an angle of:
(A) 60°
(B) 24°
(C) 12°
(D) 5°
(E) None
Rationale: 12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚
Answer: C
Answer: (C) 12°
Question: A copying machine "P" can copy 135 pages in 9 minutes, P and Q together can copy 300 pages in 12 minutes. In what time Q can copy 80 pages?
(A) 6 minute
(B) 7 minute
(C) 9 minute
(D) 8 minute
(E) 10 minute
Rationale: P copying 135 pages in 9 minutes.
so in 1 minute P copying=135/9=15 pages
P and Q both copying 300 pages in 12 minute.
so in 12 minute P coying the 12*15=180 pages.
so Q copying alone=300-180=120 pages.
according to question Q takes 12 minute for copying the pages.
so for 1 minute 120/12=10 pages.
because for 10 pages takes 1 minute
so 80 pages it's takes 8 minute
so ans is 8 minute.
ANSWER:D
Answer: (D) 8 minute
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
(A) 1:2
(B) 2:5
(C) 6"2
(D) 3:1
(E) 4:7
Rationale: Explanation:
Let speed upstream=x
hen, speed downstream =2x
Speed in still water =2x+x/2
Speed of the stream=2x-x/2
Speed in still water : Speed of the stream=3x/2:x/2=3:1
Answer:D
Answer: (D) 3:1
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 39
(B) 27
(C) 30
(D) 98
(E) 287
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: (C) 30
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
(A) 7!
(B) 8!
(C) 9!
(D) 11!
(E) 12!
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: (B) 8!
Question: If x^2 > x^7> x^5, which of the following could be the value of x?
(A) -9
(B) -2
(C) -5/8
(D) 5
(E) 9
Rationale: x^2 > x^7 > x^5
1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x.
This can be possible only if the base is negative; therefore, the variable, x, must be a negative number.
2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1.
With this information, we know that x is a negative number between 0 and -1; therefore, C (-5/8) is the only option.
Answer: (C) -5/8
Question: Carrie likes to buy t-shirts at the local clothing store. They cost $8.55 each. One day, she bought 9 t-shirts. How much money did she spend?
(A) $150
(B) $248.75
(C) $200
(D) $171.6
(E) $73.1025
Rationale: $8.55*9=$73.1025. Answer is E.
Answer: (E) $73.1025
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 25% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate?
(A) 28%
(B) 30%
(C) 32%
(D) 34%
(E) 36%
Rationale: Let x be Mork's income, then Mindy's income is 4x.
The total tax paid is 0.4x + 1.0x = 1.4x
1.4x / 5x = 0.28
The answer is A.
Answer: (A) 28%
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 37 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
(A) 36
(B) 2^4*3
(C) 24
(D) 38
(E) 47
Rationale: Working backward from the day it's covered:
day 37: fully covered
day 36: half covered
So 36 days
ANSWER:A
Answer: (A) 36
Question: There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of sections A is 40 kg and that of sections b is 35 kg. Find the average weight of the whole class
(A) 36.25
(B) 37.25
(C) 38.35
(D) 39.25
(E) None
Rationale: Solution
Total weight of(36+44)Students	= (36x40+44x35)Kg
= 2980 kg.
Average weight of the whole class	= (2980 / 80)
= 37.25.
Answer B
Answer: (B) 37.25
Question: Few years ago on 31st January on her 26th birthday a lady laid a baby. Now what's the sum of their ages?
(A) 37
(B) 38
(C) 43
(D) 51
(E) 52
Rationale: All other options have thier unit place digit odd while we require even digit because before x years she laid a baby. That time she is 26years old
so now sum of thier ages is 26 + 2x. The total should be even number
ANSWER:B
Answer: (B) 38
Question: 5,9,16,28,48,__
(A) 79
(B) 80
(C) 81
(D) 82
(E) 83
Rationale: (9+5) +2 = 16
(16+9) +3 = 28
(28+16)+4 = 48
(48+28)+5 = 81
ANSWER:C
Answer: (C) 81
Question: Vikas bought a grinder with 15% discount on the labelled price. He sold the grinder for Rs.2880 with 20% profit on the labelled price. At what price did he buy the grinder?
(A) Rs 2000
(B) Rs 2040
(C) Rs 2240
(D) Rs 2400
(E) None of these
Rationale: Explanation :
Let the labelled price be Rs.x. Then, 120% of x = 2880
Therefore x=(2880100/120) = 2400.
C.P = 85% of Rs.2400 = Rs(85/100x2400) =Rs.2040.
Answer : B
Answer: (B) Rs 2040
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
(A) 11 1/8%
(B) 11 8/9%
(C) 11 1/9%
(D) 19 1/9%
(E) 11 1/1%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer: C
Answer: (C) 11 1/9%
Question: It took Malcom 3.5 hours to drive from city A to city B. On his way back to city A, he increased his speed by 20 km per hour and it took him 3 hours.
Find the average speed for the whole journey.
(A) 134.9 km/hr
(B) 129.2 km/hr
(C) 119.6 km/hr
(D) 140.5 km/hr
(E) 155.3 km/hr
Rationale: Let x and x + 20 be the speeds of the car from A to B and then from B to A. Hence the distance from A to B may expressed as 3.5 x and the distance from B to A as 3(x + 20)
The average speed = total distance / total time = (3.5 x + 3 (x + 20)) / (3.5 + 3)
The distance from A to B is equal to the distance from B to A, hence: 3.5 x = 3(x + 20). Solve for x to obtain x = 120 km/hr.
We now substitute x by 120 in the formula for the average speed to obtain.
average speed = 129.2 km/hr
correct answer B)129.2 km/hr
Answer: (B) 129.2 km/hr
Question: Three dice are thrown together, Find the probability of getting a total of atmost 5?
(A) 2/35
(B) 1/8
(C) 3/31
(D) 2/9
(E) 5/108
Rationale: Three different dice are thrown at the same time.
Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.
Number of events of getting a total of atmost 5 = 10
i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1) and (1, 2, 2).
Therefore, probability of getting a total of atmost 5
P(E) = Number of favorable outcomes/Total number of possible outcome
= 10/216
= 5/108
Answer: (E) 5/108
Question: if (64)2 - (36)2 = 10x, then x = ?
(A) 200
(B) 220
(C) 210
(D) 280
(E) None of these
Rationale: Explanation :
a2−b2=(a−b)(a+b)
(64)2 - (36)2 = (64 - 36)(64 + 36) = 28 × 100
Given that (64)2 - (36)2 = 10x
=> 28 × 100 = 10x
=> x = 280. Answer : Option D
Answer: (D) 280
Question: There is rain at a rate of 12 centimeters per hour all over New Jersey. Somewhere downtown in New Jersey a group of students are waiting for the rain to stop. If the rain filled a tank the with a base area of 250 square centimeters and a depth of 6 centimeters, how long did the students wait for the rain to stop?
(A) 8 hours
(B) 4 hours 25 minutes
(C) 3 hours 15 minutes
(D) 6 hours
(E) 2 hours
Rationale: Answer is : E, 4 hours and 30 mins
The volume of the tank is irrelevant and only height matters since rain fell all over the city.
Thus, it takes only . 12 / 6 = 2 hours of rain to fill the tank.
Answer: (E) 2 hours
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 8 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 17:7
(B) 18:8
(C) 19:9
(D) 19:5
(E) 19:4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 8 = 5 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5 + 7/2 = 17/2 = 8.5 litres
As 12 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 8.5 : 3.5 = 17 : 7.
Answer:A
Answer: (A) 17:7
Question: If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24?
(A) 101
(B) 187
(C) 191
(D) 201
(E) 287
Rationale: here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 24 = t 3 + 3 + 4 + 5 + 6....+ 23
the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 23 sequence is equal to n*(n+1)/2 with n being 23, so equal to 23 * 24 / 2 = 276
so :
t 20 = t 3 + 276 - 3
t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E
Answer: (E) 287
Question: The difference between simple and compound interest on Rs. 1300 for one year at 10% per annum reckoned half-yearly is?
(A) 8.0
(B) 3.25
(C) 9.15
(D) 3.13
(E) 2.0
Rationale: S.I. = (1300 * 10 * 1)/100 = Rs. 130
C.I. = [1300 * (1 + 5/100)2 - 1300]
= Rs. 133.25 Difference = (133.25 - 130)
= Rs.3.25
Answer:B
Answer: (B) 3.25
Question: If the ratio of the roots of the equation x2+3px-6=0 is equal to that of the roots x2+6rx-12=0, then:
(A) 5r=3p
(B) 2p=r
(C) r=p
(D) 2r=p
(E) None
Rationale: x2+3px-6=0 for this eqn... roots are R1=-3p R2=6
x2+6rx-12=0 for this eqn... roots are R3=-6r R4=12
As per Question, -3p/6=-6r/12
=> r=p
ANSWER:C
Answer: (C) r=p
Question: A car averages 45 mph for the first 4 hours of a trip and averages 75 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip?
(A) 12
(B) 11
(C) 10
(D) 9
(E) 8
Rationale: Let the time for which car averages 75 mph = t
65*(t+4)= 45*4 + 75 t
=>10 t= 80
=> t = 8
Total duration of the trip = 8+4=12
Answer A
Answer: (A) 12
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) 16
(C) 13
(D) 18
(E) 19
Rationale: C
13
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
30 x 6 x x = 39 x 5 x 12
x = (39 x 5 x 12)/(30 x 6)
x = 13
Answer: (C) 13
Question: A reduction of 15% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 12
(B) 16
(C) 24
(D) 28
(E) 32
Rationale: 800*(15/100) = 120 ---- 5
? ---- 1 => Rs.24
Answer: C
Answer: (C) 24
Question: Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 20% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?
(A) 1 to 4
(B) 1 to 8
(C) 3 to 5
(D) 3 to 4
(E) 3 to 2
Rationale: Correct Answer: B
Solution: B. We know that when Pam and Stanley were both working, the ratio was 1 boxes by Pam to 4 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 1 to 8. Answer B is correct.
Answer: (B) 1 to 8
Question: A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of Rs. 200 each. For each rise of Rs. 4 in the selling price she will sell 2 less suits a week. If she sells the suits for Rs. x each, how many rupees a week will she receive from the sales of the suits?
(A) x2/2
(B) 200−x/2
(C) 50x - (x^2)/4)
(D) 150x - (x^2)/4)
(E) 200x - (x^2)/2)
Rationale: Explanatory Answer
Assume that she sells the suits at Rs.204; then she will sell two suits lesser or 98 suits.
Substitute x = 204 in each of the answer choices and check where the answer is 98.
For choice (2), the answer is 98 and this is the quickest way to find the answer.
Answer B
Answer: (B) 200−x/2
Question: Which of the following is equal to 1(1/6)%?
(A) 0.012/100
(B) 0.12/100
(C) 1.1/100
(D) 12/100
(E) 12/10
Rationale: This notation may be confusing for some, since it looks like we're multiplying 1 and 1/6
How about adding a space:Which of the following is equal to (1 1/6)%
(1 1/6)% = 1.1% = 1.1/100
Answer:
C
Answer: (C) 1.1/100
Question: A rectangular window is twice as long as it is wide. If its perimeter is 18 feet, then what are its dimensions in feet?
(A) 3/2 by 7/2
(B) 5/3 by 10/3
(C) 2 by 4
(D) 3 by 6
(E) 10/3 by 20/3
Rationale: Let x be the width of the window. Then the length is 2x.
x+2x+x+2x = 18
6x = 18
x = 18/6 = 3
The width is 3 and the length is 6.
The answer is D.
Answer: (D) 3 by 6
Question: If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.36 then sum is
(A) s.5000
(B) s.5100
(C) s.5800
(D) s.6000
(E) s.3600
Rationale: p(r/100)^2=C.I-S.I
P(10/100)^2=36
3600
ANSWER:E
Answer: (E) s.3600
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 338
(B) 125
(C) 726
(D) 268
(E) 171
Rationale: D = 90 * 5/18 * 5
= 125 m
Answer:B
Answer: (B) 125
Question: The salaries of A and B together amount to $500. A spends 90% of his salary and B, 80% of his. If now, their savings are the same, what is A's salary?
(A) $50
(B) $150
(C) $69
(D) $34
(E) $52
Rationale: Let A's salary is x
B's salary = 500-x
(100-90)% of x = (100-80)% of (500-x)
x = $34 (approximately)
Answer is D
Answer: (D) $34
Question: A gardener changed the size of his rectangle shaped garden by increasing it's length by 40% & decreasing is's width by 20%.Find area of new garden.
(A) 1.04
(B) 1.12
(C) 1.24
(D) 1.4
(E) 1.5
Rationale: A1= l*b
A2= (l*140/100)*(b*80/100)=1.12*lb
so, area of garden is by 1.12 times of old area.
ANSWER:B
Answer: (B) 1.12
Question: d, q, and r are positive integers. If d, q, and r are assembled into the six-digit number dqrdqr, which one of the following must be a factor of dqrdqr?
(A)  23
(B)  19
(C)  17
(D)  7
(E)  none of the above
Rationale: One short way -
dqrdqr = 1000dqr + dqr = (1000+1)dqr = 1001dqr
Therefore any factor of 1001 is a factor of dqrdqr
7 is a factor of 1001
So D
Answer: (D)  7
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $288 per week. How much does she earn in dollars per hour?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $288 per week
36x =288
x =8
Correct Option : D
Answer: (D) 8
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 20 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/50
(E) 1/100
Rationale: So there are 900 cars that they have to search.. Each takes 20mins, total of 18000 mins.. Have to find in 180 mins.. Prob180/18000 = 1/100
Answer: (E) 1/100
Question: ♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠3.32 - ♠2.42 =
(A) 1.05
(B) 0.9
(C) -1.05
(D) -1.0
(E) -0.1
Rationale: ♠3.32 - ♠2.42 =
3.3 - 2.4 = 0.9
Answer : B
Answer: (B) 0.9
Question: In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 35 and 200, then the least and greatest integer on the card would be
(A) 3 and 15
(B) 3 and 20
(C) 4 and 13
(D) 4 and 14
(E) 5 and 14
Rationale: Given: 35<x(x+1)<200.
Now, it's better to test the answer choices here rather than to solve:
If x=5 then x(x+1)=30>35 --> so, the least value is 5. Test for the largest value: if x=14 then
x(x+1)=14*15=210>200
Answer: E.
Answer: (E) 5 and 14
Question: David received Rs.6000 as his share out of the total profit of Rs.9000 which he and Dave earned at the end of 1 years. If David invested Rs.120000 for 6 months, whereas Dave invested his amount for the whole yr, what was the amount invested by Dave?
(A) 28000
(B) 30000
(C) 34000
(D) 35000
(E) 36000
Rationale: Suppose Ramesh invested Rs. x. Then,
Manoj : Ramesh = 120000 * 6 : x *12.
720000/12x: 6000/3000
x = 30000
(B)
Answer: (B) 30000
Question: I. a^2 - 9a + 20 = 0,
II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?
(A) a < b
(B) a ≤ b
(C) the relationship between a and b cannot be established
(D) a > b
(E) a ≥ b
Rationale: I. (a - 5)(a - 4) = 0
=> a = 5, 4
II. (2b + 3)(b - 4) = 0
=> b = 4, -3/2 => a ≥ b
Option E
Answer: (E) a ≥ b
Question: In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?
(A) 180
(B) 196
(C) 286
(D) 288
(E) 324
Rationale: let say number= XYZ
Z= units digit
Y= tenths digit
X= Hundredth's digit
For any 3 digit number to be odd, Unit digit must be odd
So Z can be filled with 1,3,7,9 (we are excluding digit 5) = 4 ways.
Y can be filled with 0,1,2,3,4,6,7,8,9 (we are excluding digit 5) = 9 ways
X can be filled with 1,2,3,4,6,7,8,9 (we are excluding digits 0 and 5..) = 8 ways
No of ways= 4*9*8= 288
Answer : D
Answer: (D) 288
Question: A car gets 33 miles to the gallon. If it is modified to use a solar panel, it will use only 75 percent as much fuel as it does now. If the fuel tank holds 16 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified?
(A) 168
(B) 172
(C) 176
(D) 180
(E) 184
Rationale: Originally, the distance the car could go on a full tank was 16*33=528 miles.
After it has been modified, the car can go 33/0.75=44 miles per gallon.
On a full tank, the car can go 16*44= 704 miles, thus 176 miles more.
The answer is C.
Answer: (C) 176
Question: A train 275 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 15
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [275 * 3/55] sec = 15 sec
Answer: A
Answer: (A) 15
Question: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 27th in an arithmetic progression if the sum of the 12th and 16th terms of the sequence is 98?
(A) 47
(B) 49
(C) 51
(D) 53
(E) 55
Rationale: Let x be the difference between any two consecutive terms.
The mean of a sequence like this is the middle term, thus the 14th term in the sequence.
Then the mean of the 13th and 15th term is also equal to the overall mean, because the 13th term is (14th term - x) and the 15th term is (14th term + x).
Similarly the mean of the 12th and 16th term is also equal to the mean.
etc...
Thus the mean is 98/2 = 49
The answer is B.
Answer: (B) 49
Question: In 120 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
(A) 24 m
(B) 25 m
(C) 22.5 m
(D) 9 m
(E) 12 m
Rationale: Distance covered by B in 9 sec. =	120/45 x 9	m = 24 m.
A beats B by 24 metres.
Answer: Option A
Answer: (A) 24 m
Question: If A is the average (arithmetic mean) of 3 consecutive negative integers, which of the following must be true?
I. A is a negative integer.
II. A is a nonzero integer.
III. A is a multiple of 3.
(A) I only
(B) II only
(C) III Only
(D) I and III only
(E) I and II only
Rationale: Consider any negative integer , a
we can form a series as a , a-1 , a-2
Arithmetic Mean = a+(a-1)+(a-2)/3 = a-1
So,
I) is always true, since 'a' is a negative integer
II) is always true, even if 0 is in the series. i.e. 0, -1, -2
III) not always true, a can be any integer as we considered, not necessarily multiple of 3
Ans - E
Answer: (E) I and II only
Question: If x = -7/8 and y = -1/2, what is the value of the expression -2x – y^2?
(A) -3/2
(B) -1
(C) 1
(D) 3/2
(E) 7/4
Rationale: -2X- y^2
-2x-7/8 - (1/2)^2
7/4-1/4
3/2
D correct
Answer: (D) 3/2
Question: The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 8 cm each. The radius of the sphere is
(A) 3 cm
(B) 4 cm
(C) 6 cm
(D) 8 cm
(E) None
Rationale: Solution
4Î R2	= 2Î 4x8
â‡’ R2 = (4x8/2)
â‡’ 16
â‡’ R = 4 cm.
Answer B
Answer: (B) 4 cm