mathewhe/aqua_rat huggingface dataset:
Question: A vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the lengths OP and AB respectively. Suppose ∠APB = 60°, then the relationship between h and b can be expressed as :
(A) 2b^2 = h^2
(B) 2h^2 = b^2
(C) 3b^2 = 2h^2
(D) 3h^2 = 2b^2
(E) None of these
Rationale: Explanation :
As OP is at centre of square so clearly PA = PB.
so, angle ∠PAB = ∠ PBA.
and as ∠APB = 60,so we can see that in ∆ APB, ∠ PAB = ∠ PBA = 60.
Hence, its an equilateral triangle thus making AP = PB = AB = b.
Now lets see ∆ AOB ,
O is centre of square so angle AOB=900​.
giving us AO = OB = AB/√2.
so AO= b/√2
Now in triangle AOP right angled at O,
=> AO2 + OP2 = PA2 .
=> b2/2 + h2 = b2 .
=> h2 = b2/2
Answer : B
Answer: (B) 2h^2 = b^2
Question: Circles X and Y are concentric. If the radius of circle X is seven times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?
(A) 13
(B) Pi/3
(C) Pi/2
(D) 5/6
(E) 48/49
Rationale: Small circle radius = a, so area = PI a ^ 2
Large circle radius = 7a, so area = 9. PI a ^ 2
Area of shaded region = 49PI a^2 - PI a^2 = 48 PI a^2
So, probability = ( 48 PI a^2 ) / (49 PI a^2 )
=48/49 = Answer = E
Answer: (E) 48/49
Question: If x is an odd integer, which of the following is an odd integer?
(A) 2x
(B) 3x-1
(C) 5x+6
(D) x+x^2
(E) 6x-6
Rationale: Plug in an odd integer; in this case 3
(2*3) = 6 Even
(3*3)-1 = 8 Even
(5*3)+6 = 15 + 6 = 21 Odd
3+3^2 = 3 + 9 = 12 Even
(6*3)-6 = 18 - 6 = 12 Even
Answer: C
Answer: (C) 5x+6
Question: The least perfect square, which is divisible by each of 21, 36 and 66 is:
(A) 213444
(B) 214344
(C) 214434
(D) 231444
(E) 23444
Rationale: L.C.M. of 21, 36, 66 = 2772.
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 22 x 32 x 72 x 112 = 213444
Answer: Option A
Answer: (A) 213444
Question: The average of first 15 natural numbers is?
(A) 6
(B) 5.5
(C) 5.1
(D) 8
(E) 5
Rationale: Sum of 15 natural no.
= 240/2 = 120
Average =120/15
= 8
Answer:D
Answer: (D) 8
Question: In what time a sum of money double itself at 2% per annum simple interest?
(A) 60%
(B) 58%
(C) 55%
(D) 40%
(E) 50%
Rationale: P = (P*2*R)/100
R = 50%
ANSWER:E
Answer: (E) 50%
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) Rs.480
(B) Rs.420
(C) Rs.430
(D) Rs.440
(E) Rs.490
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer:A
Answer: (A) Rs.480
Question: If the average (arithmetic mean) of a and b is 110, and the average of b and c is 170, what is the value of a − c?
(A) −120
(B) −100
(C) 100
(D) 135
(E) It cannot be determined from the information given
Rationale: a+b = 220
b+c = 340
a-c = -120.
IMO option A.
Answer: (A) −120
Question: 3 candidates in an election and received 3000, 5000 and 15000 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 65.21%
(B) 50.16%
(C) 57%
(D) 60%
(E) 65.24%
Rationale: Total number of votes polled = (3000 + 5000 + 15000) = 23000
So, Required percentage = 15000/23000 * 100 = 65.21%
A
Answer: (A) 65.21%
Question: A corporation that had $115.19 billion in profits for the year paid out $250.10 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
(A) 50%
(B) 20%
(C) 5%
(D) 2%
(E) 0.22%
Rationale: required answer = [employee benefit/profit] *100
=[(250.10 million)/(115.19 billion)]*100
=[(250.10*10^6)/(115.19*10^9)]*100
=(2.2/1000)*100
=0.22%
So answer is (E)
Answer: (E) 0.22%
Question: A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)?
(A) 0
(B) 20
(C) 75
(D) 5
(E) 10
Rationale: Explanation :
Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0
Answer : A
Answer: (A) 0
Question: When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 3), the quotient is 15 and the remainder is 1. What is the value of N?
(A) 151
(B) 331
(C) 511
(D) 691
(E) 205
Rationale: N/P=18 7/P= 18P+7
N/(P+2)=15 1/(P+3)=15P+45+1
solving these two equations
we get P=11 N= 205 answer is E.
Answer: (E) 205
Question: If 15 toys cost Rs, 234, what do 35 toys cost?
(A) 645
(B) 564
(C) 546
(D) 654
(E) None of them
Rationale: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
.	15 : 35 : : 234 : x = (15 x x) = (35 x 234) = x=(35 X 234)/15 =546
Hence, the cost of 35 toys is Rs. 546.
Answer is C
Answer: (C) 546
Question: What is the difference between the compound interest on Rs.12000 at 24% p.a. for one year when compounded yearly and half yearly?
(A) 399.8
(B) 383.8
(C) 120.8
(D) 288.8
(E) 172.8
Rationale: When compounded annually, interest
= 12000[1 + 24/100]1 - 12000 = Rs.2880
When compounded semi-annually, interest
= 12000[1 + 12/100]2 - 12000 = Rs.3052.80
Required difference = 3052.80 - 2880 = Rs.172.80
Answer:E
Answer: (E) 172.8
Question: The duplicate ratio of 1:4 is?
(A) 1:2
(B) 1:4
(C) 1:8
(D) 1:18
(E) 1:13
Rationale: 1^2: 4^2 = 2:16=1:8
ANSWER:C
Answer: (C) 1:8
Question: Two men A and B start from place X walking at 4 Â½ kmph and 5 Â¾ kmph respectively. How many km apart they are at the end of 3 Â½ hours if they are walking in the same direction ?
(A) 1 3/8 km
(B) 3 3/8 km
(C) 5 3/8 km
(D) 4 3/8 km
(E) 7 3/8 km
Rationale: Explanation:
Relative Speed = 5 Â¾ - 4 Â½ = 1 Â¼
Time = 3 Â½ h.
Distance = 5/4 x 7/2 = 35/8 = 4 3/8 km.
Answer: D
Answer: (D) 4 3/8 km
Question: What proximate value should come in place of the question mark (?) in the following question?
6.595 × 1084 + 2568.34 – 1708.34 = ?
(A) 6,000
(B) 12,000
(C) 10,000
(D) 8,000
(E) 9,000
Rationale: ? ≈ 6.6 × 1080 + 2560 – 1700 ≈ 7128 + 860 ≈ 8000
Answer D
Answer: (D) 8,000
Question: A man wants to sell his scooter.There are two offers,one at Rs.12,000 cash and the other at a credit of Rs. 12,880 to be paid after 8 months,money being at 18% per annum. Which is the better offer ?
(A) Rs. 12,000 in cash
(B) Rs. 12,880 at credit
(C) Both are equally good
(D) none of these
(E) Cannot be determined
Rationale: Solution
P.W. of Rs. 12,880 due 8 months hence
= Rs. [12880 x100/100 +( 18x8/12) ] = Rs. ( 12880x100/112)= Rs.11500.
Clearly, Rs.12,000 in cash is a better offer.
Answer A
Answer: (A) Rs. 12,000 in cash
Question: Noelle walks from point A to point B at an average speed of 3 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 4 kilometers per hour?
(A) 5.75
(B) 6
(C) 7.25
(D) 7.5
(E) 7.75
Rationale: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
4= 2*3*x/3+x
x= 6
B is the answer
Answer: (B) 6
Question: c is the product of each integer from 1 to 50, inclusive and d=100^k, where k is an integer . What is the greatest value of k for which y is a factor of c?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 9
Rationale: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*50 = 50!
No. of trailing zeros in 50! = 50/5 + 50/5^2 = 10+2 = 12
100^k = 10^2k → k = 12/2 = 6
B
Answer: (B) 6
Question: The distance from City A to City B is 60 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?
(A) 45
(B) 48
(C) 50
(D) 52
(E) 60
Rationale: The time it takes Bob to drive to City B is 60 / 40 = 1.5 hours.
Alice needs to take less than 1 hour for the trip.
Alice needs to exceed a constant speed of 60 / 1 = 60 miles per hour.
The answer is E.
Answer: (E) 60
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is?
(A) 1
(B) 2
(C) 6
(D) 8
(E) 9
Rationale: Let the ten's and unit digit be x and 8 respectively.
x
Then, 10x + 8 + 18 = 10 x 8 + x
x x
10x2 + 8 + 18x = 80 + x2
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
Option B
Answer: (B) 2
Question: What could be the range of a set consisting of odd multiples of (6+1)?
(A) 70
(B) 24
(C) 35
(D) 62
(E) 21
Rationale: Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 7*(2n+1) where n is any positive integer.
Range = 7*(2m + 1) - 7*(2n + 1) = 7*2*(m-n) = 14 * (m-n).
m, n - any positive integers
The answer must be divisible by 14, which is only 70.
The correct answer is A.
Answer: (A) 70
Question: In a 120 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
(A) 22 seconds
(B) 12 seconds
(C) 10 seconds
(D) 8 seconds
(E) 28 seconds
Rationale: B runs 56 m in 7 sec.
=> B runs 120 m in 7/56*120 = 15 seconds
Since A beats B by 7 seconds, A runs 120 m in (15-7) = 8 seconds
Hence, A's time over the course = 8 seconds
ANSWER:D
Answer: (D) 8 seconds
Question: The triplicate ratio of 1:3 is?
(A) 1:64
(B) 1:62
(C) 1:27
(D) 3:64
(E) 5:64
Rationale: 1^3: 3^3 = 1:27
ANSWER:C
Answer: (C) 1:27
Question: 36 welders work at a constant rate they complete an order in 5 days. If after the first day, 12 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
(A) 5
(B) 2
(C) 8
(D) 4
(E) 6
Rationale: 1. We need to find out the time taken by 24 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 36*5= 180 days
4. But on day 1 thirty-six workers had already worked finishing 1/5 of the job. So 24 workers have to finish only 4/5 of the job.
5. Total time taken by 24 workers can be got from formula used at (2). i.e., 24* total time taken = 180. Total time taken by 6 workers to finish the complete job is 180/ 24 = 7.5 days.
6. Time taken by 24 workers to finish 4/5 of the job is 4/5 * 7.5 = 6 days.
The answer is choice E
Answer: (E) 6
Question: A straight pipe 5 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
(A)  1/6 and 1/4 only
(B)  1/4 and 1/3 only
(C)  1/6, 1/4, and 1/3
(D)  1/12, 1/6 and 1/4
(E)  1/12, 1/6, and 1/3
Rationale: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/4, 6-4=2=2/12=1/6meters long pieces.
Answer: A.
Answer: (A)  1/6 and 1/4 only
Question: A rectangular block 10cm by 20cm by 35cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
(A) 6
(B) 56
(C) 15
(D) 40
(E) 22
Rationale: Volume of the block = 10*20*35 = 7000 cm^3
Side of the largest cube = H.C.F of 10,20,35 = 5cm
Volume of the cube = 5*5*5= 125 cm^3
Number of cubes = 7000/125 = 56
Answer is B
Answer: (B) 56
Question: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 500 feet. What is its area, in square feet?
(A) 12,000
(B) 19,600
(C) 20,000
(D) 20,400
(E) 20,800
Rationale: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.
diagonal = 200
2x + 2y = 560, or x + y = 280
a^2 + b^2 = c^2 for each the sides of the triangle
using the ratio 3:4:5 for sides, and knowing c = 500, you can deduce the following
a=300
b=400
300x400=120,000
A is the answer.
Answer: (A) 12,000
Question: 8 years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 8 = 1/3 (b - 8) --- (1)
b = a + 12
Substituting b = a + 12 in first equation,
a - 8 = 1/3 (a + 4) => 3a - 24 = a + 4
=> 2a = 28=> a = 14.
ANSWER:C
Answer: (C) 14
Question: Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race?
(A) 450 m
(B) 680 m
(C) 700 m
(D) 900 m
(E) 1000 m
Rationale: Explanation:
When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race
ANSWER C
Answer: (C) 700 m
Question: A man loses 1/3rd of his money, then wins Rs. 10 loses 1/3rd of what he has and wins Rs. 20 and finds that he has exactly what be had at the beginning. What was the amount he originally bad ?
(A) 25
(B) 36
(C) 10
(D) 48
(E) 45
Rationale: let x be that amount
so accordind to question , eqn will be like:
(((x-x/3)+10)-(((x-x/3)+10)/3))+20=x
=> ((2x/3+10)-((2x/3+10)/3))+20=x
=>3x-4x/3=80
=>x=48
ANSWER:D
Answer: (D) 48
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
(A) 33
(B) 77
(C) 265
(D) 21
(E) 88
Rationale: WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer: D
Answer: (D) 21
Question: A train travels 210 km in 3 hours and 270 km in 4 hours.find the average speed of train.
(A) 80 kmph
(B) 69 kmph
(C) 70 kmph
(D) 90 kmph
(E) None of these
Rationale: As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 210 + 270 = 480 km
Thus, Total Speed = 7hrs
or,Average Speed = 480/7
or, 69kmph.
ANSWER:B
Answer: (B) 69 kmph
Question: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(9)?
(A) 53/32
(B) 55/34
(C) 57/36
(D) 59/38
(E) 61/40
Rationale: A(n+1)=1+(1/A(n))
A(1) = 1
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5
A(6) = 13/8
A(7) = 21/13
A(8) = 34/21
A(9) = 55/34
The answer is B.
Answer: (B) 55/34
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 502 m
(B) 298 m
(C) 500 m
(D) 189 m
(E) 171 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer:C
Answer: (C) 500 m
Question: Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 15. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?
(A) 1
(B) 11
(C) 15
(D) 19
(E) 47
Rationale: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.
What does this imply?If the sum of the first n terms of the sequence is n
Since number of terms will definitely be positive, we are looking for a positive sum.
10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on
Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...
Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.
Answer (B)
Answer: (B) 11
Question: . The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
(A) 10 a.m
(B) 10.30 a.m
(C) 11 a.m
(D) 11.30 a.m
(E) 11.15 a.m
Rationale: Suppose they meet x hrs after 8 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330
60x + 75(x - 1) = 330 => x = 3
So, they meet at (8 + 3) i.e., 11 a.m.
ANSWER:C
Answer: (C) 11 a.m
Question: In how many ways can you seat 5 people on a bench if one of them does not want to sit on the middle seat or at either end?
(A) 40
(B) 44
(C) 48
(D) 52
(E) 56
Rationale: One person can choose 2 possible chairs to sit. The remaining 4 people can sit in 4! ways.
The number of arrangements is 2*4! = 48.
The answer is C.
Answer: (C) 48
Question: A racng car travels k kilometres in n hours. How many miles will it travel in x hours at the same rate?
(A) knx
(B) k⁄n
(C) kn⁄x
(D) kx
(E) kx⁄n
Rationale: Given Speed = k/n
To Find distance in x hours with same speed
Distance = speed * time
Distance = k/n*x = kx/n
Answer E
Answer: (E) kx⁄n
Question: Of 30 applicants for a job, 16 had at least 4 years' experience, 21 had degrees, and 5 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?
(A)  12
(B)  10
(C)  9
(D)  7
(E)  5
Rationale: set A : people with more than 4 years exp
set B : people with degree
AUB = total - (less than 4 exp and no degree)
AUB = 30-5=25
AUB = A + B - AiB
AiB = 21+16-25
=12
Answer A
Answer: (A)  12
Question: Six balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
(A) 60
(B) 90
(C) 210
(D) 150
(E) 180
Rationale: Since the balls are all of different colors, let's permute them and then decide how many balls we put in each box.
For example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box.
Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.
For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.
For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.
Total of 120 + 90 = 210 possibilities.
Answer C.
Answer: (C) 210
Question: Subtract the absolute value from the local value of 4 in 564823
(A) 196
(B) 1996
(C) 2996
(D) 3996
(E) 6000
Rationale: Explanation:
Place value = Local value
Face value = Absolute value
The place value of 4 in 564823 is 4 x 1000 = 4000
The face value of 4 in 564823 is nothing but 4.
=> 4000 - 4 = 3,996
Answer: Option D
Answer: (D) 3996
Question: Find the simple interest on Rs 4000 at 20% per annum for the period from 2nd March 2016 to 4th May 2016.
(A) Rs. 133.1
(B) Rs. 228.1
(C) Rs. 131.1
(D) Rs. 128.1
(E) Rs. 138.1
Rationale: Explanation:
One thing which is tricky in this question is to calculate the number of days.
Always remember that the day on which money is deposited is not counted while the day on which
money is withdrawn is counted.
So lets calculate the number of days now,
Time = (29+30+4) days = 63/365 years = 1/5 years
P = 4000
R = 20%
S.I. = =4000Ã—20Ã—0.17260273972/100=138.1
Answer: E
Answer: (E) Rs. 138.1
Question: P cando a work in 15 days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
(A) 3/5
(B) 4/5
(C) 8/15
(D) 7/11
(E) 3/41
Rationale: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
C
Answer: (C) 8/15
Question: Jeni has 7 flavors of cake in his bakery. How many options are there for Sheera to pick a one-flavor, two-flavor,three-flavor, four-flavor, five-flavor, six-flavor or seven-flavor order?
(A) 423
(B) 325
(C) 142
(D) 171
(E) 127
Rationale: 7C1 + 7C2+ 7C3+7C4+7C5+7C6+7C7 =127 .
Answer: E
Answer: (E) 127
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: B
15
In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.
Answer: (B) 15
Question: A butler stole wine from a butt of sherry which contained
40% of spirit and he replaced,what he had stolen by wine
containing only 16% spirit. The butt was then of 24%
strength only. How much of the butt did he steal?
(A) 1/3
(B) 2/3
(C) 1/4
(D) 1/8
(E) 1/9
Rationale: Wine containing 40%spirit Wine containing 16% spirit
Wine containing 24% spirit
8 16
They must be mixed in the ratio of =1:2.
Thus 1/3 of the butt of sherry was left
hence the butler drew out 2/3 of the butt.
ANSWER B
Answer: (B) 2/3
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 27
(B) 50
(C) 98
(D) 77
(E) 51
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.Answer: B
Answer: (B) 50
Question: In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled a quarter that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?
(A)  d
(B)  1/3*d
(C)  1/2*d
(D) 5/8*d
(E)  3/2*d
Rationale: Solution:
Lets look at the information given in the question...
Total time travelled = 2 hrs
Distance travelled first hour = d
Distance travelled second hour = d/4
The question is asking for the avg speed at which the car travels for 2 hrs
We know that avg speed = total distance/total time
Lets place the information given in the question to the formula above = (d+d/4)/2
= 5/8*d
We find that option D is the answer as it gives the same expression as found in our calculation above. Answer option D.
Answer: (D) 5/8*d
Question: How many zeros does 135^19 x 42^17 end with?
(A) 0
(B) 2
(C) 5
(D) 13
(E) 17
Rationale: To know the zeros we need to know how many 10's are there for this need to find number of 2s and 5s ( 2 * 5 = 10)
135 = (5 x 3 ^3)^19 So Number of 5s are = 19
42 = (2x7x3)^17 so number of 2s = 17
So tot number of 10s in this number is (17-> 2s x 17-> 5s)
So answer is 17
ANSWER:E
Answer: (E) 17
Question: How many integers from 10 to 180, inclusive, are divisible by 3 but not divisible by 7?
(A) 45
(B) 49
(C) 50
(D) 52
(E) 56
Rationale: We should find # of integers divisible by 3 but not by 3*7=21.
# of multiples of 21 in the range from 10 to 180, inclusive is (168-21)/21+1=8;
57-8=49.
Answer: B.
Answer: (B) 49