mathewhe/aqua_rat huggingface dataset:
Question: An athlete decides to run the same distance in 1/4th less time that she usually took. by how much percent will she have to increase her average speed?
(A) 40
(B) 44.4
(C) 33.3
(D) 22.2
(E) 12.2
Rationale: simple logic (1-1/4)=3/4 then reverse it so 4/3=1.333
1.33-1=33.33
ANSWER:C
Answer: (C) 33.3
Question: Suppose 3 monkeys take 3 minutes to eat 3 bananas. How many monkeys would it take to eat 6 bananas in 6 minutes?
(A) 9
(B) 10
(C) 11
(D) 3
(E) 13
Rationale: One monkey takes 3 min to eat 1 banana , so in 6 mins 1 monkey will eat 2 bananas , so for 6 bananas in 6 min we need 6/2 =3 monkeys
ANSWER:D
Answer: (D) 3
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
(A) 278 km
(B) 390 km
(C) 267 km
(D) 286 km
(E) 296 km
Rationale: The total distance covered by the car in the first 10 hours
= 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48
= sum of 10 terms in AP whose first term is 30 and last term is 48
= 10/2 [30 + 48] = 390 km.
Answer: B
Answer: (B) 390 km
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 93.5 cm
(C) 94.5 cm
(D) 92.5 cm
(E) None of these
Rationale: Explanation:
Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
ANSWER IS A
Answer: (A) 91.5 cm
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
(A) 140
(B) 130
(C) 150
(D) 200
(E) 160
Rationale: Speed=(60x5/8)m/sec = (50/3) m/sec.
Length of the train = (Speed x Time).
Length of the train = (50/3 x 12)m = 200 m.
Answer is D.
Answer: (D) 200
Question: Simplify: (8-5)+(10-2+3)-5
(A) 8
(B) 9
(C) -8
(D) -9
(E) 5
Rationale: Solution:
(8-5)+(10-2+3)-5
=3+8+3-5
=14-5
=9
Answer: (B)
Answer: (B) 9
Question: You are a cashier at a grocery store. Your customer, David, buys a pound of bacon
$1.39, one dozen eggs for $1.29, and a pound of coffee for $2.79. What is the sum
total of his purchases?
(A) $5.47
(B) $6.47
(C) $7.47
(D) $8.47
(E) $9.47
Rationale: Add $1.39+ $1.29+$2.79
we have the sum $5.47
correct answer A
Answer: (A) $5.47
Question: The total marks obtained by a student in Mathematics and Physics is 32 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 26
(C) 27
(D) 28
(E) 22
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 32 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (32 + 20) / 2 = 26.Answer:B
Answer: (B) 26
Question: A person is 80 years old in 490 and only 70 years old in 500 in which year is he born?
(A) 400
(B) 550
(C) 570
(D) 440
(E) 450
Rationale: 490(80),500(70),510(60),520(50),530(40),540(30),550(20),560(10),570(0)
ANSWER:C
Answer: (C) 570
Question: Complete the sequence:
6 7 9 8 6 8 ?
(A) 9
(B) 2
(C) 2
(D) 8
(E) 1
Rationale: A
9
Number of alphabets in the days of a week. Monday contains 6 letters; Tuesday contains 7 letters and so on.
Answer: (A) 9
Question: The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?
(A) 1:7
(B) 1:3
(C) 1:8
(D) 1:9
(E) 1:1
Rationale: 4πr12 : 4πr22 = 1 : 4
r1 : r2 = 1 : 2
4/3 πr13 : 4/3 πr23
r13 : r23 = 1:8
Answer:C
Answer: (C) 1:8
Question: A manufacturer of a certain product can expect that between 0.1 percent and 0.3 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?
(A)  Between $15,000 and $25,000
(B)  Between $50,000 and $150,000
(C)  Between $60,000 and $100,000
(D)  Between $150,000 and $250,000
(E)  Between $300,000 and $500,000
Rationale: Number of defective units is between = .1 % of 20000 and .3% of 20000
= 20 and 60
Retail Price per unit = 2500 $
Expected price of refund is between = 2500 x 20 and 2500 x 60
=50,000 and 1,50,000 dollars
Answer B
Answer: (B)  Between $50,000 and $150,000
Question: An engagement team consists of a 2 project managers, 3 team leaders, and four consultants. There are 3 candidates for the position of project manager, 4 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?
(A) 25
(B) 35
(C) 150
(D) 210
(E) 300
Rationale: Answer= Total number combinations - Total number of combinations with constraints
Total number of combinations = 3C2*4C3*7C4= 420
Total number of combinations with constraints = 3C2*4C3*5C2=120
Answer=420-120=300
ANSWER: E
Answer: (E) 300
Question: What is the value of (P + Q)/(P - Q) if P/Q is 10?
(A) 4/3
(B) 2/3
(C) 2/6
(D) 11/9
(E) 8/7
Rationale: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]
= (10 + 1)/(10 - 1)
= 11/9
= 11/9
ANSWER:D
Answer: (D) 11/9
Question: A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 6 new non-fiction books in the right window. Assuming she can put the six fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
(A) 86400
(B) 65777
(C) 89000
(D) 34560
(E) 12420
Rationale: Two displays books could be arranged n! # of total arrangements are combinations multiplied together,
5!*6! =120*720=86400
Answer is A
Answer: (A) 86400
Question: Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 20 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)
(A) 40 mph
(B) 45 mph
(C) 48 mph
(D) 52 mph
(E) 60 mph
Rationale: Let t be the number of hours he would need to reach office on time.
when he is driving with over speed, he reached office 4 min earlier! so the equation for this is s(t - 4/60) = 30
where s is the speed and 30 is the distance.
if he decreases his speed by 5mph then he would have reached his office on time: (s-5)t = 30
if you solve above equations, you will arrive at t = 2/3 hr and s = 40mph
therefore answer is A
Answer: (A) 40 mph
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
(A) 72
(B) 55
(C) 44
(D) 66
(E) 98
Rationale: Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average = 864/12 = 72.
Answer: A
Answer: (A) 72
Question: A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 6 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
(A) (a) 24/5
(B) (b) 6
(C) (c) 26/5
(D) (d) 27/5
(E) (e) 28/5
Rationale: from the uphill we can find out the distance = 6*2 = 12
average speed = total distance/total time
= 24/ (2+ (12/6)) = 6
Answer is B.
Answer: (B) (b) 6
Question: A student got 72% in math and 84% in history. To get an overall average of 75%, how much should the student get in the third subject?
(A) 65%
(B) 67%
(C) 69%
(D) 71%
(E) 73%
Rationale: 72 + 84 + x = 3*75
x = 69
The answer is C.
Answer: (C) 69%
Question: A sum amount to Rs.1344 in two years at simple interest. What will be the compound interest on the same sum at the same rate of interest for the same period?
(A) 10.28%
(B) 10.95%
(C) 10.25%
(D) 12.25%
(E) 10.55%
Rationale: 100
5 ---- I
5
0.25 --- II
-----------
10.25%.Answer:C
Answer: (C) 10.25%
Question: 180 students appeared for a test, of which 162 passed. The pass percentage is
(A) 80%
(B) 85%x1/2%
(C) 90%
(D) 93x1/3%
(E) None of these
Rationale: Explanation :
Pass percentage = (162/180 100)%
= 90%
Answer : C
Answer: (C) 90%
Question: The H.C.F. of two numbers is 15 and their L.C.M. is 420. If one of the numbers is 375, then the other is:
(A) 12.21
(B) 283
(C) 16.8
(D) 318
(E) 32.4
Rationale: Other number =	(15 x 420)/375 = 16.8.
ANSWER :C
Answer: (C) 16.8
Question: Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.
(A) Rs.512
(B) Rs.552
(C) Rs.612
(D) Rs.622
(E) None
Rationale: Solution
Amount	= Rs[7500x(1+4/100)²]
=Rs.(7500x26/25x26/25)
= Rs.8112.
C.I	= Rs(8112 - 7500)
=Rs.612.
Answer C
Answer: (C) Rs.612
Question: In how many possible ways you can write 3240 as product of 3 positive integers x,y,z .
(A) 420
(B) 450
(C) 350
(D) 320
(E) 380
Rationale: 3240=2^3*3^4*5
we have to distribute three 2 to three numbers : 3+3-1C3-1=5C2=10
similarly for 3 and 5
therefore total=10*15*3=450
ANSWER:B
Answer: (B) 450
Question: In how many ways can a committee consisting of three men and four women be formed from a group of six men and seven women?
(A) (7C4)(6C9)
(B) (7C4)(6C5)
(C) (7C4)(6C3)
(D) (7C4)(8C3)
(E) (7C3)(6C3)
Rationale: The group contain six men and seven women
Three men can be selected from six men in 6C3 ways.
Four women can be selected from seven women in 7C4 ways.
Total number of ways = (7C4)(6C3).
Answer:C
Answer: (C) (7C4)(6C3)
Question: When positive integer N is divided by positive integer J, the remainder is 12. If N/J = 134.08, what is value of J?
(A) 22
(B) 56
(C) 78
(D) 150
(E) 175
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 12
So, 134.08 = 134 + 12/J
So, J = 150 ANS D
Answer: (D) 150
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 140?
(A) 65
(B) 77
(C) 25
(D) 18
(E) 12
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (140 - 75) = 65 points to C.
Answer:A
Answer: (A) 65
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
(A) 12%
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: Sol. Required change = (20*100)/(100-20)=25%
C
Answer: (C) 25%
Question: If x and y are positive integers such that x/y = 4.25, which of the following numbers could be y?
(A) 5
(B) 4
(C) 3
(D) 17
(E) 50
Rationale: With the given information, we are trying to find the value of y.
To achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.
Take the decimal x/y = 4.25 and because it's in the hundreds decimal place, put the given value (x/y = 4.25/1) and multiply it by 100.
Take the resulting fraction (x/y = 425/100) and reduce it to it's lowest form.
Both of the numbers are divisible by 25.
The result is x/y = 17/4.
Thus y = 4.
The correct answer is B.
Answer: (B) 4
Question: The area of Circle O is added to its diameter. If twice the circumference of Circle O is then subtracted from this total, the result is 8. What is the radius of Circle O?
(A) 2/π
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: area+diameter-2*circumference=8
pi*r^2+2r=8+2*2pi*r
isolate r and get r(pi*r+2)=8+4pi*r
r=(8+4pi*r)/(pi*r+2) =>4(pi*r+2)/(pi*r+2)
r=4
D
Answer: (D) 4
Question: A set of data consists of the following 9 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8
Rationale: If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.
Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.
1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2
2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8
3. 3 , 5
Distance is - 1.8 and 1.8
4. 2 , 6
Distance is - 0.8 and 0.8
5. 0 , 8
Distnace is - 1.2 and 1.2
Hence from above , we see that adding -1 and 9 , results in a value that would change the SD to the least. Hence A
Answer: (A) -1 and 9
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.10 of money?
(A) 1500
(B) 1992
(C) 9921
(D) 1000
(E) 2789
Rationale: P = 10(100/10)2
=> P = 1000
Answer: D
Answer: (D) 1000
Question: If a is the smallest positive integer such that 3,150 multiplied by a is the square of an integer, then a must be
(A)  2
(B)  5
(C)  6
(D)  7
(E)  14
Rationale: Solution:
This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor's exponent is an even number.
Let’s start by prime factorizing 3,150.
3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2
3,150 = 2^1 x 3^2 x 5^2 x 7^1
(Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square.)
We also are given that 3,150 multiplied by a is the square of an integer. We can write this as:
2^1 x 3^2 x 5^2 x 7^1 x a = square of an integer
According to our rule, we need all unique prime factors' exponents to be even numbers. Thus, we need one more 2 and one more 7. Therefore, a = 7 x 2 = 14
Answer is E.
Answer: (E)  14
Question: Which is the middle even number between 1 and 9?
(A) 10
(B) 25
(C) 5
(D) 8
(E) 6
Rationale: 1+x = 9-x
2 x = 8
X = 4
Now 1+x = 5
ANSWER:C
Answer: (C) 5
Question: A person lent a certain sum of money at 5% per annum at simple interest and in 8 years the interest amounted to $480 less than the sum lent. What was the sum lent?
(A) 700
(B) 800
(C) 900
(D) 1000
(E) 1100
Rationale: P - 480 = (P*5*8)/100
P = 800
The answer is B.
Answer: (B) 800
Question: If, 4 years ago, Jamie was half as old as he is now, how old will he be in x years?
(A) x + 10
(B) x + 5
(C) x + 8
(D) x – 5
(E) 2x
Rationale: let his age be a. a-4=a/2 hence a=8. 8 years hence, a =x+8
Answer C
Answer: (C) x + 8
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
(A) 8 months
(B) 2 months
(C) 6 months
(D) 4 months
(E) 5 months
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Answer:E
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer: (E) 5 months
Question: Multiply: (x-4)(X+5)
(A) xpower2 + 5x-20
(B) xpower2 - 4x - 20
(C) xpower2 - x - 20
(D) xpower2 + x - 20
(E) x - 20
Rationale: (x-4)(x+5)=x(X+5)-4(x+5), = xpower2 + 5x - 4x - 20, =xpower2 + x - 20 . the correct answer : (D)
Answer: (D) xpower2 + x - 20
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
(A) 55 kmph
(B) 52 kmph
(C) 57 kmph
(D) 54 kmph
(E) 59 kmph
Rationale: D
54 kmph
D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5 = 54 kmph
Answer: (D) 54 kmph
Question: Andrew earns $2000 a month from his job. His income increased and now makes $2125 a week. What is the percent increase?
(A) 6.25%
(B) 5.25%
(C) 7.25%
(D) 4.25%
(E) 12.5%
Rationale: Increase = (125/2000)*100 = (1/16)*100 = 6.25%.
A
Answer: (A) 6.25%
Question: In a kilometer race, If A gives B a 40m start, A wins by 19sec. But if A gives B a 30 sec start, B wins by 40 m. Find the time taken by B to run 5,000m?
(A) 2275
(B) 2375
(C) 2475
(D) 2575
(E) 2675
Rationale: Let A travells 1000m in x sec and b in (x+19)sec
Therefore, speed of B is 1000/(x+19)
B travel 960m in x sec from here equation of speed=960/x
speed of B is constant so boht the speed equation for B are equal
960/x = 1000/(x+19)
On solving we get x=456sec
Time taken by B for 5000m : 5000/(960/456)=2375
ANSWER:B
Answer: (B) 2375
Question: In a certain warehouse, 70 percent of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80 percent of the packages weigh at least 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds?
(A) 8
(B) 64
(C) 120
(D) 102
(E) 144
Rationale: If 80% of the packages weigh at least 25 pounds
This means that 20% of the packages weigh LESS THAN 25 pounds
Let T = TOTAL number of packages
So, 20% of T = # of packages that weigh LESS THAN 25 pounds
48 packages weigh LESS THAN 25 pounds
GREAT. So, 20% of T = 48
Rewrite to get: 0.2T = 48
Solve:T = 240
70% of the packages weigh less than 75 pounds
So, 70% ofT= number of packages that weigh less than 75 pounds
70% of240=168, so168packages weigh less than 75 pounds
OF THOSE168packages that weigh less than 75 pounds,48packages weigh less than 25 pounds.
So, the number of packages that weight BETWEEN 25 and 75 pounds =168-48= 120 = C
Answer: (C) 120
Question: What is the ratio between perimeters of two squares one having 8 times the diagonal then the other?
(A) 3: 6
(B) 3: 3
(C) 3: 8
(D) 8: 1
(E) 3: 2
Rationale: d = 8d d = d
a√2 = 8d a√2 = d
a = 8d/√2 a = d/√2 => 8: 1
Answer: D
Answer: (D) 8: 1
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
(A) 7%
(B) 9%
(C) 4 percent
(D) 2%
(E) 4%
Rationale: 150 = (750*5*R)/100
R = 4%
Answer: C
Answer: (C) 4 percent
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 150 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
(A) 110
(B) 146
(C) 152
(D) 162
(E) 170
Rationale: The probability of survival for each of the first 3 months of life is 1-1/10=9/10, so of 150 newborn 150*9/10*9/10*9/10=~110 is expected to survive.
Answer: A.
Answer: (A) 110
Question: If Albert’s monthly earnings rise by 26%, he would earn $693. If, instead, his earnings rise by only 20%, how much (in $) would he earn this month?
(A) 643
(B) 652
(C) 660
(D) 690
(E) 693
Rationale: =693/1.26∗1.2
=660=660
Answer is C
Answer: (C) 660
Question: If a and b are prime numbers, which of the following CANNOT be the sum of a and b?
(A) 5
(B) 9
(C) 23
(D) 16
(E) 13
Rationale: All answer choices but C are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.
Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers.
Answer: C
Answer: (C) 23
Question: A train 440 meters long is running with a speed of 50 kmph. The time taken by it to cross a tunnel 180 meters long is?
(A) 40.33 sec
(B) 41.33 sec
(C) 42.33 sec
(D) 40 sec
(E) 44.64 sec
Rationale: D = 440 + 180 =620
S = 50 * 5/18 = 13.88889 mps
T = 620/13.88889 = 44.64
E
Answer: (E) 44.64 sec
Question: A = {0, 1, 3, 6, -8}
B = {-1, 2, -4, 7,-5}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
(A) 1/4
(B) 1/3
(C) 2/5
(D) 9/25
(E) 1/2
Rationale: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 3/5*2/5 = 6/25;
P(negative, negative) = 1/5*3/5 = 3/25.
P = 6/25 + 3/25
= 9/25
Answer: D
Answer: (D) 9/25
Question: The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit?
(A) 136
(B) 187
(C) 600
(D) 750
(E) 733
Rationale: Explanation:
Let C.P be Rs. x
900 - x = 2(x - 450)
=> x = Rs.600
C.P = 600 gain required is 25%
S.P = [(100+25)*600]/100
= Rs.750
Answer: D
Answer: (D) 750
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 10 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 - 10 = 1/3 (b - 10) --- (1)
b = a + 10
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a + 0) => 3a - 30 = a
=> 2a = 30=> a = 15.
ANSWER:D
Answer: (D) 15
Question: A group of men can complete a job in X hours. After every 4 hours, half the number of men working at that point of time leave the job. Continuing this way if the job is finished in 16 hours, what is the value of X.
(A) 5.5 days
(B) 6.5 days
(C) 7.5 days
(D) 8.5 days
(E) 9.5 days
Rationale: If there are m men
job requires mX man hours.
job completed in first 4 hrs = m*4 =4m
job completed in next 4 hrs = 4*m/2 = 2m
job completed in next 4 hrs = 4.m/4 = m
job completed in last 4 hrs = 4.m/8= m/2
4m+2m+m+m/2 = mX
x= 7+1/2 = 7.5 days
ANSWER:C
Answer: (C) 7.5 days
Question: The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 24 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
(A) 30
(B) 20
(C) 18
(D) 12
(E) 16
Rationale: Given: mean=24 and SD=6.
The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=18and 2 SD below the mean ismean-2*SD=12, so the number of hours that Pat watched television was between 12 and 18 hours.
Answer: E
Answer: (E) 16
Question: Mary completes a piece of work in 160 days, Rose completes the same work in 240 days. If both of them work together, then the number of days required to complete the work is?
(A) 92
(B) 94
(C) 96
(D) 98
(E) 100
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 160 × 240/400 = 96 days
Answer is C
Answer: (C) 96
Question: David paid $5,000 for 100 shares of stock X and $3,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/8 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
(A) A gain 1.67 times as much.
(B) A loss 2 times as much
(C) A loss 3 times as much
(D) A loss 1.5 times as much
(E) No Loss No Gain
Rationale: A = 5000; B = 3000; Profit = (3/8)*3000 = 1125
After prices are reversed:
A = 3000; B =5000; Profit = (3/8)*5000 =1875
1875 --> Gain of 1.67 times 1125
Answer: A
Answer: (A) A gain 1.67 times as much.
Question: Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 4 hours?
(A) 675
(B) 900
(C) 1,800
(D) 5,900
(E) 7,500
Rationale: 8 machines/ 360 cans = 5 machines/ x cans
8x= 1800
x=225
(225)(4 hours)= 900 cans. The answer is B.
Answer: (B) 900
Question: The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
(A) Rs.8790
(B) Rs.8721
(C) Rs.8891
(D) Rs.8768
(E) Rs.8730
Rationale: Actual price = 95% of 90% of 85% of Rs. 12000
= 95/100 * 90/100 * 85/100 * 12000
= Rs.8721.
Answer: B
Answer: (B) Rs.8721