mathewhe/aqua_rat huggingface dataset:
Question: Of the employees in a company, 40 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?
(A) 54%
(B) 52%
(C) 50%
(D) 51%
(E) 55%
Rationale: Let E be total no. of employees and F be total no of female employees.
Question asked what is F/E X 100%?
No. of female employees with Masters = 0.4 x E (From the question)
No. of female employees without masters = 0.2 x F (From the question)
Therefore No. of female employees with masters = F - 0.2 F = 0.8 F
The 2 expressions equal each other therefore 0.8F = 0.4E; F/E = 0.4/0.8 = 50%
Ans: C
Answer: (C) 50%
Question: Two numbers are 30% and 37% are less than a third number .How much percent is the second number less than the first?
(A) 15%
(B) 12%
(C) 10%
(D) 5%
(E) 18%
Rationale: I II III
70 63 100
70 -------- 7
100 ------ ? => 10%
ANSWER:C
Answer: (C) 10%
Question: A broker invested her own money in the stock market. During the first year, she increased her stock market wealth by 50 percent. In the second year, largely as a result of a slump in the stock market, she suffered a 30 percent decrease in the value of her stock investments. What was the net increase or decrease on her overall stock investment wealth by the end of the second year?
(A) −5%
(B) 5%
(C) 15%
(D) 20%
(E) 80%
Rationale: Assume the broker invested $100.
After year 1 (50% increase in wealth): $100 * 0.5 = $50 increase + $100 = $150
After year 2 (30% decrease in wealth): $150 * 0.3 = $45; $150 - $45 decrease = $105
Net increase = $105/$100 - 1 = 5%
Answer is B.
Answer: (B) 5%
Question: Four consecutive traffic signals each show either red or green. How many different arrangements of the four signals are possible?
(A) 16
(B) 9
(C) 8
(D) 7
(E) 6
Rationale: Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 4 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 4 signals are possible.
Total Options: 16
Final Answer:
A
Answer: (A) 16
Question: If x*y = xy – 2(x + y) for all integers x and y, then 2* (–3) =
(A) –16
(B) –11
(C) –4
(D) 4
(E) 16
Rationale: The quickest (rather only) way is to apply the given formula:
2*(-3) = 2*(-3) - 2 (2 + (-3) ) = -6 +2 = -4
Option (C)
Answer: (C) –4
Question: Rs.1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
(A) 387
(B) 736
(C) 300
(D) 345
(E) 635
Rationale: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300
Answer:C
Answer: (C) 300
Question: The average expenditure of a labourer for 6 months was 90 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
(A) 70
(B) 72
(C) 75
(D) 78
(E) 81
Rationale: Income of 6 months = (6 × 90) – debt
= 540 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 810
Average monthly income = 810 ÷ 10 = 81
Answer E
Answer: (E) 81
Question: Solve for x: 2x â€“ y = (3/4)x + 8.
(A) (y + 6)/5
(B) 4(y + 8)/5
(C) (y + 6)
(D) 4(y - 6)/5
(E) 5/4(y-6)
Rationale: Solution:
2x â€“ y = (3/4)x + 8.
or, 2x - (3/4)x = y + 8.
or, (8x -3x)/4 = y + 8.
or, 5x/4 = y + 8.
or, 5x = 4(y + 8).
or, 5x = 4y + 32.
or, x = (4y + 32)/5.
Therefore, x = 4(y + 8)/5.
correct answer B
Answer: (B) 4(y + 8)/5
Question: A large field of 900 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?
(A) 435 hectares.
(B) 425 hectares.
(C) 445 hectares.
(D) 415 hectares.
(E) 405 hectares.
Rationale: Let the areas of the parts be x hectares and (900 - x) hectares.
Difference of the areas of the two parts = x - (900 - x) = 2x - 900
one-fifth of the average of the two areas = 1/5[x+(900−x)]/2
= 1/5 × (900/2) = 450/5 = 90
Given that difference of the areas of the two parts = one-fifth of the average of the two areas
=> 2x - 900 = 90
=> 2x = 990
⇒ x = 990/2 = 495
Hence, area of smaller part = (900 - x) = (900 – 495) = 405 hectares.
Answer is E.
Answer: (E) 405 hectares.
Question: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number Q of people surveyed by the company?
(A) 46
(B) Q.80
(C) Q.90
(D) Q.100
(E) 200
Rationale: 100 = x + x - 20 + 23 - 23
x = 60,
So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%
23% of the total no. of people should be an integer. So, A,BC are out.
60% of D and 40% of D are both integers. So, D satisfies all conditions.
So, answer is D.
Answer: (D) Q.100
Question: If the average of 6 digits is 16 and the average of 4 of them is 10, calculate the average of the remaining 2 numbers?
(A) 36
(B) 35
(C) 28
(D) 33
(E) 21
Rationale: Explanation:
Total of the 6 digits - 6*16 = 96
Total of the 4 digits - 4*10 = 40
Total of the remaining 2 digits - 96-40 = 56
average of the remaining 2 numbers = 56/2 = 28
ANSWER: C
Answer: (C) 28
Question: 32% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
(A) 25
(B) 30
(C) 50
(D) 55
(E) 80
Rationale: I came up with (E) 80
Think of 100 people total:
From the first fact, 32 of these are women with fair hair.
From the second fact, these 30 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*32 equals the number of fair haired men, which is 48 men with fair hair.
Add this 48 to the 32 women and get 80 fair haired men and women out of 100 total men and women.
80%
E
Answer: (E) 80
Question: On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 20. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?
(A) (3, 7)
(B) (-8, 4)
(C) (5, -8)
(D) (-2, 10)
(E) (-5, -5)
Rationale: The area of the triangle formed will be:
1/2 * base * height =
1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 20
Thus |product of coordinates of point C| = 40
The answer is C.
Answer: (C) (5, -8)
Question: A bonus of Rs.2800 is to be divided among 3 people such that Alex gets twice as much as David, who receives one-fourth as much as Peter. What amount did Peter get?
(A) 1200
(B) 2000
(C) 1600
(D) 1500
(E) 2500
Rationale: Explanation:
Let Peter’s share be x.
Hence, David gets x/4 and Alex gets x/2.
x + x/4 + x/2 = 2800
7x/4 = 2800
x = Rs.1600
ANSWER: C
Answer: (C) 1600
Question: The average of four consecutive even numbers is 27. Find the largest of these
numbers.
(A) 29
(B) 25
(C) 32
(D) 30
(E) 27
Rationale: Let the four consecutive even numbers be x, x + 2, x + 4 and x + 6.
Then, sum of these numbers = (27 x 4) = 108.
So, x + (x + 2) + (x + 4) + (x + 6) = 108 or 4x = 96 or x = 24.
:. Largest number = (x + 6) = 30.
Answer is D.
Answer: (D) 30
Question: A can complete a work in 18days and B can do the same work in 10days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work?
(A) 2days
(B) 8days
(C) 6days
(D) 7days
(E) 10days
Rationale: The required answer = (18-3)*5 / 18 = 150/18 = 8days
Answer is B
Answer: (B) 8days
Question: If x2 - y2 = -12 and x + y = 6, find x and y.
(A) x = 2 , y = 4
(B) x = 3 , y = 5
(C) x = 4 , y = 6
(D) x = 5 , y = 7
(E) x = 6 , y = 8
Rationale: x2 - y2 = (x - y)(x + y) = -12 : given
6(x - y) = -12 : substitute x + y by 6
(x - y) = -2 : solve for x - y
(x - y) = -2 and x + y = 6 : 2 by 2 system.
x = 2 , y = 4 : solve above system.
correct answer A
Answer: (A) x = 2 , y = 4
Question: If n is the smallest integer such that 108 times n is the square of an integer, what is the value of n?
(A)  2
(B)  3
(C)  6
(D)  12
(E)  24
Rationale: 108 can written as = 2 * 2 * 3 * 3 * 3 --> 2^2* 3^3 ---(1)
so for 108 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of.
here 2 already has even power -> So n has to be 2 to make the power of 2 in (1) even
Option A is correct
Answer: (A)  2
Question: A bag contains 6 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 3/4
(B) 5/11
(C) 1/7
(D) 1/8
(E) 4/3
Rationale: Let number of balls = (6 + 5) = 11.
Number of white balls = 5
P (drawing a white ball) =5/11
Option B.
Answer: (B) 5/11
Question: If p and r are integers, and p^2 = 20r, then r must be divisible by which of the following?
(A) 2
(B) 4
(C) 5
(D) 7
(E) 14
Rationale: Ans: D
Solution: for p to be an int 20 r must be whole square of a number.
20r= 5*2*2*r
to make it whole square we need 5
so r can must be divisible by 5y where y is itself a whole square.
so C is the ans
Answer: (C) 5
Question: Find the value of x from this equation? 7(x - 1) = 21
(A) 2
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: 1. Divide both sides by 7:
2. Simplify both sides:
x - 1 = 3
3. Add 1 to both sides:
x - 1 + 1 = 3 + 1
4. Simplify both sides:
x = 4
B
Answer: (B) 4
Question: The difference between the weights of two girls is 10 kgs. Five years ago, the heavier one was twice as heavy as the lighter one. The present age of the heavier person is
(A) 15kg
(B) 10kg
(C) 20kg
(D) 25kg
(E) 30kg
Rationale: Let their weights of x kgs and (x + 10) kgs respectively.
Then, (x + 10) - 5 = 2(x - 5)
⇔ x +5= 2x - 10
⇔ 3x = 15
∴ Present weight of the heavier person = (5 + 10)
= 15kgs.
Answer :15kgs
Answer: (A) 15kg
Question: If 25 men do a work in 96 days, in how many days will 40 men do it?
(A) 66
(B) 53
(C) 55
(D) 60
(E) 61
Rationale: 25 * 96 = 40 * x
x = 60 days
Answer: D
Answer: (D) 60
Question: Four different children have jelly beans: Aaron has 7, Bianca has 7, Callie has 8, and Dante has 11. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?
(A)  2
(B)  3
(C)  4
(D)  5
(E)  6
Rationale: Since Bianca and Callie are both within 1 jelly bean of each other and Aaron has 5, Dante must provide 3 of his 11 jelly beans so each child has no more than 1 fewer jelly bean than any other child.
Dante + Aaron = 11+7 =18/2 = 9
11-9 = 2 so Dante must provide 3 jelly beans to Aaron.
Answer (A)
Answer: (A)  2
Question: The ratio between the number of sheep and the number of horses at the Stewar farm is 3 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??
(A) 24
(B) 28
(C) 32
(D) 56
(E) 58
Rationale: et no of sheep and horses are 3k and 7k
no of horses= 12880/230=56
now 7K=56 and k=8
no of sheep=(3*8) =24
ANSWER:A
Answer: (A) 24
Question: On average, the bottle-nosed dolphin comes up for air once every two minutes; the beluga whale, a close relative, comes up for air on average once every five minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
(A) 50%
(B) 100%
(C) 150%
(D) 200%
(E) 250%
Rationale: Soln;-
30∗24−12∗24/12∗24=30−12/12=18/1230∗24−12∗24/12∗24=30−12/12=18/12
So 150%, Answer is C.
Answer: (C) 150%
Question: Set A consists of all the prime numbers between 12 and 32. What is the range of set A?
(A) 12
(B) 18
(C) 16.6
(D) 17
(E) 23
Rationale: The range of a set of data is the difference between the highest and lowest values in the set
In this set,
Highest number = 31
Lowest number = 13
Range = Highest - Lowest = 31 - 13 = 18
Option B
Answer: (B) 18
Question: 12.5 * 3.2 * 6.8 = ?
(A) 352
(B) 272
(C) 224
(D) 646
(E) 742
Rationale: B
272
? = 12.5 * 3.2 * 6.8 = 352
Answer: (B) 272
Question: By how much is three-fifth of 250 greater than four- seventh of 210 ?
(A) 30
(B) 110
(C) 25
(D) None of these
(E) Cannot be determined
Rationale: Solution
3/5of 250 - 4/7of 210 = 60.
Answer A
Answer: (A) 30
Question: Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
(A) 187
(B) 187
(C) 300
(D) 176
(E) 158
Rationale: 1/2:1/3:1/4
= 6:4:3
3/13*1300
= 300
Answer: C
Answer: (C) 300
Question: One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 3 robots altogether, if the robots build only one robot at a time?
(A) 40 min
(B) 94 min
(C) 110 min
(D) 112 min
(E) 120 min
Rationale: First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
And now we have 3 robots in 40 minutes
Answer -A
Answer: (A) 40 min
Question: In a mayoral election, Candidate X received 1/3 more votes than candidate Y, and Candidate Y received 1/7 fewer votes than Z. If Z received 21,000 votes how many votes did candidate X received?
(A) 18000
(B) 22000
(C) 24000
(D) 26000
(E) 32000
Rationale: Z=21 --> Y received 1/7 fewer votes than Z --> Y=Z-1/7*Z=18;
X received 1/3 more votes than Y --> X=Y+1/3*Y=24.
Answer: C.
Answer: (C) 24000
Question: There are n cities. What is the number of airlines that connected 4 different cities (airline from city A to city B is different with airline from city B to city A)?
(A) n(n-1)
(B) n(n-3)
(C) n(n-1)/2
(D) n(n+1)/2
(E) n2
Rationale: First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-3). Hence, the answer is n(n-3), which makes A an answer choice.
B
Answer: (B) n(n-3)
Question: 3x^2-6x+3 = 0 Find the above equation find the value of x
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: (B) 1
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 36 years now, the son's age five years back was:
(A) 13
(B) 17
(C) 19
(D) 22
(E) 24
Rationale: Let the son's present age be x years. Then, (36 - x) = x
2x = 36.
x = 18.
Son's age 5 years back (18 - 5) = 13 years.
answer :A
Answer: (A) 13
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
(A) 20:15:15
(B) 20:15:10
(C) 20:15:12
(D) 20:15:11
(E) 20:15:13
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12.Answer: C
Answer: (C) 20:15:12
Question: 25 * 25* 25 * 25 * 25 = 5^ ?
(A) 4
(B) 6
(C) 5
(D) 3
(E) 10
Rationale: Solution:
5^2 * 5^2 * 5^2 * 5^2 * 5^2 = 5 ^(2+2+2+2+2) = 5^10
Answer : E
Answer: (E) 10
Question: Three numbers A,B,Care in ratio 1:2:3. Their average is 600. If A is increased by 10% and B is increased by 20%, then to get the average increased by 5%, C will increased by:
(A) 90
(B) 100
(C) 150
(D) 180
(E) 190
Rationale: Let be A= x, B=2x, and C=3x.
(x+2x+3x)/3=600
this will be x=300
so, the numbers will be 300,600,900
new average= 105%of 600= 630
Let 110% of 300+80% of 600 + y= 630*3
solve it for y, you will get, y=1080
so, increase in C= 1080-900 =180 ans
ANSWER:D
Answer: (D) 180
Question: Look at this series: 83, 73, 93, 63, __, 93, 43, ... What number should fill the blank?
(A) 33
(B) 53
(C) 73
(D) 93
(E) 83
Rationale: Explanation: This is a simple subtraction series in which a random number, 93, is interpolated as every third number. In the subtraction series, 10 is subtracted from each number to arrive at the next.
Answer: Option B
Answer: (B) 53
Question: A boy has eight trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 88
(B) 96
(C) 106
(D) 108
(E) 111
Rationale: Explanation:
The boy can select one trouser in eight ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 8 * 12 = 96 ways
B)
Answer: (B) 96
Question: How many numbers from 10 to 31 are exactly divisible by 3?
(A) 13
(B) 15
(C) 16
(D) 7
(E) 18
Rationale: 12, 15, 18, 21, 24, 27, 30.
7 Numbers.
10/3 = 3 and 31/3 = 10 ==> 10 - 3 = 7. Therefore 7 digits
D)
Answer: (D) 7
Question: Kim purchased n items from a catalog for $5 each. Postage and handling charges consisted of $3 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
(A) 8n + 2
(B) 8n + 4
(C) 6n + 2
(D) 6n + 3
(E) 6n + 4
Rationale: its C
n items for $5 each
total price $5n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [3+ (n-1)]
= $ n+2
total cost
5n+n+2 = 6n+2
Answer: (C) 6n + 2
Question: A bag contains 9 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
(A) 8/17
(B) 2/5
(C) 3/5
(D) 11/15
(E) 7/15
Rationale: Drawing two balls of same color from nine green balls can be done in 9C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 9C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 8/17
ANSWER:A
Answer: (A) 8/17
Question: A certain office supply store stocks 2 sizes of self-stick notepads, each in 3 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 6
(B) 8
(C) 16
(D) 24
(E) 32
Rationale: Notepads of the same color = 3 (we have 3 colors). As we have two sizes then total for the same color=3*2=6
Notepads of the different colors = 3C3=1 (we should choose 3 different colors out of 4). As we have two sizes then total for the different color=1*2=2
Total=6+2=8
Answer: B.
Answer: (B) 8
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
(A) 2999
(B) 2787
(C) 2097
(D) 9680
(E) 2886
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}2
= Rs.9680
Answer: D
Answer: (D) 9680
Question: A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 2.6
(B) 8.6
(C) 7.6
(D) 3.6
(E) 1.6
Rationale: Explanation:
40*(48/100) = 19.2 --- 64
? --- 12 => Rs.3.6
Answer: D
Answer: (D) 3.6
Question: 5.005/2.002 =
(A) 2.05
(B) 2.50025
(C) 2.501
(D) 2.5025
(E) 2.5
Rationale: 5.005/2.002 = 5005/2002 = 5(1001)/2(1001) = 5/2 = 2.5
The answer is E.
Answer: (E) 2.5
Question: A merchant marks his goods up by 30% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?
(A) 8%
(B) 10%
(C) 21%
(D) 15%
(E) 4%
Rationale: Let the price be 100.
The price becomes 130 after a 30% markup.
Now a discount of 20% on 130.
Profit=104-100
4%
answer E
Answer: (E) 4%
Question: The average of three consecutive odd numbers is 14 more than one-third of the first of these numbers, what is the last of these numbers?
(A) 17
(B) 19
(C) 15
(D) Data inadequate
(E) None of these
Rationale: Let the three consecutive odd numbers be
x – 2, x, x + 2 respectively.
According to question,
x=x−2/3+14
∴ 3x – x + 2 = 42 ⇒ 2x = 40
∴ x = 20 = an even number, which goes against our supposition.
Answer D
Answer: (D) Data inadequate
Question: Mr. Bhaskar is on tour and he has Rs. 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by Rs. 3. for how many days is Mr. Bhaskar on tour?
(A) 10
(B) 50
(C) 30
(D) 40
(E) 20
Rationale: Suppose Mr. Bhaskar is on tour for x days. Then,
= 360/x - 360/x+4 = 3 <=> 1/x - 1/x+4
= 1/120 x(x+4) =4 x 120 =480
<=>x2 +4x –480 = 0 <=> (x+24) (x-20) = 0
<=> x =20.
Hence Mr. Bhaskar is on tour for 20 days.
Answer is E.
Answer: (E) 20
Question: A bag contains eight white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/8
(B) 16/33
(C) 25/63
(D) 15/33
(E) 5/1
Rationale: Two balls can be picked from twelve balls in 12Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (8 * 4) = 32/66 = 16/33
Answer: B
Answer: (B) 16/33
Question: If all 6 are replaced by 9,the algebric sum of all numbers from 1 to 100 (both inclusive)varies by,
(A) 980
(B) 330
(C) 660
(D) 990
(E) 300
Rationale: 6,16,26,36,46,56,76,86,96 replace by 9 then 3*9=27
60,61,62,63,64,65,66,67,68,69 then increase by 30 i.e, 30*10=300+3
99-66=33-30
It will be 330
ANSWER:B
Answer: (B) 330
Question: A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo
(A) 61
(B) 62
(C) 63
(D) 64
(E) 65
Rationale: 4C1+4C2+4C3+4C4=15.
If their positions also takes into consideration then the ans will be 64
ANSWER:D
Answer: (D) 64
Question: A started a business with Rs.21,000 and is joined afterwards by B with Rs.36,000. After how many months did B join if the profits at the end of the year are divided equally?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Solution
Suppose B joined after x months.
Then,	21000×12=36000×(12 - x)
‹=›36x=180
= x= 5.
Answer C
Answer: (C) 5
Question: When a=3+(2/3) and b=3-(2/3), (2^a^2)/(2^b^2)=?
(A) 256
(B) 156
(C) 250
(D) 150
(E) 125
Rationale: --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=4/3 and a+b=6, 2^(a-b)(a+b)=2^(4/3)(6)=2^8=256
Therefore, the answer is A
Answer: (A) 256
Question: On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is?
(A) 120
(B) 10%
(C) 93%
(D) 84%
(E) None of these
Rationale: Explanation:
Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.
S.I for one year = Rs. 330.
S.I. on Rs. 330 for 1 year = Rs. 36.30
Rate = (100 * 36.30)/(330 * 1) = 11%
Answer: Option E
Answer: (E) None of these
Question: If A,B,C,D,E,F,G,H,I,J are in an increasing Arithmetic Progression as such. Then Which of the following operations will result in either mean or the median being modified.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed
(A) A and B
(B) A and E
(C) A,C,E
(D) All of them
(E) None of them
Rationale: There are 10 equidistant numbers on the number line.
Mean and median will be the average of middle two numbers.
If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers.
Here answer will be (B).
Answer: (B) A and E
Question: It takes David 30 minutes to walk to the car park and 60 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
(A) 7:30 a.m
(B) 5:50 a.m
(C) 7:50 a.m
(D) 6:50 a.m
(E) 9:50 a.m
Rationale: The time it takes David to get to work: time to walk to car park + time to drive
30 + 60 = 90 minutes = 1 hour and 30 minutes
David needs to get out of the house 1 hour and 30 minutes before 9:00 am at
9:00 - 1:30 = 7:30 a.m
correct answer A
Answer: (A) 7:30 a.m
Question: The population of a town increases 25% and 30% respectively in two consecutive years. After the growth the present population of the town is 1950. Then what is the population of the town 2 years ago?
(A) A)800
(B) B)900
(C) C)1000
(D) D)1100
(E) E)1200
Rationale: Explanation:
Formula: (After =100 denominator
Ago = 100 numerator)
1950 * 100/125 * 100/130 = 1200
Answer: Option E
Answer: (E) E)1200