RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Of the following, which is greater than 1/2 ?
Indicate ALL such fractions
A.4/9
B.4/7
C.4/3
D.4/2
Answer: B.4/7
Explanation: One way to deal with fractions is to convert them all to decimals.
In this case all you would need to do is to see which is greater than 0.5.
Otherwise to see which is greater than ½, double the numerator and see if the result is greater than the denominator. In B doubling the numerator gives us 8, which is bigger than 7.
Answer: B
Question: In how many different ways can the letters of the word "POLICE" be rearrangement?
A.710
B.725
C.720
D.770
Answer: C.720
Explanation: Option 'C'
The total number of arrangements is
6P6 = 6! = 720
Question: What is the units digit of 16^83 × 13^82 × 11^87?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: To find : the units digit of 17^83 × 13^82 × 11^87
Let's reduce the clutter and simplify the product
(7^83) (3^82) (1^87)
7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4th power
so 7^5 has the same last digit as 7^1, 7^9, 7^13
Thus , 7^83 has the same last digit as 7^3, 7^7, 7^11 i.e.3
3 has a cyclicity of 4 : exactly the same routine as above
Thus , 3^82 has the same last digit as 3^2, 3^6, 3^10 i.e.9
Any power of 1 will result in1as the last digit
So, product of our last digits = 3 x 9 x 1 = 27....last digit is 6
Correct Option : C
Question: Sandhiya purchased a briefcase with an additional 10% discount on the reduced price after deducting 20% on the labelled price. If the labelled price was Rs. 1400, at which price did she purchase the briefcase?
A.Rs. 980
B.Rs. 999
C.Rs. 1008
D.Rs. 1120
Answer: C.Rs. 1008
Explanation: Solution
C.P. 90% of 80% of Rs. 1400	= Rs.(90/100x80/100x1400)
‹=›Rs. 1008.
Answer C
Question: A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be
A.7744
B.2388
C.3778
D.2992
Answer: A.7744
Explanation: Explanation:
length of wire = {\color{Blue}2 \Pi r}= 2 *(22/7 )*56 = 352 cm
side of the square = 352/4 = 88cm
area of the square = 88*88 = 7744sq cm
Answer: A) 7744
Question: The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 3 ?
A.95
B.106
C.122
D.116
Answer: A.95
Explanation: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 * 20 = 640
Now increase in avg = 4 runs. So, new avg = 32+3 = 35 runs
Total runs = new avg x new no. of innings = 35 * 21 = 735
Runs made in the 11th inning = 735-640 = 95
ANSWER:A
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 13 men
do it ?
A.65 hours
B.69 hours
C.30 hours
D.62 hours
Answer: B.69 hours
Explanation: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
13 : 36 : : 25 : x	(13 x x) = (36 x 25)	(36 x 25)/13= 69
Hence, 15 men can do it in 60 hours.
Answer is B.
Question: If one of the followings is the product of the two 3-digit integers 8L7 and 6K9 (K and L denote the tens digit of the respective integers), then that product must be
A.511,913
B. 478,823
C. 531,875
D. 538,424
Answer: A.511,913
Explanation: To know the unit digit you can multiply both digit number: 7 x 9 = 63
This eliminates C, D, and E, because the number must end with a 3
To know the answer you can multiply both the thousand digit giving 8 x 6 = 48 so the number must be bigger than 480.000.
So the answer is A
Question: If a = 105 and a^3 = 21 × 25 × 45 × z, what is the value of z?
A.35
B.42
C.45
D.49
Answer: D.49
Explanation: a=105 = 3* 5 *7
a^3 = 21 × 25 × 45 × z
=> a^3 = (7*3) x (5*5) x ( 3^2 * 5) x z
=> a^3 = 3^3 * 5^3 * 7 x z
=>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x z
z = 7^2 = 49
Answer D
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 60 kmph respectively. In what time will they cross each other completely?
A.15 sec
B.19 sec
C.12 sec
D.12.9 sec
Answer: D.12.9 sec
Explanation: Explanation:
D = 250 m + 250 m = 500 m
RS = 80 + 60 = 140 * 5/18 = 350/9
T = 500 * 9/350 = 12.9 sec
Answer: Option D
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3649
A.3649
B.9654
C.5945
D.7963
Answer: A.3649
Explanation: The product of first two digits in a number equals the last two digits, except in 3649. Hence, it is the odd one.
The answer is 3649.
ANSWER:A
Question: 60% of a number is added to 120, the result is the same number. Find the number?
A.300
B.388
C.776
D.2991
Answer: A.300
Explanation: (60/100) * X + 120 = X
2X = 600
X = 300
Answer: A
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
A.4
B.5
C.6
D.7
Answer: A.4
Explanation: Explanation:
132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 -> 11,3,4 (/)
396 ->11,3,4 (/)
462 ->11,3 (X)
792 ->11,3,4 (/)
968 ->11,4 (X)
2178 ->11,3 (X)
5184 -> 3,4 (X)
6336 ->11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
ANSWER IS A
Question: In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
A.20%
B.40%
C.50%
D.60%
Answer: D.60%
Explanation: 70 + 55 + 35 = 160%
The number is 60% above 100% because 60% of the counties were counted twice.
The answer is D.
Question: Insert the missing number.
2, 6, 12, 20, 30, 42, 56,72, 90, 110 (....)
A.22
B.132
C.72
D.66
Answer: B.132
Explanation: Explanation:
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8,8 x 9, 9 x 10,10 x 11.
So, the next number is 11 x 12 = 132.
Answer: B) 132
Question: If 0.75 : x : : 5 : 8, then x is equal to
A.1.12
B.1.25
C.1.20
D.1.3
Answer: C.1.20
Explanation: Sol.
(x×5) = (0.75×8) ⇒ x = 6/5 = 1.20.
Answer C
Question: There are 14 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
A.1/5
B.11/22
C.81/724
D.91/946
Answer: D.91/946
Explanation: 14/44*13/43 = 91/946
The answer is D.
Question: What Should come in place of the question mark in the following number series ?
Q. 5 8 10 12 16 (?)
A.15
B.18
C.17
D.21
Answer: B.18
Explanation: Explanation :
The series is 5, and 5 + odd prime numbers 5 + 3 = 8, 5 + 5 = 10, 5 + 7 = 12, 5+ 11 = 16, 5 + 13 = 18
Answer : Option B
Question: A furniture dealer purchased a desk for $180 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
A.$40
B.$60
C.$80
D.$120
Answer: D.$120
Explanation: Purchase price = 180
Selling price = x
180 + 0.4*x = x
0.6*x = 180
x = 300
Profit = 300 - 180 = 120
ANSWER:D
Question: Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2:3, then find the number of pens that D gets?
A.45 pens
B.65 pens
C.75 pens
D.95 pens
Answer: C.75 pens
Explanation: Let the number of pens that A, B, C and D get be a, b, c and d respectively.
a:b = 2:1
a = c + 25
b:c = 2:3
a:b:c:d = 4:2:3:3
a, d get 4p, 3p pens
=> 4p - 3p = 25 => p = 25
=> D gets 3p = 3 * 25 = 75 pens.
Answer: C
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
A.2 hours
B.8 hours
C.6 hours
D.1 hours
Answer: A.2 hours
Explanation: |-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer:A
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is a jack?
A.1/52
B.1/13
C.5/13
D.1/4
Answer: B.1/13
Explanation: The question should ask about the probability not the odds.
There are 13 spades, the probability that the spade we already have is a jack is therefore 1/13.
Answer: B.
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 2028 sq m, then what is the breadth of the rectangular plot?
A.11
B.17
C.26
D.101
Answer: C.26
Explanation: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 2028
3b2 = 2028
b2 = 676 = 26 (b > 0)
b = 26 m.
Answer: C
Question: Stacy and Heather are 40 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?
A.4 miles
B.8 miles
C.17 miles
D.6 miles
Answer: C.17 miles
Explanation: Original distance between S and H = 40 miles.
Speed of S = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.
Now, the total distances traveled by S and H = 40 miles ---> 6*(t+2/5)+5*t=40 ---> t= 188/55 hours. Thus H has traveled for 188/55 hours giving you a total distance for H = 5*188/55 = 17 miles.
C is thus the correct answer.
P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Question: How many different 6-letter sequences are there that consist of 1A, 3B's and 4C's ?
A.6
B.80
C.120
D.360
Answer: B.80
Explanation: How many different 6-letter sequences are there that consist of 1 A, 3B's, and 4 C's?
(A) 6
(B) 80
(C) 120
(D) 360
(E) 720 (ANS B)
Question: Given distinct positive integers 1, 11, 4, x, 2, and 9, which of the following could be the median?
A.2
B.3
C.6
D.8
Answer: C.6
Explanation: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.
Arrange numbers in ascending order: 1, 2, 4, 9, 11, and x.
Now, x can not possibly be less than 4 as given that all integers are positive and distinct (and we already have 1, 2, and 4).
Next, if x is 4<x<9 then the median will be the average of 4 and x. As all answers for the median are integers, then try odd values for x:
If x=5, then median=(4+5)/2=4.5 --> not among answer choices;
If x=8, then median=(4+8)/2=6 --> OK;
Answer: C
Question: How many pounds of salt at 80 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?
A.5
B.15
C.40
D.50
Answer: A.5
Explanation: Selling price is 48 cents/lb
For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)
Basically, you need to mix 35 cents/lb (Salt 1) with 80 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg)
weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (80 - 40)/(40 - 35) = 8/1
We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 5 lbs.
Answer (A)
Question: The average (arithmetic mean) of the even integers from 0 to 200 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 100 inclusive?
A.10
B.25
C.50
D.100
Answer: C.50
Explanation: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 200 is 200/2 = 100
The average of the even numbers from 0 to 100 is 100/2 = 50
The answer is C.
Question: The distance between Delhi and Mathura is 100 kms. A starts from Delhi with a speed of 50 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 45 kmph at 8 p.m. from Delhi. When will they meet?
A.11
B.77
C.8 3/4
D.8 1/2
Answer: D.8 1/2
Explanation: D = 100 – 50 = 50
RS = 45 + 50 = 95
T = 90/45 = 0.5 hours
8 a.m. + 0.5 = 8 1/2 a.m..Answer: D
Question: There are 4 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament?
A.10
B.8
C.40
D.60
Answer: B.8
Explanation: Each person is one participant of 4 games. So there are in all 4*4 = 16 instances of one participant games. But each game has 2 participants so total number of games = 16/2 = 8
B
Question: What is the greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 3, 4, 5, 6 and 7 respectively?
A.456780
B.678910
C.997479
D.997917
Answer: D.997917
Explanation: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 7 when we divide by 10, so D is the only possible answer.
Question: If Reena says, “Anjali's father Raman is the only son of my father-in-law Ramanand”, then how is Piyu, who is the sister of Anjali, related to Ramanand ?
A.Grand-daughter
B.Wife
C.Daughter
D.None of these
Answer: A.Grand-daughter
Explanation: Explanation:
Only son of Reena's father-in-law Ramanand is Reena's husband. So, Raman is Reena's husband and Anjali & Piyu are his daughter's, Thus, Piyu is Grand-daughter of Ramanand.
ANSWER: A
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin
A.24.58
B.24.5
C.24.3
D.24.9
Answer: B.24.5
Explanation: If Rahul age is x, then Sachin age is x-7,
so (x-7)/x = 7/9
=> 9x-63 = 7x
=> 2x = 63
=> x = 31.5
So Sachin age is 31.5 - 7 = 24.5
Answer: B
Question: A train covers a distance of 1250 km in 25hrs. Find the speed of the train?
A.30km/hr
B.40km/hr
C.50km/hr
D.60km/hr
Answer: C.50km/hr
Explanation: Speed = 1250/25 = 50km/hr
Answer is C
Question: Arrange fractions in descending order
A.9/11 > 8/9 > 3/5 > 4/7
B.9/11 > 8/9 > 4/7 > 3/5
C.8/9 > 9/11 > 3/5 > 4/7
D.9/11 >3/5 > 8/9 > 4/7
Answer: C.8/9 > 9/11 > 3/5 > 4/7
Explanation: Explanation:
9/11 = .818 , 8/9 = .88 , 3/5 = .6, 4/7 = .571
So order is 8/9 > 9/11 > 3/5 > 4/7
Option C
Question: In an exam, Bobby scored 38 percent, Bonny scored 56 percent, Vijay scored 66 percent and Libin scored 75 percent. The maximum score awarded in the exam is 500. Find the average mark scored by all the three boys?
A.293
B.293.75
C.294
D.295.5
Answer: B.293.75
Explanation: Average mark scored by all the three boys =
[38/100 (500) + 56/100 (500) + 66/100 (500) + 75/100(500)] / 4
(190+280+330+375)/4
= 293.75
Answer: B
Question: A man borrowed Rs 24000 from two money lenders. For one loan, he paid 15% per annum and for the other 18% per annum. At the end of one year, he paid Rs 4050. How much did he borrow at each rate ?
A.Rs.16000
B.Rs.12000
C.Rs.15000
D.Rs.13000
Answer: C.Rs.15000
Explanation: Explanation:
Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x).
{(x * 15 * 1)/100 } + { [(24000 – x) * 18 * 1]/100 } = 4050
or 15 x + 432000 - 18x = 405000 or x = 9000.
Money borrowed at 15% = Rs 9000 .
Money borrowed at 18% = Rs 15000.
Answer: C
Question: The faces of pyramid are to be painted by 4 different colors. In how many ways can be this be done?
A.A.720
B.B.256
C.C.24
D.D.12
Answer: C.C.24
Explanation: If I have to paint 4 sides with 4 different colour...
First face can have 4c1 options,
2nd would have 3c1, and subsequent ones would have 2c1 and 1 options respectively.
Total options = 4c1 x 3c1 x 2c1 x 1 = 24 distinct ways
Correct answer - C
Question: Two pipes A and B can fill a tank in 36 hours and 46 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
A.20.195 hrs
B.21.195 hrs
C.22.195 hrs
D.23.195 hrs
Answer: A.20.195 hrs
Explanation: a fill in one hour = 1/36
b fill in one hour = 1/46
both fill in one hour = 1/36+1/46
= 82/1656
time taken by both pipes = 1656/82
=20.195 hrs
ANSWER:A
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 800 per sq.metre.
A.Rs.15500
B.Rs.16500
C.Rs.17500
D.Rs.18500
Answer: B.Rs.16500
Explanation: Area = 5.5 × 3.75 sq. metre.
Cost for 1 sq. metre. = Rs. 800
Hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = Rs. 16500
Answer: B
Question: Which number is the odd one out in the list ?
A.38442
B.78426
C.84029
D.67626
Answer: C.84029
Explanation: C
84029
All the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27.
Answer: C
Question: If n is a prime number greater than 3, what is the remainder when n^2 is divided by 13?
A.0
B.1
C.2
D.13
Answer: D.13
Explanation: There are several algebraic ways to solve this question including the one under the spoiler. But the easiest way is as follows:since we can not have two correct answersjust pick a prime greater than 3, square it and see what would be the remainder upon division of it by 13.
n=5 --> n^2=25 --> remainder upon division 25 by 13 is 12.
Answer: D.
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
A.227
B.299
C.270
D.585
Answer: C.270
Explanation: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer: C
Question: The average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
A.107 kg
B.80 kg
C.120 kg
D.90 kg
Answer: A.107 kg
Explanation: Solution
Total weight increased	= (10 x 4.2)kg
= 42 kg.
Weight of new person	= (65 + 42)kg
= 107kg.
Answer A
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
A.22
B.21
C.22
D.28
Answer: D.28
Explanation: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m.Answer: D
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
A.Rs.128
B.Rs.129
C.Rs.125
D.Rs.198
Answer: C.Rs.125
Explanation: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2
=Rs.125
Answer:C
Question: At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?
A.24min
B.44min
C.14min
D.21min
Answer: A.24min
Explanation: In this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart
Case 1 : (5*x + t) * 12/11
(5*5 + 3) * 12/11
28 * 12/11 = 336/11= min
therefore the hands will be 3 min apart at 31 5/11 min past 5.
Case 2 : (5*x - t) * 12/11
(5*5 -3 ) * 12/11
22 *12/11 = 24 min
therefore the hands will be 3 min apart at 24 min past 5
Answer: A
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases?
A.8:6
B.8:7
C.8:9
D.8:4
Answer: B.8:7
Explanation: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer: B
Question: The perimeter of a semi circle is 108 cm then the radius is?
A.17
B.21
C.19
D.11
Answer: B.21
Explanation: 36/7 r = 108 => r
= 21
Answer: B
Question: In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
A.6
B.5
C.4
D.3
Answer: A.6
Explanation: Let us first find the fraction of green, blue and yellow balls
1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator
= 11 / 24 , add numerators
The fraction of white balls is given by
24 / 24 - 11 / 24 = 13 / 24
So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then
(13 / 24) of x = 26 balls
or (13 / 24) ? x = 26
x = 26 ? (24 / 13) = 48 , total number of balls
The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by
(1 / 8) of 48 = 6 balls.
correct answer A
Question: The number obtained by interchanging the digits of a two-digit number is less than the original number by 36. The sum of the digits of the number is 8. What is the original number ?
A.71
B.62
C.53
D.35
Answer: B.62
Explanation: Explanation :
Let the number be 10x + y.
∴ x + y = 8 .....(i)
10x + y - (10y + x) = 36 ∴ 9(x - y) = 3
∴ x - y = 4 .......(ii)
From equation (i) and (ii): x = 6, y = 2
∴ Number = 62
Answer : Option B
Question: Solution for 2.12+.004+.345
A.2.91
B.2.911
C.2.469
D.2.586
Answer: C.2.469
Explanation: 2.12+.004+.345
0=0-2.12-0.004-0.345
0=-2.469
answer :C
Question: How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr ?
A.25
B.30
C.40
D.45
Answer: B.30
Explanation: Solution
Speed of train relative to man =(63-3)km/hr=60km/hr
=(60x5/18)m/sec =50/3 m/sec
Time taken to pass the man =(500x3/50)sec =30sec
Answer B
Question: Which is better investment, 12% stock at par with an income tax at the rate of 5paise per rupee or 14 2/7 % stock at 120 free from income tax?
A.12%
B.14 2/7%
C.Both are equally good
D.Cannot be compared
Answer: B.14 2/7%
Explanation: Let the investment in each (100*120)
Income in first case = (12/100*100*120)=1440
Net income =(1440-5/100*1440)=1368
Income in second case=((100/2*20)*100*120)=1428.57
Clearly, 14 2/7 % stock at 120 is better
Option B
Question: If a(a - 4) = 12 and b(b -4) = 12, where a ≠ b, then a + b =
A.−48
B.−5
C.4
D.46
Answer: C.4
Explanation: i.e. if a = 6 then b = -2
or if a = -2 then b = 6
But in each case a+b = -2+6 = 4
Answer: option C
Question: Two trains travelling in the same direction at 55 and 40 kmph completely pass off another in 1 minute. If the length of the first train is 139 m, what is the length of the second train?
A.387 m
B.139 m
C.111 m
D.125 m
Answer: C.111 m
Explanation: RS = 55 â€“40 = 15 * 5/18 = 25/6 mps
T = 60 sec
D = 25/6 * 60 = 250 m
139
--------
111 m
Answer: C
Question: In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?
A.22
B.25
C.88
D.17
Answer: B.25
Explanation: The toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2, 2, 1
b. 3, 1, 1
Case a. Number of ways of achieving the first option 2 - 2 - 1
Two toys out of the 5 can be selected in \inline {\color{Black} 5C_{2}} ways. Another 2 out of the remaining 3 can be selected in \inline {\color{Black} 3C_{2}} ways and the last toy can be selected in \inline {\color{Black} 1C_{1}} way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2
Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways \inline {\color{Black} 5C_{2}\times 3C_{2}}= 15 ways
Case b. Number of ways of achieving the second option 3 - 1 - 1
Three toys out of the 5 can be selected in \inline {\color{Black} 5C_{3}} ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3 - 1 - 1 option is \inline {\color{Black} 5C_{3}} = 10 = 10 ways.
Total ways in which the 5 toys can be packed in 3 identical boxes
= number of ways of achieving Case a + number of ways of achieving Case b
= 15 + 10 = 25 ways.
Answer: B