RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: 36 men can complete a piece of work in 18 days. In how many days will 9 men complete the same work ?
A.24
B.77
C.88
D.72
Answer: D.72
Explanation: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
9 : 36 :: 18 : x
x = 72
Answer: D) 72 days
Question: Two airplanes fly the same exact route from Atlanta to Chicago. Plane A flies 200 mph while plane B flies 300 mph (assume that simple model versus actual acceleration/deceleration near the airports). If plane A took off exactly 40 minutes before plane B, after how many minutes will plane B overtake plane A?
A.65
B.80
C.90
D.115
Answer: B.80
Explanation: We can use some form of the equation D=RT [distance = rate * time]
rate of plane A: 200 mph
rate of plane B: 300 mph
Plane A will be in the sky 40 minutes longer than plane B (2/3 of an hour)
time of plane A when B overtakes it: T+(2/3) use 2/3 of an hour since the rate is in hours
time of plane B when B overtakes A: T
At the time that B overtakes A, they will have travelled the same distance so RT is equal for each plane:
200*(T+2/3) = 300*T
200T + 400/3 = 300T
400/3 = 100T
4/3 = T
this is 1 and a third hour, so 60 minutes + 20 minutes = 80 minutes
B
Question: If the average (arithmetic mean) of 5 positive temperatures is m degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
A.6m
B.4m
C.5m/3
D.3m/2
Answer: B.4m
Explanation: The sum of three greatest should be more than sum of two lowest.
The total sum is; 5m
A. 6m; 6m is more than 5m. Not possible.
B. 4m; 5m-4m=m(Possible)
C. 5m/3; 10m/3; 10m/3 > 5m/3. Not possible
D. 3m/2; 7m/2; 7m/2 > 3m/2. Not possible
E. 3m/5; 22m/5; 22m/5 > 3m/5. Not possible.
Ans:B
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.253
B.366
C.298
D.266
Answer: A.253
Explanation: Explanation:
Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352
Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit.
Hence, required number = 253.
Answer: A) 253
Question: Solve below question 2x + 1 = -21
A.-11
B.-9
C.9
D.8
Answer: A.-11
Explanation: 2x + 1 = -21
x = -11
A
Question: If z is a positive integer, which of the following could NOT be the square of z?
A.4932
B.9126
C.4566
D.6815
Answer: A.4932
Explanation: A number ending in 2 cannot be a perfect square.
4932 ends in a number 2, making that the correct answer
(A) 4932
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.14, 2
B.14, 9
C.14, 5
D.14, 4
Answer: D.14, 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: Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible?
A.90
B.79
C.64
D.57
Answer: C.64
Explanation: Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible.
Total Options: 64
Final Answer:
C
Question: John makes $60 a week from his job. He earns a raise and now makes $110 a week. What is the % increase?
A.16%
B.83.33%
C.17%
D.17.61%
Answer: B.83.33%
Explanation: Increase = (50/60)*100 = (5/6)*100 = 83.33%.
B
Question: Find the greatest number which on dividing 1255 and 1490, leaves a reminder of 8 and 11 respectively
A.27
B.29
C.33
D.39
Answer: B.29
Explanation: Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (1255 - 8) and (1490 -11)
= HCF (1247, 1479) = 29
Option B
Question: A train running at the speed of 60 km/hr crosses a pole in 3 seconds. What is the length of the train?
A.20 metres
B.50 metres
C.32 metres
D.70 metres
Answer: B.50 metres
Explanation: Speed= 60 x	5/18	m/sec	= 50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3	x 3 m = 50 m.
Option B
Question: In how many no. between 10 and 50 exactly Two of the digits is 5?
A.47
B.65
C.1
D.35
Answer: C.1
Explanation: It's simple can be solved by elimination of answer choices.
Option B and D are too large, not possible. Even AE are large to have correct choice.
Ans : C
Question: The cash difference between the selling prices of an book at a profit of 5% and 10% is $3. The ratio of the two selling prices is:
A.21:22
B.52:33
C.52:53
D.45:53
Answer: A.21:22
Explanation: Let C.P. of the book be $x.
Then, required ratio = 105% of x / 110% of x
= 105/110 = 21/22 = 21:22
A
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
A.1078
B.1276
C.1000
D.1021
Answer: C.1000
Explanation: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 10 * 10 * 10 = 1000
Answer:C
Question: A right circular cylinder has a height of 21 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
A.500(π – 3)
B.500(π – 2.5)
C.510(π – 1.5)
D.500(π – 2)
Answer: C.510(π – 1.5)
Explanation: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
The square base has sides of sqrt(50) due to the 45-45-90 triangle
21*25*pi - 15*sqrt(50)^2
=510(π – 1.5)
C. 510(π – 1.5)
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
A.31.7
B.31.3
C.31.6
D.31.9
Answer: C.31.6
Explanation: 100*(80/100)*(90/100)*(95/100)
= 68.4
100 - 68.4
= 31.6
Answer: C
Question: The mean of 50 observations was 36. It was found later that an observation 29 was wrongly taken as 23. The corrected new mean is :
A.36.1
B.36.5
C.36.22
D.36.12
Answer: D.36.12
Explanation: Explanation:
Correct Sum = (36 * 50 + 29 - 23) = 1806.
Correct mean = = 1806/50 = 36.12
Answer: D) 36.12
Question: 2 dice are tossed. What is the probability that the total score is a prime no. is?
A.2/11
B.5/12
C.6/13
D.7/15
Answer: B.5/12
Explanation: 5/12
B
Question: The difference between a number and its two-fifth is 510. What is 5% of that number?
A.425
B.300
C.255
D.300
Answer: A.425
Explanation: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
5% of 850 = 425.
Answer:A
Question: Raffle tickets numbered consecutively from 101 through 250 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?
A.51/250
B.2/7
C.33/83
D.99/250
Answer: A.51/250
Explanation: SOLUTION
The number of integers from 101 to 250, inclusive is 250, out of which 100 (from 200 to 250) will have a hundreds digit of 2. Thus the probability is 51/250.
Answer: A.
Question: A train covers a distance of 12 km in 10 min. If it takes 15 sec to pass a telegraph post, then the length of the train is?
A.300 m
B.168 m
C.120 m
D.168 m
Answer: A.300 m
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 15
= 120 m.
Answer: A
Question: It takes 10 days for digging a trench of 100 m long, 50 m broad and 10 m deep. What length of trench,
25 m broad and 15 m deep can be dug in 30 days ?
A.400 m
B.200 m
C.100 m
D.89m
Answer: A.400 m
Explanation: Expl : More days, more length (Direct)
Less breadth, more length (Indirect)
More depth, less length (Indirect
Days 10 : 30;
Breadth 25 : 50; : : 100 : x
Depth 15 : 10;
:. 10 * 25* 15 * x = 30 *50 * 10 *100
x= (30*50*10*100)/10*25*15 = 400
So the required length = 400m
Answer: A
Question: Machine P and Machine Q are each used to manufacture 330 sprockets. It takes Machine P 10 hours longer to produce 330 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
A.5
B.15
C.3
D.95
Answer: C.3
Explanation: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
330/x = 330/1.1x + 10
1.1(330) = 330 + 11x
11x = 33
x = 3
The answer is C.
Question: A certain number of men can do a work in 40 days . If there were 5 men less it could be finished in 10 days more . How many men are there?
A.15 men
B.25 men
C.18 men
D.12 men
Answer: B.25 men
Explanation: Explanation:
x*40 =(x-5)*50
5x-4x =25
X=25 men
Answer: Option B
Question: The sum of two numbers is 40 and their difference is 20. Find their product.
A.300
B.108
C.114
D.325
Answer: A.300
Explanation: Sol.
Let the numbers be x and y.
Then, x + y = 40 and
x - y = 20.
2x = 60 => x = 30 So y = 10
xy = 30 * 10 = 300
Answer : A
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
A.8
B.10
C.11
D.12
Answer: B.10
Explanation: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer: Option B
Question: If xy = 3 and x^2 + y^2 = 12, then x/y + y/x =
A.4
B.3 1/7
C.5 1/3
D.7
Answer: A.4
Explanation: We can make simplifying of question and get it in view: (x^2 + y^2) / xy and as we know the meaning of this parts:
x^2 + y^2 = 12
xy = 3
we can calculate the answer 12/3 -> 4 so answer is A
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
A.10
B.13
C.18
D.19
Answer: C.18
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer: Option C
Question: A certain restaurant offers 7 different salads, 5 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?
A.120
B.240
C.480
D.600
Answer: D.600
Explanation: MAGOOSHOFFICIAL SOLUTION:
To count the number of meals, we have to count the possibilities for the three components, and then, according to theFundamental Counting Principle, we multiply. For more on the FCP, seethis blog.
For salads, there are 8 possibilities. Done.
For main courses, there are 5 different possibilities. Done.
For desserts, there are 6 choices, but we pick two different choices. This would be 6C2. To calculate this, we can usethe shortcut, nC2 = (n*(n-1))/2.
6C2 = (6*5)/2 = 15
So, there are 15 combinations of two different desserts.
For the number of meals, we multiply 7*5*15. We know 8*5 = 525
Answer = (D)
Question: Each of the integers from 1 to 18 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even
A.19
B.12
C.11
D.10
Answer: D.10
Explanation: Out of the 18 integers: 9 are odd and 9 are even.
If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:
1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first
2. 10th number will be the first even number
So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even.
So, answer will be 10. (D)
Question: A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party T. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
A.15
B.20
C.30
D.35
Answer: A.15
Explanation: S=100
not( T and B ) =35
only T=20
(T and B)/B=1/2
let ( T and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.40
B.88
C.26
D.18
Answer: A.40
Explanation: Explanation:
The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100 = 40%
Answer:A
Question: which of the following statement is not correct?
A.log10 10 = 1
B.log(2+3)= log(2*3)
C.log10 1= 0
D.log(1+2+3)= log1 + log2 + log3
Answer: B.log(2+3)= log(2*3)
Explanation: a) loga a=1, so log10 10 = 1
b) log(2+3) = log 5 and log(2*3) = log 6 = log 2 + log 3
therefore log(2+3) # log (2*3)
c) since loga 1=0, so log10 1 = 0
d) log(1+2+3) = log 6= log(1*2*3)= log 1+log 2+log 3
e)none
Correct Answer (B)
Question: The difference between the length and breadth of a rectangle is 28 m. If its perimeter is 120 m, then its area is:
A.704 m2
B.720 m2
C.620 m2
D.820 m2
Answer: A.704 m2
Explanation: EXPLANATION
We have: (l â€“ b) = 28 and 2(l + b) = 120 or (l + b) = 60.
Solving the two equations, we get: l = 44 and b = 16.
Area = (l x b) = (44x 16) m2 = 704 m2.
Answer A
Question: 47% of the students in a class of 36 students has glasses or contacts. How many students in the class have either glasses or contacts?
A.15
B.16
C.17
D.18
Answer: C.17
Explanation: a=r⋅b
47%=0.47a
=0.47⋅36
a≈17
Option C is correct.
Question: A used car dealer sold one car at a profit of 25 percent of the dealers purchase price for that car and sold another car at a loss of 20 percent of the dealers purchase price for that car. If the dealer sold each car for $20,000 , what was the dealers total profit or loss, in dollars, for the two transactions combined?
A.1000 profit
B.2000 profit
C.1000 loss
D.2000 loss
Answer: C.1000 loss
Explanation: car 1 :
P1*1.25 = 20000
P1 = 16000
car2
P2*0.8 = 20000
P2 = 25000
P1+P2 = 41000
Final sale = 40000
1000 loss .. option C
Question: A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
A.2/91
B.3/91
C.5/91
D.6/91
Answer: A.2/91
Explanation: Total number of balls = 4 + 5 + 6 = 15
Let S be the sample space.
n(S) = Total number of ways of drawing 3 balls out of 15 = 15C3
Let E = Event of drawing 3 balls, all of them are yellow.
n(E) = Number of ways of drawing 3 balls, all of them are yellow
= Number of ways of drawing 3 balls from the total 5 = 5C3
(∵ there are 5 yellow balls in the total balls)
P(E) = n(E)/n(S)
=5C3/15C3
=5C2/15C3 [∵ nCr = nC(n - r). So 5C3 = 5C2. Applying this for the ease of calculation]
= 2/(7*13)
= 2/91
Answer : Option A
Question: In a college the ratio of the numbers of boys to the girls is 8:5. If there are 120 girls, the total number of students in the college is?
A.312
B.356
C.452
D.416
Answer: A.312
Explanation: Let the number of boys and girls be 8x and 5x
Then , 5x = 120
x= 24
Total number of students = 13x = 13*24 = 312
Answer is A
Question: A building is to be completed in 48 days. To meet the deadline 54 men were employed and were made to work for 10 hours a day. After 30 days 5/9th of the work was completed. How many more workers should be employed to meet the deadline if each workers are now made to work 8 hours a day?
A.36
B.55
C.40
D.45
Answer: A.36
Explanation: Explanation :
54 men work 10 hours a day for 30 days and 5/9th of the work is completed.
Now, let x workers be employed to work 8 hours a day for the rest 18 days to complete 4/9th of the work.
M1D1T1W2 = M2D2T2W1
54*30*10*4/9 = x*18*8*5/9
x = 90
Hence, 36 more workers should be employed.
Answer : A
Question: What is the median from the below series 90, 89, 93, 88, 95, 88, 97, 87, and 98
A.80
B.85
C.90
D.97
Answer: C.90
Explanation: Ordering the data from least to greatest, we get:
87, 88, 88, 89, 90, 93, 95, 96, 98
The median quiz score was 90. (Four quiz scores were higher than 90 and four were lower.)
C
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
A.1: 5
B.1: 8
C.1: 9
D.1: 1
Answer: C.1: 9
Explanation: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1: 9
Answer:C
Question: The average age of a husband and his wife was 29 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
A.11
B.23
C.19
D.287
Answer: B.23
Explanation: Explanation:
Sum of the present ages of husband, wife and child = (29 * 2 + 5 * 2) + 1 = 69 years.
Required average = (69/3) = 23 years.
Answer: B
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
A.7 min
B.8 min
C.9 min
D.10 min
Answer: B.8 min
Explanation: Explanation:
1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
ANSWER IS B
Question: If 100<y<199 and 10<x<100, then the product xy CANNOT be equal to:
A.19,104
B.19,303
C.19,356.732
D.19,910
Answer: D.19,910
Explanation: Correct Answer: (E)
Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 100 * 10. The largest value must be less than 199 * 100. This means that 1000 < xy < 19,900. (D) is outside of this range, so it is not a possible product of xy.
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
A.200 m
B.225 m
C.245 m
D.250 m
Answer: C.245 m
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
ANSWER:C
Question: In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
A.1/6
B.2/9
C.6/11
D.9/16
Answer: C.6/11
Explanation: # defective pens = 3
# good pens = 9
Probability of the 1st pen being good = # of favorable outcomes / # of total outcomes = 9/12
Probability of the 2nd pen being good = # of remaining favorable outcomes / # of total remaining outcomes = 8 / 11
Total probability = 9/12 * 8/11 = 6/11
answer will be C
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
A.20%
B.30%
C.50%
D.70%
Answer: C.50%
Explanation: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
A.22 1/8 days
B.22 1/2 days
C.22 6/2 days
D.72 1/2 days
Answer: B.22 1/2 days
Explanation: 1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 1/4 *2 = 22 1/2 days
Answer: B
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
A.6
B.7
C.8
D.6
Answer: A.6
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 = (1/6 - 1/10) = 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) = 6 min.
So, the tank will be emptied in 6 min.Answer: A
Question: How many even numbers greater than 300 can be formed with digits 1,2,3,4,5 no digit being repeated ?
A.111
B.123
C.124
D.132
Answer: A.111
Explanation: Number can be 3, 4, or 5 digit (4 and 5 digit number will obviously be more than 300).
5 digit even numbers:
Last digit must be either 2 or 4 (for number to be even), so 2 choices. First 4 digits can be arranged in 4! # of ways. So total # of 5 digit even numbers possible is 4!∗2=484!∗2=48;
4 digit even numbers:
Last digit again must be either 2 or 4, so 2 choices. # of ways to choose rest 3 digits out of 4 digits left when order of the digits matters is P34P43. So total # of 4 digit even numbers possible is P34∗2=48P43∗2=48;
3 digit even numbers:
Last digit again must be either 2 or 4, so 2 choices. # of ways to choose rest 2 digits out of 4 digits left when order of the digits matters is P24P42. So total # of 3 digit even numbers possible is P24∗2=24P42∗2=24.
But out of these 24 3-digit even numbers some will be less than 300, the ones starting with 1 or 2. There are 9 such numbers (1X2 and 3 options for the second digit X, so 3 plus 1X4 and 3 options for X, so 3 plus 2X4 and 3 options for X, so 3), which means that # of 3 digit even numbers more than 300 is 24−9=1524−9=15;
So total 48+48+15=11148+48+15=111.
ANS:A
Question: The inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters. A cylindrical drum is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such drums that could be used, what is the volume, in cubic meters, of the one that has maximum volume?
A.20π
B.24π
C.25π
D.96π
Answer: C.25π
Explanation: You have three options here. Approach is to calculate volumes for all of them and see which one is greatest.
1. Cylinder's base rests on a 4x5 side of the box. So, height becomes 6 and the maximum possible radius becomes 4/2.
So, maximum volume = π.(4/2)^2.6=π24
2. Cylinder's base rests on a 5x6 side of the box. So, height becomes 4 and the maximum possible radius becomes 5/2.
So, maximum volume = π.(5/2)^2.4=π25
3. Cylinder's base rests on a 4x6 side of the box. So, height becomes 5 and the maximum possible radius becomes 4/2.
So, maximum volume = π.(4/2)^2.5=π20
Option 2 gives maximum value and so that should be the answer, π25.
ANSWER:C
Question: From a pack of 52 cards,two cards are drawn at random together at random what is the probability of both the cards being kings?
A.1/221
B.8/221
C.4/589
D.4/587
Answer: A.1/221
Explanation: let S be the sample space then
n(S)=52C2=(52*51)/(2*1)=1326
let E be the event of getting 2 kings out of 4
n(E)=4C2=(4*3)/(2*1)=6
P(E)=n(E)/n(S)=6/1326=1/221
Answer (A)
Question: Working alone, Mary can pave a driveway in 6 hours and Hillary can pave the same driveway in 6 hours. When they work together, Mary thrives on teamwork so her rate increases by 25%, but Hillary becomes distracted and her rate decreases by 20%. If they both work together, how many hours will it take to pave the driveway?
A.3 hours
B.4 hours
C.5 hours
D.6 hours
Answer: A.3 hours
Explanation: Initial working rates:
Mary = 1/6 per hour
Hillary = 1/6 per hour
Rate when working together:
Mary = 1/6+ (1/4*1/6) = 1/5 per hour
Hillary = 1/6 - (1/5*1/6) = 2/15 per hour
Together they work 1/5 + 2/15 = 1/3 per hour
So they will need 3 hours to complete the driveway. The correct answer is A.