mathewhe/aqua_rat huggingface dataset:
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 45 meters. How many times did the ball bounce?
(A) 5
(B) 4
(C) 7
(D) 8
(E) 9
Rationale: Going down = 16 m
Going Up = 8 --> Total = 24
Going down = 8 --> Total = 32
Going Up = 4 --> Total = 36
Going down = 4 --> Total = 40
Going up = 2 --> Total = 42
Going down = 2 --> Total = 44
Going up = 1 --> Total = 45 (Caught)
No of bounce = 4
Answer : B
Answer: (B) 4
Question: Statement : Until our country achieves economic equality, political freedom and democracy would be meaningless.
Conclusions :
I. Political freedom and democracy go hand in hand.
II. Economic equality leads to real political freedom and democracy.
(A)  I only
(B)  II only
(C)  I and II only
(D)  I and III only
(E)  II and III only
Rationale: Explanation:
Nothing about first conclusion is stated in statement.
Only II conclusion follows.
(B) II only
Answer: (B)  II only
Question: What is the value of 28^2 + 29^2 + 30^2 + 31^2 + 32^2 ?
(A) 4298
(B) 4508
(C) 4510
(D) 4528
(E) 4538
Rationale: This is what I did, all the nos are close to 30, and squared, so 30^2 plus there are 5 numbers, so (30)^2 x 5 =4500,
now squaring the last digits of each no individually comes up to (4+1+0+1+4) = 10.
when you add the 2 up it gives you a (4500+10) =4510,
Answer is C.
Answer: (C) 4510
Question: If three numbers are added in pairs, the sums equal 10, 19 and 21. Find the numbers
(A) 6, 4, 15
(B) 7, 8, 6
(C) 5, 15, 45
(D) 12, 8, 13
(E) 10, 15, 20
Rationale: Let the numbers be x, y and z. Then,
x+ y = 10 ...(i) y + z = 19 ...(ii) x + z = 21 …(iii)
Adding (i) ,(ii) and (iii), we get: 2(x + y + z ) = 50 or (x + y + z) = 25.
Thus, x= (25 - 19) = 6; y = (25 - 21) = 4; z = (25 - 10) = 15.
Hence, the required numbers are 6, 4 and 15.
Answer A)6, 4, 15
Answer: (A) 6, 4, 15
Question: If d=1/(2^3*5^6) is expressed as a terminating decimal, how many nonzero digits will d have?
(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten
Rationale: Another way to do it is :
We know x^a*y^a=(X*Y)^a
given = 1/(2^3*5^6)
= Multiply and divide by 2^3
=2^3/(2^3*2^3*5^6)
=2^3/10^6
=> non zero digits are 8 => Ans A
Answer: (A) One
Question: Three cows work to fill a tub at at different rate. Hose A and B, working together, can fill the tub in 3/5 of an hour. Hoses A and C can fill it in 1/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 cows, working together, to fill the tub?
(A) 3/10
(B) 2/5
(C) 6/11
(D) 1
(E) 6/5
Rationale: We have ,in 1 hourwhen two hose working together can fill the tub as follow:
1/a + 1/b = 1/3/5 of the work
1/a + 1/c = 1/1/2 of the work
1/b + 1/c = 1/2 of the work
=>Get total both sides we got : 2(1/a +1/b +1/c) = 10+30+15/30 of the work
or 1/a +1/b +1/c = 55/30=11/6 of the work
Calculate total amount of time taken when three hoses work together 11/6 = 6/11
C
Answer: (C) 6/11
Question: How many of the positive factors of 24 , 16 and how many common factors are there in numbers?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: factors of 24 - 1, 2, 3, 4, 8, 12 and 24
factors of 16 - 1 , 2, 4, 8 and 16
Comparing both, we have three common factors of 45,16-4
Answer D
Answer: (D) 4
Question: Which of the following is between 27/37 and 29/35?
(A) 1/3
(B) 3/8
(C) 1/2
(D) 5/8
(E) 7/9
Rationale: I see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:
1) I estimate 27/37 to be ~3/4+ (approximately slightly greater than 3/4)
2) I estimate 29/35 to be ~4/5+ (approximately slightly greater than 4/5)
3) So now I'm looking for an answer choice that is .75 < x < .80
It should be pretty easy to identify which answer choices are less than .75 (or 3/4) if you have had practice with fractions.
A) clearly wrong - it's less than 3/4
B) also clearly wrong - it's less than 3/4
C) also clearly wrong - it's less than 3/4
D) also clearly wrong - it's less than 3/4
I would just stop here and select E. But to verify:
E) 7/9 ~ .77 which is greater than .75 and less than .80
Answer: (E) 7/9
Question: a, b, c, d, and e are five consecutive integers in increasing order of size. Which one of the following
expressions is not odd?
(A) a + b + c
(B) ab + c
(C) ab + d
(D) ac + d
(E) ac + e
Rationale: lets see the choices..
(A) a + b + c
a+a+1+a+2=3a+2..
if a is even, it is EVEN..
if a is odd, it is ODD..
(B) ab + c
a(a+1)+a+2=a^2+2a+2..
a(a+2)+2...
This will be O/E if a is O/E..
(C) ab + d
a(a+1)+a+3=a^2+2a+3..
a(a+2)+3...
This will be opposite of a.
.
(D) ac + d
a(a+2)+a+3=a^2+3a+3..
a(a+3)+3...
This will always be odd, as a(a+3) will always be even
(E) ac + e
a(a+2)+a+3=a^2+3a+3..
a(a+3)+4...
This will always be even, as a(a+3) will always be even
E must be the correct answer.
Answer: (E) ac + e
Question: If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?
(A) 23
(B) 20
(C) 11
(D) 5
(E) 2
Rationale: Soln:
{22} + {20} = 22*{20} +{20} = 23*{20}
ANSWER:A
Answer: (A) 23
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
(A) 5%
(B) 6%
(C) 6.125%
(D) 7.12%
(E) 8.13%
Rationale: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Answer: (C) 6.125%
Question: Jack and Christina are standing 150 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 7 feet per second and Christina walks in a straight line toward Jack at a constant speed of 8 feet per second. Lindy runs at a constant speed of 10 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
(A) 40
(B) 60
(C) 80
(D) 100
(E) 120
Rationale: The relative speed of Jack and Christina is 7 + 8 = 15 feet per second.
The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 150/15 = 10 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 10*10 = 100 feet.
Answer: D.
Answer: (D) 100
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 $216 per week. How much does she earn in dollars per hour?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 6
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 $216 per week
36x =216
x =6
Correct Option : E
Answer: (E) 6
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 61.50, his capital is?
(A) 24,602
(B) 28,888
(C) 24,600
(D) 24,628
(E) 24,6012
Rationale: Let the capital be Rs. x. Then,
(x * 8 * 1)/100 - (x * 31/4 * 1/100) = 61.50
32x - 31x = 6150 * 4
x = 24,600.
Answer: C
Answer: (C) 24,600
Question: A large box contains 21 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
(A) 250
(B) 350
(C) 450
(D) 550
(E) 525
Rationale: The number of chocolate bars is equal to
21 * 25 = 525
correct answer E
Answer: (E) 525
Question: A glass was filled with 12 ounces of water, and 0.03 ounce of the water evaporated each day during a 22-day period. What percent of the original amount of water evaporated during this period?
(A) 5.002%
(B) 5.5%
(C) 0.5%
(D) 5%
(E) 20%
Rationale: In 22 days 22*0.03=0.66 ounces of water evaporated, which is 0.66/12âˆ—100=5.5 of the original amount of water.
Answer: B.
Answer: (B) 5.5%
Question: A, B, and C working alone can finish constructing a house in 4, 8, and 12 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
(A) 11:12 am
(B) 11:32 am
(C) 11:49 am
(D) 12:07 pm
(E) 12:35 pm
Rationale: A completes 1/4 of the job each hour.
B completes 1/8 of the work each hour.
C completes 1/12 of the work each hour.
A completes 1/4 of the work in the first hour.
Working together, A and B complete another 3/8 for a total of 5/8.
Working together, A, B, and C can complete 11/24 of the work each hour.
To complete 3/8, the time required is (3/8) / (11/24) = 9/11 hours.
The work will be completed at 11:00 plus 9*60/11 minutes which is about 11:49 am.
The answer is C.
Answer: (C) 11:49 am
Question: 331, 482, 551, 263, 383, 242, 111
(A) 263
(B) 383
(C) 242
(D) 111
(E) None of these
Rationale: Solution
In each number except 383,the product of first and third digits is the middle one. Answer B
Answer: (B) 383
Question: An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
(A) 2
(B) 9
(C) 8
(D) 7
(E) 4
Rationale: Explanation:
In sixteen kg of alloy 10 kg of zinc and 6 kg copper is present
To make the ratio 3:1 we must add 8 kg of zinc to make it 18 kg of zinc and 6 kg copper
So answer is 8.
Answer: C
Answer: (C) 8
Question: I. a3 - 988 = 740,
II. b2 - 72 = 72 to solve both the equations to find the values of a and b?
(A) a > b
(B) a ≥ b
(C) a < b
(D) a ≤ b
(E) a = b or the relationship between a and b cannot be established.
Rationale: a3 = 1728 => a = 12
b2 = 144 => b = ± 12
a ≥ b
ANSWER:B
Answer: (B) a ≥ b
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
(A) (a) 4/10
(B) (b) 4/9
(C) (c) 1/2
(D) (d) 6/10
(E) (e) 5/9
Rationale: Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability B= 50/90 = 5/9
Correct answer E
Answer: (E) (e) 5/9
Question: If 3a – 3b – 2c = 32 and √3a-√(2b+2c)=4, what is the value of a + b + c?
(A) 3
(B) 9
(C) 10
(D) 12
(E) 14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
C
Answer: (C) 10
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 5 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 28%
(B) 40%
(C) 85.5%
(D) 70%
(E) 72%
Rationale: original price = 100
day 1 discount = 10%,price = 100-10 =90
day 2 discount = 10%,price = 90-9=81
day 3 discount = 5%,price = 81-4.05= 76.95
which is 76.95/90 *100 of the sale price on day 1= ~8
Answer C
Answer: (C) 85.5%
Question: The average monthly income of P and Q is Rs. 6050. The average monthly income of Q and R is Rs. 7050 and the average monthly income of P and R is Rs. 8000. The monthly income of P+Q+R is:
(A) 41100
(B) 42000
(C) 21100
(D) 42200
(E) 21000
Rationale: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (6050 x 2) = 12100 .... (i)
Q + R = (7050 x 2) = 14100 .... (ii)
P + R = (8000 x 2) = 16000 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 42200 or P + Q + R = 21100 .... (iv)
(P+Q+R)'s monthly income = Rs. 21100.
Answer: C
Answer: (C) 21100
Question: $600 will become $720 in 4 years find the rate of interest?
(A) 10%
(B) 15%
(C) 5%
(D) 7%
(E) 20%
Rationale: SI = simple interest = A-P = 720-600 = $120
R = 100SI/PT = 100*120/600*4 =5%
Answer is C
Answer: (C) 5%
Question: Hardy and Andy start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Andy. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 50 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
(A) 65
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: let x=length of pool
at first meeting, combined distance=x
at second meeting, combined distance=3x
if andy swims 18.5 m of x, then he will swim 3*18.5=55.5 m of 3x
andy's total distance to second meeting=x+10.5 m
x+10.5=55.5 m
x=45 m
D
Answer: (D) 45
Question: A train covers a certain distance at a speed of 280kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
(A) 500km/hr
(B) 540km/hr
(C) 560km/hr
(D) 600km/hr
(E) 650km/hr
Rationale: Explanation:
Distance = 280×4 = 1120km
Required speed = (1120/2) = 560km/hr
Answer: Option C
Answer: (C) 560km/hr
Question: If the units digit of n^27 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47
(A) Only I
(B) Only II
(C) Only III
(D) I and II
(E) II and III
Rationale: I tried in this way.
Given n^27 units digit is 7.
If at all we have to get 7 as units digits only 3 and 7 series has 7
3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81
7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)
We have n^27 - then divide 27 by 4 = reminder 3.
Then we have for only 7^3 - we have units digit as 3.
Hence 47^27 = 7 (units).
Option B is correct answer , and with 41^27 we always get 1 as units digit and 43^27 - we get units as 3.
Answer: (B) Only II
Question: Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
(A) 2197 feet
(B) 2420 feet
(C) 2500 feet
(D) 2629 feet
(E) None of these
Rationale: Distance =(1100*11/5)feet=2420 feet.
Correct Option: B
Answer: (B) 2420 feet
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
(A) $900
(B) $800
(C) $1000
(D) $700
(E) $1500
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $200. So 1 / 4 of her savings is $200. So her original savings are 4 times $200 = $800
correct answer B
Answer: (B) $800
Question: I bought a book for Rs 60 , I sold off to a friend for Rs 70 but after a while i felt sorry , that i sold it and bought it back for Rs 80, how much loss did I incur?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: profit 70-60 = 10
b p =80-60 =20
20-10=10 loss.
ANSWER:A
Answer: (A) 10
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number T?
(A) 126
(B) 1386
(C) 3108
(D) 308
(E) 13986
Rationale: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.
So,Total possible numbers with these digits=3 X 3 X 3 =27.
First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D
Second, If you imagine numbers T with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.
You are left withanswer E.
Answer: (E) 13986
Question: Due to 10% decrease in the price of sugar and John can buy 6kg more sugar in Rs100 , then find the CP of sugar?
(A) s. 1(23/27)
(B) s. 2(2/9)
(C) s. 2(1/9)
(D) s. 3(2/7)
(E) s. 4(2/9)
Rationale: Here r = 10 % ,x = 100 and A = 6 kg
Actual price of sugar = 10*100/((100-10 )*6) = Rs. 1(23/27)
A
Answer: (A) s. 1(23/27)
Question: If a copier makes 20 copies every 6 seconds, then continues at this rate, how many minutes will it take to make 2,000 copies?
(A) 13
(B) 15
(C) 12
(D) 11
(E) 10
Rationale: 20 copies 6 seconds
2000 copies = (2000*6)/20 seconds
= 600/60 minutes
= 10 minutes
Answer : E
Answer: (E) 10
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs.200
(B) Rs.250
(C) Rs.290
(D) Rs.300
(E) Rs.310
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
B)
Answer: (B) Rs.250
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 2007
(B) 2008
(C) 2002
(D) 2000
(E) 2001
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: D
Answer: (D) 2000
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
(A) 233
(B) 37
(C) 25
(D) 27
(E) 11
Rationale: Explanation:
Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: C
Answer: (C) 25
Question: If a book is sold at 6% profit instead of 6% loss, it would have brought Rs 15 more. Find out the cost price of the book
(A) 75
(B) 72
(C) 60
(D) 70
(E) 125
Rationale: Let C.P. of the book be Rs. ’X’
Given, 1.06 X - 0.94X = 15
=> 0.12 X = 15 = 15/0.12 = Rs 125
ANSWER:E
Answer: (E) 125
Question: A man walking at 3/4th of the speed, reaches his office late by 2 hours. What is the usual time?
(A) 5 hours
(B) 3 hours
(C) 6 hours
(D) 12 hours
(E) 15 hours
Rationale: at 3/4th of speed he is late by' 2hrs'
x-3/4(x)=2
x=8
so 8-2=6hrs(since 2 hrs late)
ANSWER:C
Answer: (C) 6 hours
Question: The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 660 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)
(A) 150π
(B) 240π
(C) 300π
(D) 480π
(E) 1,200π
Rationale: Distance traveled in 1 revolution = 2πr= 2π10/5280
Revolutions in one second= 660
Revolutions in 60 seconds (one minute)= 660*60
Total distance traveled= total revolutions *distance traveled in one revolution
660*60 *2π10/5280= 150π
A is the answer
Answer: (A) 150π
Question: A man sells two flats at the rate of Rs.1.995 lakhs each. On one he gains 5% and on the other, he loses 5%. His gain or loss percent in the whole transaction is
(A) 0.25% loss
(B) 0.25% gain
(C) 2.5% loss
(D) 25% loss
(E) None
Rationale: Solution
Loss %	= (5/ 10) ²%
=(0.5) ²%
= 0.25%.
Answer A
Answer: (A) 0.25% loss
Question: Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 40 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?
(A)  3
(B)  5
(C)  6
(D)  8
(E)  24
Rationale: Total work = 4*40 machine hrs
Time taken = 4* 40 /5 => 32 hours...
Thus all five machines, operating simultaneously will take ( 40 - 32 ) 8 hours..
Answer will be (D) 8
Answer: (D)  8
Question: Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 15 min
(B) 20 min
(C) 25 min
(D) 30 min
(E) 12 min
Rationale: A in 1 min = 1/20
B in 1 min = 1/30
(A+B) in 1 min = 1/12
both pipes fill in =>12 min
ANSWER E
Answer: (E) 12 min
Question: add 20% of 40 and 25% of 60.
(A) 9.5
(B) 23
(C) 25
(D) 22
(E) 15
Rationale: 20% of 40 + 25% of 60
40*20/100+60*25/100
8+15=23
answer B
Answer: (B) 23
Question: If (2^x)(3^y) = 576, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
(A) 16
(B) 24
(C) 32
(D) 96
(E) 144
Rationale: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=6, y=2. now quickly 2^5(3^0)=32. Than answer should be number 3.
C
Answer: (C) 32
Question: find cp when sp=rs51.70:loss=12%
(A) Rs 58.75
(B) Rs 88.75
(C) Rs 68.75
(D) Rs 98.75
(E) Rs 78.75
Rationale: cp=Rs{(100/88)*51.87}=Rs58.75
Answer is A.
Answer: (A) Rs 58.75
Question: If 72 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?
(A) 120 hours
(B) 110 hours
(C) 100 hours
(D) 90 hours
(E) 80 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
15 : 72 : : 25 : x<=>(15 x x) =(72 x 25)<=>(72 x 25)/15 = 120
Hence, 15 men can do it in 60 hours
Answer is A.
Answer: (A) 120 hours
Question: The sum of the even numbers between 1 and n is 85*86, where n is an odd number, then n=?
(A) 163
(B) 171
(C) 179
(D) 185
(E) 191
Rationale: Let n-1 = 2a.
2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 85*86
Then a = 85 and n = 171.
The answer is B.
Answer: (B) 171
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
(A) 2277
(B) 2987
(C) 4400
(D) 2678
(E) 2681
Rationale: X * (95/100) * (85/100) = 3553
X = 4400
Answer:C
Answer: (C) 4400
Question: The difference between simple and compound interest on Rs. 1200 for one year at 10% per annum reckoned half-yearly is?
(A) 7
(B) 3
(C) 4
(D) 5
(E) 1
Rationale: S.I. = (1200 * 10 * 1)/100 = Rs. 120
C.I. = [1200 * (1 + 5/100)2 - 1200] = Rs. 123 Difference = (123 - 120) = Rs. 3.
Answer: B
Answer: (B) 3
Question: The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time T all five colored lights will all flash together at the exact same time?
(A) 0:03 AM
(B) 0:04 AM
(C) 0:06 AM
(D) 0:12 AM
(E) 0:24 AM
Rationale: Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
Answer: (D) 0:12 AM