RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is:
A.32 years
B.36 years
C.38 years
D.40 years
Answer: C.38 years
Explanation: Let Rajan's present age be x years.
Then, his age at the time of marriage = (x - 8) years.
x = 6/5 (x - 8)
5x = 6x - 48 => x = 48
Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.
Rajan's sister's present age = (30 + 8) = 38 years.
ANSWER:C
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A.11
B.60
C.77
D.55
Answer: C.77
Explanation: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer: C
Question: If x < 0 and 0 < y < 1, which of the following has the greatest value Q?
A.x^2
B.(xy)^2
C.(x/y)^2
D.x^2/y
Answer: C.(x/y)^2
Explanation: Given, x < 0 and 0 < y < 1
Let, x = -2 and y = 1/2
A. x^2 = (-2)^2 =4
B. (xy)^2 = (-2*1/2)^2 =1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16
D. x^2/y = (-2)^2 / (1/2) = 4*2 =8
E. x^2*y = (-2)^2*(1/2) =2
Answer: option C
Question: man is 15 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A.13years
B.26 years
C.17 years
D.18 years
Answer: A.13years
Explanation: Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 15) + 2 = 2(x + 2)
x + 17 = 2x + 4
x = 13.
answer :A
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
A.220
B.222
C.223
D.224
Answer: D.224
Explanation: distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x
Distance covered in the the second half = 24(10 - x)
But distance covered in the the first half = Distance covered in the the second half
=> 21x = 24(10 - x)
=> 21x = 240 - 24x
=> 45x = 240
=> 9x = 48
=> 3x = 16
⇒x=16/3
Hence Distance covered in the the first half = 21x=21×16/3=7×16=112 km
Total distance = 2×112=224 km
Answer is D.
Question: The ratio of two quantities is 4 : 3. If each of the quantities is decreased by 8, their ratio changes to 3:1 then the smallest number is?
A.5.2
B.6.9
C.9.6
D.7.8
Answer: C.9.6
Explanation: Let the numbers be 4x and 3x
Then 4x-8 / 3x-8 = 3/1
4x-8 = 9x-24
5x = 16
x = 3.2
smallest number = 3*3.2 = 9.6
Answer is C
Question: Find the missing in the series: 70, 54, 45, 34,___
A.22
B.287
C.266
D.2767
Answer: C.266
Explanation: Answer:C
Question: A man is 37 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
A.78 years
B.22 years
C.88 years
D.35 years
Answer: D.35 years
Explanation: Let's Son age is x, then Father age is x+37.
=> 2(x+2) = (x+37+2)
=> 2x+4 = x+39
=> x = 35 years
Answer: D
Question: 85 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
A.75
B.80
C.85
D.90
Answer: A.75
Explanation: Answer = A
Please refer diagram below
85 - 10 = 75
Question: CONVERT 1.8 hectares in ares
A.130 ares.
B.160 ares.
C.180 ares.
D.230 ares.
Answer: C.180 ares.
Explanation: 1.8 hectares in ares
1 hectare = 100 ares
Therefore, 1.8 hectares = 1.8 × 100 ares
= 180 ares.
ANSWER- C
Question: How many 4-letter words with or without meaning can be formed out of the letters of the word,'LOGARITHMS',if repetition of letters is not allowed?
A.5040
B.2520
C.400
D.40
Answer: A.5040
Explanation: 'LOGARITHMS' contains 10 different letters
Required number of words=Number of arrangements of 10 letters taking 4 at a time
=10P4
=10*9*8*7
=5040
Option A
Question: A Jar contains a mixture of A & B in the ratio 4:1. When 10 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.
A.12
B.15
C.16
D.20
Answer: C.16
Explanation: 10 litres of mixture that is replaced will contain 8 litres of A and 2 litres of B (as A:B = 4:1)
Let the initial volume of the mixture be 4K + 1K = 5K
So by condition ,
[ 4K-8 ]/ [ K-2+10 ] = 2/3
Solve for K which is K = 4
So initial volume of liquid A = 4K = 16 litres
ANSWER:C
Question: Dravid rented a power tool from a rental shop. The rent for the tool was $8 for the first hour and $3 for each additional hour. If Dravid paid a total of $38, excluding sales tax, to rent the tool, for how many hours did she rent it?
A.10
B.11
C.12
D.13
Answer: B.11
Explanation: 8 + 3n = 38
n = 10
Total time = n+1 hrs = 10+1 hrs = 11 hrs
Answer : B
Question: If x,y ,and z are positive real numbers such that x+y-z =100 , y-z+x =120 , and z-x+y = 50, then find the x+y+z value?
A.100
B.120
C.150
D.200
Answer: B.120
Explanation: x+y-z =100, ------1)
y-z+x =120 , ------2)
z-x+y = 50------3)
from (1)&(2)
2z=20
z=10
from (2)&(3)
2y = 170
y=85
then x=100-75= 25
x+y+z = 120
correct option is B
Question: A seven-digit phone number is divisible by 7. After adding the two digits of the area code the number is not divisible by 7, which of the following cannot be the area code?
A.07.
B.07.
C.05.
D.04.
Answer: B.07.
Explanation: Given that 7 digit number is divisible by 3
we know any number will not be divisible by 7 if the sum of all digits of the number is not the multiple of 7.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 07 as adding it will make it divisible by 7... hence answer is B
Question: The ratio of buses to cars on River Road is 1 to 3. If there are 40 fewer buses than cars on River Road, how many cars are on River Road?
A.60
B.75
C.85
D.95
Answer: A.60
Explanation: B/C=1/3
C-B=40.........> B=C-40
(C-40)/C=1/3
Testing answers. Clearly Eliminate BCDE
Put C=60.........> (60-40)/60=20/60=1/3
Answer: A
Question: Three numbers are in the ratio 5 : 4 : 6 and their average is 750. The largest number is :
A.30
B.98
C.900
D.21
Answer: C.900
Explanation: Explanation:
Let the numbers be 5x, 4x and 6x, Then, (5x + 4x + 6x ) / 3 = 750
=> 15x = 750*3
=> x = 150
Largest number 6x = 6*150 = 900
Answer: C
Question: The sides of a square region, measured to the nearest centimeter, are 9 centimeters long. The least possible value of the actual area of the square region is
A.60.25 sq cm
B.66.25 sq cm
C.56.25 sq cm
D.72.25 sq cm
Answer: C.56.25 sq cm
Explanation: Though there might be some technicalities concerning the termnearest(as 7.5 is equidistant from both 7 and 8) the answer still should be : 7.5^2=56.25.
Answer: C
Question: 3x^2 - 10x + 8 =
A.(3x-4)(x-2)
B.(3x-4)(x+2)
C.(3x-4)(x-3)
D.(3x-2)(x+4)
Answer: A.(3x-4)(x-2)
Explanation: 3x^2 - 2x + 8
= 3x^2 - 6x - 4x + 8
= 3x (x - 2) - 4 (x-2)
= (3x-4) (x-2)
Option A
Question: In a garden, 26 trees are planted at equal distances along a yard 500 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
A.20
B.8
C.12
D.14
Answer: A.20
Explanation: 26 trees have 25 gaps between them.
Length of each gap = 500/25 = 20
i.e., distance between two consecutive trees = 20
Answer is A.
Question: Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 18 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.
A.25 days
B.100 days
C.120 days
D.110 days
Answer: A.25 days
Explanation: Rate of both = 1/20
Together they do = 1/20*18 = 9/10
Left work = 1 - 9/10 = 1/10
Adam completes 1/10 work in 10 day
so he took 10*10 = 100 days to complete the left work alone.
Thus the rate of adam is 1/100
Rate of Micheal = 1/20 - 1/100 = 1/25
Thus micheal takes 25 days to complete the whole work.
ans. A.
Question: In a given set of X = {70,55,98,45,62} what is the difference of median and mean of the set X?
A.25
B.30
C.32
D.40
Answer: C.32
Explanation: mean = 70+55+98+45+62 / 5 = 330/5 = 66
Median = 98
Difference = 98-66 = 32
Answer is C
Question: Two partners in a business (Carol and Ben) invested $500 and $850 in a business respectively. At the end of the year they made a profit of $250. Find share of each partner?
A.$92.59,$157.41
B.$96.59,$157.41
C.$92.59,$159.41
D.$92.59,$127.41
Answer: A.$92.59,$157.41
Explanation: A:B = 500:850
A:B = 10 : 17
A's share = 250*10/27 = $92.59
B's share = 250*17/27 = $157.41
Answer is A
Question: If a and b are positive integers of T such that a/b=2.86, which of the following must be a divisor of a?
A.10
B.B.13
C.18
D.26
Answer: B.B.13
Explanation: The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).
The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 143
B = 50
143/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Final Answer:
B
Question: John was 35 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/8 of John's. How old is Betty?
A.24
B.35
C.28
D.30
Answer: B.35
Explanation: Assume Betty's age on marriage = x years.
John's age on marriage = 35
John's age after 5 years = 40 years.
Betty's age after 5 years = x + 5
Given: x + 5 = 7/8 (40) = 35
Therefore Betty's current age = 35
Option B
Question: five mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the five arrange themselves in line such that Frankie’s requirement is satisfied?
A.80
B.66
C.60
D.72
Answer: C.60
Explanation: 5 mobsters can stand in 5! ways = 120
in half of the cases one person will be ahead and in the other person in the other half.
thus 60 cases.
C
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.3146 in 3 years. Find the rate percent?
A.11
B.30
C.28
D.24
Answer: B.30
Explanation: Explanation:
2420 --- 726
100 --- ? => 30%
Answer: Option B
Question: The circumference of a circle is equal to 72 pi. Find the radius of this circle.
A.32
B.33
C.36
D.37
Answer: C.36
Explanation: The circumference of a circle is given by
C = 2 pi r, where r is the radius of the circle.
Substitute C by 72 pi to obtain the equation
72 pi = 2 pi r
Simplify and solve for r to obtain
r = 36
correct answer C
Question: The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 4 months. At this time, the construction was behind schedule by how many projects?
A.28
B.96
C.198
D.204
Answer: A.28
Explanation: Project/month : 612/18 = 34
Project in 6 month to be completed = 34*4 =136
Lag :136-108 = 28
A is the answer
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference?
A.12
B.13
C.14
D.15
Answer: A.12
Explanation: total circuit=16/4=4
total feet squirrel travels=4*3=12 feet
ANSWER:A
Question: The difference of the squares of two consecutive odd integers is divisible by which of the following integers ?
A.4
B.6
C.2
D.8
Answer: D.8
Explanation: Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,
(2n + 3)^2 - (2n + 1)^2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)
= (4n + 4) x 2
= 8(n + 1), which is divisible by 8.
ANSWER D
Question: Having scored 94 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?
A.28
B.27
C.26
D.22
Answer: D.22
Explanation: Explanation :
Let the average score of the first 18 innings be n
18n + 94 = 19(n+4)=> n = 18
So, Average score after 19th innings = x+4 =22.
Answer : D
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 3/7. What is the probability that they agree in stating the same fact?
A.17/35
B.17/37
C.17/39
D.17/33
Answer: A.17/35
Explanation: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 3/7 + 2/5 * 4/7
= 17/35
Answer:A
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
A.337
B.268
C.198
D.646
Answer: D.646
Explanation: 840 = P [1 + (10*3)/100]
P = 646'
Answer:D
Question: Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is
A.70
B.71
C.72
D.73
Answer: C.72
Explanation: Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=264
<=>11x/3=264
=>x=72
Answer: Option C
Question: Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution?
A.62.0
B.65.25
C.68.75
D.70.15
Answer: C.68.75
Explanation: SOL:
Lets assume that 46L of sol1 was mixed with 10L of sol2.
Alcohol in Sol1: 46*3/4 = 34.5L
Alcohol in Sol2: 10*2/5 = 4L
Total Alcohol in the mixed solution of 56L = 34.5 + 4 = 38.5L
Alcohol concentration in the new sol: (38.5/56)*100 = 68.75%
ANSWER:C
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 5% of bananas were rotten. Find the percentage of fruits in good condition?
A.92.5%
B.89.0%
C.85.2%
D.96.8%
Answer: B.89.0%
Explanation: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 5% of 400
= 20
Therefore, total number of rotten fruits = 90 + 20= 110
Therefore Number of fruits in good condition = 1000 - 110 = 890
Therefore Percentage of fruits in good condition = (890/1000 × 100)%
= (89000/1000)%
= 89.0%
Answer:B
Question: A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 10 minutes. How much time will be take to cover a distance of 10 kilometres?
A.148 min.
B.150 min.
C.145 min.
D.155 min.
Answer: B.150 min.
Explanation: Rest time = Number of rest Ã— Time for each rest
= 9 Ã— 10 = 90 minutes
Total time to cover 10 km
= (10 â„10 Ã— 60)minutes + 90 minutes = 150 minutes
Answer B
Question: Find the length of a rectangle isdecreased by 40cm & the width is increased by 3cm, a square with the samearea as the original rectangle result. Find the perimeter of the original rectangle?
A.30 cm
B.40 cm
C.50 cm
D.64 cm
Answer: C.50 cm
Explanation: Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(1)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(2)
Solving 1 & 2 , we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
C
Question: If the LCM of two integers M, N (where N> M and M>1) is M*N, then which of the following can not be true?
A.Both M and N can be Prime Numbers.
B.Both M and N can be consecutive integers.
C.M and N do not share any Prime factors.
D.All Prime factors of M must be Prime factors of N.
Answer: D.All Prime factors of M must be Prime factors of N.
Explanation: If LCM of two numbers M and N is the product MN then both numbers are Co- prime.
(Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).
Numbers that can be Co-Prime are :
1) Two consecutive natural numbers.
2) Two consecutive odd numbers.
3) Two prime numbers.
4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.
With above four statements it can be concluded that Options A, B, C and E are all true.
Only Option D cannot be true.
Hence answer is D.
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
A.4/9
B.4/1
C.4/7
D.4/2
Answer: A.4/9
Explanation: 2/3 ---- 12
? ----- 8 ==> 4/9
Answer:A
Question: An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 16 times the difference between the two numbers. How many coins did the old man have?
A. 24
B. 26
C. 30
D. 16
Answer: D. 16
Explanation: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.
x^2 - y^2 = 16(x - y) --> x + y = 16.
Answer: D.
Question: At a meeting, 3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
A.2
B.7
C.C)120
D.D)144
Answer: C.C)120
Explanation: The number of arrangements of n distinct objects in a row is given by n!
The number of arrangements of n distinct objects in a circle is given by (n−1)!
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
R=n!-n=(n−1)!
(n−1)!=(7−1)!=720
Answer: E
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John’s weekly allowance?
A.$2.40
B.$3.00
C.$3.20
D.$3.60
Answer: D.$3.60
Explanation: Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$0.96
Therefore, X=$3.60. Answer D
Question: If (c - a)/(c - b) = 3, then (5b - 5a)/(c - a) =
A.0.5
B.1
C.1.5
D.3.33
Answer: D.3.33
Explanation: Let's say c=7, b=5, a=1 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 3.33
Answer D (hopefully )))
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively The ratio of their speeds is
A.2 : 3
B.4 : 3
C.6 : 7
D.9 : 16
Answer: B.4 : 3
Explanation: Solution
Let us name the trains
as A and B.	= (A'S speed) : (B's speed)
=√b : √a
= √16 : √9
= 4 : 3
Answer B
Question: What is the value of n if the sum of the consecutive odd intergers Q from 1 to n equals 169?
A.47
B.25
C.37
D.33
Answer: B.25
Explanation: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.
Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.
a=1 (first term)
d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2
*On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.
But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.
Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.
It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Question: If 0 < X < Y, X is an odd number and Y is a prime number, which of the following can be the value of X + Y ?
A.11.
B.13.
C.17.
D.10
Answer: D.10
Explanation: If x is odd ,implies x(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2 & x=1 since 0<X<Y therefore X+Y =3. But 3 is not an option
which implies y is odd,
Now X(odd)+Y(odd)=Even
10 is the only option that is even.
Ans is D: 10
Question: If the complement of a certain angle is twice the measure of that certain angle, then what is the measure of that certain angle?
A.45°
B.30°
C.22.5°
D.18°
Answer: B.30°
Explanation: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is 2x, and together, these add up to 90 degrees.
x + 2x = 90
3x = 90
x = 30°
Answer = (B)