mathewhe/aqua_rat huggingface dataset:
Question: A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
(A) 17
(B) 23
(C) 77
(D) 26
(E) 30
Rationale: Explanation :
Let, the number of apples be 100.
On the first day he sells 60% apples i.e.,60 apples. Remaining apples =40.
He throws 15% of the remaining i.e., 15% of 40 = 6.Now he has 40−6=34 apples
The next day he throws 50% of the remaining 34 apples i.e., 17.
Therefore, in total he throws 6+17= 23 apples.
Answer : B
Answer: (B) 23
Question: Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum?
(A) 30
(B) 45
(C) 50
(D) 25
(E) 60
Rationale: Let capacity of P be x liters
Then capacity of Q = x/3 liters
capacity of the drum = 60x
Required number of turns = 60x/(x+x/3) = 60x * 3/4x = 45
Answer is B
Answer: (B) 45
Question: In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?
(A) 22
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: T = (100 * 16500)/(15 * 5000) = 22 years
ANSWER A
Answer: (A) 22
Question: If x= (y-1)(y+2), then what is the least possible value of x?
(A) -9/4
(B) 9/4
(C) 7/4
(D) 2
(E) 1
Rationale: Answer : A
Answer: (A) -9/4
Question: The area of a triangle is with base 4m and height 5m?
(A) 11
(B) 10
(C) 99
(D) 17
(E) 12
Rationale: 1/2 * 4 * 5 = 10 m2
Answer: B
Answer: (B) 10
Question: A call center has two teams. Each member of Team A was able to process 1/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B?
(A) 3/2
(B) 3/4
(C) 8/9
(D) 1/2
(E) 1/5
Rationale: Let team B has 8 agents, so team A has 5 agents
Let each agent of team B picked up 5 calls, so total calls by team B = 40
So, each agent in Team A picked up 1 calls, so total calls for team A = 5
Fraction for team B = 40/(40+5) = 8/9 = Answer = C
Answer: (C) 8/9
Question: How many multiples of 5 are there between 1 and 89 ?
(A) 15
(B) 20
(C) 13
(D) 17
(E) 22
Rationale: 5 multiples are 5,10,15,---------,80,85
It should be mentioned whether 1 and 89 are inclusive.
the answer is (85-5)/5+1=17
Answer is D
Answer: (D) 17
Question: A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
(A) 2 hour 20 minutes
(B) 1 hour 80 minutes
(C) 1 hour 20 minutes
(D) 8 hour 20 minutes
(E) 1 hour 50 minutes
Rationale: Let the distance and original speed be d km and k kmph respectively.
d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3
=> (5d - 4d)/4k = 1/3 => d = 4/3 k
Time taken to cover the distance at original speed
= d/k = 4/3 hours = 1 hour 20 minutes.
Answer:C
Answer: (C) 1 hour 20 minutes
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 90 terms?
(A) 0
(B) 1
(C) 25
(D) 89/90
(E) 90/91
Rationale: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a90 = 1/90 - 1/91
The sum of these terms is 1-1/91 = 90/91
The answer is E.
Answer: (E) 90/91
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 70/7 sec
(B) 80/7 sec
(C) 40/7 sec
(D) 60/7 sec
(E) 90/7 sec
Rationale: B
Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer: (B) 80/7 sec
Question: What is the difference between the place value of 1 in the numeral 7119?
(A) 150
(B) 160
(C) 180
(D) 90
(E) 210
Rationale: 100 - 10 = 90
D
Answer: (D) 90
Question: A person incurs 5% loss by selling a watch for $1140. At what price should the watch be sold to earn 5% profit?
(A) $1260
(B) $1150
(C) $1542
(D) $1000
(E) $1292
Rationale: Let the new selling price be $x
(100-loss%): (1st S.P.) = (100+gain%):(2nd S.P.)
(100-5)/1140 = (100+5)/x
x = 105*1140/95 = 1260
Answer is A
Answer: (A) $1260
Question: An unbiased cubic die is thrown.What is the probability of getting a multiple of 2 and 3?
(A) 1/6
(B) 2/6
(C) 3/6
(D) 1
(E) 1/12
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
Let F be the event of getting the multiple of 2
then ,E={2,4,6}
Let G be the event of getting the multiple of 2 and 3
then ,G={6}
P(G)=n(G)/n(S)=1/6
answer option A) 1/6.
Answer: (A) 1/6
Question: In a mixture of a, b and c, if a and b are mixed in 3:5 ratio and b and c are mixed in 8:5 ratio and if the final mixture is 35 liters, find the amount of b?
(A) 15.73
(B) 15.79
(C) 15.77
(D) 15.72
(E) 15.71
Rationale: Ans: As b is common in both ratios, we should equate b in both ratios by multiplying suitable numbers.
a:b = 3 : 5 = 24 : 40
b:c = 8 : 5 = 40 : 25
Now a : b : c = 24 : 40 : 25.
Amount of b in the mixture = 4089×354089×35 = 15.73
Answer:
Answer: (A) 15.73
Question: A garden has 50,000 trees. 12% of the trees are guava trees, 15% are orange trees, 10% are coconut trees and the rest are mango trees. Find the number of mango trees.
(A) 30000
(B) 30200
(C) 30800
(D) 31200
(E) 31500
Rationale: Mango Trees = (100 - 12 - 15 - 10) = 63%.
Number of Mango trees = 63% of 50000 = 31,500.
ANSWER : OPTION E
Answer: (E) 31500
Question: How many numbers with distinct digits are possible product of whose digits is 28?
(A) 6
(B) 4
(C) 8
(D) 12
(E) 14
Rationale: DETAILED SOLUTION
Two digit numbers; The two digits can be 4 and 7: Two possibilities 47 and 74.
Three-digit numbers: The three digits can be 1, 4 and 7: 3! Or 6 possibilities.
We cannot have three digits as (2, 2, 7) as the digits have to be distinct.
We cannot have numbers with 4 digits or more without repeating the digits.
So, there are totally 8 numbers.
Correct Answer: C
Answer: (C) 8
Question: A man’s wages were decreased by 50%. Again, the reduced wages were increased by 50%. He has a loss of?
(A) 35%
(B) 25%
(C) 20%
(D) 30%
(E) none of these
Rationale: Here, x = - 50 and y = 50
Therefore, the net % change in value
= ( x + y + xy/100) %
= [- 50 + 50 + ( -50 x 50)/100]% or - 25%
Since the sign is negative, there is loss of 25%
ANSWER:B
Answer: (B) 25%
Question: Convert the 13/36 m/s into kilometers per hour?
(A) 1.8 kmph
(B) 1.6 kmph
(C) 1.3 kmph
(D) 3.3 kmph
(E) 1.9 kmph
Rationale: 13/36 m/s
= 13/36 * 18/5
= 13/10
= 1.3 kmph.
Answer:C
Answer: (C) 1.3 kmph
Question: A can do a piece of work 60 days. B can do work in 20 days. In how many days they will complete the work together?
(A) 12 days
(B) 16 days
(C) 15 days
(D) 17 days
(E) 18 days
Rationale: LCM = 60, Ratio= 60:20=3:1
No of days= 60/(3 + 1) = 90/4 = 15 days
ANSWER:C
Answer: (C) 15 days
Question: 2, 7, 36, 4, 14, 225, 6, 21, ?
(A) 576
(B) 476
(C) 376
(D) 584
(E) 594
Rationale: 2, 7, 36, 4, 14, 225, 6, 21, ?
2+7=9 and 9-3=6 and 6^2=36
4+14=18 and 18-3=15 and 15^2=225
6+21=27 and 27-3=24 and 24^2=576
ANSWER:A
Answer: (A) 576
Question: A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is
(A) 36
(B) 40
(C) 15
(D) 20
(E) 10
Rationale: Explanation :
Let the person has x Rs , then price of 50 oranges or 40 mangoes is x Rs.
Therefore, from given information x = (x / 10) + (x / 2) + Amount left.
Hence, the amount left to buy oranges is (2x / 5) , since price of 50 oranges or 40 mangoes is x Rs , hence price of 1 orange, 1 mango is (x / 50), (x / 40) respectively.
Hence, he can buy (2 /5) x 50 = 20 oranges.
Answer : D
Answer: (D) 20
Question: Before a salary increase, the weekly salary of a worker for 42 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let x be the original salary per hour.
Let y be the salary per hour after the increase.
40y=42x
y=(42/40)x=1.05x
The salary increased 5%.
The answer is C.
Answer: (C) 5
Question: How can a cake(circular) be cut into 8 pieces by making just 3 cuts?
(A) 21
(B) 787
(C) 37
(D) 26
(E) 01
Rationale: Explanation:
Cut the cake using three mutually perpendicular planes. It leaves 8 pieces, one each in each octant.
AnswerA
Answer: (A) 21
Question: Kathleen can paint a room in 2 hours, and Anthony can paint an identical room in 7 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
(A) 28/9
(B) 4/3
(C) 15/8
(D) 9/4
(E) 15/4
Rationale: (1/2 + 1/7)t=2
t=28/9
Answer: A
Answer: (A) 28/9
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 34
(A) 2
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: P Ã· 44 = 432
=> P = 432 * 44 = 19008
P / 34 = 19008 / 34 = 559, remainder = 2
A
Answer: (A) 2
Question: How should be added in order to make 2345672 this number is divisible by 9?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Sum of the numbers 2345672 is 29 which is not multiple of 9
Add 7 which makes the sum 36 which is multiple of 9
So digit becomes 2345679 (as we know that if sum multiple of 9 then it is divisible of 9)
Answer:C
Answer: (C) 7
Question: If 8 spiders make 8 webs in 8 days, then 1 spider will make 1 web in how many days?
(A) 7
(B) 6
(C) 5
(D) 8
(E) 3
Rationale: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:8
Webs 8:1
1 x 8 x x = 8 x 1 x 8
=> x= 8
Answer is D
Answer: (D) 8
Question: How many multiples of 5 are there between 1 and 36, exclusive?
(A) 2
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: 7
multiples of 5 between 1 and 36 exclusive.
from 5 * 1 upto 5*7, (1,2,3,4,...,7). Hence, 7 multiples !
correct option is D
Answer: (D) 7
Question: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Regine
II. Stephanie
III. Brian
(A) I only
(B) II only
(C) III only
(D) I or II only
(E) II, or III
Rationale: Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.
Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.
There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.
Answer: E.
Answer: (E) II, or III
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg. How much amount did he pay to the shopkeeper?
(A) A)1055
(B) B)1075
(C) C)1145
(D) D)1070
(E) E)1080
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 65 × 9 = 585.
Total cost he has to pay = 560 + 585 = 1145.
C)
Answer: (C) C)1145
Question: Determine the value of (25/32+50/64)*2
(A) 25/8
(B) 25/4
(C) 25/6
(D) 3
(E) none
Rationale: Solution:
Both fractions should be reduced before performing arithmetic operations. We get (25/32+2.25/2.32)*2=(25/32+25/32)*2=2*(25/32)*2=4(25/32)=25/8
Answer A
Answer: (A) 25/8
Question: Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 330 grams of compound X?
(A) 54
(B) 162
(C) 250
(D) 275
(E) 322
Rationale: total number of fractions =2+10=12
element B constitutes =10 out of 12 parts of X
So in 330 gms of X have 330*10/12=275 gms of B
and 330-275=55 gms of A.
cross check:- A/B = 55/275 =2/10 (as given)
Ans D
Answer: (D) 275
Question: A 16% stock yielding 10% is quoted at :
(A) 83.33
(B) 110
(C) 112
(D) 120
(E) 160
Rationale: Solution
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160.
âˆ´ Market value of Rs. 100 stock =Rs. 160
Answer E
Answer: (E) 160
Question: You collect flowers. Suppose you have 89 flowers. You plucked 77 flowers from tree. How many flowers do you have now.?
(A) 89
(B) 166
(C) 77
(D) 12
(E) 37
Rationale: Solution
You have 89 flowers..
you plucked 77 flowers : 89 + 77 = 166 flowers
So you have 166 flowers
Correct answer: B
Answer: (B) 166
Question: Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full?
(A) 2hrs
(B) 4hrs
(C) 5hrs
(D) 6hrs
(E) 7hrs
Rationale: A's work in 1 hour = 1/6
B's work in 1 hour = 1/4
A+B 2 hour's work when opened alternately = 1/6 + 1/4 = 5/12
A+B 4 hour's work when opened alternately = 10/12 = 5/6
Remaining part = 1-5/6 = 1/6
it is A's turn and 1/6 part is filled by A in 1 hour.
Total time taken to fill the tank = 4+1 = 5hrs
Answer is C
Answer: (C) 5hrs
Question: A cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 12 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 5.2 hrs
(B) 2.9 hrs
(C) 12 hrs
(D) 7.2 hrs
(E) 1.4 hrs
Rationale: Net part filled in 1 hour = (1/6 - 1/12) = 1/12
The cistern will be filled in 12/1 hrs i.e., 12 hrs.
Answer:C
Answer: (C) 12 hrs
Question: A train covers a distance of 36km in 12 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
(A) 300 m
(B) 1000 m
(C) 120 m
(D) 200 m
(E) 500 m
Rationale: Speed = (36/12 * 60) km/hr
= (180 * 5/18) m/sec
= 50 m/sec.
Length of the train
= 50 * 10
= 500 m.
Answer: E
Answer: (E) 500 m
Question: If air is called green , green is called blue, blue is called water, sky is called yellow, yellow is called water and water is called water, then what is the color of clear sky ?
(A) Blue
(B) Sky
(C) Water
(D) Yellow
(E) Black
Rationale: Explanation:The colour of clear sky is 'blue' and as given, 'blue' is called 'water'.So, the colour of clear sky is 'water'.Answer: C
Answer: (C) Water
Question: A jar full of whiskey contains 40% alcohol. A part of
this whiskey is replaced by another containing 19% alcohol
and now the percentage of alcohol was found to be 26%.
The quantity of whiskey replaced is?
(A) 2/3
(B) 1/3
(C) 1/5
(D) 1/4
(E) 1/8
Rationale: Strength of first jar 40% Strength of 2nd jar 19%
Mean Strength 26%
7 14
So,ratio of 1st and 2nd quantities =7:14 =1:2
Therefore required quantity replaced =2/3.
ANSWER A
Answer: (A) 2/3
Question: A corporation paid $7 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $100 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $100 million in profits?
(A)  6%
(B)  14%
(C)  114%
(D)  23%
(E)  43%
Rationale: Difference in Ratios = (30/100) - (7/50) = (8/50)
% Change = (Change (8/50) / Original ratio (7/50)) *100 = 114%
Answer - C
Answer: (C)  114%
Question: 7 people average age is 30. youngest person age is 7. find average of the people when youngest was born.
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: average age of people =30
so have total age =210
before 7 years we have to deduct each person age by seven years 210-49=161
so average age would be 161/7=23
ANSWER:A
Answer: (A) 23
Question: George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare and buys 10 mangoes. How many oranges can he buy?
(A) 25
(B) 30
(C) 20
(D) 16
(E) 12
Rationale: Let the amount of money be 200
Let cost of 1 Orange be 4
Let cost of 1 mango be 5
He decides to retain 10% of 200 = 20 for taxi fare, so he is left with 180
He buys 20 mangoes ( @ 5) so he spends 100
Money left is 80 (180 - 100)
No of oranges he can buy = 80/4 =>20
So, George can buy 10 Oranges.
C
Answer: (C) 20
Question: If selling price is doubled, the profit triples. Find the profit percent?
(A) 187
(B) 100
(C) 177
(D) 165
(E) 122
Rationale: Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
Answer: B
Answer: (B) 100
Question: A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?
(A) 2 days
(B) 4 days
(C) 5 days
(D) 6 days
(E) 9 days
Rationale: sax Work done by Afar 3 days : i
J
.. Remzming war — 1
.Work done by (A + B) for 1 day :
. Work done by a for 1 day
6 days
D
Answer: (D) 6 days
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 8 sec
(B) 6 sec
(C) 4 sec
(D) 3 sec
(E) 1 sec
Rationale: Speed of train relative to man = 60 + 6
= 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55
= 6 sec
Answer:B
Answer: (B) 6 sec
Question: The greatest possible length which can be used to measure exactly the length 6m ,2m 85cm, 4m 95 cm is?
(A) 25cm
(B) 101cm
(C) 56cm
(D) 42cm
(E) 15cm
Rationale: Required length = H.C.F of 600cm, 285cm, 495cm = 15cm
Answer is E
Answer: (E) 15cm
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
(A) 1/129
(B) 1/199
(C) 1/122
(D) 1/121
(E) 1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= 4C4/9C4 = 1/126
Answer:E
Answer: (E) 1/126
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: dividend rs 20 = 9/200*20 = 9/5
Rs 12 is an income Rs 100
9/5 is an income (100/12*9/5) = Rs 15
ANSWER E
Answer: (E) 15
Question: Aaron will jog from home at 4 miles per hour and then walk back home by the same route at 8 miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking?
(A) 2
(B) 10
(C) 12
(D) 8
(E) 15
Rationale: xyt/(x+y)
x= 4, y=8 t= 3
4*8*3/4+8 = 96/12 = 8
Answer : D
Answer: (D) 8
Question: When the integer x is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6 ?
I. 2x
II. 6x
III. 4x + 6
(A)  I only
(B)  II only
(C)  III only
(D)  I and II only
(E)  I, II, and III
Rationale: is it E.
x= 12*a + 3
2x = 12*2*a + 6
6x = 12*6*a + 18 ( 18 = 12+6)
4x + 6 = 12*4*a + 18 (18 = 12 + 6)
Answer: (E)  I, II, and III
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 55 sq. cm. Find the length of the rectangle.
(A) 16cm
(B) 18cm
(C) 15cm
(D) 20cm
(E) 23cm
Rationale: Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 55 => 5x - 25 = 55 => x = 16.
Length of the rectangle = 16 cm.
Answer: Option A
Answer: (A) 16cm
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 7 kmph
(B) 8 kmph
(C) 4 kmph
(D) 9 kmph
(E) 3 kmph
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: (B) 8 kmph
Question: A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)?
(A) 16
(B) 20
(C) 24
(D) 28
(E) 32
Rationale: The height:length ratio will be equal in both cases.
18 / 45 = x / 50
x = 20
The answer is B.
Answer: (B) 20
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) Rs.2500
(B) Rs.2700
(C) Rs.2800
(D) Rs.5000
(E) Rs.6000
Rationale: Explanation:
(x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 â€“ 5x/100 = 144
2x/100 = 56 Ã¨ x = 2800
ANSWER IS C
Answer: (C) Rs.2800
Question: A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A
(A) 26.2 km
(B) 25.7 km
(C) 23.2 km
(D) 26.67 km
(E) None of these
Rationale: Explanation:
Distance travelled by each of them is to be made equal.
=> Distance travelled walking = Distance covered cycling.
Let after 4 hours of walking, A walk for x hours more before B catches up with him.
=> Distance = Speed * Time
(4+x)4 = 10x
x = 8/3
Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67
ANSWER: D
Answer: (D) 26.67 km
Question: The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 2x)^4 is between
Bunuel, can you please explain this one?
(A) 0 and 0.5
(B) 0.5 and 1
(C) 1 and 1.5
(D) 1.5 and 2
(E) 2 and 2.5
Rationale: Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).
Try x=1 --> LHS=3^5=81*3=243 and RHS=4^4=64*4=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1.
Answer: B.
Answer: (B) 0.5 and 1
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is?
(A) 52:56
(B) 52:53
(C) 52:50
(D) 22:56
(E) 52:51
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
Answer: B
Answer: (B) 52:53
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 17
(B) 10
(C) 178
(D) 162
(E) 72
Rationale: 7*5: 5*x = 7:10
x = 10
Answer:B
Answer: (B) 10
Question: What is the greatest number of 4 digits that when divided by any of the numbers 6, 9, 12, 17 leaves a remainder of 2?
(A) 9792
(B) 9982
(C) 9794
(D) 9906
(E) None of these
Rationale: Apply hit and trial method at each option
9792/9= 0 remainder (failed)
9982/9= 1 remainder (failed)
9794/6= 2
9794/9= 2
9794/12=2
9793/17= 2
ANSWER:C
Answer: (C) 9794
Question: A 4-letter code word consists of letters A, B, and C. If the code includes all the three letters, how many such codes are possible?
(A) 72
(B) 48
(C) 36
(D) 24
(E) 18
Rationale: 3 letters A, B and C can be arranged in 3! ways = 6 ways
4th letter can be chosen in 3 ways
Total number of ways = 6*3=18
ANS E: 18
Answer: (E) 18
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.9
(B) 1.5
(C) 1.4
(D) 1.1
(E) 1.2
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: (B) 1.5
Question: Two unemployed young men decided to start a business together. They pooled in their savings, which came to Rs. 2,000. They were both lucky, their business prospered and they were able to increase their capital by 50 per cent every three years. How much did they have in all at the end of eighteen years?
(A) Rs. 22,781.25
(B) Rs. 24,150.25
(C) Rs. 28,140.50
(D) Rs. 18,000
(E) Rs. 19,000
Rationale: P = 2000, r = 50/100 = 0.5, t =18/3= 6 (number of years)
C = P ( 1 + r )^(t)
C = 2000 ( 1 + 0.5)^(6)
C = 22781.25rs.
ANSWER:A
Answer: (A) Rs. 22,781.25
Question: In a circle with a radius of 6, what is the area of the biggest rectangle that can be cut out of this circle ?
(A) 12
(B) 96
(C) 50
(D) 72
(E) 144
Rationale: The biggest rectangle would be a square, whose diagonal is 12 (6+6)
if side of square is a, 144=a^2+a^2=2a^2
so area of square=a^2=144/2=72
ANSWER: D
Answer: (D) 72