mathewhe/aqua_rat huggingface dataset:
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 320 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 600
(B) 640
(C) 500
(D) 520
(E) 720
Rationale: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 320) = 2 + 2(extra)
=> 2x - 640 = x => x = 640.
ANSWER:B
Answer: (B) 640
Question: Ramesh spends 40% of his monthly salary on food, 40% of the remaining on conveyance and clothes and saves 50% of the remaining amount. If his monthly salary is Rs.17,000, how much money does he save every month ?
(A) 3060
(B) 2787
(C) 2697
(D) 2671
(E) 1922
Rationale: Explanation:
Ramesh's monthly income = Rs.17,000
He spends 40% on food.
The total money spent on food = 40/100 * 17000 = Rs. 6800
Now, his monthly remaining income = Rs.17000 – Rs.6800 = Rs. 10200
Out of Rs. 10200, he spends 40% on conveyance and clothes.
The total money spent on conveyance and clothes = 40/100 * 10200 = Rs. 4080
Now, his monthly remaining income = Rs.10200 – Rs.4080 = Rs. 6120
Out of Rs. 6120, he saves 50%.
Amount saved = 50/100 * 6120 = Rs. 3060
ANSWER:A
Answer: (A) 3060
Question: A set S = {x, -8, -5, -2, 2, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
(A) 1
(B) 0
(C) 2
(D) -1
(E) Cannot be determined
Rationale: Median of the set = (-2+2)/2 = 0
As per statement, Mean of the set = 0
Mean of the set
|y|- |x| +17-15 = 0 (where x is negative n y is positive)
|y|- |x| = -2
So the absolute difference between two numbers is 2
Answer C
Answer: (C) 2
Question: Which of the following must be true?
1) Every prime number greater than 5 can be written as either as 7n+1 or 7n-1
2) Every prime number greater than 5 can be written as 4n+1 or 4n-1
3) Every number greater than 5 of the form 7n+1 or 7n-1 is a prime number.
(A) 1,2,3
(B) 2,3
(C) only 2
(D) only 1
(E) 1,2
Rationale: Every prime number greater than 3 can be written in the form of 7n+1 or 7n-1 where n is an integer. So 1 can be possible.
3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 7n+1 or 7n-1.
E
Answer: (E) 1,2
Question: Find the value of y from (12)^1 x 6^4 ÷ 432 = y?
(A) 2134
(B) 2234
(C) 2540
(D) 2560
(E) 36
Rationale: 36
E
Answer: (E) 36
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 70 km/hr. When will he overtake the thief?
(A) 6:34 p.m
(B) 9:34 p.m
(C) 6:00 p.m
(D) 2:30 p.m
(E) 1:34 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 70(x - 1/2) => x = 7/2 hrs.
So, the thief is overtaken at 5:34 p.m.'
Answer: C
Answer: (C) 6:00 p.m
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 36, Find x and y ?
(A) x=4,y=8
(B) x=9,y=64
(C) x=4,y=7
(D) x=4,y=9
(E) x=5,y=8
Rationale: 9+64=73
when reversed 37
73-37=36
x=9,y=64
ANSWER:B
Answer: (B) x=9,y=64
Question: If P(A) = 2/15, P(B) = 4/15, and P(A ∪ B) = 6/15 Find P(A|B)
(A) 1/2
(B) 2/3
(C) 3/2
(D) 4/5
(E) 4/7
Rationale: P(A|B) = P(A ∪ B)/P(B)
P(A|B) = (6/15)/(4/15) = 3/2.
C
Answer: (C) 3/2
Question: If 16% of 40% of a number is 8, then the number is
(A) 200
(B) 225
(C) 125
(D) 320
(E) None of these
Rationale: Explanation:
Let 16/100×40/100×a=8
a = 8×100×100/16×40=125
Correct Option: C
Answer: (C) 125
Question: P and Q started a business investing Rs 60000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
(A) 7:5
(B) 17:3
(C) 4:1
(D) 17:7
(E) 5:8
Rationale: Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 60000:15000
= 60:15
= 4:1
Option C
Answer: (C) 4:1
Question: In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is?
(A) 24
(B) 26
(C) 28
(D) 30
(E) None
Rationale: Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
Option A
Answer: (A) 24
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 778
(B) 280
(C) 288
(D) 111
(E) 121
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: (B) 280
Question: A shopkeeper buys mangoes at the rate of 8 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 33 4/3 %
(B) 33 1/7 %
(C) 62.5 %
(D) 32 1/3 %
(E) 33 2/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 24.
If he buys 8 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 8
Profit = SP - CP = 8 - 3 = 5
Profit Percent = 5/8 * 100 = 62.5 %
Answer:C
Answer: (C) 62.5 %
Question: Find the value of (√1.21)/(√0.81) + (√1.44)/(√0.49) is
(A) 195/63
(B) 145/63
(C) 155/63
(D) 125/63
(E) 185/63
Rationale: (√1.21)/(√0.81) + (√1.44)/(√0.49)
11/9 + 12/7 => (77 + 108)/63 => 185/63
Answer is E.
Answer: (E) 185/63
Question: A man bought pens at 3 for a dollar. How many for a dollar must he sell to gain 50%?
(A) 3
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: C.P. of 3 pens = $1
S.P. of 3 pens = 150% of $1 = 3/2
for $3/2 pens sold = 3
for $1 pens sold = 3*2/3 = 2
Answer is C
Answer: (C) 2
Question: If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is
(A) A decrease of 99%
(B) No change
(C) A decrease of 1%
(D) A increase of 1%
(E) none
Rationale: initially assume 100 rupees
10% discount in 100 gives price of 90 rupees
then 10% raise in 90 is only 9 rupees.
therefore total price =99 rupees.
hence 1% is the loss
ANSWER:C
Answer: (C) A decrease of 1%
Question: the reciprocal of the hcf and lcm of two are 1/17 and 1/312 .if one of the number is 24 then other no. is
(A) 126
(B) 136
(C) 146
(D) 221
(E) 266
Rationale: reciprocal of the hcf and lcm of two are 1/17 and 1/312
so, HCF = 17 , LCM = 312
LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a
so, other = 17*312 / 24 = 221
ANSWER:D
Answer: (D) 221
Question: A departmental store bought some grapes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of grapes in the two stacks if the store broke even after having sold all of its grapes?
(A) 1:6
(B) 1:4
(C) 2:3
(D) 1:2
(E) 2:5
Rationale: To avoid fractions, assume there were 45 mangoes. So the store bought them for 45/5 = 9 dollars.
To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these.
45 split in the ratio 1:4 gives 9 and 36.
9 grapes split into 3 grapes each will give $3.
36 grapes split into 6 grapes each will give $6.
They add up to $9 so we have hit the right answer.
Answer (B)
Answer: (B) 1:4
Question: If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 24, what is the value of r-p?
(A) 28
(B) 10
(C) 30
(D) 40
(E) 5
Rationale: Arithmetic mean expression for p and q:
(p+q)/2=10 ; p+q=20 ----eq1
Arithmetic mean expression for q and r:
(q+r)/2=20 ; q+r=48 ----eq2
Subtracting eq1 from eq2 we get: r-p=28
Hence, the correct answer is A
Answer: (A) 28
Question: 2+2+2²+2³ ... +2^7
(A) 2^9
(B) 2^10
(C) 2^16
(D) 2^35
(E) 2^8
Rationale: 2+2=2^2
2^2+2^2=(2^2)*(1+1)=2^3
2^3+2^3=(2^3)*(1+1)=2^4
so you can notice the pattern... in the end you will have 2^7+2^7, which will give you 2^8
Answer E
Answer: (E) 2^8
Question: Simplify: 702 x 698
(A) 489996
(B) 490000
(C) 492800
(D) 487200
(E) 490004
Rationale: 702 x 698 = (700 + 2)(700 - 2)
= 490000 + 1400 -1400 -4
=489996
Answer is A
Answer: (A) 489996
Question: When two dice are rolled, what is the probability that the difference between the two numbers is 4?
(A)  1/9
(B)  2/9
(C)  1/3
(D)  2/3
(E)  None of the above
Rationale: We have 4 outcomes that satisfy the question:
1-5
2-6
5-1
6-2.
the probability is (1/6*1/6)*4= 1/9.
I think the answer is A
Answer: (A)  1/9
Question: A school has received 40% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
(A) $200
(B) $177.78
(C) $100
(D) $277.78
(E) $77.78
Rationale: Let the amount school needs = X
Let total people school plans to solicit = T
School has received 60 % of X => (3/5) X
People already solicited = 40% of T => (2/5) T
Now, as per the information given in the question :
(3/5)X = $400 . (2/5) . T --------------------------- 1
Remaning Amount is 40 % i.e ( 2/5 ) X ------because school has already received 60%
And the remaining people are 60 % i.e (3/5) .T -----because 40% of the people are already solicited
So, average contribution required from the remaining targeted people is
(2/5) X = (Amount required) . (3/5) . T ----------------------------------- 2
Divide eqn 1 by eqn 2
Amount required = $77.78
E
Answer: (E) $77.78
Question: A clock shows the time as 9 a.m. If the minute hand gains 6 minutes every hour, how many minutes will the clock gain by 6 p.m.?
(A) 30 min
(B) 35 min
(C) 45 min
(D) 50 min
(E) 54 min
Rationale: there are 9 hours in between 9 a.m. to 6 p.m.
9*6=54 minutes.
ANSWER:E
Answer: (E) 54 min
Question: If 8 workers can build 8 cars in 8 days, then how many days would it take 5 workers to build 5 cars?
(A) 4
(B) 5
(C) 8
(D) 10
(E) 12
Rationale: 8 workers can build 1 car per day on average.
1 worker can build 1/8 of a car per day.
5 workers can build 5/8 car per day.
The time required to build 5 cars is 5 / (5/8) = 8 days
The answer is C.
Answer: (C) 8
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 48
(B) 93
(C) 26
(D) 23
(E) 12
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer:A
Answer: (A) 48
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
(A) 277
(B) 288
(C) 600
(D) 273
(E) 126
Rationale: D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km
Answer: C
Answer: (C) 600
Question: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 34 pints of Perfect Pink paint?
(A) 9
(B) 16
(C) 18
(D) 25 1/3
(E) 28 1/2
Rationale: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
34 pints will require 9/17 * 34= 18 points..
Second way..
get both red and white paints in same denominator...
3/4 + 2/3 = (9/12)+(8/12) pints..
from here we get the ratio of red:white = 9:8..
so in 34 pints red will be 9/(9+8) * 34 =18..
ANSWER:C
Answer: (C) 18
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 90, 40 kmph
(B) 80, 40 kmph
(C) 80, 70 kmph
(D) 80, 80 kmph
(E) 50, 40 kmph
Rationale: Speed downstream
= 60 + 20 = 80 kmph
Speed upstream
= 60 - 20 = 40 kmph
Answer:B
Answer: (B) 80, 40 kmph
Question: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 11 multiples of 14, how many multiples of 7 are there in Q?
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 11+10 = 21.
The answer is C.
Answer: (C) 21
Question: Solution Y is 30 percent liquid J and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid J?
(A) 30%
(B) 33 1/3%
(C) 37 1/2%
(D) 40%
(E) 50%
Rationale: Answer:C
Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid J and 70% water, and then I was able to get the answer. That was a bit tricky and nice question=C
Answer: (C) 37 1/2%
Question: A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?
(A) 10.25 days
(B) 11.5 days
(C) 12.75 days
(D) 9 days
(E) 8 days
Rationale: Explanation:
A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work.
=> In one day A came complete 1/9th of the task(x/9)
=> In one day B can complete 1/12th of the job.(x/12)
First day x/9th work will be done next day x/12th and so on:
Together A and B can do x/9 + x/12 work.
=>(x/9) + (x/12) = 7/36th work done
In 10 days 35/36th of the work will be done.
On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work.
So, 1/36th work will be done in 1/4 days.
=>10.25 days
ANSWER A
Answer: (A) 10.25 days
Question: If D is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of D?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: D = 30!
8
D = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3
3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3
So we have a total of 14 three's ...
Therefore the maximum value of K can be 14 (C)
Answer: (C) 14
Question: If Rs.10 be allowed as true discount on a bill of Rs.110 due at the end of a certain time,then the discount allowed on the same sum due at the end of double the time is :
(A) Rs. 20
(B) Rs. 21.81
(C) Rs. 22
(D) Rs. 18.33
(E) None
Rationale: Solution
S.I. on Rs.(110 -10) for a certain time =Rs.10.
S.I. on Rs. 100 for double the time =Rs. 20.
T.D. on Rs. 120 =Rs.(120 -100)=Rs. 20.
T.D. on Rs. 110 =Rs.(20/120x120) =Rs.18.33.
Answer D
Answer: (D) Rs. 18.33
Question: Ram, Krish and Bhim can complete a work in 30 days. If Ram and Krish together can complete the same work in 40 days, then how long will Bhim take to complete it?
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Rationale: Ram + Krish + Bhim’s work = 1/30
Ram and Krish’s work= 1/40
Bhim’s work = 1/30 - 1/40 = 1/120
ANSWER:D
Answer: (D) 120
Question: Alice and Paul have a plate with 37 cookies on it. They both eat cookies off of the plate every minute. Paul takes a drink of milk instead of eating a cookie every third minute. Alice eats two cookies instead of one every fourth minute. How many minutes does it take them to eat all of the cookies?
(A) 13 minutes
(B) 12 minutes
(C) 11 minutes
(D) 10 minutes
(E) 9 minutes
Rationale: Alice eats 6 cookies every 4 minutes. Paul eats 2 cookies every 3 minutes. In 9 minutes, Alice eats 6*2 + 1 = 13 cookies, and Paul eats 2*3 = 6 cookies, for a total of 13+6 = 19 cookies. In 10 minutes, Alice eats 6*2 + 2 = 14 cookies, and Paul eats 2*3 + 1= 7 cookies, for a total of 14+7 = 21 cookies. In 11 minutes, Alice eats 6*2 + 3 = 15 cookies, and Paul eats 2*3 + 2= 8 cookies, for a total of 15+8 = 23 cookies.Thus, the answer is C.
Answer: (C) 11 minutes
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train?
(A) 150 meter
(B) 170 meter
(C) 250 meter
(D) 168 meter
(E) 154 meter
Rationale: Speed = 60*(5/18) m/sec
= 50/3 m/sec
Length of Train (Distance)
= Speed * Time
(50/3) * 15
= 250 meter
Answer:C
Answer: (C) 250 meter
Question: Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?
(A) 11:9
(B) 11:20
(C) 9:20
(D) 11:8
(E) None
Rationale: Sol.
In the same time, they cover 110 km and 90 km respectively.
∴ Ratio of their speeds = 110 : 90 = 11 : 9.
Answer A
Answer: (A) 11:9
Question: All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
A.
B.
C.
D.
E.
(A) 2 (26)^5
(B) 26(26)^4
(C) 27(26)^4
(D) 26(26)^5
(E) 27(26)^5
Rationale: There are two slightly different ways of doing this question:
No of different four letter codes:
26*26*26*26 = 26^4
No of different five letter codes:
26*26*26*26*26 = 26^5
Total number of codes = 26^4 + 26^5 = 27*26^4
ANS:C
Answer: (C) 27(26)^4
Question: (8956231 x 465) = ?
(A) 4584638125
(B) 4164647415
(C) 4584638135
(D) 4584638140
(E) 4584638145
Rationale: 8956231 x 465=4164647415Ans B
Answer: (B) 4164647415
Question: Two numbers are 35% and 42% are less than a third number .How much percent is the second number less than the first ?
(A) 11.769%
(B) 10.769%
(C) 12.769%
(D) 11.69%
(E) 11.89%
Rationale: Explanation:
I II III
65 58 100
65 -------- 7
100 ------ ? => 10.769%
Answer B
Answer: (B) 10.769%
Question: Find the average of the series : 256,254,350, 1110,1200 ?
(A) 129
(B) 308
(C) 634
(D) 207
(E) 174
Rationale: Average = (256+254+350+1110+1200) /5
= 3170/5
= 634
Answer: C
Answer: (C) 634
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 57 .6 m
(B) 127.5 m
(C) 87 .9 m
(D) 123.5 m
(E) 157.5 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 =127.5 m
Answer:B
Answer: (B) 127.5 m
Question: A customer asks the clerk for a paintbrush and a bucket of whitewash for a total price of B dollars. If the paintbrush costs 400 cents less than twice the price of a bucket of whitewash, what is the price of half a bucket of whitewash in dollars?
(A) (B + 200)/2.
(B) (B + 2)/6.
(C) (2B + 200)/3.
(D) (B + 2)/3.
(E) (B - 2)/6.
Rationale: P = 2w - 200
thus total price in cents as given should be
2w-200 +w = 100B
3w - 200 = 100 B
3w = 100 B+200
3w =b+2 (in dollars)
w/2 = (b+2)/6
Ans:E
Answer: (E) (B - 2)/6.
Question: Amar, Bhavan and Chetan divide an amount of Rs.5600 among themselves in the ratio 3:6:5. If an amount of Rs.400 is deducted from each of their shares, what will be the new ratio of their shares of the amount?
(A) 2:5:6
(B) 2:5:0
(C) 2:5:4
(D) 2:5:3
(E) 2:5:1
Rationale: Let the shares of Amar, Bhavan and Chetan be 3x, 6x and 5x respectively.
3x + 6x + 5x = 5600
14x = 5600 => x = 400
Required ratio = 3x - 400 : 6x - 400 : 5x - 400
= 3x - x : 6x - x : 5x - x
= 2x : 5x : 4x => 2:5:4
Answer:C
Answer: (C) 2:5:4
Question: A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
(A) 40
(B) 50
(C) 54
(D) 60
(E) 64
Rationale: (A + B)'s 20 day's work =	(1/30 x 20	)	=	2/3	.
Remaining work =	(1 -	2/3 )	=	1/3	.
Now,	1/3	work is done by A in 20 days.
Therefore, the whole work will be done by A in (20 x 3) = 60 days.
Answer : D
Answer: (D) 60
Question: Two trains of equal 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 36 sec. The length of each train is?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: Option A
Answer: (A) 50
Question: P and Q walk around a circular track. They start at 7 a.m from the same point in the opposite directions. P and Q walk at a speed of 4 rounds per hour and 7 rounds per hour respectively. How many times shall they cross each other before 10 a.m
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: Explanation:
Relative speed = (4+7) =11 rounds per hour
So, they cross each other 11 times in an hour hence, they cross 33 times before 10 a.m
Answer: Option D
Answer: (D) 33
Question: Of the 30 employees of a certain company, 10 are accountants. 2 employees of the company will be selected at random. Which of the following is closest to the probability that neither of the employees selected will be an accountant?
(A) 0.43
(B) 0.36
(C) 0.31
(D) 0.52
(E) 0.63
Rationale: We can Solve this by two ways:
either find the probability by = 1-(both accountant+atleast one accountant)
or direct from = P(both non accountant)
second is easier but requires calculation if don't do the approximation.
So probability= (20/30)*(19/29) = 0.43
so the answer is A
Answer: (A) 0.43
Question: Marcella has 27 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?
(A) 22
(B) 20
(C) 19
(D) 16
(E) 15
Rationale: Marcella has 27 pairs of shoes and loses 9 shoes.
To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes).
The 27 pairs of shoes minus the 5 'destroyed' pairs yields 22 pairs that still fulfill the requirements.
Answer: A
Answer: (A) 22
Question: Sonika bought a V.C.R. at the list price of 18,900. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.
(A) 20,412
(B) 19,780
(C) 19,680
(D) 19,380
(E) None of these
Rationale: Sol. List price of V.C.R. =18,900
Rate of sales tax = 8%
∴ Sales tax = 8% of 18,900
= 8⁄100 × 18500 = 1512
So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,900 + 1512
= 20,412. Answer A
Answer: (A) 20,412
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in teh same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
(A) 27 7/9 m
(B) 28 m
(C) 29
(D) 30
(E) None
Rationale: Sol.
Relative speed = (40-20) km/hr = [20 * 5/18] m/sec = [50/9] m/sec.
Length of faster train = [50/9 * 5] m = 250/9 m = 27 7/9 m.
Answer A
Answer: (A) 27 7/9 m
Question: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 180 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
(A)  280
(B)  400
(C)  540
(D)  900
(E)  840
Rationale: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:
2/3*3/4 = 1/2 survived the first month.
Of the geese that survived the first month, 3/5 did not survive the first year:
(1-3/5)*1/2 = 1/5 survived the first year.
180 geese survived the first year:
1/5*(total) = 180 --> (total) = 900.
Answer: D.
Answer: (D)  900