RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?
A.6 days
B.18 days
C.21 days
D.3 days
Answer: B.18 days
Explanation: We have the important relation, More work, More time (days)
A piece of work can be done in 6 days.
Three times of work of same type can be done in 6 x 3
= 18 days
Answer B
Question: A man invested Rs. 4940 in Rs. 10 shares quoted at Rs. 9.50. If the rate of dividend be 14%, his annual income is
A.Rs.728
B.Rs.648
C.Rs.720
D.Rs.622
Answer: A.Rs.728
Explanation: Explanation :
Market Value of a share = Rs.9.50
Investment = Rs.4940
Number of shares = 4940/9.50 = 520
Face Value of a share = Rs.10
dividend = 14%
dividend per share = (10×14)100 = Rs. 1.4
His annual income = 520 × 1.4 = Rs.728
Answer : Option A
Question: Twenty percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
A.15%
B.20%
C.25%
D.60%
Answer: D.60%
Explanation: Initially 80% and 20% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗80
so, the required % is [(3/4)∗80/100]∗100 = 60%
ANSWER:D
Question: At a dinner party, 4 people are to be seated around a circular table. Two seating arrangement 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.5
B.10
C.6
D.32
Answer: C.6
Explanation: Has to be C.
Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle
hence (4-1)! = 3!= 6
Question: In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1100 employees, then the no. of female employees who are computer literate ?
A.462
B.674
C.672
D.960
Answer: A.462
Explanation: Solution: Total employees,
= 1100
Female employees, 60% of 1100.
= (60 *1100) /100 = 660.
Then male employees,
= 440
50 % of male are computer literate,
= 220 male computer literate.
62 % of total employees are computer literate,
= (62 *1100) /100 = 682 computer literate.
Thus, Female computer literate = 682 - 220
= 462.
Answer: Option A
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $215 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
A.17,010
B.2,150
C.1,890
D.1,701
Answer: B.2,150
Explanation: 10% ---- 215 millions
for 100% => ( 215 * 100% )/10% = 2150.
Option B.
Question: A box contains 3 blue marbles, 2 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
A.1/286
B.2/455
C.1/91
D.4/455
Answer: A.1/286
Explanation: Given that there are three blue marbles, two red marbles, six green marbles and one yellow marbles.
Probability that all the three marbles picked at random are blue = 3C₃/13C₃ = (1 * 3 * 2 * 1)/(13 * 12 * 11) = 1/286
ANSWER:A
Question: If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2 SDs from the mean?
A.a. 12
B.b. 14.5
C.c. 17
D.d. 23.5
Answer: A.a. 12
Explanation: Value ismore than 2SDfrom the mean means that the distance between the mean and the value must be more than 2SD=6. So the value either <20-6=14 or >20+6=26.
Answer: A.
Question: The lowest number which should be added to 11390 so that the sum is exactly divisible by 7, 9, 10 and 12 is:
A.1010
B.2210
C.1250
D.1210
Answer: D.1210
Explanation: L.C.M. of 7, 9, 10 and 12 = 1260.
On dividing 11390 by 1260, the remainder is 50.
Number to be added = (1260 - 50) = 1210. Answer: Option 'D'
Question: A group consists of 8 men, 6 women and 4 children. In how many ways can 1 man , 2 woman and 2 child selected from the given group?
A.780
B.750
C.720
D.620
Answer: C.720
Explanation: One man, two women and two child can be selected in 8C1 * 6C2 * 4C2 ways
8*6*5/2*1*4*3/2*1
= 720 ways
Answer : C
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 16, then v=
A.30
B.33
C.36
D.39
Answer: C.36
Explanation: (v*)* = (v - v/3) - (v - v/3) / 3
16 = 2v/3 - 2v/9 = 4v/9
v = 36
The answer is C.
Question: how many such letters pairs r in word SMUGGLER having same no. of letters left between them in the word as they have in the series
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: 2 letter pair.S-U,G-E.
ANSWER:B
Question: How many words can be formed by using all letters of the word “MANFUL”
A.720
B.240
C.750
D.860
Answer: A.720
Explanation: The word MANFUL contains 6 different letters.
Required number of words = 6p6 = 6! = (5x4x3x2x1) = 720.
Answer A.
Question: If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers?
A.108
B.99
C.128
D.135
Answer: B.99
Explanation: Let the 2 positive numbers x and y
x+ y = 20 -- 1
x^2 - y^2 = 40
=> (x+y)(x-y)=40 -- 2
Using equation 1 in 2 , we get
=> x-y = 2 -- 3
Solving equation 1 and 3 , we get
x= 11
y= 9
Product = 11*9 = 99
Answer B
Question: The sum of the present ages of A, B, C is 39 years. Three years ago their ages were in the ratio 1:2:3. What is the present age of A?
A.5
B.6
C.7
D.8
Answer: D.8
Explanation: Three years ago:
a:b:c = 1:2:3
Let a = 1x, b = 2x, and c = 3x.
Today:
(x+3) + (2x+3) + (3x+3) = 39
x = 5
So the present age of A is x+3 = 8
The answer is D.
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 17 more than the first integer. Find the three integers?
A.11,13,15
B.7, 2, 10
C.7, 9, 10
D.7, 9, 11
Answer: A.11,13,15
Explanation: Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 17 => x = 11
Hence three consecutive odd integers are 11, 13 and 15
Answer: A
Question: If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8?
A.a. 25%
B.b. 50%
C.c. 62.5%
D.d. 72.5%
Answer: C.c. 62.5%
Explanation: There is another way I approach such questions if I am short of time (otherwise I prefer the logical approach given above) - Brute Force/Pattern Recognition/Intuition - whatever you may want to call it.
We need to find the numbers in which the product is a multiple of 8. I know I get a multiple of 8 after every 8 numbers. I will also get an 8 when I multiply 4 by an even number. In first 8 numbers, I have exactly two multiples of 4.
Basically, I figure that I should look at the first 8 cases. In all other cases, the pattern will be repeated. It helps that n can be from 1 to 96 i.e. a multiple of 8:
1*2*3 N
2*3*4 Y
3*4*5 N
4*5*6 Y
5*6*7 N
6*7*8 Y
7*8*9 Y
8*9*10 Y
5 of the first 8 products are divisible by 8 so my answer would be 5/8 = 62.5% C
Question: If 2 : 9 :: x : 18, then find the value of x
A.2
B.3
C.4
D.6
Answer: C.4
Explanation: Explanation:
Treat 2:9 as 2/9 and x:18 as x/18, treat :: as =
So we get 2/9 = x/18
=> 9x = 36
=> x = 4
ANSWER IS C
Question: If the area of a circle is 81pi square feet, find its circumference.
A.18 pi feet
B.28 pi feet
C.38 pi feet
D.48 pi feet
Answer: A.18 pi feet
Explanation: The area is given by pi *r* r. Hence
pi * r *r = 81 pi
r * r = 81 ; hence r = 81 feet
The circumference is given by
2 * pi * r = 2 * pi * 9 = 18 pi feet
correct answer A
Question: One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 16 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
A.2,000
B.5,000
C.10,000
D.40,000
Answer: D.40,000
Explanation: out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 2 bulbs, have broken glass
i.e 2 broken glass out of 5000 bulbs
16 broken glass will be from 40000 bulbs
Answer is D
Question: Kanul spent $80000 in buying raw materials, $30000 in buying machinery and 20% of the total amount he had as cash with him. What was the total amount?
A.$135656
B.$137500
C.$134446
D.$123265
Answer: B.$137500
Explanation: Let the total amount be x
then, (100-20)% of x = 80000+30000
80% of x = 110000
80x/100 = 110000
x = $1100000/8
x = $137500
Answer is B
Question: A TaTa company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 14 hrs and a machine of type S does the same job in 7 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
A.3
B.4
C.6
D.9
Answer: A.3
Explanation: Rate of machine R =1/14
Rate of machine S =1/7
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/14 +x/7 =1/2
3x/14=1/2
x=14/6=2.3=3
So no of machine R is 3
Answer A
Question: In one hour, a boat goes 6 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
A.3 km/hr
B.4 km/hr
C.5 km/hr
D.6 km/hr
Answer: B.4 km/hr
Explanation: Upstream relative speed is u + v=6km/hr
Downstream speed is u-v = 2
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =6+2
2u=8
Finally, u=4.
ANSWER : B
Question: Albert borrowed a total of $ 6000 from john and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years?
A.571
B.581
C.441
D.445
Answer: C.441
Explanation: Let x be the amount borrowed form john. So amount borrowed form Charlie = 6000-x.
1494 = 21/100x + 27/100(6000-x)
=>x = 2100.
Interest paid = 3*7/100*2100 = 441.
C
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 5 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
A.4 min. to empty
B.6 min. to full
C.9 min. to empty
D.9 min. to full
Answer: A.4 min. to empty
Explanation: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/5 - 1/10) = 1/10
1/10 : 2/5 :: 1 : x
x = (2/5 * 1 * 10) = 4 min.
So, the tank will be emptied in 4 min.
ANSWER:A
Question: A can do a piece of work in 5 days and B can do it in 7 days how long will they both work together to complete the work?
A.6/11
B.8/11
C.7/12
D.9/12
Answer: D.9/12
Explanation: Explanation:
A’s one day work = 1/5
B’s one day work = 1/7
(A+B)’s one day work = 1/5 + 1/7 = 12/35 => time = 35/12 = 2 9/12 days
Answer: Option D
Question: Fourteen people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
A.1/15
B.1/14
C.1/13
D.13/14
Answer: C.1/13
Explanation: Let P = total cost of the rental van.
The original share per person is P/14.
The new share per person is P/13.
P/13 = P/14 * 14/13 = (1 + 1/13)*original share
The answer is C.
Question: A $72.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?
A.18%
B.20%
C.25%
D.60%
Answer: A.18%
Explanation: Listed selling price of chair = 72.95 $
Discounted selling price of chair = 59.95 $
Discount = 72.95 - 59.95 = 13 $
% decrease in price of chair = (13/72.95) * 100% = 18 % approx
Answer A
Question: 6% of a towns eligible voters did not vote in a recent election. If 30 of the towns eligible voters did not vote, how many did vote?
A.470
B.500
C.440
D.400
Answer: A.470
Explanation: 30 is 6% of the total number of voters.
If the total number of voters in the town is X, then 6/100 = 30/X
Therefore 100/6 * 30 = X
3000/6 = X
There are 500 total voters in the town.
500 - 30 = 470
A)
Question: Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 3 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
A.1/3
B.2/5
C.3/10
D.7/15
Answer: D.7/15
Explanation: Tom paints 1/6 of the room in the first hour.
Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.
The three people then paint the remaining 2/6 in a time of (2/6) / (5/6) = 2/5 hours
Peter worked for 7/5 hours so he painted 7/5 * 1/3 = 7/15 of the room.
The answer is D.
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
A.14029
B.14027
C.11867
D.14000
Answer: D.14000
Explanation: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Question: The difference of two numbers is 1515. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
A.A)270
B.B)280
C.C)290
D.D)300
Answer: D.D)300
Explanation: Let the smaller number be x. Then larger number = (x + 1515).
x + 1515 = 6x + 15
5x = 1500
x = 300
Smaller number = 300.
D)
Question: Two brother X and Y appeared for an exam. The probability of selection of X is 1/3 and that of B is 2/7. Find the probability that both of them are selected.
A.2/69
B.2/21
C.2/23
D.2/29
Answer: B.2/21
Explanation: Explanation:
Let A be the event that X is selected and B is the event that Y is selected.
P(A) = 1/3, P(B) = 2/7.
Let C be the event that both are selected.
P(C) = P(A) Ã— P(B) as A and B are independent events:
= (1/3) Ã— (2/7) = 2/21
Answer: B) 2/21
Question: The product of three consecutive numbers is 720. Then the sum of the smallest two numbers is ?
A.11
B.15
C.17
D.38
Answer: C.17
Explanation: Product of three numbers = 720
720 = 8*9*10
So, the three numbers are 8, 9 and 10.
And Sum of smallest of these two = 8 + 9 = 17.
ANSWER : OPTION C
Question: find the number of 5 digits numbers can be formed using the digits 1,2,3,4,5 if no digit is reapeted and two adjoint digits are not together
A.11
B.12
C.13
D.14
Answer: B.12
Explanation: 13524
14253
24153
24135
25314
31425
31524
+ 6 more numbers replicas of above numbers (total 12)
ANSWER:B
Question: Twelve men and six women together can complete a piece of work in four days. The work done by a women in one day is half the work done by a man in one day. If 12 men and six women started working and after two days, six men left and six women joined, then in hoe many more days will the work be completed?
A.2 (1/8) days
B.2 (1/6) days
C.3 (1/2) days
D.2 (1/2) days
Answer: D.2 (1/2) days
Explanation: Work done by a women in one day = 1/2 (work done by a man/day)
One women's capacity = 1/2(one man's capacity)
One man = 2 women.
12 men = 24 women.
12 men + 6 women = 30 women
30 women can complete the work in four days. In the first 2 days they can complete 1/2 of the work. Remaining part of the work = 1/2. If 6 men leave and 6 new women join, then new work force = 30 women - 12 women + 6 women = 24 women.
Time taken by them to complete the remaining work = 1/2 (Time taken by 24 women to complete the work) = 1/2 * (30 * 4)/24 = 2 (1/2) days.
Answer: D
Question: At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 232 students study Scramjet rocket engines and 114 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
A.438
B.436
C.430
D.442
Answer: C.430
Explanation: 312 + 232 - 114 (since 112 is counted twice )= 430
C is the answer
Question: If 2 : 9 :: x : 18, then find the value of x
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: Explanation:
Treat 2:9 as 2/9 and x:18 as x/18, treat :: as =
So we get 2/9 = x/18
=> 9x = 36
=> x = 4
Option C
Question: How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?
A.56
B.72
C.48
D.60
Answer: B.72
Explanation: The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged amongst themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48 ways.
Total number of words formed by using all the letters of the given words
= 5! = (5x4x3x2x1) = 120.
Number of words, each having vowels never together = (120-48) = 72.
Ans: B
Question: A can finish a work in 18 days and B can do the same work in 15 days. B
worked for 10 days and left the job. In how many days A alone can finish the
remaining work?
A.6days
B.5days
C.4days
D.3days
Answer: A.6days
Explanation: B's 10 day's work=10/15=2/3
Remaining work=(1-(2/3))=1/3
Now, 1/18 work is done by A in 1 day.
Therefore 1/3 work is done by A in 18*(1/3)=6 days.
ANSWER A 6days
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability q that the World Series will consist of fewer than 7 games?
A. 12.5%
B. 25%
C. 31.25%
D. 68.75%
Answer: D. 68.75%
Explanation: In order to determine the probability that the World Series will last less than 7 games, we can first determine the probability q that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
A.15 m,80 m
B.15 m,18 m
C.15 m,60 m
D.15 m,10 m
Answer: D.15 m,10 m
Explanation: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer:D
Question: A man whose bowling average is 22.2, takes 4 wickets for 36 runs and thereby decreases his average by 1.2. The number of wickets, taken by him before his last match is :
A.14
B.22
C.38
D.40
Answer: D.40
Explanation: Explanation :
Let the number of wickets taken before the last match is x.
Then, (22.2x + 36)/(x + 4) = 21
=> 22.2x+36 = 21x+84
=> 1.2x = 48
=> x = 48 / 1.2
= 40
Answer : D
Question: Find the average of first 25 natural numbers?
A.12
B.16
C.13
D.18
Answer: C.13
Explanation: Sum of first 100 natural numbers = 25*26/2 = 325Required average = 325/25 = 13Answer is C
Question: Seventy five percent of a number is 21 less than four fifth of that number. What is the number ?
A.240
B.340
C.420
D.130
Answer: C.420
Explanation: Let the number be x.
Then, 4*x/5 â€“(75% of x) = 21
4x/5 â€“ 75x/100 = 21
x = 420.
Answer C.
Question: A retailer sells 5 shirts. He sells first 2 shirts for $30 and $20. If the retailer wishes to sell the 5 shirts for an overall average price of over $30, what must be the minimum average price of the remaining 3 shirts?
A.$28.50
B.$30.50
C.$33.33
D.$40.50
Answer: C.$33.33
Explanation: First 2 shirts are sold for $30 and $20=$50.
To get average price of $30,total sale should be 5*$30=$150
So remaining 3 shirts to be sold for $150-$50=$100
Answer should be 100/3=$33.33 that is C
Question: Two good train each 750 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
A.12 sec
B.24 sec
C.48 sec
D.72 sec
Answer: D.72 sec
Explanation: Sol.
Relative Speed = (45 + 30) km / hr
= (75 x 5 / 18) m/sec
= (125/6) m/sec.
Distance covered = (750 + 750) m = 1500m.
Required time = (1500 x 6 / 125) sec = 72 sec.
Answer D
Question: One litre of water is evaporated from 6 litre of a solution containing 5% salt. The percentage of salt ?
A.4 4/19%
B.5 5/7%
C.5%
D.6%
Answer: D.6%
Explanation: Answer
Salt in 6 liter = 5% of 6 = 0.30 liter
Salt in new solution = (0.30/5) x 100% = 6%
Correct Option: D
Question: A leak in the bottom of a tank can empty the full tank in 4 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?
A.7580
B.7960
C.8290
D.2160
Answer: D.2160
Explanation: Solution
Work done by the inlet in 1 hour	= (1/4 - 1/12)
= 1/6.
Work done by the inlet in 1 min.	= (1/6 × 1/60)
= 0.002778
Volume of 0.002778 part = 6 litres.
Therefore, Volume of whole	= (.002778×6)
‹=› 2160 litres.
Answer D
Question: One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
A.5L/7 miles
B.4L/7 miles
C.3L/7 miles
D.2L/7 miles
Answer: A.5L/7 miles
Explanation: This is an infinite round problem means the bird will complete infinite rounds in this manner now for finding the total distance traveled by the bird let us consider the total distance between the two given stations as L. Here since the distance between these two stations is not given so answer will be in terms of L.
speed of the two trains moving in opposite directions are 15 mph and 20 mph.
so time taken for the collision between the trains will be L/(15+20) = L/35
In this much time the bird will move 25*L/35 miles = 5L/7 miles
ANSWER:A
Question: If x and y are positive numbers and z = xy^2, a 60 percent increase in x and a 30 percent decrease in y would result in which of the following changes in z?
A.decrease of 12.5%
B.decrease of 21.6%
C.increase of 4.8%
D.increase of 12.5%
Answer: B.decrease of 21.6%
Explanation: After the changes, z = 1.6x*(0.7y)^2 = (1.6*0.49)xy^2 = 0.784*z
The answer is B.
Question: The probability that a computer company will get a computer hardware contract is 2/3 and the probability that it will not get a software contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts ?
A.14/45
B.4/9
C.4/5
D.4/6
Answer: A.14/45
Explanation: Explanation :
Let, A ≡ event of getting hardware contract
B ≡ event of getting software contract
AB ≡ event of getting both hardware and software contract.
P(A) = 2/3, P(~B) =5/9
=> P(B) = 1- (5/9) = 4/9.
A and B are not mutually exclusive events but independent events. So,
P(at least one of A and B ) = P(A) + P(B) - P(AB).
=> 4/5 = (2/3) + (4/9) -P(AB).
=> P(AB) = 14/45.
Hence, the required probability is 14/45.
Answer : A