mathewhe/aqua_rat huggingface dataset:
Question: If the average of 1, 2, 4, 5, 6, 9, 9, 10, 12 and x is 7, what is the value of x?
(A) 7
(B) 9
(C) 11
(D) 12
(E) 13
Rationale: Sum of the deviations of the numbers in the set from the mean is always zero
1, 2, 4, 5, 6, 9, 9, 10, 12
mean is 7
so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 7 + 5 = 12
D
Answer: (D) 12
Question: A boat takes 38 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?
(A) 240 km
(B) 120 km
(C) 360 km
(D) 180 km
(E) None of these
Rationale: Explanation :
velocity of the stream = 4 kmph
Speed of the boat in still water is 14 kmph
Speed downstream = (14+4) = 18 kmph
Speed upstream = (14-4) = 10 kmph
Let the distance between A and B be x km
Time taken to travel downstream from A to B + Time taken to travel upstream from B to C(mid of A and B) = 38 hours
⇒x/18+(x/2)10=38
⇒x/18+x/20=38
⇒19x/180=38
⇒x/180=2
⇒ x = 360
i.e., the distance between A and B = 360 km. Answer : Option C
Answer: (C) 360 km
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 7
(B) 4
(C) 12
(D) 19
(E) 28
Rationale: Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).
Answer: D
Answer: (D) 19
Question: a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a - b'?
(A) 28
(B) 29
(C) 34
(D) 38
(E) 36
Rationale: possible values of a and b can be 5,4; 4,5 and 1,20; 20,1
maximum possible value for a-b is 20-1=19
minimum possible value for a-b is 1-20=-19
19-(-19)=38 ans is D
Answer: (D) 38
Question: Three candidates contested in an election and received 1136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
(A) 45%
(B) 49%
(C) 57%
(D) 51%
(E) 62%
Rationale: Total number of votes polled = 1136+7636+11628 = 20400
Required percentage = 11628*100/20400 = 57%
Answer is C
Answer: (C) 57%
Question: If 50% of (x-y) = 20% of (x+y), then what percent of x is y?
(A) 50.5%
(B) 42.8%
(C) 22.2%
(D) 33.3%
(E) 25%
Rationale: 50% of (x-y) = 20% of (x+y)
50/100 (x-y) = 20/100 (x+y)
3x = 7y
Required percentage = y/x *100 = 3y/7y * 100 = 42.85%
Answer is B
Answer: (B) 42.8%
Question: A departmental store charges the commission of 15 percent on the first sale of items worth $50,000 and then an additional 12 percent on any sale price that exceeds the initial $50,000. If the department store earned $24,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?
(A)  $215,000
(B)  $365,000
(C)  $115,000
(D)  $240,000
(E)  $187,500
Rationale: 24,000 = 0.15 *(50000) + 0.12 (x - 50000)
24000 - 7500 = 0.12 (x-50000)
137500 = x - 50000
x = 1,87,500
Answer : E
Answer: (E)  $187,500
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number R?
(A) 126
(B) 1386
(C) 3108
(D) 308
(E) 13986
Rationale: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.
So,Total possible numbers with these digits=3 X 3 X 3 =27.
First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D
Second, If you imagine numbers R with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.
You are left withanswer E.
Answer: (E) 13986
Question: In how many years, Rs. 300 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?
(A) 4 years
(B) 6 years
(C) 8 years
(D) 9 years
(E) 12 years
Rationale: Explanation :
Let Simple Interest for Rs.300 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years
300×6×n/100=800×9/2×2/100
300×6×n=800×9/2×2
300×6×n=800×9
n=4 years
Answer : Option A
Answer: (A) 4 years
Question: What is the units digit of 32! + 50! + 2! + 4!?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: For all N greater than 4, the units digit of N! is 0.
The sum of the four units digits is 0 + 0 + 2 + 4 = 6
The units digit is 6.
The answer is D.
Answer: (D) 6
Question: Sharmila works 10 hours per day on Monday, Wednesday and Friday, and 8 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $460 per week. How much does she earn in dollars per hour?
(A) 8
(B) 9
(C) 9.5
(D) 10
(E) 11
Rationale: So, she works 30 hours in 3 days
So, she works 16 hours in 2 days
So in a week she works 46 hours ( 30 + 16 ) and earns $460
So, Hourly wage is 460/46 => 10
Hence answer will be (D) 10
Answer: (D) 10
Question: If (4 - x)/(5 + x) = x, what is the value of x^2 + 6x - 4?
(A) -3
(B) 0
(C) 2
(D) 4
(E) 6
Rationale: (4-x) = x*(5+x)
(4-x) = 5x+x^2
0 = x^2+6x-4
The answer is B.
Answer: (B) 0
Question: A whale goes on a feeding frenzy that lasts for 12 hours. For the first hour he catches and eats 30 kilos of plankton. In every hour after the first, it consumes 2 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 600 kilos of plankton, how many kilos did he consume on the 10th hour?
(A) 36
(B) 45
(C) 28
(D) 48
(E) 52
Rationale: Therefor in 10th hour he consume x+2*9=30+18=48
correct option is D
Answer: (D) 48
Question: From a class consisting of 12 computer science majors, 10 mathematics majors, and 9 statistics majors, a committee of 4 computer science majors, 4 mathematics majors, and 3 statistics majors is to be formed. How many distinct committees are there?
(A) 15200
(B) 16200
(C) 17200
(D) 18000
(E) 19500
Rationale: From a class consisting of 12 computer science majors, 10 mathematics majors, and 9 statistics majors, a committee of 4 computer science majors, 4 mathematics majors, and 3 statistics majors is to be formed. How many distinct committees are there?
Alright, I just started learning combinations tonight, but I have hit a wall. I ran across this problem but cannot get the answer right. Apparently, the answer is 8-some-thousand, but I keep coming up with 16,200. This is how I am working it.
12!/4!(12-4)! * 10!/4!(10-4)! * 9!/3!(9-3!)
(12*...*1/4*...*1*8*...1) * (10*...*1/4*...1*6...*1) * (9*...1/3*2*1*6*...1)
(12*10*9/4*3*2*1) * (10*9*8*7/4*3*2*1) * (9*8*7/3*2*1)
(3*5*3/1*1*1) * (5*3*7/1*1*1) * (3*4*7/1*1*1)
45 * 30 * 12
Answer: 16,200 B
Answer: (B) 16200
Question: A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
(A) $18,400
(B) $19,700
(C) $20,200
(D) $20,400
(E) $21,100
Rationale: Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 1000
Net price of the car in 02 = 18700 + 1000 = $19700
Correct Option: B
Answer: (B) $19,700
Question: Four hundred multiples of seven are chosen at random, and 100 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?
(A) 30%
(B) 50%
(C) 60%
(D) 55%
(E) 40%
Rationale: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....
Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.
So approx. 50 % of the 400 multiples are odd i.e 200 multiples.
--> Similalrly, for 8 multiples are:8,16,24...
All are even so 0 % are odd.
Total odd= (200+0)/(400+100)= 200/500=(2/5) = 40%
Answer E
Answer: (E) 40%
Question: What is the area M of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?
(A) 60.
(B) 85.
(C) 125.
(D) 225.
(E) It cannot be determined from the information given
Rationale: Length of one side= 15 (20-5)
Since, its a square, the area will be M= 15^2= 225
D is the answer
Answer: (D) 225.
Question: The speed of a car is 120 km in the first hour and 70 km in the second hour. What is the average speed of the car?
(A) 72 kmph
(B) 75 kmph
(C) 95 kmph
(D) 80 kmph
(E) 82 kmph
Rationale: S = (120 + 70)/2
= 95 kmph
ANSWER:C
Answer: (C) 95 kmph
Question: An air conditioner can coo the hall in 12 minutes while another takes 15 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
(A) about 7 minutes
(B) about 8 minutes
(C) about 9 minutes
(D) about 10 minutes
(E) about 5 minutes
Rationale: Take LCM of 12 and 15 = 60
12*5=60/ 15*4=60.
So if both are switched on together , room cooled in 60/(5+4)=60/9=6.66 minutes
6.66 can be round to 7 minutes , so about 7 minutes
ANSWER: A
Answer: (A) about 7 minutes
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/71%
(B) 18 2/11%
(C) 18 2/15%
(D) 18 2/19%
(E) 18 2/21%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: (B) 18 2/11%
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
(A) 2800
(B) 2500
(C) 3000
(D) 3500
(E) 4000
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 â€“ 5x/100 = 144
2x/100 = 56 Ã¨ x = 2800
ANSWER A
Answer: (A) 2800
Question: John deposited $10,000 to open a new savings account that earned 6 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?
(A) $10,100.30
(B) $10,101.50
(C) $10,200.75
(D) $10,302.25
(E) $10,400.25
Rationale: 6 percent annual interest compounded quarterly --> 1.5% in 3 moths.
For the first 3 moths interest was 1.5% of $10,000, so $150;
For the next 3 moths interest was 1.5% of $10,000,plus2.25 earned on previous interest of $150, so $150+$2.25=$152.25;
Total interest for 6 months was $150+$152.25=$302.25, hence balance after 6 months was $10,000+ $302.25=$10,302.25.
Answer: D.
Answer: (D) $10,302.25
Question: 90kg of an alloy A is mixed with 140 kg of alloy B. If alloy A has lead and tin in the ratio 3:4 and alloy B has tin and copper in the ratio 2:5, then the amount of tin in the new alloy is?
(A) 100.6kg
(B) 95.4kg
(C) 117.5kg
(D) 91.4kg
(E) 92kg
Rationale: Quantity of tin in 90kg of A = 90*4/7 = 51.4kg
Quantity of tin in 140kg of B = 140*2/7 = 40kg
Quantity of tin in the new alloy = 51.4+40 = 91.4kg
Answer is D
Answer: (D) 91.4kg
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.)
(A)  1
(B)  4
(C)  5
(D)  11
(E)  10
Rationale: We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 3 ingredients...
3 ingredient blends:
ABC
ABD
ACD
BCD
4 ingredient blends:
ABCD
Total blends =4+1 = 5
C
Answer: (C)  5
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of four consecutive even integers starting with 10, respectively, what is the probability that b/a will not be an integer?
(A) 3/16
(B) 1/4
(C) 5/16
(D) 3/8
(E) 1/2
Rationale: a is from the following set {1,2,3,4}
b is from the following set {10,12,14,16}
The total number of ways of choosing 2 integers, one from each set is 4*4 = 16 ways.
The possibilities where b/a is not an integer is for the following outcomes:
{b,a} = {10,3},{10,4},{14,3},{14,4},{16,3} = 5 ways
Thus the probability is 5/16
The answer is C.
Answer: (C) 5/16
Question: Lastly, jenny compared Canada’s CN Tower and Seattle’s Space
Needle. How tall is the Space Needle if the CN Tower stands at 553m
high and it is taller than the Space Needle by 369m?
(A) 127
(B) 184
(C) 170
(D) 113
(E) 099
Rationale: 553-369=184.Answer is B.
Answer: (B) 184
Question: A student chose a number, multiplied it by 6, then subtracted 250 from the result and got 122. What was the number he chose?
(A) 59
(B) 60
(C) 61
(D) 62
(E) 63
Rationale: Let x be the number he chose, then
6⋅x−250=122
6x=372
x=62
correct answer D
Answer: (D) 62
Question: Min (a, b, c)=min of a, b, c Max (a, b, c,)=max of a, b, c then what is the value of MAX {min (2,5,7), max (-7, -2, -3), 3}
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: MAX {min (2,5,7), max (-7, -2, -3), 3}
= MAX {2,-2,3}
=3
ANSWER:C
Answer: (C) 3
Question: A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
(A) 12
(B) 15
(C) 10
(D) 48
(E) 17
Rationale: Two students can be selected from 6 in 6C2 =15 ways.
Therefore, the teacher goes to the zoo 15 times.
Ans: B
Answer: (B) 15
Question: If x and y are positive integers such that x/y = 2.60, which of the following numbers could be y?
(A) 3
(B) 4
(C) 6
(D) 5
(E) 10
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 = 2.60 and because it's in the hundreds decimal place, put the given value (x/y = 2.60/1) and multiply it by 100.
Take the resulting fraction (x/y = 260/100) and reduce it to it's lowest form.
Both of the numbers are divisible by 20.
The result is x/y = 13/5.
Thus y = 5.
The correct answer is D.
Answer: (D) 5
Question: Initially two cups of same volume are present with milk filled upto 3/5th and 4/5th of their volumes.Water is then filled. Then two mixtures are mixed. Find the ratio of water to milk in the mixture
(A) 1/7
(B) 2/7
(C) 3/7
(D) 4/7
(E) 5/7
Rationale: water content can b in 1st and second is 2/5 and1/5 total:3/5.the total milk content is 7/5.the ratio is ((3/5)/(7/5))=3/7.
ANSWER:C
Answer: (C) 3/7
Question: What smallest number should be added to 8444 such that the sum is completely divisible by 7 ?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: Explanation:
8444 ÷ 7 = 1206, remainder = 2
7 - 2 = 5
Hence, 5 should be added to 8444 such that the sum is completely divisible by 7.
Answer: B
Answer: (B) 5
Question: The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
(A) 13.5
(B) 14
(C) 15
(D) 12.5
(E) None
Rationale: Solution:
At present the total age of the family = 5*20 =100.
The total age of the family at the time of the birth of the youngest member,
=[100−10−(10*4)]=50.
Therefore, average age of the family at the time of birth of the youngest member,
= 50/4 = 12.5.
Answer: Option D
Answer: (D) 12.5
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 27 seconds. What is the length of each train (in meters)?
(A) 50.5
(B) 88.5
(C) 37.5
(D) 55.5
(E) 23.5
Rationale: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 27 seconds, the relative difference in distance traveled is 27 * 25/9 = 75 meters
This distance is twice the length of each train.
The length of each train is 75/2 = 37.5 meters
The answer is C.
Answer: (C) 37.5
Question: 180 metres long yard, 11 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 18
(B) 12
(C) 14
(D) 16
(E) 17
Rationale: 11 trees have 10 gaps between them,
Required distance (180/10) = 18
A
Answer: (A) 18
Question: If x and y are integers such that x^2+4x+2y+6=2x^2+5x+y-6, we can deduce that y is
(A) not an even
(B) an even
(C) a perfect square
(D) an odd
(E) a prime
Rationale: x^2 + 4x + 2y + 6 = 2x^2 + 5x + y - 6
y = x^2 + x - 12
y = (x+4)(x-3) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B.
Answer: (B) an even
Question: A, B and C can do a work in 7 , 14 and 21 days respectively. They completed the work and got Rs.242. What is the share of C?
(A) 33
(B) 44
(C) 55
(D) 77
(E) 99
Rationale: The ratio of their working rates = 1/7 : 1/14 : 1/21 = 6 : 3 : 2.
Since, they work together, the share of C
= 2/11 * 242 = Rs.44
\Answer: B
Answer: (B) 44
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is q, what is the difference between the probability that q is even and the probability that q is odd?
(A)  1/9
(B)  1/6
(C)  2/9
(D)  1/4
(E)  1/2
Rationale: Age of Boys q:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11)(13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Answer: (A)  1/9
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 180,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?
(A) 77,500
(B) 1,860,000
(C) 2,880,000
(D) 3,720,000
(E) 4,960,000
Rationale: 180,000 × 2 × 2×2×2 = 180,000 × 16 = C
Answer: (C) 2,880,000
Question: Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.60 at the candy store. What is this student’s weekly allowance?
(A) $2.25
(B) $2.75
(C) $3.00
(D) $3.50
(E) $3.75
Rationale: Let x be the value of the weekly allowance.
(2/3)(2/5)x = 60 cents
(4/15)x = 60
x = $2.25
The answer is A.
Answer: (A) $2.25
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 5
(B) 4
(C) 7
(D) 9
(E) None of these
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = 954×60954×60 = 10 min.
Option(E) is correct
Answer: (E) None of these
Question: Four bells commence tolling together and toll at intervals of 2, 3, 4 and 5 seconds respectively. In 10 minutes, how many times do they toll together ?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: LCM of 2, 3, 4, and 5 is 60.
So, after each 60 seconds, they would toll together.
Hence, in 10 minutes, they would toll 10*60 seconds / 60 seconds = 10 times
But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second).
So, total tolls together = 10+1 = 11
Answer: B
Answer: (B) 11
Question: If 125% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 20% of m is equal to what percent of 100% of j ?
(A) 0.35
(B) 3.5
(C) 35
(D) 350
(E) 700
Rationale: IMO answer should be 350...
consider j=10, then k=50, l=150 and m=350....
20% of 350, comes out to be 70....
100% of 10 is 10....
(70*100)/10=700....
Ans : E
Answer: (E) 700
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 120 metres?
(A) 22 seconds
(B) 65 seconds
(C) 24 seconds
(D) 12 seconds
(E) 21 seconds
Rationale: Speed of the boat downstream
= 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 120/5 = 24 seconds.
Answer:C
Answer: (C) 24 seconds
Question: A straight pipe 6 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, 4-3=1=1/3 meters long pieces.
Answer: B.
Answer: (B)  1/4 and 1/3 only
Question: The average height of 20 students is 20 cm and the average height of 11 students is 20 cm . What is the average height of the 31 students?
(A) 40 cm
(B) 20 cm
(C) 30 cm
(D) 25 cm
(E) 35 cm
Rationale: The total height of the 31 students =(20 * 20) + (11 * 20) = 400 + 220 = 620 cm The required average height =620/31 = 20 cm Answer :B
Answer: (B) 20 cm
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 187 m
(B) 287 m
(C) 279 m
(D) 270 m
(E) 197 m
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: (D) 270 m
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) Rs.10000
(B) Rs.12800
(C) Rs.6000
(D) Rs.8000
(E) Rs.9000
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
ANSWER:B
Answer: (B) Rs.12800
Question: What is K's position with respect to P?
(A) Fifth to the LEFT
(B) 7
(C) Fifth to the right
(D) 8
(E) 72
Rationale: Answer: Option C
Answer: (C) Fifth to the right
Question: IF A'S INCOME IS 25%LESS THAN B'S.BY WHAT % B'S INCOME IS GREATER THAN A?
(A) 11
(B) 12
(C) 33
(D) 15
(E) 36
Rationale: If B 's income is rs 100,
A's income = Rs 75
% B'S INCOME IS GREATER THAN A = 100*25/75= 33.33 %
ANSWER:C
Answer: (C) 33
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 27 liters
(B) 18 liters
(C) 10 liters
(D) 11 liters
(E) 14 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
Answer:C
Answer: (C) 10 liters
Question: The area of a triangle is with base 4m and height 5m?
(A) 11 m2
(B) 10 m2
(C) 54 m2
(D) 86 m2
(E) 42 m2
Rationale: 1/2 * 4 * 5
= 10 m2
Answer:B
Answer: (B) 10 m2
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (5/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
(A)  3/8
(B)  1/2
(C)  9/16
(D)  5/7
(E)  3/4
Rationale: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 5/8*c:
(b+c)/2 = (5/8)*c
b = (1/4)*c
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (1/4*c)/2 = (1/8)*c
Median = (a + c)/2 = (1/8*c + c)/2 = (9/8)*c/2 = (9/16)*c (ANSWER C)
Answer: (C)  9/16