mathewhe/aqua_rat huggingface dataset:
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
(A) 2:8
(B) 2:1
(C) 2:2
(D) 2:4
(E) 2:5
Rationale: Explanation:
Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
Answer:E
Answer: (E) 2:5
Question: Find the probability if a two digit number multiplied by 3 but not 5
(A) 2/15
(B) 3/15
(C) 4/15
(D) 5/15
(E) 6/15
Rationale: sample space of 2 digit number = (99-10)+1 = 90
probability of number multiplied by 3 but not 5 = total no. multiplied by 3 - total no. multiplied by 5
= 30 - 6=24
so, probability= 24/90 = 4/15
ANSWER:C
Answer: (C) 4/15
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 5 out of 8 consecutive days in Rwanda?
(A) 4/7
(B) 3/7
(C) 7/32
(D) 4/28
(E) 28/135
Rationale: using Binomial. theorem
nCr (p)^r (q)^n-r
8C5 (1/2)^5 (1/2)^r
which is 7/32
Answer is C.
Answer: (C) 7/32
Question: The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 10 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
(A) 2
(B) 4
(C) 12
(D) 40
(E) 160
Rationale: Actual miles/gallon is = 480/40 = 12 miles/gallon.
Current engine miles/gallon is 10 miles/gallon.
Additional 2 miles/gallon is required to match the actual mileage.
IMO option A.
Answer: (A) 2
Question: Average of 5 numbers is zero. At most how many numbers may be greater than zero
(A) 0
(B) 4
(C) 5
(D) 9
(E) 10
Rationale: Answer: Option B
Answer: (B) 4
Question: A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage
(A) 25% gain
(B) 20% gain
(C) 20% loss
(D) 15% gain
(E) None
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (500 - 400)/400 = 25% gain
A
Answer: (A) 25% gain
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 150 meters, how long will it take to cross a railway platform 235 meters long
(A) 6 ½ sec
(B) 7 ½ sec
(C) 8 sec
(D) 10 ½ sec
(E) 9 sec
Rationale: Explanation:
Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (150 + 235) m = 385 m.
Time taken =385 ×(3/110) sec =21/2 sec = 710½ sec
Answer: Option D
Answer: (D) 10 ½ sec
Question: If x is a sum of all even integers on the interval 13...65 and y is their number, what is the GCD (x, y)?
(A) 1
(B) 13
(C) 26
(D) 52
(E) 1014
Rationale: x = 14 + 16 + ... + 64 = (largest + smallest)/2 *(# of terms) = (14 + 64)/2*26 = 39*26.
GCD of 26 and 39*26 is 26.
Answer: C.
Answer: (C) 26
Question: How many pages the book have, if total 300 digits are used to form the page numbers?
(A) 135 pages
(B) 136 pages
(C) 137 pages
(D) 138 pages
(E) 139 pages
Rationale: First 9 pages .. 9 digits
next 90 pages .. 180 digits
next 37 pages ... 111 digits
----------------------
Total ...136 pages ...300 digits
ANSWER:B
Answer: (B) 136 pages
Question: The sum of two numbers is 16. The difference is 4. What are the two numbers?
(A) 10-6
(B) 8-8
(C) 9-7
(D) 11-5
(E) 13-3
Rationale: Let x be the first number. Ley y be the second number
x + y = 16
x - y = 4
Solve the system of equations by elimination
Adding the left sides and the right sides gives:
x + x + y + -y = 16 + 4
2x = 20
x = 10
Since x + y = 16, 10 + y = 16
10 + y = 16
10 - 10 + y = 16 - 10
y = 6
The numbers are 10 and 6
correct answer is A)10-6
Answer: (A) 10-6
Question: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
(A) 76
(B) 88
(C) 77
(D) 67
(E) 60
Rationale: The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
Answer:E
Answer: (E) 60
Question: For the sequence a1, a2, a3. ..an, an is defined by an=1/2n−1−1/2n for each integer n≥1. What is the sum of the first 8 terms of the sequence?
(A) 63/64
(B) 127/128
(C) 255/256
(D) 511/512
(E) 513/512
Rationale: a1=1/2^0−1/2^1
a2=1/2^1−1/2^2....
a8=1/2^7−1/2^8
a1+a2+...+a8=1/2^0−1/2^8=255/256
The answer is C.
Answer: (C) 255/256
Question: A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
(A) 5 days
(B) 6 days
(C) 7.5 days
(D) 8.5 days
(E) 8 days
Rationale: Explanation:
B's 5 days work = 1/10*5=1/2
Remaining work =1âˆ’1/2=1/2
A can finish work =15âˆ—1/2=7.5days
ANSWER IS C
Answer: (C) 7.5 days
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
(A) No profit, no loss
(B) 5%
(C) 8%
(D) 10%
(E) 12%
Rationale: Explanation:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =(80/1600 x 100\ )% = 5%. Answer: B
Answer: (B) 5%
Question: Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 9kmph. For how many minutes does the bus stop per hr
(A) 12 min
(B) 11 min
(C) 13 min
(D) 20 min
(E) 50 min
Rationale: Due to stoppages,it covers 45km less.
time taken to cover 45 km is [45/54 *60] min = 50min
Answer is E.
Answer: (E) 50 min
Question: I have only 1$ and 2$ note. I want to give 95$ to John. How many maximum number of 1$ note I need?
(A) 53
(B) 35
(C) 47
(D) 95
(E) 62
Rationale: To give 95$ we need of 95 1$ notes
so ans is D
Answer: (D) 95
Question: Given that there are 11 cricket players per team, how many ways can you select 10 cricket players from 2 teams if no more than 3 players can be selected from each team?
(A) 24563
(B) 45784
(C) 14525
(D) 35658
(E) 27225
Rationale: Now from each group we have to select 5 persons only: 11C3 * 11C3= 165 * 165= 27225
Total ways=27225 ways.
Answer E
Answer: (E) 27225
Question: There are 100 students in a certain geometry class. If one half of the students are boys and one fifth of the boys are under six feet tall, how many boys in the class are under six feet tall?
(A) 6
(B) 10
(C) 18
(D) 24
(E) 27
Rationale: Total Students = 100
One half of the students are boys = 1/2*100 = 50
One fifth of the boys are under six feet tall = 1/5*50 = 10 ...
Therefore Number of boys in the class under six feet tall = 10 ... Answer B....
Alternatively... Number of boys in the class under six feet tall = 1/5 of 1/2 of Total Students = 1/5*1/2*100 = 10...
Answer B
Answer: (B) 10
Question: A company has 600 employees, 40% of whom are employed full time. If it hires 80 new employees, 15% of whom are employed part time, what will be the percent increase in part time employees?
(A) 1 2/3 %
(B) 2 2/3 %
(C) 4 %
(D) 3.33 %
(E) 9 %
Rationale: Total employee = 600
Full time Empl = 600 * 40/100 =240
Part time Emp = 600 - 240 = 360
New part time empl = 80 * (15/100)
=12
Total new part time Emp = 12+360= 372
Old part time Emp = 360
% increase = (new - old)*100/old
=12*100/360
= 3.33 %
Ans-D
Answer: (D) 3.33 %
Question: Four friends are pooling their money for pizza. Emma has 8 dollars. Daya has 25% more money than Emma, Jeff has 2/5 of the money Daya has, and Brenda has 4 more dollars than Jeff. How much money does Brenda have?
(A) 14
(B) 6
(C) 7
(D) 8
(E) 10
Rationale: D
8
Emma has 8 dollars.
Daya has 25% more dollars than Emma.
Daya= 8 + 8 x 25%
= 8 + 8 x .25
=8 + 2
=10
Jeff has 2/5 of what Daya has.
= 10 x 2/5
= 4
Brenda has 4 more dollars than Jeff.
= 4 + 4
=8
Brenda has 8 dollars.
The correct answer is D.
Answer: (D) 8
Question: If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.7 SDs from the mean?
(A) 12.5
(B) 13
(C) 14
(D) 11.8
(E) 15
Rationale: 2.7 SD's mean is equal to: +/- 2.7*3 = +/- 8.1
ie. 11.9 to 28.1
Answer is: D
Answer: (D) 11.8
Question: In a flower shop there were 8 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
(A) 12
(B) 16
(C) 8
(D) 9
(E) None of these
Rationale: Answer
Now required average
= old average x Multiplicand
= 8 x 2 = 16
Correct Option: B
Answer: (B) 16
Question: If n is the greatest positive integer for which 2^n is a factor of 6!, then n =?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 6! = 720
E. 2^10 = 512 (720/512) - this is not a factor of 6!
D. 2^8 = 256 (720/256) - this is not a factor of 6!
C. 2^6 = 64 (720/64) - this is not a factor of 6!
B. 2^4 = 16 (720/16) - this is a factor of 6!
B is answer
Answer: (B) 4
Question: For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are positive numbers, which of the following could be a value of w?
(A) 9
(B) 3
(C) 0
(D) −2
(E) −9
Rationale: Since w#Z and w are positive, we need to take the value of w such that w#z or w^3z(8 - w^2) is positive.
ANSWER:E
Answer: (E) −9
Question: Fresh fruit contains 55% water and dry fruit contains 10% water. How much dry fruit can be obtained from 100kg of fresh fruit?
(A) A)32kg
(B) B)40kg
(C) C)52kg
(D) D)50kg
(E) E)100kg
Rationale: Quantity of pulp in 100kg of fresh fruits = (100-55)% of 100kg = 45kg
Let the quantity of dry fruit obtained be x kg
then, (100-10)% of x = 45
(90/100)*x = 45
x = 50
correct option is D
Answer: (D) D)50kg
Question: Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 4.85
(B) 7.85
(C) 6.85
(D) 5.85
(E) 6.15
Rationale: T = (111 + 165)/ (80 + 65) * 18/5
T = 6.85
ANSWER:C
Answer: (C) 6.85
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 288
(B) 266
(C) 120
(D) 287
(E) 212
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Answer: (C) 120
Question: Gate A runs 3000 liters of water per minute out of a check dam that has a total volume of 360000 liters. Gate B drains a third of the dam in 6 hours.
Working together how long will it take both gates to drain the dam completely ?
(A) 2 hours and 36 minutes
(B) 1.5 hours
(C) 9 hours and 12 minutes
(D) 15 hours
(E) 1 hour and 28 minutes.
Rationale: Gate A has a rate of 300 liters per minute which equals a rate of 18,000 liters per hour.
Pipe B has a rate of 10,000 liters per hour.
10,000 + 18000 (A+B) = Together they have a rate of 28000 liters per hour.
36000 (The dam ) / 28000 = 36/28 = 1 Hour and 28 minutes
Answer -E
Answer: (E) 1 hour and 28 minutes.
Question: How many real roots does the equation x^2y+16xy+60y=0 have if y < 0?
(A) 0
(B) 1
(C) 2
(D) 3
(E) Infinite
Rationale: x^2y+16xy+60y=0
=> y ( x^2 + 16x + 60) = 0
=> y (x+8)^2 = 0
if y<0 , then x=-9
So although there are 2 factors , they are the same x=-9 .
The equations has 3 distinct real root .
Answer D
Answer: (D) 3
Question: A container contains a dry mixture of sand and stones. Mass of sand and stones in the container is in the ratio 1:3. If 12 kg sand is added to the container, the ratio of masses of sand and stones becomes 5:3. Originally, how much more was the mass of stones than sand in the container?
(A) 12
(B) 9
(C) 6
(D) 3
(E) 1
Rationale: Suppose originally the mass of sand in the container was x. So the mass of stones, originally, would be 3x because mass of sand and stones in the container is in the ratio 1:3.
If 12 kg sand is added, mass of sand becomes x + 12, and the mass of stones remains unchanged. But now the ratio of the mass of sand and stones is 5:3.
This means,
(x + 12)/3x = 5/3, which gives x = 3.
So originally, there was 3 kg sand and 9 kg stones.
So, the mass of stones was 6 kg more than the mass of sand.
Ans C
Answer: (C) 6
Question: In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?
(A) 17
(B) 18
(C) 20
(D) 21
(E) 30
Rationale: 6p2 = 6 x 5 = 30
Answer : E
Answer: (E) 30
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 10.30 a.m.?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 12
Rationale: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 8 am to 10.30 am = 2.5 hour
Hence they cross each other 12 times before 10.30 am
Answer is E
Answer: (E) 12
Question: A person borrows Rs.5000 for 2 years at 5% p.a. simple interest. He immediately lends it to another person at 61⁄4% p.a for 2 years. Find his gain in the transaction per year.
(A) 62.5
(B) 150
(C) 225
(D) 112.5
(E) 212.5
Rationale: Explanation :
The person borrows Rs. 5000 for 2 years at 5% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×5×2/100=500
He also lends it at 6 1⁄4% p.a for 2 years
Simple interest that he gets = PRT/100=5000×25/4×2/100=625
His overall gain in 2 years = Rs.625 - Rs.500 = Rs.125
His overall gain in 1 year = 125/2 = Rs.62.5
Answer : Option A
Answer: (A) 62.5
Question: A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than five people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
(A) x/4
(B) x/5
(C) x/9
(D) x/20
(E) 4x/9
Rationale: If 5 people share the rent, each person would pay x/5.
If 4 people share the rent, each person will pay x/4.
The extra amount each person pays is x/4 - x/5 = 5x/20 - 4x/20 = x/20
The answer is D.
Answer: (D) x/20
Question: 81,162,49,98,25,50,68
(A) 126
(B) 127
(C) 129
(D) 128
(E) 136
Rationale: 81*2=162
49*2=98
25*2=50
68*2=136
ANSWER:E
Answer: (E) 136
Question: The bankerâ€™s discount on Rs. 1600 at 8% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
(A) 2 months
(B) 4.5 months
(C) 6.5 months
(D) 7.5 months
(E) None
Rationale: Sol.
S.I. on Rs. 1600 = R.D. on Rs. 1680.
âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 8%.
âˆ´ Time = [100 * 80 / 1600 * 8] year = 5/8 year = 7.5 months.
Answer D
Answer: (D) 7.5 months
Question: A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
(A) Rs.3600
(B) Rs.3607
(C) Rs.3627
(D) Rs.3661
(E) Rs.3628
Rationale: X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
Answer:A
Answer: (A) Rs.3600
Question: At what time between 5.30 and 6 will the hands of a clock be at right angles?
(A) 43*8/11 min past 5
(B) 42*7/11 min past 5
(C) 43*7/11 min past 5
(D) 43*7/11 min past 7
(E) 44*7/11 min past 5
Rationale: Explanation:
At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in 60/55 * 40 min= 43*7/11 min
Required time 43*7/11 min past 5
Answer is C
Answer: (C) 43*7/11 min past 5
Question: there are 30 students in a classroom. The ratio of the # of girls to boys was 1:2, how many boys are there?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: # OF GIRLS = X
# OF BOYS =2X
X + 2X = 30
3X = 30
X = 30/3 = 10
BOYS = 2X = 2 * 10 =20
ANSWER: C
Answer: (C) 20
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs.800 per sq. metre.
(A) Rs. 12000
(B) Rs. 19500
(C) Rs. 18000
(D) Rs. 16500
(E) Rs. 18090
Rationale: Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = Rs.800
Hence, total cost=5.5×3.75×800=5.5×3000
= Rs.16500 Answer: Option D
Answer: (D) Rs. 16500
Question: When ticket sales began, Pat was the nth customer in line for a ticket, and customers purchased their tickets at the rate of r customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?
(A) (n - 1) r
(B) (n-1)/r
(C) n + r –1
(D) r/(n-1)
(E) n/(r-1)
Rationale: B. (n - 1) / r
Answer: (B) (n-1)/r
Question: Set P is composed of nine numbers, labeled P1 through P9. Set Q is also composed of nine numbers, labeled Q1 through Q9. Set Q is defined as follows: Q1 = 1 + P1; Q2 = 2 + P2; and so on, including Q9 = 9 + P9. How much larger is the sum of set Q's mean and range than the sum of set P's mean and range?
(A) 3
(B) 6
(C) 9
(D) cannot be determined
(E) 12
Rationale: Yes, the correct answer is D
Answer: (D) cannot be determined
Question: From a pack of cards, two cards are drawn one after the other, with replacement. What is the probability that the first card is a club and the second card is a red king?
(A) 1/13
(B) 1/15
(C) 1/26
(D) 1/52
(E) 1/104
Rationale: P(club) = 1/4
P(red king) = 1/26
P(club then a red king) = 1/4 * 1/26 = 1/104
The answer is E.
Answer: (E) 1/104
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
(A) 39
(B) 27
(C) 30
(D) 26
(E) 29
Rationale: 20 + 24 + 8 * 2 = 60/2 = 30
Answer: C
Answer: (C) 30
Question: A polygon has 135 diagonals. How many sides does it have?
Self made
(A)  12
(B)  13
(C)  18
(D)  15
(E)  16
Rationale: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 135
n*(n - 3) = 270
Substitute n from the answer choices. n = 18
Answer: C
Answer: (C)  18
Question: The average age of a group of 10 students was 25. The average age increased by 3 years when two new students joined the group. What is the average age of the two new students who joined the group?
(A) 22 years
(B) 30 years
(C) 32 years
(D) 43 years
(E) None of these
Rationale: The total age of 10 students with average 25 = 250
The total age of 12 students with average 28 = 336
The total age of 2 new students = 86
Their average =43
Correct Option D
Answer: (D) 43 years
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
(A) 23
(B) 46
(C) 47
(D) 76
(E) 35
Rationale: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
B
Answer: (B) 46
Question: If m and n are negative integers, which of the following statements must be true?
I. (-m)^n is positive.
II. (-m)^(-n) is positive.
III. m^(-n) is positive.
(A) None
(B) II only
(C) I and II
(D) I and III
(E) I, II and III
Rationale: Let's m = -2 and n = -3
I. (-m)^n = (2)^(-3) = 1/(2^3) --> Positive
II. (-m)^(-n) is positive. = 2^3 --> Positive
III. m^(-n) is positive. = -2^3 --> Negative
Answer: C
Answer: (C) I and II
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^2 + s^2?
(A) 0
(B) 1
(C) 2
(D) 8
(E) 9
Rationale: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).
Then the sum of r^2+s^2 will have 1+1 = 2 as a units digit.
The answer is C.
Answer: (C) 2
Question: What is the greatest possible length which can be used to measure exactly the lengths 180 m, 500 m and 15m 20 cm?
(A) 80 cm
(B) 50 cm
(C) 40 cm
(D) 10 cm
(E) 100 cm
Rationale: Required length = HCF of 18000 cm, 50000 cm, 1520 cm = 80 cm
Answer is A
Answer: (A) 80 cm
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2080 less than the principal. What was the principal?
(A) 1500
(B) 2600
(C) 2507
(D) 3200
(E) 11500
Rationale: P - 2080 = (P*5*4)/100
P = 2600
Answer: B
Answer: (B) 2600
Question: If (1/2)^25 (1/81)^k = 1/18^25, then k =
(A) 8
(B) 12.5
(C) 16
(D) 24
(E) 36
Rationale: I'm going to focus on denominator only..
(2^25) . ((3^4)^k = 18^25
(2^25) . ((3^4k) = (2. 3^2)^25
(2^25) . ((3^4k) = (2^25) . (3^2)^25
hence
4k = 50
k = 12,5
answer B
I hope it's quite clear
Answer: (B) 12.5
Question: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 6 cups of tea are prepared, 3 in one way and 3 in other. Find the different possible ways of presenting these 6 cups to the expert.
(A) 252
(B) 240
(C) 300
(D) 720
(E) None
Rationale: Solution:
Since, there are 3 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,
[6!/(3!x 3!)]= 720
Answer: Option D
Answer: (D) 720
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 17 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 11
(B) 444
(C) 2881
(D) 287
(E) 456
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 17 + 21 = 38
T = 12
D = 38 * 12 = 456
Answer:E
Answer: (E) 456
Question: One night 18 percent of the female officers on a police force were on duty. If 144 police officers were on duty that night and half of these were female officers, how many female officers were on the police force?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: Let x be the number of female police officers on the police force.
The number of female police officers on duty was 72.
0.18x = 72
x = 400
The answer is B.
Answer: (B) 400
Question: If the sample interest on a sum of money 10% per annum for 2 years is $1200, find the compound interest on the same sum for the same period at the same rate?
(A) $1260
(B) $1520
(C) $1356
(D) $1440
(E) $1210
Rationale: Rate = 10%
Time = 2years
S.I. = $1200
Principal = 100*1200/10*2 = $6000
Amount = 6000(1+10/100)^2 = $7260
C.I. = 7260-6000 = $1260
Answer is A
Answer: (A) $1260
Question: If a + b + c = 13, a2 + b2 + c2 = 69 then find the ab + bc + ca :
(A) 10
(B) 30
(C) 50
(D) 70
(E) 90
Rationale: Explanation:
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
2(ab + bc + ca) = (a + b + c)2 - a2 + b2 + c2
2(ab+bc+ca) = 169 - 69 = 100.
(ab + bc + ca) = 50.
Answer: C
Answer: (C) 50
Question: When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction w of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
(A) 11/14
(B) 13/18
(C) 4/7
(D) 3/7
(E) 3/14
Rationale: If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.
2/9 of the votes on a certain resolution have been counted--> 4 counted and 18-4=14 votes left to be counted;
3/4 of those counted are in favor of the resolution--> 3 in favor and 1 against;
Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18*2/3=12 people who voted against, so in the remaining 14 votes there should be 12-1=11 people who voted against. Thus w=11/14 of the remaining votes must be against.
Answer: A.
Answer: (A) 11/14
Question: Look at this series: 36, 34, 30, 28, ..., ... What numbers should come next?
(A) 29,27
(B) 32,30
(C) 22,20
(D) 24,22
(E) 10,9
Rationale: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.
36-2 = 34
34-4 = 30
30-2 = 28
28-4 = 24
24-2 = 22
Answer is D
Answer: (D) 24,22
Question: Of three numbers, the third is thrice the second and the second is 5 times the first. If their average is 105, the smallest of the three numbers is:
(A) 18
(B) 15
(C) 20
(D) 21
(E) 22
Rationale: Explanation:
Let first number be x.
So,2nd no. = 5x & 3rd no.=15x.
So,x+5x+15x=105× 3 = 234.
21x = 315
x = 315/21
Hence,smallest Number x=15.
Answer: B
Answer: (B) 15