RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Solve the equation :
(2x - 1)3 + 2x(2x - 3).(3 - 2x) – (3x - 1)2 = 3x2 - 2
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: Solution:
We open the brackets by using the formulas for multiplication:
8x3 - 3(2x)2.1 + 3.2x(1)2 – 13 - 2x(2x - 3)2 – (9x2 - 6x + 1) = 3x2 - 2 <=>
8x3 - 12x2 + 6x - 1 - 2x(4x2 - 12x + 9) - 9x2 + 6x - 1 = 3x2 - 2 <=>
8x3 - 21x2 + 12x - 8x3 + 24x2 - 9x = 3x2 <=>
3x2 + 3x = 3x2 <=>
3x = 0 <=> x = 0
Answer A
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.6
B.5
C.7
D.4
Answer: D.4
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: D
Question: In a 2000 m race, A beats B by 100 meters or 20 seconds. Find the speed of B?
A.10m/s
B.2m/s
C.5m/s
D.7m/s
Answer: C.5m/s
Explanation: Since A beats B by 100 m or 20 seconds,
it implies that B covers 100 m in 20 seconds.
Hence speed of B = 100/20 = 5 m/s.
Answer: C
Question: A is twice as good as B. And together they finish a piece of work in 20days. In how many days will A alone finish the work
A.30
B.25
C.12
D.10
Answer: A.30
Explanation: (A's 1day work):(B's 1day work) = 2:1
A+B 1day work = 1/20
A's 1day work = (1/20)*(2/3) = 1/30
A alone can finish the work in 30 days
Answer is A
Question: Will decides to attend a basketball game with four friends.
If the party of five sits together in five consecutive seats, and Will must NOT sit in between two of his friends, how many ways
can the five friends be arranged?
A.24
B.36
C.48
D.72
Answer: C.48
Explanation: Will have to sit at either of the ends.
If will sits on the left most corner, then other 4 friends can be arranged in 4! = 24
Will can also sit on the other end, then another 4! ways we can arrange.
So total number of ways = 24+24 = 48
ANS:Option( C)
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits are in s(99)?
A.350
B.353
C.354
D.356
Answer: B.353
Explanation: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353;
ANSWER:B
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 15th, 17th, and 18th terms in the sequence?
A.2^18
B.3(2^17)
C.7(2^16)
D.13(2^14)
Answer: D.13(2^14)
Explanation: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 15th term will be 2^14
17th term 2^16
18th term 2^17
adding all three
we get
2^14+(2^15)*4+(2^15)*8
so answer is 2^15(1+4+8)=>13(2^15)
answer D
Question: The speed of a boat in still water in 42 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 44 minutes is:
A.86.6 km
B.46.6 km
C.33 km
D.35.6 km
Answer: C.33 km
Explanation: Speed downstream = (42 + 3) = 45 kmph
Time = 44 minutes =44/60 hour = 11/15 hour
Distance travelled = Time × speed =11/15×45 = 33 km
ANSWER:C
Question: If (-3)^(2x) = 3^(12 - x) and x is an integer, what is the value of x ?
A.5
B.4
C.3
D.2
Answer: B.4
Explanation: Since x is an integer, (-3)^(2x) is always positive.
So, 3^2x = 3^(12 - x)
2x = 12 - x
3x = 12
x = 4
Answer: B
Question: In an election between two candidates first candidate got 70% of votes polled and second Candidate got 270 votes. The total number of votes polled was?
A.700 votes
B.750 votes
C.800 votes
D.900 votes
Answer: D.900 votes
Explanation: Explanation:
Total = 100 %,
First person got 70%
second person got remaining 30 % of votes.
than 30 % = 270
30% = 30*9 = 270
100% =100*9 =900votes
Answer: Option D
Question: In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs 157300 was their profit, how much amount did B receive?
A.Rs. 48000
B.Rs. 48200
C.Rs. 48400
D.Rs. 48600
Answer: C.Rs. 48400
Explanation: Solution: Assume that investment of C = x
Then, investment of A =2x
Investment of B = 4x/3
A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3
B's share = 157300 * 4/(6+4+3) = 157300*4/13
= 12100*4 = Rs. 48400.
Answer: Option C
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -7 ≤ x ≤ 1 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
A.54
B.432
C.2,160
D.3024
Answer: D.3024
Explanation: We have the rectangle with dimensions 9*7 (9 horizontal dots and 7 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*7C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 6C1, (7-1=6 as 1 vertical dot is already occupied by A).
9C1*7C1*8C1*6C1=3024
Answer: D.
Question: How many pairs (n, n+1) have one or more prime factors common, where n is an integer and 2 ≤ n ≤9 ?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: n and n+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
Question: If (x+3)^2/(3x+5)=2, then the difference between the two possible values of x is:
A.2
B.4
C.6
D.8
Answer: A.2
Explanation: (x+3)^2/(3x+5)=2
(x+3)^2=2(3x+5)
x^2+6x+9=6x+10
x^2-1=0
(x-1)(x+1)=0
x=1 or x=-1
The answer is A.
Question: If cost of 18 eggs be 75 rupees, then find out the cost of 5 dozen eggs.
A.300
B.400
C.500
D.252
Answer: D.252
Explanation: Cost of 18 eggs = 75 rupees
Cost of 1 egg = 75/18 = 4.2 rupees,
Cost of 5 dozens, i.e. 4.2 x 12 = 50.4 x 5 = 252
Answer : D
Question: The sum of two numbers is 64, and one of them is 12 more than the other. What are the two numbers?
A.26-38
B.50-34
C.60-24
D.42-42
Answer: A.26-38
Explanation: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 64:
word problem = 64
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 64 âˆ’ 12
= 52.
x = 52/2
= 26.
This is the first number. Therefore the other number is
x + 12 = 26 + 12 = 38.
The sum of 26 + 38 is 64.
A
Question: The average of 6 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?
A. 9.5
B. 8.0
C. 7.2
D. 5.0
Answer: C. 7.2
Explanation: The average of 6 numbers is 6.8
The sum of 6 numbers will be 6.8 x 6 = 40.8
The average of 6 number after one of the number is multiplied by 3 is 9.2
The sum of the numbers will now be 9.2 x 6 = 55.2
So the sum has increased by 55.2-40.8 = 14.4
Let the number multiplied by 3 be n
Then,
3n = n+14.4
or 2n = 14.4
or n = 7.2
Answer:- C
Question: In a rectangular coordinate system, if a line passes through the points (-13,-18), (17,22) and (x,2) then what is the value of x?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: The slope of the line m is rise/run = 22-(-18) / 17-(-13) = 4/3
4/3 = 22-2 / 17-x
68-4x = 66-6
x = 2
The answer is B.
Question: If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:
A.3:1
B.3:2
C.3:5
D.3:7
Answer: A.3:1
Explanation: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=27/1
=>(a/b)3=(3/1)3
a/b=3/1
=>a:b=3:1
ANSWER IS A
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A.25200
B.25100
C.25000
D.26000
Answer: A.25200
Explanation: Explanation:
Number of ways of selecting 3 consonants from 7
= 7C3
Number of ways of selecting 2 vowels from 4
= 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 × 4C2
=
(
7
×
6
×
5
3
×
2
×
1
)
×
(
4
×
3
2
×
1
)
=
210
=(7×6×53×2×1)×(4×32×1)=210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves
=
5
!
=
5
×
4
×
3
×
2
×
1
=
120
=5!=5×4×3×2×1=120
Hence, required number of ways
=
210
×
120
=
25200
Answer is A
Question: A jeep takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.48 Kmph
B.52 Kmph
C.6o Kmph
D.63 Kmph
Answer: C.6o Kmph
Explanation: Time = 6
Distance = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
C)
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?
A.27
B.30
C.20
D.99
Answer: B.30
Explanation: M = 15
S = 15
DS = 15 + 15 = 30
Answer:B
Question: X can do a piece of work in 40days. He works at it for 8 days and then Y finished it in 24 days. How long will Y take to complete the work?
A.30
B.12
C.15
D.18
Answer: A.30
Explanation: Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 24 days
Whole work will be done by Y in 24*5/4 = 30days
Answer is A
Question: Mary's income is 60 percent more than Tim's income, and Tim's income is 50 percent less than Juan's income. What percent of Juan's income is Mary's income?
A. 124%
B. 120%
C. 96%
D. 80%
Answer: D. 80%
Explanation: Juan's income = 100 (assume);
Tim's income = 50 (50 percent less than Juan's income);
Mary's income = 80 (60 percent more than Tim's income).
Thus, Mary's income (80) is 80% of Juan's income (100).
Answer: D.
Question: How many cubes of 50 cm edge can be put in a cubical box of 1 m edge.
A.17 cm
B.10 cm
C.8 cm
D.6 cm
Answer: C.8 cm
Explanation: Number of cubes =100âˆ—100âˆ—100/50*50*50=8
Number of cubes =100âˆ—100âˆ—10010âˆ—10âˆ—10=1000
Note: 1 m = 100 cm
Answer:C
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 800 grams. Find the profit percent.
A.20
B.15
C.25
D.18
Answer: C.25
Explanation: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 800
100 + g / 100 + 0 = 1000 / 800
100+g = 5/4*100
g = 25
ANSWER: C
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 5% sugar. What percentage of the gallon is dye?
A. 6
B. 4
C. 7.5
D. 8
Answer: B. 4
Explanation: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/5
=> 4/5 = x/5 => x = 4*5/5 = 4.
Answer is B
Question: 3.5 can be expressed in terms of percentage as?
A.0.35%
B.3.5%
C.35%
D.350%
Answer: D.350%
Explanation: Explanation:
3.5 = 35/10 = (35/10 * 100) = 350%
Answer IS D
Question: The average of 11 results is 45, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
A.A)46
B.B)111
C.C)66
D.D)76
Answer: B.B)111
Explanation: 1 to 11 = 11 * 45 = 495
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 495= 111
Answer:B
Question: The water from one outlet, flowing at a constant rate, can fill a swimming pool in 7 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 4 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?
A. 0.22
B. 0.31
C. 2.54
D. 3.21
Answer: C. 2.54
Explanation: Always remember RT=W i.e Rate*Time = Work
Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.
They both of them together will do a work in 1 day.
So now your question first determine both outlets rate.
1st outlet rate = 1/7 (R=W/T here W=1 work, T = 7hrs)
2nd outlet rate = 1/4 (R=W/T here W=1 work, T = 4hrs)
Both of them working together rate = 1st outlet rate + 2nd outlet rate = 1/7+1/4 = 11/28
again apply the formula RT=W
T = W/R = 1/11/28 = 28/11 =2.54
Answer is C.
Question: The total number of digits used in numbering the pages of a book having 369 pages is
A.732
B.990
C.999
D.1305
Answer: C.999
Explanation: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 270) = (9 + 180 + 810) = 999.
ANSWER:C
Question: A committee of two people is to be chosen from three married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
A.4
B.8
C.12
D.16
Answer: C.12
Explanation: Each couple can send only one representative to the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 3 to send only one representatives to the committee: 3C2=3.
But each of these 2 couples can send two persons (husband or wife): 2*2=2^2=4.
Total # of ways: 3C2*2^2=12.
Answer: C
Question: There ia truck which should reach some place at 11'o clock , if it travels with 30 mph it reaches i hour before, if it travles with 20 mph it reaches 1 hour late. what is the distance it must be travlled and what is the speed it must maintain to rech at exact time?
A.22 kmph
B.24 kmph
C.26 kmph
D.28 kmph
Answer: B.24 kmph
Explanation: let S T D are the speed time and distance
S=D/T
according to question,
30=D/(T-1)..........1
and
20=D/(T+1)..........2
dividing equation 1 by 2 we get T=5 hours
now,
for distance put value of T in equ 1
then D=120 m
now,
for exact time s=d/t
=120/5
=24 kmph
ANSWER:B
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. 5b > 5c
III.a + b + c > a^3
A.I only
B.II only
C.III only
D.II and III
Answer: A.I only
Explanation: Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4
Putting the values in the answers only 'A' seems valid.
Question: Mohit sold an article for $27000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
A.16000
B.22500
C.15000
D.18000
Answer: B.22500
Explanation: Let the CP be $x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = $1.08x = 27000 - 10/100(27000) = 27000 - 2700 = $22500
=> 1.08x = 22500
=> x = 22500
B
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is?
A.4452
B.4445
C.4330
D.4334
Answer: A.4452
Explanation: Divisor = (5 * 42) = 210
= 10 * Quotient = Divisor
=> Quotient = 210/10 = 21
Dividend = (Divisor * Quotient) + Remainder
Dividend = (210 * 21) + 42 = 4452
A
Question: If a positive integer n is divisible by both 2 and 3, then n must also be divisible by which of the following?
I. 6
II. 5
III. 18
A.None
B.I only
C.II only
D.I and II
Answer: B.I only
Explanation: A multiple of 2 and 3 is also a multiple of 6, but not necessarily a multiple of 5 or 18.
The answer is B.
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.16,500 at the end of the year, B's share is
A.Rs.4000
B.Rs.6000
C.Rs.7500
D.Rs.6600
Answer: B.Rs.6000
Explanation: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
∴ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(16500 x 4 / 11)
= Rs.6000.
Answer B
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.1.8
B.1.9
C.1.2
D.1.5
Answer: D.1.5
Explanation: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer:D
Question: If m : n = 3 : 4 and n : o = 8 : 9, then m : o is :
A.1 :3
B.3 :2
C.2 : 3
D.1 : 2
Answer: C.2 : 3
Explanation: Expl : m/n = m/n * n/o =3/4 * 8/9 = 2/3. So m : o = 2 : 3
Answer :C
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'6" tall, which of the following is the median height of the children?
A.2'2"
B.2'6"
C.3'3"
D.3'4"
Answer: B.2'6"
Explanation: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'6"+2'6")/2 = 2'6"
Ans:Option B
Question: If you are given $2, and the amount doubles every day, how much money will you have after 10 days?
A.$256
B.$512
C.$1024
D.$2048
Answer: C.$1024
Explanation: 2^10=1024
The answer is C.
Question: The sum of number of boys and girls in a school is 900. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
A.50
B.40
C.60
D.90
Answer: D.90
Explanation: We have x+x% of 900 = 900
x + x/100 * 900 = 900
10 * x = 900
x =90
Answer is D
Question: If an article with marked price of $4000 is sold at successive discount of 10%,25% and 15%,what is the price the customer has to pay?
A.3600
B.3080
C.2280
D.2760
Answer: C.2280
Explanation: discount=0.9*.75*.85=.57
so .57*4000=2280
ANSWER:C
Question: If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 682, C will receive
A.233
B.381
C.132
D.287
Answer: C.132
Explanation: Explanation:
Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (682* 6/31) = Rs, 132.
Answer: C) Rs.132
Question: In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000.
What is the median salary
A.42,000
B.43,000
C.44,000
D.45,000
Answer: D.45,000
Explanation: as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned)
Rest amounts are in the form of greater than or lesser than , Hence C $45000
answer is D
Question: There are 6 working days in a regular week and for each day, the working hours are 10. A man earns Rs. 2.10 per hour for regular work and Rs. 4.20 per hour for overtime. If he earns Rs.525 in 4 weeks, how many hours did he work?
A.245
B.285
C.275
D.255
Answer: A.245
Explanation: Explanation :
Regular working hours in 4 weeks = (4 × 6 × 10) = 240 hours
Amount earned by working in these regular working hours
= 240 × 2.10 = Rs.504
Additional amount he earned = 525 - 504 = Rs.21
Hours he worked overtime = 21/4.2 = 210/42 = 5 hours
Total hours he worked = 240 + 5 = 245 hours
Answer : A
Question: Two brothers took the GMAT exam, the higher score is A and the lower one is B. If the difference between the two scores is equal to their average, what is the value of B/A ?
A.3
B.2
C.1/2
D.1/3
Answer: D.1/3
Explanation: Answer is D : 1/3
A - B = (A + B)/2
Solving for B/A = 1/3
D
Question: There are three categories of jobs A, B and C. The average salary of the student who got the job of A and B categories is 26 lakh per annum. The average salary of the students who got the job of B and C category is 44 lakh per annum and the average salary of those students who got the job of A and C categories is 34 lakh per annum. The most appropriate (or closet) range of average salary of all the three categories (if it is known that each student gets only one category of jobs i.e. , A, B and C):
A.lies between 30 and 44
B.lies between 28 and 34
C.lies between 34 and 44
D.lies between 27 and 44
Answer: A.lies between 30 and 44
Explanation: Solution: Let the number of students who got the job of A, B and C categories is a, b and c respectively,
Then the total salary,
= [{26(a+b)+44(b+c)+34(c+a)}/2(a+b+c)]
= [(60a+70b+78c)/2(a+b+c)]
= [30(a+b+c)+(5b+9c)]/(a+b+c)
= 30 + some positive value
Thus, the minimum salary must be Rs. 30 lakh and the maximum salary can not exceed 44, which is the highest of the three.
Answer: Option A
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
A.13√8
B.13√2
C.13√0
D.53√2
Answer: B.13√2
Explanation: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer:B
Question: Two numbers are respectively 19% and 40% more than a third number. The percentage that is first of the second is?
A.15%
B.20%
C.25%
D.30%
Answer: A.15%
Explanation: I II III
119 140 100
140----------119
100-----------? => 15%
Answer:A
Question: The average (arithmetic mean) of 10, 30, and 50 is 8 more than the average of 20, 40, and x. What is x?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: The average of 10, 30, and 50 is 30.
The average of 20, 40 and x is 22.
Then 20 + 40 + x = 66.
x = 6.
The answer is C.
Question: A sum of Rs.1400 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls
A.8B, 5G
B.5B, 8G
C.4B, 9G
D.9B, 4G
Answer: B.5B, 8G
Explanation: 120B+100G=1400-----i
B+G=13-------ii
from i
100B+20B+100G=1400
100(B+G)+20B=1400
100(13)+20B=1400
By simplifing we get
B=5;G=8
ANSWER:B
Question: What approximate value will come in place of the question mark (?) in the following equation?
√625.04×16.96+136.001÷17=?
A.418
B.441
C.425
D.433
Answer: D.433
Explanation: ?=−−−−−√625.04×16.96+136.001÷17?=≈ 25 × 17 + 8
= 425 + 8 = 433
Answer D
Question: Seats for Maths, Physics and Biology are in the ratio of 8 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
A.16 : 15 : 20
B.16 : 7 : 8
C.16 : 8 : 9
D.Cannot be determined
Answer: A.16 : 15 : 20
Explanation: Reqd ratio 8 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100
= 8 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 16 : 15 : 20
Answer A
Question: A boat can move upstream at 25 kmph and downstream at 37 kmph, then the speed of the current is?
A.5 kmph
B.7 kmph
C.8 kmph
D.6 kmph
Answer: D.6 kmph
Explanation: US = 25
DS = 37
M = (37 - 25)/2 = 6
Answer:D
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
A.228
B.105
C.288
D.277
Answer: B.105
Explanation: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: B
Question: A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/9 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?
A.7x/2
B.x/2
C.2x/3
D.3x/2
Answer: A.7x/2
Explanation: x/(x+y) = 2/9
9x = 2x+2y
7x = 2y
y = 7x/2
Answer A
Question: If in a $210 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?
A.70mln
B.60mln
C.50mln
D.40mln
Answer: A.70mln
Explanation: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $210 mln portfolio, x+2x=3x=210 mln from where x=70 mln.
Answer: A
Question: If 55^4*11^6*16^3 = x, what is the units digit of x ?
A.2
B.6
C.0
D.1
Answer: C.0
Explanation: 55^4*11^6*16^3 = x
Units digit of x will be
5^4 * 1^6 * 6^3
=5* 1 *6
=30
Therefore , units digit of x = 0
Answer C
Question: For how many integers n is 1^n+1 = (n+1)^1?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: If n=0
1^0+1 = (0+1)^1
1^1 =1 ok
If n=1
1^2 =1 ; (2)^1=2 not OK
So, Answer : A