mathewhe/aqua_rat huggingface dataset:
Question: A man can row 7.5 km/hour in still water & he finds that it takes him twice aslong to row up as to row down the river. Find the rate of stream?
(A) 2 km/hr
(B) 2.5 km/hr
(C) 3 km/hr
(D) 4 km/hr
(E) 4.3 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream =x
Then speed downstream =2x
we have, 12(x+2x) = speed in still water
⇒12(3x)=7.5⇒3x=15⇒x=5
i.e., speed upstream = 5 km/hr
Rate of stream =12(2x−x)=x2=52=2.5 km/hr
B
Answer: (B) 2.5 km/hr
Question: A bag contains 6 black and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 3/4
(B) 1/3
(C) 1/7
(D) 1/8
(E) 4/3
Rationale: Let number of balls = (6 + 3) = 9.
Number of white balls = 3.
P (drawing a white ball) =3/9=1/3.
Option B.
Answer: (B) 1/3
Question: If a chair was sold for $ 990 at a loss of $ 110. Find the cost price of the chair.
(A) $ 1000
(B) $ 1100
(C) $ 1200
(D) $ 1300
(E) $ 1400
Rationale: Selling Price = $ 990,
Loss = $ 110
Cost Price = Selling Price + Loss
Cost Price = 990 + 110
= $ 1100
Therefore, cost price of the chair = $ 1100
Answers: B
Answer: (B) $ 1100
Question: a, b, c and d are four consecutive numbers. If the sum of a and dis 111, what is the product of b and c?
(A) 2652
(B) 2578
(C) 2534
(D) 3080
(E) 4234
Rationale: Here d = a + 3
a + a + 3 = 111
2a = 108
a = 54
So, numbers are 54, 55, 56 and 57
∴ b × c= 55 × 56 = 3080
D
Answer: (D) 3080
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) 22277
(B) 26782
(C) 22882
(D) 15000
(E) 28761
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000
= Rs.15000
Answer: D
Answer: (D) 15000
Question: It costs $18 for the first 1/2 hour to rent a bike. After the first 1/2 hour it costs $10 per hour. If a certain customer uses the bike for 2 hours, how much will it cost him?
(A) $12
(B) $45
(C) $33
(D) $95
(E) $30
Rationale: 2 hours = 120 minutes
First 30 min ------> $18
Time left is 90 min...
Now, 60 min costs $ 10
1 min costs $ 10/60
90 min costs $ 10/60*90 => $ 15
So, Total cost will be $15 + $18 => $ 33
The answer will be (C) $ 33
Answer: (C) $33
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35,x
(A) 23
(B) 26
(C) 38
(D) 35
(E) 45
Rationale: (C)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 35 + 3 = 38.
Answer: (C) 38
Question: In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
(A) 10
(B) 11
(C) 8
(D) 9
(E) 12
Rationale: Let the number of papers be x. Then,
63x + 20 + 2 = 65x
= 2x = 22
= x = 11.
ANSWER B
Answer: (B) 11
Question: A basketball player succeeds with 40% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
(A) 0.343
(B) 0.472
(C) 0.555
(D) 0.657
(E) 0.784
Rationale: P(missing all 3 free throws) = 0.6^3 = 0.216
P(succeeding at least once) = 1 - 0.216 = 0.784
The answer is E.
Answer: (E) 0.784
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 5
(B) 6
(C) 8
(D) 4
(E) 1
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: (C) 8
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Y of races we need to conduct to get the top 3 fastest horses?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: Y=7 is the correct answer.
Good solution Buneul.B
Answer: (B) 7
Question: A, B, C subscribe Rs. 50000/- for a business. A subscribes Rs. 4000/- more than B and B Rs. 5000/- more than C. out of a total profit of Rs. 35,000/- A receives:
(A) Rs. 8400/-
(B) Rs. 11900/-
(C) Rs. 13600/-
(D) Rs. 14700/-
(E) None of these
Rationale: Explanation:
Let the investments of C, B and A be Rs. X,
Rs. (x + 5000) and (x + 9000) = 50000
3x = 36000
X = 12000
C = Rs. 12000/- , B = Rs. 17000/- and A = Rs. 21000/-
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
A’s share = Rs. (35000 * 21/50) = Rs. 14700/-
Answer: Option D
Answer: (D) Rs. 14700/-
Question: Which of the following values is the greatest
(A) a) 11% of 89
(B) b) 22% of 78
(C) c) 33% of 67
(D) d) 65% of 45
(E) e) 44% of 56
Rationale: Are you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says D.
Answer: (D) d) 65% of 45
Question: The average age of 22 students in a group is 12 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
(A) 31
(B) 36
(C) 35
(D) 53
(E) 57
Rationale: age of the teacher=(23*13-22*12)
=35 years.
ANSWER:C
Answer: (C) 35
Question: Raju age after 4 years will be 10 times his age 5 years back, What is the present age of Raju
(A) 9 years
(B) 10 years
(C) 7 years
(D) 6 years
(E) 8 years
Rationale: Explanation:
Clearly,
x+4= 10(x-5)
<=> 9x = 54 => x = 6
Option D
Answer: (D) 6 years
Question: If n divided by 8 has a remainder of 1, what is the remainder when 3 times n is divided by 8?
(A) 1
(B) 3
(C) 7
(D) 5
(E) 6
Rationale: As per question => N=8P+1 for some integer p
hence 3N => 24Q + 3 => remainder => 3 for some integer Q
hence B
Answer: (B) 3
Question: Set J consists of 18 consecutive even numbers. If the smallest term in the set is -22, what is the range of the positive integers in set J?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Since there are only 18 integers, another approach is the just list all 18.
We get:-22, -20, -18, -16, -14,-12,-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12
Range of POSITIVE INTEGERS =12 - 2= 10
Answer: E
Answer: (E) 10
Question: Certain number of worms are placed in a container. The number of worms increases by three times every day and the container is completely filled with worms in 12 days. On what day, the worms were
1/3rd of the container ?
(A) 9 days
(B) 3 days
(C) 4 days
(D) 11 days
(E) 14 days
Rationale: As every day the worms increases by 3 times
1/3 × 3 = 1 [full]
Therefore on 11th day
Option D
Answer: (D) 11 days
Question: Which of the following is always true?
(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
(A) I and III
(B) I, II and III
(C) II
(D) I and II
(E) None
Rationale: he average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(-10+-9+-8+-7+-6)/5 = -40/5 = -8 same as (-10+-6)/2 = -8 True
The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(2+3+4+5)/4 = 14/4 same as (5+2)/2 = 7/2 always true
(1+2+3+4)/4 = 10/4 same as (4+1)/2 = 5/2
The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
(3+4+5+6+7)/5 = 5 same as (7+3)/2 = 5 True
ANSWER:B
Answer: (B) I, II and III
Question: A can do a work in 20 days and B can do it in 8 days. In how many days A and B can do the work?
(A) 5 5/7 days
(B) 10 days
(C) 6 days
(D) 8 days
(E) 7 days
Rationale: Explanation:
A's 1day's work = 1/20
B's 1day's work = 1/8
They work together = 1/20 + 1/8 = 7/40 = 40/7 = 5 5/7days
Answer: Option A
Answer: (A) 5 5/7 days
Question: A man counted his animals, 80 heads and 260 legs (ducks and goats). how many goats are there?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=260 and divide 2d+4g=260 by 2 we get d+2g=130 -----------> eq2
subtract eq1 from eq2
we get no of goats=50
ANSWER:C
Answer: (C) 50
Question: Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is
(A) 1/36
(B) 3/36
(C) 11/36
(D) 20/36
(E) 23/36
Rationale: 1. The probability of getting an even number at the first die is 1/2 (as the probability of even = the probability of odd = 1/2);
2. The probability of getting a total of 8 is 5/6^2, as there are 5 different favorable scenarios: (2,6), (6,2), (3,5), (5,3) and (4,4);
3. The probability of getting an even number at the first die AND a total of 8 is 3/6^2 (from above case);
Hence, The probability of getting an even number at the first die OR a total of 8 is 1/2+5/36-3/36=20/36.
Answer: D
Answer: (D) 20/36
Question: In a certain pond, 60 fish were caught, tagged, and returned to the pond. A few days later, 60 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
(A) 400
(B) 625
(C) 1818
(D) 2500
(E) 10 000
Rationale: The percent of tagged fish in the second catch is 2/60*100 = 3.33%.
We are told that 3.33% approximates the percent of tagged fish in the pond. Since there are 60 tagged fish, then we have 0.033x = 60 --> x = 1,818.
Answer: C.
Answer: (C) 1818
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 10 a.m. and travels towards B at 100 km/hr. Another starts from B at 11 a.m. and travels towards A at 150 km/hr. At what time do they meet?
(A) 11am.
(B) 12p.m.
(C) 3pm.
(D) 2p.m.
(E) 1p.m.
Rationale: Suppose they meet x hrs after 10 a.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 10+5 = 3 p.m.
Answer is C
Answer: (C) 3pm.
Question: Find the sum of first 70 odd numbers
(A) 4900
(B) 4970
(C) 4990
(D) 4980
(E) 4960
Rationale: Explanation:
n2 = 702 = 4900
Answer: Option A
Answer: (A) 4900
Question: (39,897)(0.0096)/198.76 is approximately
(A) 0.02
(B) 0.2
(C) 2
(D) 20
(E) 200
Rationale: 39,897 can be written as 40,000 (approximately)
0.0096 can be written as 0.01 (approximately
198.76 can be written as 200 (approximately)
40,000*0.01/ 200= 2 (approximately)
C is the answer
Answer: (C) 2
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 8^a and y = 7^b, which of the following is a possible units digit of xy?
(A) 1, 4
(B) 4, 1, 2
(C) 5, 8
(D) 2, 4, 6 and 8
(E) 8, 6
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=8
a=2; X=64
a=3; X=512
a=4; X=2048........ Units digit repeat in a cycle of 8,4,2,8......
Similarly, Finding all values ofYfor positive values ofb
When,
b=1; Y=7
b=2; Y= 49
b=3; Y= 343
b=4; Y=2041
b=5; Y=16807....... Units digit repeat in cycle of 7,9,3,1,7,9,3....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=8 and Y=7: Units digit of XY = 56
When X=8 and Y=9: Units digit of XY = 72
When X=8 and Y=3: Units digit of XY = 24
When X=4 and Y=7: Units digit of XY = 28
When X=4 and Y=9: Units digit of XY = 36
When X=4 and Y=3: Units digit of XY = 12
When X=2 and Y=7: Units digit of XY = 14
When X=2 and Y=9: Units digit of XY = 18
When X=2 and Y=3: Units digit of XY = 6
Only four possibilities for Units digit of XY i.e. 2, 4, 6 and 8
therefore answer is D
Answer: (D) 2, 4, 6 and 8
Question: In a consumer survey, 82% of those surveyed liked at least one of three products: 1, 2, and 3. 45% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 4% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
Rationale: 45 + 30 + 20 = 95
The number 95 includes some people counted twice and some people counted three times.
95 - 82 = 13, and this number represents people counted twice or three times.
4% of the people are counted two extra times.
The percentage of people counted one extra time is 13 - 4(2) = 5.
The percentage of people who liked more than one product is 4% + 5% = 9%.
The answer is A.
Answer: (A) 9
Question: How many words can be formed by using all the letters of the word, 'ALLAHABAD' ?
(A) 3780
(B) 1890
(C) 7560
(D) 2520
(E) 5420
Rationale: The word 'ALLAHABAD' contains 9 letters, namely 4A, 2L, 1H, 1B and 1D.
Requisite number of words =9!/(4!)(2!)(1!)(1!)(1!) =7560
Answer is C
Answer: (C) 7560
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x
(A) 2546
(B) 2753
(C) 2864
(D) 2975
(E) 3158
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
E
Answer: (E) 3158
Question: Kavi had a stock of 600 bags in his bookshop. He sold 25 on Monday, 70 on Tuesday, 100 on Wednesday, 110 on Thursday and 145 on Friday. What percentage of the bags were not sold?
(A) 10%
(B) 25%
(C) 64%
(D) 42%
(E) 17%
Rationale: Let N be the total number of bags sold. Hence
N = 25 + 70 + 100 +110 + 145 = 450
Let M be the bags NOT sold
M = 600 - N = 600 - 450 = 150
Percentage
Bags not sold / total number of bags = 150/600= 0.25 = 25%
correct answer B
Answer: (B) 25%
Question: Mr. Karthik drives to work at an average speed of 48 km/hr. Time taken to cover the first 60% of the distance is 20 minutes more than the time taken to cover the remaining distance. Then how far is his office ?
(A) 23
(B) 98
(C) 28
(D) 80
(E) 19
Rationale: Explanation:
Let the total distance be 'x' km.
Time taken to cover remaining 40% of x distance is
But given time taken to cover first 60% of x distance is
\Rightarrow
\small \Rightarrow x=80 km.
Answer: D
Answer: (D) 80
Question: The number of arrangements that can be made with the letters of the word PETER so that the vowels occupy the even places?
(A) 14
(B) 18
(C) 12
(D) 15
(E) 11
Rationale: The word PETER has 5 letters of which 2 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways.
Hence the total ways are 6 * 2 = 18.
Answer:B
Answer: (B) 18
Question: What is the sum of the different positive prime factors of 720?
(A) 5
(B) 10
(C) 15
(D) 17
(E) 21
Rationale: Prime factorization of 720
=72 * 10
=6*12 * 10
=2*3 * 2*6 * 2*5
=2*3 * 2 * 2*3 * 2*5
=2^4 * 3^2 * 5
Sum of the different positive prime factors of 720 = 2+3+5
=10
Answer B
Answer: (B) 10
Question: If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?
(A) 29
(B) 30
(C) 31
(D) 32
(E) 33
Rationale: A two-digit number "cd" can be expressed algebraically as 10c+d.
The sum of A + B = (10c+d)+(10d+c)=11(c+d).
The only answer that is a multiple of 11 is 33.
The answer is E.
Answer: (E) 33
Question: College T has 1000 students. Of the 250 students majoring in one or more of the sciences,140 are majoring in Chemistry and 170 are majoring in Biology. If at least 50 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
(A) 110 to 150
(B) 110 to 140
(C) 110 to 130
(D) 120
(E) 130
Rationale: Total = Chemistry + Biology - Both + Neither
250 = 140 + 170 - Both + N
We know that N (Neither) must be at least 30, so set N=30 and solve:
250 = 140 + 170 - Both + 50
250 = 360 - Both
Both = 110
Even if you're not sure whether 110 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range,
Both can not be greater than 140, because even if every chemistry major was also a biology major, there are only 140 chemistry majors total. B the solution.
Answer: (B) 110 to 140
Question: A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 8 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
(A) 11:30am
(B) 10:30am
(C) 9:30am
(D) 8:30am
(E) 7:30am
Rationale: In 8 hours the inlet pipe will pump in water equal to 8*1/5 = 8/5 of the pool. So, 3/5 more than necessary, which should be compensated by the outlet pipe. To pump out 3/5 of the water the outlet pipe needs 30/5 = 6 hours.
Therefore, the outlet pipe should be opened at 9:30am + 8 hours - 6 hours = 11:30am.
Answer: A
Answer: (A) 11:30am
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
(A) 4/5 km
(B) 2/3 km
(C) 8/2 km
(D) 1/3 km
(E) 9/6 km
Rationale: x/3 – x/4 = 4/60
x = 4/5 km
Answer:A
Answer: (A) 4/5 km
Question: Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
(A)  0
(B)  25
(C)  49
(D)  81
(E)  100
Rationale: 144 =12 *12
(1!)^3=1
2!=2, therefore (2!)^3=2*2*2=8
3!=6, therefore (3!)^3=6*6*6=216
4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144
thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0
now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144
now remainder when 225 is divided by 144 is 81. hence answer should be D
Answer: (D)  81
Question: Alex deposited x dollars into a new account that earned 9 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
(A) w/(1+1.08)
(B) w/(1.08+1.16)
(C) w/(1.16+1.24)
(D) w/(1.09+1.09^2)
(E) w/(1.08^2+1.08^2)
Rationale: Account at the end of the first year would be 1.09x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.09x+x) dollars. Account at the end of the second year would be (1.09x+x)*1.09=w --> x(1.09^2+1.09)=w --> x=w/(1.09+1.09^2).
Answer: D.
Answer: (D) w/(1.09+1.09^2)
Question: The diagonals of the two squares are in the ratio of 2:5 find the ratio of their area .
(A) 5:89
(B) 7:96
(C) 4:25
(D) 5:84
(E) 8:96
Rationale: Let the diagonals of the square be 2x and 5x respectively .
ratio of their areas =1/2(2x)^2:1/2(5x)
= 4x^2:25x^2=4:25
Answer(C)
Answer: (C) 4:25
Question: A worker's daily wage is increased by 50% and the new wage is $30 per day. What was the worker's daily wage before the increase?
(A) $15
(B) $18
(C) $20
(D) $22
(E) $25
Rationale: Let x be the daily wage before the increase.
1.5x = $30
x = $20
The answer is C.
Answer: (C) $20
Question: If six persons sit in a row, then the probability that three particular persons are always together is ?
(A) 1/3
(B) 1/9
(C) 1/5
(D) 1/7
(E) 1/1
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer:C
Answer: (C) 1/5
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 2% per first year and 3% for the second year?
(A) 3377
(B) 2678
(C) 5460
(D) 1976
(E) 5253
Rationale: 5000 * 102/100 * 103/100 => 5253
Answer: E
Answer: (E) 5253
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 84 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
(A)  16%
(B)  32%
(C)  48%
(D)  84%
(E)  92%
Rationale: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.
So, if 84% is one st.Dev, then on either side of m we have 84/2 =42%. So, 84% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 42 = 92% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 92% of the values are below m + d.
Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it
E
Answer: (E)  92%
Question: A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 355 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
(A)  90
(B)  115
(C)  120
(D)  130
(E)  220
Rationale: Orchestra Seats - a
Balcony Seats - b
a+b = 355
and 12a + 8b = 3320
Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)
4a = 3320 - 8*355 = 3320 - 2840 = 480
i.e. a = 120
and b = 355-120 = 235
More seats in balcony than orchestra = b-a = 235 - 120 = 115
Answer: option B
Answer: (B)  115
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
(A) 2997
(B) 1900
(C) 2887
(D) 2898
(E) 27912
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900.Answer: B
Answer: (B) 1900
Question: he population of a city is 120,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
(A) 137787
(B) 134832
(C) 139776
(D) 139728
(E) 139718
Rationale: Population after n years = P [1 + (R/100)]2
Population after 2 years = 120000 * [1 + 6/100]2 = (120000 x 53/50 x 53/50) = 134832
ANSWER: B
Answer: (B) 134832
Question: The largest 4 digit number exactly divisible by 88 is?
(A) 9934
(B) 9938
(C) 9940
(D) 9942
(E) 9944
Rationale: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
E)
Answer: (E) 9944
Question: Three seventh of a number is 12 more than 40% of that number. What will be the 90% of that number?
(A) A)148
(B) B)210
(C) C)189
(D) D)248
(E) E)258
Rationale: 3/7 x – 40/100 x = 12
x = 35 * 12
35 * 12 * 90/100 = 378/2 = 189
ANSWER:C
Answer: (C) C)189
Question: Bob finishes the first half of an exam in one-fifth the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?
(A) 20
(B) 24
(C) 27
(D) 36
(E) 40
Rationale: Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/5's the time of the second half (6/6's), we can see that the hour the entire exam took to finish can be broken down into sixth's. (Another way to look at this problem is via ratio's - first half is 1:6 and the second half is 5:6). With each sixth of an hour being 10 minutes (60/6), the first half of the exam would have taken 20 minutes. Correct answer is A.
Answer: (A) 20