RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.277
B.267
C.240
D.882
Answer: C.240
Explanation: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C
Question: If 18 is 15 percent of 10 percent of a certain number, what is the number?
A.9
B.1200
C.40
D.81
Answer: B.1200
Explanation: Let the certain number be x.
=> (15/100)*(10/100)*x = 18;
=> x=1200;
Ans is (B).
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number?
A.1875
B.2000
C.2375
D.2500
Answer: B.2000
Explanation: the five-digit number: abcde
a have 4 choice of even numbers: 2, 4, 6, 8
b have 4 choice of even numbers: 0, 2, 6, 8 because 4 cannot appear more than once
c, d and e each have 5 choice from 1, 3, 5, 7, 9
So total: 4*4*5*5*5=2000 ANS:B
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A.50
B.100
C.150
D.200
Answer: B.100
Explanation: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer is B.
Question: When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?
A.$1,600
B.$1,850
C.$2,250
D.$2,400
Answer: C.$2,250
Explanation: Let the value of the item be $x, then 0.07(x−1,000)=87.5--> x−1,000=1,250x−1,000=1,250 --> x=2,250.
Answer: C.
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 16 miles, how many miles was Mike's ride?
A.32
B.36
C.40
D.44
Answer: B.36
Explanation: The cost of Annie's ride was 2.5+5+(0.25*16) = $11.50
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 11.5
0.25*x = 9
x = 36 miles
The answer is B.
Question: In the xy-coordinate system, if (m,n) and (m+2, n+k) are two points on the line perpendicular to x=2y+5, then k=?
A.-5
B.-8
C.2
D.-4
Answer: D.-4
Explanation: the slope= k/2
the line perpendicular to x=2y+5 or y=1/2x-5/2 has
a slope= -1/ (1/2) =-2 --->k/2=-2 --> k=-4
Answer is D
Question: A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price
A.Rs.500/-
B.Rs.540/-
C.Rs.600/-
D.Rs.640/-
Answer: B.Rs.540/-
Explanation: 100 % ------> 600 (100 * 6 = 600)
90 % ------> 540 (90 * 6 = 540)
Selling price = Rs.540/-
B
Question: After paying a 10 percent tax on all income over $3,000, a person had a net income of $12,000. What was the income before taxes?
A.$13,300
B.$13,000
C.$12,900
D.$10,000
Answer: B.$13,000
Explanation: Let x be the income over 3000
Then (x-x/10) + 3000 = 12000
=> x = 10000
Therefore income before taxes = 10000 + 3000 = 13000
Option (B)
Question: In a throw of dice what is the probability of geÆ«ing number greater than 2
A.2/3
B.1/3
C.1/5
D.1/6
Answer: A.2/3
Explanation: Explanation:
Number greater than 2 is 3, 4, 5 & 6, so only 4 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 4/6 = 2/3
Answer: A
Question: In xyz business school,88% are taking their specialization as finance at the same time 76% taking their specialization as marketing.If 90% are taking their specialization as finance then, what is % of marketing specialization students?
A.55
B.75
C.43
D.52
Answer: C.43
Explanation: Percentage of finance specialization = 88; Percentage of marketing specialization = 75%; Total =90*100;Percentage of finance specialization= 90 - 88= 2; Percentage of marketing specialization= 100 - 75 =25; then Percentage of marketing specialization = 0.75*24=18. Then total percentage of marketing specialization = 25+18=43. Answer: C
Question: Out of seven given numbers, the average of the first four numbers is 4 and that of the last four numbers is also 4. If the average of all the seven numbers is 3, fourth number is
A.3
B.4
C.7
D.fourth no=11
Answer: D.fourth no=11
Explanation: (a+b+c+d)/4=4
=>(a+b+c+d)=16...........(1)
(d+e+f+g)/4=4
=>(d+e+f+g)=16
=>(e+f+g)=16-d...........(2)
Also, (a+b+c+d+e+f+g)/7=3 (Given)
using (1) and (2) equations
16+16-d=21
=> d=11
ANSWER:D
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
A.15
B.16
C.18
D.25
Answer: B.16
Explanation: EXPLANATION
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.
Suppose Tanya takes x days to do the work.
5 : 4 :: 20 : x => x =(4x20/5)
x = 16 days.
Hence, Tanya takes 16 days to complete the work.
Answer B
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 8% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
A.$100
B.b $115
C.c $125
D.d $130
Answer: D.d $130
Explanation: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 8% less than the price each head sold for on the day before i.e , (92/100)*0.5 = $ 0.46
Hence selling cost for the remaining cabbage = 500 * 0.46 = $ 230
Total selling cost = 500 + 230 = $ 730
Gross profit = $ 730 - $ 600 = $ 130
Hence Answer is D.
Question: Three pounds of 05 grass seed contain 10 percent herbicide. A different type of grass seed, 20, which contains 20 percent herbicide, will be mixed with three pounds of 05 grass seed. How much grass seed of type 20 should be added to the three pounds of 05 grass seed so that the mixture contains 15 percent herbicide?
A.3
B.3.75
C.4.5
D.6
Answer: A.3
Explanation: 05 grass seed contains 5% herbicide and its amount is 3 pound
20 grass seed contains 20% herbicide and its amount is x
when these two types of grass seeds are mixed, their average becomes 15%
thus we have
3(10)+x(20)/(x+3) = 15
30+20x=15x +45
5x=15
or x=3
A
Question: The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday?
A.39oC
B.44oC
C.38oC
D.41oC
Answer: A.39oC
Explanation: Solution: Average temperature for Wednesday, Thursday and Friday = 40oC
Total temperature = 3*40 = 120oC
Average temperature for Thursday, Friday and Saturday = 41oC
Total temperature = 41*3 = 123oC
Temperature on Saturday = 42oC
Now,
(Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120;
Saturday - Wednesday = 3
Wednesday = 42-3 = 39oC.
Answer: Option A
Question: Machine R and machine B are each used to manufacture 660 sprockets. It takes machine R 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine R. How many sprockets per hour does machine R produces?
A.6
B.6.6
C.60
D.100
Answer: A.6
Explanation: I think the correct answer is A.
Machine R produces at a speed of R sp/hour and B at a speed of B sp/hour.
so, 660/R=(660/B)+10 and B=1,1 R--->1,1*660=660+11R--->A=6, so answer A is correct
Question: A can finish a work in 24 days, B n 9 days and C in 12 days. B&C start the
work but are forced to leave after 3 days. The remaining work done by A in:
A.12days
B.13days
C.11days
D.10days
Answer: D.10days
Explanation: (B+C)'s one day's work=1/9+1/12=7/36
Work done by B & C in 3 days=3*7/36=7/12
Remaining work=1-(7/12)=5/12
Now , 1/24 work is done by A in 1 day.
So, 5/12 work is done by A in 24*5/12=10 days
ANSWER D 10days
Question: The number of boxes in a warehouse can be divided evenly into 7 equal shipments by boat or 28 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?
A. 28
B. 33
C. 54
D. 81
Answer: A. 28
Explanation: Answer is the LCM of 7 and 28
= 28
Answer A
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
A.276
B.299
C.322
D.336
Answer: C.322
Explanation: the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer: Option C
Question: Two pipes A and B can separately fill a cistern in 24 minutes and 48 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 12 minutes. In how much time, the third pipe alone can empty the cistern?
A.90 min
B.48 min
C.54 min
D.120 min
Answer: B.48 min
Explanation: 1/12-(1/24+1/48)=-1/48
third pipe can empty in 48 minutes
ANSWER:B
Question: There are 6 people in the elevator. Their average weight is 154 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.
A.133
B.168
C.189
D.190
Answer: A.133
Explanation: Solution
Average of 7 people after the last one enters = 151 .
âˆ´ Required weight = (7x151)-(6x154)
= 1057- 924
= 133.
Answer A
Question: A, Band C can do a piece of work in 11 days, 45 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?
A.7 days
B.8 days
C.9 days
D.10 days
Answer: C.9 days
Explanation: (A+B)'s 1 day's work = 1/11+1/45 = 56/495
(A+C)'s 1 day's work = 1/11+1/55 = 6/55
work done in 2 day's = 56/495+6/55 =2/9
2/9th work done in 2 days
work done= 9/2*2 = 9 days
ANSWER:C
Question: What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, 216, x
A.23
B.34
C.36
D.42
Answer: C.36
Explanation: Go on dividing by 6 to the next number
C)
Question: A baseball card decreased in value 40% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
A.46%
B.30%
C.32%
D.36%
Answer: A.46%
Explanation: Let the initial value of baseball card = 100
After first year , value of baseball card = (1- 40/100)* 100 = 60
After second year , value of baseball card =(1 - 10/100)* 60 = 54
total percent decrease of the card's value over the two years = (100-54)/100 *100%
=46%
Answer A
Question: A student scored an average of 75 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
A.86
B.16
C.76
D.95
Answer: D.95
Explanation: Given M + P + C = 75 * 3 = 225 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 225
= 95
Answer:D
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
A.28882
B.27772
C.23123
D.13500
Answer: D.13500
Explanation: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer: D
Question: A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
A.145
B.253
C.370
D.352
Answer: B.253
Explanation: we can easily solve the ans using the result
all options are fullfill 1st condition ie the sum of digit is 10
now only B and D are full fill the 2nd condition ie middle digit = sum of the side digit
now finally B is the result bcze if we add two number the number must be increase but here if we reverse 352 then it become 253 but if we add 99 the itnever be a small number so thats why result is 253
ANSWER:B
Question: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
A.285
B.377
C.366
D.288
Answer: A.285
Explanation: Since the month begins with a Sunday, there will be five Sundays in the month
Required average = (510 * 5 + 240 * 25) / 30 = 8550/30 = 285
Answer: A) 285
Question: There are two numbers. If 55% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
A.A)5/6
B.B)5/8
C.C)5/11
D.D)6/7
Answer: C.C)5/11
Explanation: Let the two numbers be x and y.
55/100 * x + y = 5/4y
=> 11/20 x = 1/4 y => x/y = 5/11
C)
Question: A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 4 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
A.1/3
B.1/4
C.1/5
D.1/6
Answer: B.1/4
Explanation: Let x be the fraction of her take-home pay that the worker saved.
Let P be the monthly pay.
12xP = 4(1-x)P
12xP = 4P - 4xP
16xP = 4P
x = 1/4
The answer is B.
Question: How many digits are required to number a book containing 250 pages?
A.756
B.642
C.492
D.372
Answer: B.642
Explanation: 9 pages from 1 to 9 will require 9 digits.
90 pages from 10 to 99 will require 90*2=180 digits.
250-(90+9)=151 pages will require 151*3=453 digits.
The total number of digits is 9+180+453=642.
The answer is B.
Question: In how many ways can the letters of the word ACTUAL be rearranged such that the vowels always appear together?
A.6!/2!
B.3!*3!
C.4!/2!
D.(4! *3!)/2!
Answer: D.(4! *3!)/2!
Explanation: In the word ABACUS , there are 3 vowels - 2 A's and U
Number of ways the letters of word ACTUAL be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Question: If x and y are both prime numbers greater than 10, which of the following CANNOT be true?
I. xy is an even number.
II. x - y = 117.
III.The sum of x and y is even.
A.A)I and II only
B. I only
C. I and III only
D. II and III only
Answer: D. II and III only
Explanation: MANHATTAN GMATOFFICIAL SOLUTION:
Since x and y are both prime numbers greater than 10, they must both be odd. Therefore xy must be an odd number, so Statement I cannot be true. Similarly, if x and y are both odd, then x - y cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since x and y are both odd, x + y must be even, so Statement III will always be true. Since Statements I and II CANNOT be true, but Statement III IS true,the correct answer is (D).
Answer : D
Question: There is a total of 84 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/7. What is the probability that the marble will be either red or blue?
A.4/7
B.9/14
C.11/14
D.17/28
Answer: D.17/28
Explanation: P(red or blue) = 1 - P(white) - P(green) = 28/28 - 7/28 - 4/28 = 17/28
The answer is D.
Question: A chessboard is an 8×8 array of identically sized squares. Each square has a particular designation, depending on its row and column. An L-shaped card, exactly the size of four squares on the chessboard, is laid on the chessboard as shown, covering exactly four squares. This L-shaped card can be moved around, rotated, and even picked up and turned over to give the mirror-image of an L. In how many different ways can this L-shaped card cover exactly four squares on the chessboard?
A.256
B.336
C.424
D.512
Answer: B.336
Explanation: Select 3 squares which are in a line together first. We will call them a block of 3 squares. Consider just the vertical arrangement for now (for horizontal, we will multiply everything by 2 at the end).
Consider a block of 3 squares lying vertically on the left edge (the first column of the chess board). You can place another square on the right to make an L at either extreme of the block. So for each such block, you can make an L in 2 ways. There will be 12 such blocks (6 on either edge).
You get 12*2 Ls.
Now consider the blocks of 3 squares lying vertically in columns 2 to 7. You can make an L by placing a square on left or right at either end. So for each block of 3 squares, you can make 4 Ls. There are 6 such blocks in each of the 6 columns
You get 6*6*4 Ls.
Total you get 12*2 + 6*6*4 = 168 Ls.
Now you just multiply it by 2 to account for the Ls lying horizontally too. Since it is a square, the number of Ls found vertically will be the same as the number of Ls found horizontally.
Total = 168*2 = 336
Answer (B)
Question: A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is
A.1:10
B.1:12
C.1:15
D.1:20
Answer: A.1:10
Explanation: Milk = m liters;
Water = w liters;
Cost of m+w liters = 6.4m;
Selling price of m+w liters = 8(m+w).
Given that 6.4m*1.375 = 8(m+w) --> w/m=1/10.
Answer: A.
Question: The number 94 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?
A.2
B.5
C.7
D.8
Answer: C.7
Explanation: Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-2, +/-3 and +/-9, so the difference could be 7, 11 or 12. Since only one of them is among the choices, then it must be the correct answer.
Answer: C
Question: The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 9!?
A.3(5!)
B.4(5!)
C.6(5!)
D.5(5!)
Answer: D.5(5!)
Explanation: GCF is the product of common factors of the numbers involved.
GCF = 5!
a = 9! = 9*8*7*6*5!
b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)
Looking at the answers only 5 (5!) and 9! will have GCF as 5!
Ans D
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 72 seconds. What is the length of each train (in meters)?
A.70
B.80
C.90
D.100
Answer: D.100
Explanation: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 72 seconds, the relative difference in distance traveled is 72 * 25/9 = 200 meters
This distance is twice the length of each train.
The length of each train is 200/2 = 100 meters
The answer is D.
Question: A certain article of clothing was discounted during a special sale to 2/3 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?
A.50%
B.22.22%
C.25%
D.16.66%
Answer: B.22.22%
Explanation: Say the original retail price of the item was $200.
The price after the first sale = 2/3 * $200 = $400/3.
The price after the second sale = 1/2 * $200 = $100.
The percent change from the first sale to the second = (400/3 - 100) / 150 = 1/3 = 22.22%.
Answer: B.
Question: In a lottery, there are 10 prizes and 20 blanks. A lottery is drawn at random. What is the probability of getting a prize?
A.1/10
B.2/5
C.1/3
D.5/7
Answer: C.1/3
Explanation: Solution
P(getting a prize)	= 10 / (10+20)
‹=› 10 / 30
‹=› 1/ 3.
Answer C
Question: In a 500 m race, Ravi beats Ramesh by 5 seconds or 100 m. They decide to run another race and this time Ravi gives Ramesh a head tart of 200 m. If Ravi’s speed is twice his previous speed and Ramesh’s speed is one and half times his previous speed, how far from the starting point should the winning post be so that they finish at the same time?
A.500 m
B.1000 m
C.1500 m
D.2000 m
Answer: A.500 m
Explanation: Ravi beats ramesh by 5 sec or 100 mtr....means ramesh cover 100mtr in 5 sec....by this we can get ramesh speed in 20m/sec
20.............in 1 sec
500........in 500/20=25 sec(Ramesh's time)
so ravi take 20 sec to cover 500 mtr......by this we can get that ravis speed is 25m/sec
now assume x be the distance from staring line where we need to put the winning post.
According to question ravi’s speed will be 25*2=50m/sec & ramesh’s speed will be 20*1.5=30 m/sec
now assume x be the distance from staring line where we need to put the winning post.
they will take same time to reach the wining post.
As ravi gives Ramesh a 200 m ahead start so he has to accede x meter and Ramesh has to accede (x-200) meter
Hence we may write,
x/50=(x-200)/30
x=500 meter
ANSWER:A
Question: What is the Compound Interest on Rs.9500 at 6% p.a. compounded half-yearly for 1 1/2 years.
A.810.91
B.840.91
C.880.91
D.887.91
Answer: C.880.91
Explanation: Compound interest : A = P(1 + r/n)nt
A = 10,380.91
C.I. >> 10,380.91 - 9500 >> Rs. 880.91
Answer:C
Question: Five farmers have 7,9,11,13 & 14 apple trees respectively in their orchards.last year each of them discovered that every tree in their own orchard bore exactly d same no of apples.further,if d 3rd farmer gives one apple to the 1st,& the 5th gives 3 to each of the 2nd & d 4th,they would all exactly have the same no of apples, what were d yields per tree in the orchards of d 3rd & 4th farmers?
A.8,9
B.10,11
C.11,12
D.11,9
Answer: D.11,9
Explanation: Let a, b, c, d & e be the number of apples bored last year in each farmer's tree.
Given that 7a + 1 = 9b + 3 = 11c - 1 = 13d + 3 = 14e - 6
But the question is to find the number of apples bored per tree in 3rd nd 4th orchard.It is enough to consider 11c - 1 = 13d + 3..
Therefore 11 c - 1 = 13 d + 3
By trial and error method, we get the value for c and d as 11 and 9.
5th nd 4th
14e - 6 = 13d + 3
14e - 13d = 9
here if u put e=d=1, result ll be 1, e=d=2 difference ll be 2, .... e=d=9 ,result ll be 9
so e=9 , d=9
So 5ht tree ll give 14 * 9 = 126 no. of apples
4th tree ll give 13 * 9 = 117 no. of apples
for 5th nd 2nd
14 * 9 -6 = 9 * b + 3
120=9b + 3
b = 13
So 2nd tree ll give 9 * 13 = 117
A= 119 , per tree = 17
B= 117 , per tree = 13
C= 121, per tree = 11
D= 117, per tree = 9
E = 126 , per tree = 9
3'rd farmer have 11 apples per tree and
4'th farmer have 9 apples per tree.
ANSWER:D
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
A.17/27
B.17/25
C.17/76
D.17/20
Answer: D.17/20
Explanation: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20
= 17/20
Answer: D
Question: Of the 200 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 45 percent of the employees prefer City Y and 55 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?
A. 65
B. 100
C. 115
D. 130
Answer: D. 130
Explanation: 110 prefer X (Group 1);
90 prefer Y (Group 2).
City Y needs 150 people: letall 90 who prefer Y (entire Group 2) be relocated there, the rest 60 will be those who prefer X from Group 1;
City X needs 40 people: 110-60=40 from Group 1 will be relocated to X, which they prefer.
So, the highest possible number of employees who will be relocated to the city they prefer is 90+40=130.
Answer: D.