RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A grocer has 400 pounds of coffee in stock, 30 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
A.28%
B.30%
C.36%
D.36%
Answer: D.36%
Explanation: 1. 30% of 400=120 pounds of decaffeinated coffee
2. 60% of 100=60 pounds of decaffeinated coffee
3. Wt have 180 pounds of decaffeinated out of 500 pounds, that means 180/500*100%=36%. The correct answer is D.
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
A.7
B.8
C.9
D.10
Answer: D.10
Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
Answer: Option D
Question: A monkey start climbing up a tree 20ft tall.Each hour it hops 3 ft and slips back 2ft.How much time would it take the monkey to reach the top.
A.15 hrs
B.18 hrs
C.19 hrs
D.17 hrs
Answer: B.18 hrs
Explanation: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 17hrs it wil be 17ft.
Bt since the height of the tree is 20ft, so if the monkey hops up the tree in the next hr i.e 18th hr then it reaches at the top of the tree.
hence it takes 18 hrs for monkey to reach at the top
ANSWER:B
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 2 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?
A.A)5
B.B)61
C.C)8
D.D)6
Answer: D.D)6
Explanation: Relative speed = 2 + 2 = 4 rounds per hour.
So, they cross each other 4 times in an hour and 2 times in half an hour.
Hence, they cross each other 6 times before 9.30 a.m.
ANSWER:D
Question: How many digits are in the number 50^8 × 8^3 × 11?
A.18
B.20
C.19
D.22
Answer: A.18
Explanation: Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10
50^8 × 8^3 × 11 = (5^2*2)^8*2^9*11 = 5^16*2^17*11 = 2*11*10^16 = 22*10^16
Hence we would have 16 trailing 0's and the three digits from 22
Total digits = 2 + 16 = 18
Correct Option: A
Question: If [x] is the greatest integer less than or equal to x, what is the value of [-6.2]+[-3.4]+[12.7] ?
A. -1
B. 0
C. 1
D. 2
Answer: A. -1
Explanation: You are asked what the closest lesser integer value to [x] is.
[-6.2] = -7.0
[-3.4] = -4.0
[12.7] = 12.0
Therefore , answer is: -7.0 -4.0 + 12.0 = -1.0
Option A.
Question: Pipe P can drain the liquid from a tank in 1/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?
A.9/29
B.3/23
C.3/8
D.17/29
Answer: B.3/23
Explanation: Suppose Q can drain in 1 hr. So, rQ = 1/1 = 1
So, rP = 1/[(1/4)rQ] = 4
Also, rP = rR/(2/3) => 4 = rR/(2/3) => rR = 8/3
Let H is the time it takes to drain by running all 3 pipes simultaneously
So combined rate = rC = 1/H = 1 + 4 + 8/3 = 23/3 = 1/(3/23)
Thus running simultaneously, Pipe Q will drain 3/23 of the liquid.
Thus answer = B.
Question: Find the sum which will yield an interest of Rs.910 in 2 1/2 years at 7% p/a simple interest.
A.Rs.3200
B.Rs.4200
C.Rs.6200
D.Rs.5200
Answer: D.Rs.5200
Explanation: 70 = (P*4*7/2)/100
P = (910x100x2)/(5x7)=Rs.5200
Answer: D
Question: The H.C.F. of two numbers is 59 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is:
A.678
B.944
C.456
D.323
Answer: B.944
Explanation: :	Explanation:
Clearly, the numbers are (59 x 13) and (59 x 16).
{\color{Blue} \therefore } Larger number = (59 x 16) = 944.
Answer: B)944
Question: In the first M games of a team's season, the ratio of the team's wins to its losses was 1:2. In the subsequent N games, the ratio of the team´s wins to losses was 1:4. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games?
A.7:20
B.9:23
C.11:27
D.23:54
Answer: A.7:20
Explanation: M = 4/9 of total games
N = 5/9 of total games
Wins = 1/3*4/9 + 1/5*5/9 = 4/27 + 3/27 = 7/27
Losses = 1 - 7/27 = 20/27
The ratio of wins to losses is 7:20.
The answer is A.
Question: A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be
A.1,2
B.2,3
C.3,7
D.2,7
Answer: B.2,3
Explanation: 4 | x y = (5 x 1 + 4) = 9
--------
5 | y -1 x = (4 x y + 1) = (4 x 9 + 1) = 37
--------
| 1 -4
Now, 37 when divided successively by 5 and 4, we get
5 | 37
---------
4 | 7 - 2
---------
| 1 - 3
Respective remainders are 2 and 3.
Correct Option is B
Question: Which of the following is equal to 10^-(-3)^3?
A.1/(10^30)
B.1/(10^28)
C.1/(10^29)
D.1/(10^27)
Answer: D.1/(10^27)
Explanation: 10^-(-3)^3 => 10^-(-3^3) => 10^-(27) = 1/(10^27)
Answer : D
Question: 3 men or 6 women can do a piece of work in 24 days. In how many days will 12 men and 8 women do the same work?
A.15/9 days
B.9/2 days
C.18/4 days
D.11/4 days
Answer: B.9/2 days
Explanation: 3M = 6W ---- 24 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 24 32 -----?
6 * 24 = 32 * x => x = 9/2 days
Answer:B
Question: In what time will Rs.5000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
A.6 2/3
B.6 1/6
C.6 1/3
D.6 1/2
Answer: A.6 2/3
Explanation: (5000*3*R)/100 = (5000*5*4)/100
R = 6 2/3
Answer: A
Question: Jack takes a loan of $120,000 with 12% annual interest: the interest is paid once, at the end of the year. Jill takes a loan of $120,000 with 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Jack's loan interest, approximately how much more does Jill have to repay?
A.Zero
B.$81.90
C.$8190.03
D.$819.00
Answer: D.$819.00
Explanation: Jack's interest= $120,000*0.12 = $14400 or $1,200 each month.
Jills’s interest, 12%/12 = 1% each month:
For the 1st month = $120,000*0.01 = $1,200;
For the 2nd month = $1,200 + 1% of 1,200 = $1,212, so we would have interest earned on interest (very small amount);
For the 3rd month = $1,212 + 1% of 1,212 = ~$1,224;
For the 4th month = $1,224 + 1% of 1,224 = ~$1,236;
...
For the 12th month = $1,320 + 1% of 1,320 = ~$1,332.
The difference between Jack's interest and Jill’s interest = ~(12 + 24 + ... + 132) = $792.
Answer: D.
Question: shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
A.8%
B.9%
C.3%
D.4%
Answer: D.4%
Explanation: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100
=0.04 * 100 = 4%
Answer:D
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
A.400
B.625
C.1250
D.2500
Answer: C.1250
Explanation: This is a rather straight forward ratio problem.
1. 50 fish tagged
2. 2 out of the 50 fish caught were tagged thus 2/50
2/50=50/x
thus, x=1250
Think of the analogy: 2 fish is to 50 Fish as 50 fish is to ...?
You've tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch
ANSWER C
Question: A group of two women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
A. 7! – 2!3!2!
B. 7! – 4!3!
C. 5! – 3!3!
D. 7 × 2!3!2!
Answer: C. 5! – 3!3!
Explanation: 5 people can sit in 5! different ways. But because 3 men cannot sit together, we take them as a unit.
This unit of men, among themselves can sit in 3! ways.
Hence, 5! - 3!.
This unit of men along with 2 women can sit in 3! different ways which also needs to be eliminated.
Hence 5! - 3!3!
C
Question: The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is?
A.7
B.2
C.3
D.4
Answer: B.2
Explanation: Let the numbers be 13a and 13b.
Then, 13a * 13b = 2028 => ab = 12.
Now, co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 * 1, 13 * 12) and (13 * 3, 13 * 4).
Clearly, there are 2 such pairs.
Answer: B
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.276 m
B.256 m
C.120 m
D.216 m
Answer: C.120 m
Explanation: Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer:C
Question: The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 24th of September 1990?
A.Monday
B.Tuesday
C.Wednesday
D.Thursday
Answer: A.Monday
Explanation: 19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 24th September was a Monday.
The answer is A.
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is :
A.7.5 %
B.8 %
C.9.7 %
D.None of these
Answer: B.8 %
Explanation: Solution
By investing Rs. 1552,income = Rs. 128.
By investing Rs. 97, income = Rs. (128/1552x97) =Rs.8
∴ Dividend = 8%.
Answer B
Question: If a man were to sell his chair for Rs. 720, he would lose 25%. To gain 25% he should sell it for:
A.Rs. 1,200
B.Rs. 1,000
C.Rs. 960
D.Rs. 900
Answer: A.Rs. 1,200
Explanation: Solution: Let the Cost price of the Chair is X.
SP = X - 25% of X
720 = 0.75X
X = 960.
CP = Rs. 960.
So, To gain 25%, SP would be
= 960 + 25% of 960 =Rs. 1200.
Short-cut
CP of chair = (100/75)*720 = Rs. 960;
To gain 25%, SP = (125/100)*960 = Rs. 1200.
Answer: Option A
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.288
B.298
C.245
D.200
Answer: C.245
Explanation: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m. Answer: C
Question: A and B invests Rs.10000 each, A investing for 4 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.4000, find their shares?
A.1000,3500
B.1000,3000
C.1000,2000
D.1000,5000
Answer: B.1000,3000
Explanation: The ratio of their profits A:B = 4:12 =1:3
Share of A in the total profit = 1/4 * 4000 = Rs.1000
Share of B in the total profit = 3/4 * 4000 = Rs.3000
Answer:B
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 28 years. Find the average age of the women?
A.87
B.98
C.32
D.28
Answer: C.32
Explanation: 20 + 28 + 8 * 2
= 64/2
= 32
Answer:C
Question: Each of the following equations has at least one solution EXCEPT C. Is it true?
A.2* -a = (–2)*a
B.2*a = (–2)*-a
C.-2*a = -2-a
D.(–2)a = –2a
Answer: C.-2*a = -2-a
Explanation: If we put a = 1 then
A. -2
B. 2
D. -2
E. -3
Answer : C
Question: A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs.482 more, if the interest was payable half yearly than if it was payable annually . The sum is
A.200000
B.20000
C.200029
D.288778
Answer: B.20000
Explanation: Explanation:
Let sum=Rs.x
C.I. when compounded half yearly =
C.I. when compounded annually =
=> x=20000
Answer: B) 20000
Question: One-third less than 15% of 180 is equal to:
A.18
B.30
C.35
D.40
Answer: A.18
Explanation: Lots of ways to tackle this.
15% of 180 =27
1/3 of 27= 9
So, 1/3less than 27 is equal to 27- 9 = 18
Answer: A
Question: Let y=1+1/2+1/3+1/2+......, what is the value of y ?
A.(√11 + 3 ) / 2
B.(√11 - 3 ) / 2
C.(√15 + 3 ) / 2
D.(√15 - 3 ) / 2
Answer: D.(√15 - 3 ) / 2
Explanation: Explanation :
=> y = 1 / (2 + 1 / ( 3 + y) ).
=> y = (3 + y) / (7 + 2y).
=> 2y2 + 6y - 3 = 0.
=> y = −6±36+24/√4
=> −6±60/√4= −3±15/√2.
Since 'y' is a +ve number, therefore:
y = ( √15 - 3 ) / 2.
Answer : D
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
A.1
B.2
C.4
D.6
Answer: B.2
Explanation: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
B
Question: A person says that their speed while going to a city was 10mph however while
returning as there is no much traffic they came with a speed of 15mph. what is their
average speed?
A.12
B.13
C.14
D.15
Answer: A.12
Explanation: Avg speed= 2xy/x+y
Hence Ans: 12
ANSWER:A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
A.150 m
B.145 m
C.140 m
D.135 m
Answer: A.150 m
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
ANSWER:A
Question: Rahim bought 65 books for Rs.1160 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?
A.Rs.18.28
B.Rs.20
C.Rs.18.08
D.Rs.28.08
Answer: C.Rs.18.08
Explanation: Average price per book = (1160 + 920) / (65 + 50) = 2080 / 115 = Rs.18.08
ANSWER:C
Question: Meena wrote all the numbers from 1 to 29,999 inclusive. How many digits did she write in total?
A.118,889
B.138,889
C.159,889
D.188,789
Answer: B.138,889
Explanation: 1-9=>1*9 digits
10-99=>2*90=180 (numbers between 10-99 is 90 where each has 2 digits)
100-999=>3*900=2700
1000-9999=>4*9000 = 36,000
10000-29999=>5*20,000 = 100,000
The answer is 138,889
The answer is B.
Question: In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are marketing majors?
A.3
B.5
C.7
D.11
Answer: C.7
Explanation: pqrs = 1365 = 3 * 5 * 7 * 13
Since 1< p < q < r < s, the number of students who are marketing majors is r = 7.
The answer is C.
Question: What is the probability of getting a sum 9 from two throws of dice
A.1/3
B.1/9
C.1/12
D.2/9
Answer: B.1/9
Explanation: Explanation:
Total number of cases = 6*6 = 36
Favoured cases = [(3,6), (4,5), (6,3), (5,4)] = 4
So probability = 4/36 = 1/9
Answer: B
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
A.3901
B.3909
C.3929
D.3900
Answer: D.3900
Explanation: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Question: In an examination, a student scores 4 marks for every correct answer and loses I mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number of questions he attempts correctly, is:
A.35
B.38
C.40
D.42
Answer: B.38
Explanation: = 4x – (60 – x) = 130
= 5x = 190 x = 38
Answer: Option B
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 25 percent on food, and 25 percent on other items. If Jill paid a 10 percent tax on the clothing, no tax on the food, and an 20 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
A.5
B.10
C.15
D.20
Answer: B.10
Explanation: Assume she has $200 to spend.
TAX
Clothing = 50% = $100= $10.00
Food = 25% = $ 50 = $0.00
Items = 25% = $ 50 = $ 10.00
Total tax = $20.00
% of total amount = 20/200 * 100 = 10%
Answer B
Question: When x - p is divided by p , the quotient is n and there is no remainder. Which of the following must be the value of x?
A.p(n + 1)
B.n(p + 1)
C.p(n + 1) + 2n
D.p(n - 1) + 2n
Answer: A.p(n + 1)
Explanation: Given in question (x-p)/p= n
=> x-p= np
=>x= np+p
Now we are good to check the options
x= p(n+1)
Answer A
Question: Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 8% greater than any other employee, what is the lowest possible salary that any one employee earned?
A. $40,000
B. $41,667
C. $42,000
D. $46,460.17
Answer: D. $46,460.17
Explanation: Employee 1 earned $x(say)
Employee 2 will not earn more than $1.08x
Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees
(1.08x*20)+x=1,050,000
Solving for x=$46,460.17
Answer D
Question: 2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost?
A.26
B.56
C.110
D.28
Answer: D.28
Explanation: Let the cost of 1 chair = x, let the cost of 1 table = y
2x + y = 110
y = 110 - 2x
Again,
4x + y = 166
4x + (110 - 2x) = 166
4x + 110 - 2x = 166
2x + 110 = 166
2x = 56
x = 28
Answer: D
Question: Find a sum for first 4 prime no's from number series?
A.24
B.28
C.30
D.17
Answer: D.17
Explanation: Required sum = (2 + 3 + 5 + 7 ) = 17
Note: 1 is not a prime number
Option D
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 12%. What is the selling price of the cycle?
A.s. 1090
B.s. 1160
C.s. 1232
D.s. 1202
Answer: C.s. 1232
Explanation: since,c.p=1400
loss%=(c.p-s.p)/c.p*100
12=(1400-s.p)/1400*100
so,after solving answer=1232.
ANSWER:C
Question: The cost of painting the four walls of a room is Rs.350. The cost of painting a room three times in length, breadth and height will be :
A.Rs.1050
B.Rs.1400
C.Rs.3150
D.Rs.4200
Answer: C.Rs.3150
Explanation: Explanation:
Area of 4 walls of the room = [2(l+b)×h]m2
Area of 4 walls of new room = [2(3l+3b)×3h]m2 = 9[2(l+b)×h]m2
Cost of painting the 4 walls of new room = Rs.(9×350)=Rs.3150
Correct Option: C
Question: The average of 13 numbers is 59. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
A.59
B.83
C.45
D.53
Answer: A.59
Explanation: Sum of all the 13 numbers = 13 * 59 = 767
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 767 = 59.
Answer:A
Question: An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 24 metre of cloth ?
A.175 seconds
B.195 seconds
C.155 seconds
D.188 seconds
Answer: D.188 seconds
Explanation: Explanation:
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,
0.128 : 1 :: 24 : x => x = {\color{Blue} \frac{24\times 1}{0.128}}
=> x = 187.5
So time will be approx 188 seconds
Answer: D
Question: An investor bought a 1-year $7,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
A.$350
B.$367.25
C.$700
D.$717.50
Answer: D.$717.50
Explanation: 1.05*1.05*7000 = $7717.50
The answer is D.
Question: A sum of Rs.2200 has been divided among A, B and C such that A gets 1/4 of what B gets and B gets 1/5 of what C gets. What is B's share?
A.342
B.352
C.322
D.332
Answer: B.352
Explanation: Let C's share = Rs. x
Then B's share = x/5
A's share = x/5×1/4=x/20
Hence, x+x/5+x/20=2200
⇒x(1+1/5+1/20)=2200
⇒x(25/20)=2200
⇒x(5/4)=2200
⇒x=2200×4/5=440×4=Rs.1760
B's share = x/5=1760/5=Rs.352
Answer is B.
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
A.157
B.169
C.197
D.280
Answer: D.280
Explanation: 80* 7: x* 3
= 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Question: A pet store owner has 12 cats and 20 dogs. They want to have 20% more cats than dogs. How many dogs do they have to sell to achieve their goal of having 20% more cats than dogs assuming they do not sell any cats in this time.
A.6
B.8
C.10
D.12
Answer: D.12
Explanation: You can use basic arithmetic to solve the answer by testing each of the possible answers.
Lets test C:
if they sold 10 dogs they would have 12 cats and 10 dogs and a total of 22 pets
12/22= 54.5%
10/22= 45.5%
for a difference of 9%
lets test D:
if they sold 12 dogs they would have 12 cats and 8 dogs and a total of 20 pets
12/20=60%
8/20=40%
for a difference of 20%
The answer is D
Question: A inlet pipe can fill a tank in 12 hours and an outlet pipe can empty the tank in 16 hours. If both the pipes are opened simultaneously, find the time taken to fill the tank.
A.36 hours
B.12 hours
C.4 hours
D.48 hours
Answer: D.48 hours
Explanation: Explanation:
As the inlet can fill the tank in 12 hours, in one hour it will fill 1/12th of the tank.
Similarly, the outlet pipe in one hour can empty 1/16th part of the tank.
If both are opened simultaneously, the part of the tank filled in one hour is:
1/12 - 1/16 = 1/48
Hence, the tank gets filled in 48 hours.
ANSWER D
Question: If the average of 20 digits is 500 and the average of 14 of them is 390, calculate the average of the remaining 6 numbers?
A.756.7
B.751.7
C.753.7
D.752.7
Answer: A.756.7
Explanation: Explanation:
Total of the 20 digits - 20 * 500= 10000
Total of the 14 digits - 14*390 = 5460
Total of the remaining 6 digits - 10000-5460 = 4540
average of the remaining 6 numbers = 4540/6 = 756.7
ANSWER: A
Question: An investment of y dollars at p percent simple interest yields $600 interest over a 3-year period. In terms of y, what dollar amount invested at the same rate will yield the same amount of interest over a 2-year period?
A.2/3 y
B.3/4 y
C.3/2 y
D.2y
Answer: C.3/2 y
Explanation: Let's start by assigning suitable values to some variables so that we can easily calculate the answer.
$600 simple interest earned in 3 yrs means $200 earned every year. So if dollar amount y = 1000, rate of interest p = 20%
We need $600 in 2 yrs i.e. $300 every year at 20% rate.
300 = 20% of Amount invested
Amount invested = $1500 i.e. (3/2)y
Answer (C)
Question: If x is an integer that has exactly three positive divisors (these include 1 and x), how many positive divisors does x^3 have?
A.4
B.5
C.6
D.7
Answer: D.7
Explanation: Since factors of '4'are {1,2,4}
4^3=64
Number of factors/divisors of 64= 2^6
We know that when a number is expressed as a product of the prime factors as below:
N = a^x * b^y * c^z
Then no. of divisors = (x+1)*(y+1)*(z+1)
Then here (6+1) = 7
ANSWER:D
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 250 girls, the total number of
students in the college is
A.420
B.520
C.620
D.650
Answer: D.650
Explanation: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 250
=> x = 50
Total students = 8x+5x = 13x = 13(50) = 650
Answer: D
Question: If u, v, w, x, y, and z are six different prime numbers, which of the following is the smallest possible value of u + v + w + x + y + z?
A.35
B.37
C.39
D.41
Answer: D.41
Explanation: The sum of the six small smallest primes numbers is 2+3+5+7+11+13=41.
The answer is D.
Question: For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers V are there between #6 +2 and #6 +6 , inclusive?
A.None
B.One
C.Two
D.Three
Answer: A.None
Explanation: None is the answer. A.
Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.A
Question: The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paisa per meter is Rs. 36. The breadth of the room is ?
A.6 meters
B.8 meters
C.9 meters
D.10 meters
Answer: A.6 meters
Explanation: Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m2
= 90 m2
∴ Area of the room = 90 m2
Breadth of the room = Area /Length
= 90 / 15 m
= 6m
ANSWER :A