RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The ages of 2 persons differ by 18 years. If 12 years ago the elder one be 6 times as old as the younger one, find the present age of elder person.
A.33.6
B.47
C.50.4
D.52.4
Answer: A.33.6
Explanation: age of the younger person = x
age of the elder person = x+18
6(x-12) = x+18-12
x= 15.6
age of elder person = 15.6+18=33.6
Answer is A
Question: How many 3-digit numerals begin with a digit that represents a odd prime and end with a digit that represents a prime number?
A.16
B.80
C.160
D.120
Answer: D.120
Explanation: prime digits 2,3,5 and 7.
three digit numbers _ _ _
1st place can be filled in 3 ways
2nd place can be filled in 10 ways
3rd place can be filled in 4 ways
Total=3*10*4=120
Ans : D
Question: X is a set containing 8 different positive odd numbers. Y is a set containing 7 different numbers, all of which are members of X. Which of the following statements CANNOT be true?
A.The range of Y is even.
B.The mean of X is even.
C.The mean of Y is even.
D.The range of X is equal to the range of Y.
Answer: C.The mean of Y is even.
Explanation: Option C.
Given: X is a set containing 8 different positive odd numbers
Easily inferred: Y is a set containing 7 different odd numbers
(A) The range of Y is even. - Always even, since it is a difference of two odd numbers
(B) The mean of X is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of Y is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of X is equal to the range of Y.
(E) The median of Y is equal to the mean of Y
C
Question: If x > 1, which of the following decreases as x decreases?
I. 1/(x + x^2)
II. 2x^2 − x
III. 1/(x + 1)
A.I only
B.II only
C.III only
D.I and II only
Answer: B.II only
Explanation: let x= 4 and 3 b old and new values
ST1: x= 4 -> 4+16 =1/ 20
x=3-> 3+9 = 1/12 ...increased
ST2:x= 4-> 2*16-4 = 28
x=3->2*9-3 = 15
decreased
St3: x=4-> 1/4 = .25
x=3->1/3 = .33
Ans: B
Question: A watch passes through three hands and each person gains 25%. If the third person sells it for $187.50, what did the first person pay for it?
A.$84
B.$88
C.$92
D.$96
Answer: D.$96
Explanation: 1.25*1.25*1.25 * original price = 187.5
(5/4)^3 * original price = 187.5
original price = 64*187.5 / 125 = $96
The answer is D.
Question: One ton has 2500 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons?
A. 2000
B. 1700
C. 2350
D. 2500
Answer: A. 2000
Explanation: 16 pounds and 4 ounces= 16*16 + 4 = 260 ounces.
13 tons = 13*2500 pound = 13*2500*16 ounces.
Hence the answer is (13*2500*16)/260 =2000.
Answer: A.
Question: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
A.66
B.26
C.42
D.27
Answer: C.42
Explanation: x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42
Answer: C
Question: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 10. Which of the following is NOT a possible value for y + b?
A.24
B.21
C.20
D.16
Answer: D.16
Explanation: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>10 --> y+b>16.
Answer: D.
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 360 m long platform?
A.19
B.27
C.29
D.48
Answer: D.48
Explanation: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +360)/ 36 * 5/18
= 48 min.
Answer:D
Question: At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using six colors?
A.20
B.35
C.105
D.135
Answer: A.20
Explanation: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.
As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:
ABC
ACB
BAC
BCA
CAB
CBA
By extension, the first part of your calculation would be the number of possible substances that could be identified with 6 colors: 6c3 = 20 possible substances
A
Question: Lane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?
A.30
B.36
C.70
D.80
Answer: B.36
Explanation: Method I: the rates solution
“Lane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Lane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Lane + Zane is
R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12
That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:
T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36
BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Lane and Zane need 36 weeks to make 15 drums.
Answer = B.
Question: Two trains are approaching each other at 60 mph each. The length of each train is 1/6 miles. When
the two locomotives(engines) meet, how many seconds will it take for them to pass each other
completely?
A.15 sec
B.12 sec
C.10 sec
D.18 sec
Answer: C.10 sec
Explanation: Explanation :
Total distance to cover = 2*(1/6) = 2/6 miles
Relative speed = 60+60 = 120mph
Time taken = (2/6)/120*3600 = 10 sec.
Hence (C) is the answer.
Answer : C
Question: There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
A.18
B.21
C.35
D.42
Answer: B.21
Explanation: Note that each handshake includes two people.
The total number of handshakes is 14*3/2 = 21
The answer is B.
Question: How many numbers between 100 and 900 begin or end with 3?
A.80
B.100
C.150
D.170
Answer: D.170
Explanation: How many numbers between 100 and 900 begin or end with 3?
Just think that those numbers are:
i) The ones ending in 3: 103, 113, 123, ... , 893 --> 80 numbers
ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers
BUT 10 out of the first 80 numbers are repeated in the second set.
THEREFORE, the solution is 170 numbers.
Answer: D
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
A.1 : 1
B.2 : 3
C.5 : 2
D.4 : 3
Answer: A.1 : 1
Explanation: Mixture A has a total of 5 + 3 = 8 parts. If in the final mixture this represents 4 parts, then the total number of parts in mixture B should be (8/4)*3 = 6.
So, we should take of mixture B a quantity with 2 and 4 parts, respectively.
This will give us in the final mixture (5 + 2) : (3 + 4), which means 7:7, or 1:1.
Answer A.
Question: How many combinations of three letters taken from letters (a, a, b, c, c, d) are possible?
A.12
B.13
C.10
D.36
Answer: C.10
Explanation: So 4C3 for abcd - 4 choices
3 more for aa(b,c or d)
3 more for cc(a,b or d)
total 10
Ans :C
Question: A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days?
A.7 days
B.8 days
C.9 days
D.10 days
Answer: B.8 days
Explanation: (A+B)'s 1 day's work=(1/11+1/20)=31/220;
(A+C)'s 1 day's work=(1/11+1/55)=6/55;
work done in 2 days=(31/220+6/55)=55/220=1/4
Now, 1/4 work is done by A in 2 days.
Whole work will be done in (2*4)=8days.
Correct Option: B
Question: What approximate value should come in place of the question mark (?) in the following equation?
1.542 × 2408.69 + 3134.632 = ?
A.6800
B.4800
C.5200
D.6400
Answer: A.6800
Explanation: Explanation 3700 + 3100 = 6800
Answer A
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
A.153
B.150
C.140
D.138
Answer: D.138
Explanation: Let x be the original 2-digit number.
If each digit is halved, then the sum of G and H is 3x/2.
Note the sum must be a multiple of 3 and less than 150.
Of these five choices, only 138 satisfies these two conditions.
The answer is D.
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
A.1/4
B.4/7
C.2/3
D.2/5
Answer: B.4/7
Explanation: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
B
Question: A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?
A.315
B.339
C.288
D.299
Answer: A.315
Explanation: Explanation:
Let the areas of the two parts be x and (700-x) hectares
therefore,
So, the two parts are 385 and 315.
Hence, Area of the smaller = 315 hectares
Answer: A) 315
Question: A man is 26 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
A.23 years
B.22 years
C.24 years
D.20 years
Answer: C.24 years
Explanation: Let present age of the son =x years
Then, present age the man =(x+26) years
Given that, in 2 years, man's age will be twice the age of his son
â‡’(x+26)+2=2(x+2)
â‡’x=24
ANSWER:C
Question: Out of a classroom of 4 boys and 7 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions?
A.3/11
B.5/11
C.5/33
D.7/33
Answer: D.7/33
Explanation: The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 7C3=35.
P(only girls are chosen)=35/165=7/33
The answer is D.
Question: Difference of two numbers is 15. Two times of the first exceeds by 2 from the three times of the other. Then the numbers will be
A.28, 43
B.43, 28
C.15, 30
D.30, 15
Answer: B.43, 28
Explanation: Explanation:
x - y = 15
2x Ã¢â‚¬â€œ 3y = 2
x = 43 y = 28 Answer: B
Question: A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
A.1/4
B.1/2
C.1/2
D.5/8
Answer: D.5/8
Explanation: Let the 5 black balls be BBBBB and 3 Red Balls be RRR
They can be arranged in 8 slots _ _ _ _ _ _ _ _
in (8!)/ (5!x3!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 7 slots and 4 Black (BBBB) and 3 Red (RRR)
They can be arranged in (7!)/ (4!x3!)
Hence required probability = [(7!)/ (4!x3!)] / [(8!)/ (5!x3!)]
Ans = 5/8 D
Question: Which of the following year is not a leap year?
A.1960
B.2080
C.2024
D.2100
Answer: D.2100
Explanation: SOLUTION :
The two conditions that decide that a year is a leap year or not is:
• For a year to be a leap year, it should be divisible by 4.
• No century is a leap year unless it is divisible by 400.
Hence, the year 2100 is not a leap year as it is not divisible by 400.
ANSWER IS D
Question: Evaluate combination
96C94=96!/(94)!(2)!
A.6170
B.5560
C.4170
D.4560
Answer: D.4560
Explanation: Explanation:
nCr=n!/(r)!(n−r)!
96C94=96!/(94)!(2)!
=96*95*94!/(94)!(2)!
=96*95/2∗1
=4560
Option D
Question: The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
A.2
B.8
C.7
D.6
Answer: D.6
Explanation: 33 + 43 + 53 = a3 => a = 6
Answer:D
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
A.3/18
B.3/10
C.3/11
D.3/12
Answer: C.3/11
Explanation: The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
Answer: C
Question: A sum of $3310 is to be paid back in 3 equal installments. How much is each installment if the interest is compounded annually at 10% per annum.
A.1311
B.1331
C.1103
D.2331
Answer: A.1311
Explanation: Assume each installment = X
Initial value = 3310
End of 1st year, value = 3310*1.1 AND we pay the first installment, so remaining value = 3310*1.1 - X = 3641 - X
End of 2nd year, value = (3641 - X)*1.1 AND we pay the second installment, so remaining value = (3641 - X)*1.1 - X = 4005 - 2.1X
End of 3rd year, value = (4005 - 2.1X)*1.1 = 4405 - 2.31X
KEY is the value at the end of 3rd year = X (the last installment)
=> 4405 - 2.31X = X
=> 4405 = 3.31X
=> X = 1331
ANSWER:A
Question: Sara works 5 days a week at d dollars per day for m weeks out of the month. Which of the following represents her monthly pay?
A.m/(5d)
B.20d
C.5d
D.5dm
Answer: D.5dm
Explanation: Total income of Sara in a month = d*5*m dollars. = d*5*m = 5dm Answer is D
Question: The average age of a group of 10 students was 24. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
A.22 years
B.36 years
C.32 years
D.44 years
Answer: B.36 years
Explanation: The total age of 10 students with average 24 = 240
The total age of 12 students with average 26 = 312
The total age of 2 new students = 72
Their average =36
Correct Option B
Question: Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
A.40
B.72
C.84
D.90
Answer: A.40
Explanation: A is the answer....
D = TS where D=distance, T=Time and S=Speed
To travel half distance, (2+2T) = 8T ==> T = 1/3 ==> 20 minutes
To travel double distance, 2(2+2T) = 8T ==> 1 ==> 60 minutes
Difference, 40 minutes
A
Question: Of the three numbers, the sum of the first two is 45; the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. The third number is
A.10
B.20
C.30
D.40
Answer: C.30
Explanation: Solution
Let the number be x, y and Z.
= Then, x+y=45, y+z=55&3x+z=90
‹=›y=45-x, z=55-y = 55-(45-x) = 10+x
‹=›Therefore 3x+10+x = 90 or x = 20.
y=(45-20)=25 and z=(10+20)= 30.
Therefore Third number = 30
Answer C
Question: Romi has a collection of 10 distinct books (8 small and 2 large). In how many ways can he select 5 books to take with him on a trip if he has room for only 1 large book?
A.56
B.126
C.152
D.196
Answer: D.196
Explanation: 5 Small books out of 8 AND 0 large book out of 2 books
OR
4 Small book out of 8 AND 1 large book out of 2 books
We know AND represents multiplication and OR addition;
Thus; to convert the above statement into combinations:
first select 5 books i.e. 10C5 and then subtract the remainder i.e. All big + 3 small
10C5 - 8C3 = 196
Ans: "D"
Question: Last year Department Store X had a sales total for December that was 7 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
A.1/4
B.4/15
C.1/3
D.7/18
Answer: D.7/18
Explanation: Let avg for 11 mos. = 10
Therefore, Dec = 70
Year total = 11*10 + 70 = 180
Answer = 70/180 = 7/18 = D
Question: A = {2, 3, 5, 7, 15}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
A.15
B.16
C.19
D.22
Answer: D.22
Explanation: By looking at Set A, we can see that it's all primes. Thus, we should immediately break down the elements in Set B to their prime factors. That gives :
Set A = {2,3,5,7,11}
Set B = {2, 2x2, 3x2, 13}
Apart from 2x3x2 (taking 2 from set A) which is the same as 3x2x2(taking 3 from set A); there is nothing which can be repeated. Thus, the total unique product = 20-1 = 22.
D
Question: College T has 1000 students. Of the 210 students majoring in one or more of the sciences,135 are majoring in Chemistry and 155 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
A.110 to 135
B.110 to 130
C.130
D.110
Answer: A.110 to 135
Explanation: Total = Chemistry + Biology - Both + Neither
210 = 135 + 155 - Both + N
We know that N (Neither) must be at least 30, so set N=30 and solve:
210 = 135 + 155 - Both + 30
210 = 320 - Both
Both = 110
Even if you're not sure whether 110 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range.
Both can not be greater than 135, because even if every chemistry major was also a biology major, there are only 135 chemistry majors total. A the solution.
Question: On selling a pencil at 5% loss and a book at 15% gain, Kiran gains Rs 7. If he sells the pencil at 5% gain and the book at 10% gain, then he gains Rs 13. The actual price of the book is
A.Rs 100
B.Rs 80
C.Rs 90
D.Rs 400
Answer: A.Rs 100
Explanation: Let actual price of the book = Rs X
Let actual price of the pen = Rs Y
Therefore, ( X + 15% of X) + (Y – 5% of Y) = X + Y + 7
15X - 5Y = 700 …….(i)
Also (X + 10% of X) + (Y + 5% of Y) = X + Y + 13
10X + 5Y = 1300
Using (i) and (ii) we get X = 80, Y = 100
Therefore, actual price of the book = Rs 80
ANSWER:A
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
A.81 min
B.108 min
C.144 min
D.192 min
Answer: C.144 min
Explanation: Explanation:
Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.
ANSWER IS C
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
A.30
B.15
C.20
D.25
Answer: A.30
Explanation: Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min
ANSWER A
Question: How many numbers up to 100 are divisible by 7?
A.14 Numbers
B.17 Numbers
C.16 Numbers
D.25 Numbers
Answer: A.14 Numbers
Explanation: Explanation:
100/7 = 14 2/7 => 14 Numbers
Answer:A
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
A.230 m
B.240 m
C.260 m
D.270 m
Answer: D.270 m
Explanation: Speed =	(72 x(5/18))m/sec = 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	((x + 250)/26)	= 20
x + 250 = 520
x = 270.
D
Question: A batch of cookies was divided amomg 2 tins: 2/3 of all the cookies were placed in either the blue or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction of the cookies that were placed in the other tins were placed in the green tin
A.15/2
B.9/4
C.5/11
D.7/5
Answer: C.5/11
Explanation: This will help reduce the number of variables you have to deal with:
G + B = 2/3
R = 1/2
B = 1/4
We can solve for G which is 5/12
What fraction (let it equal X) of the cookies that were placed in the other tins were placed in the green tin?
So..
X*(G+R)=G
X*(5/12 + 1/2) = 5/12
X = 5/11
ANSWER: C. 5/11
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 162° of the circle, what percentage of MegaTek employees are in manufacturing?
A.20%
B.25%
C.30%
D.45%
Answer: D.45%
Explanation: ANSWER: D 162° divided by 360° equals 0.45, therefore the sector is equal to 45% of the total
Question: Line m lies in the xy-plane. The y-intercept of line m is -4, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -8). What is the slope of line m ?
A.-2
B.-1
C.-1/3
D.0
Answer: A.-2
Explanation: Ans: A
Solution: line m goes through midpoint of (2, 4) and (6, -8). midpoint is (4,-2)
as we can see that the y axis of intercept point is (0,-4) means line m is parallel to x axis
slope M= -2
Ans: A
Question: A towel, when bleached, lost 30% of its length and 15% of its breadth. What is the percentage decrease in area?
A.24%
B.40.5 %
C.44%
D.54%
Answer: B.40.5 %
Explanation: percentage change in area
=(−30−15+(30×15)/100)%=−40.5%
i.e., area is decreased by 40.5%
ANSWER:B
Question: A corporation five times its annual bonus to 10 of its employees. What percent of the employees’ new bonus is the increase?
A.12%
B.18%
C.80%
D.20%
Answer: C.80%
Explanation: Let the annual bonus be X.
A corporation triples its annual bonus.
So new bonus = 5X.
Increase = 5X-X =4X
The increase is what percent of the employees’ new bonus
= (4X/5X)*100
= 80%
Hence C.
Question: A vendor bought bananas at 6 for Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss value.
A.45
B.12
C.36
D.18
Answer: D.18
Explanation: Suppose , number of bananas bought = LCM of 6 and 4=12
CP=Rs.[(10/6)*12]=Rs.20 ; SP= Rs[(6/4)*12]=Rs.18
Ans: D
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 men?
A. 1/14
B. 1/7
C. 3/7
D. 2/7
Answer: C. 3/7
Explanation: Total ways to choose 4 employees from 8 employees = 8C4
Two women = 5C2
Two Men = 3C2
P = (5C2 * 3C2)/8C2 = 3/7 hence C.
Question: In how many different ways can 7 people be seated in a room with 9 chairs?
A.40,320
B.181,440
C.403,200
D.1,814,400
Answer: B.181,440
Explanation: Order doesn't matter
With 9 chairs and only 7 to seat
7!- Number of ways the 7 can seat on the chair
9C2 - Number of ways the 2 empty sits can be vary with the 7 seated
7! * 9C2 = 1,81,440 Answer - B
Question: Pipe X that can fill a tank in an hour and pipe Y that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe Y is shut 15 minutes before the tank overflows. When will the tank overflow?
A.35 mins
B.30 mins
C.40 mins
D.32 mins
Answer: B.30 mins
Explanation: The last 15 minutes only pipe X was open. Since it needs 1 hour to fill the tank, then in 15 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.
The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 3/4th of the tank they need (time) = (work)/(rate) = (3/4)/3 = 1/4 hours = 15 minutes.
Total time = 15 + 15 = 30 minutes.
Answer: B