mathewhe/aqua_rat huggingface dataset:
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
(E) $8.19
Rationale: 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.
Answer: (D) $819.00
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%
(E) 2%
Rationale: 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
Answer: (D) 4%
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
(E) 10000
Rationale: 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
Answer: (C) 1250
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!
(E)  2!3!2!
Rationale: 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
Answer: (C)  5! – 3!3!
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
(E) 9
Rationale: 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
Answer: (B) 2
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
(E) 268 m
Rationale: Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer:C
Answer: (C) 120 m
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
(E) Friday
Rationale: 19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 24th September was a Monday.
The answer is A.
Answer: (A) Monday
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
(E) Cannot be determined
Rationale: Solution
By investing Rs. 1552,income = Rs. 128.
By investing Rs. 97, income = Rs. (128/1552x97) =Rs.8
∴ Dividend = 8%.
Answer B
Answer: (B) 8 %
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
(E) None
Rationale: 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
Answer: (A) Rs. 1,200
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
(E) 212
Rationale: 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
Answer: (C) 245
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
(E) 1000,2500
Rationale: 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
Answer: (B) 1000,3000
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
(E) 37
Rationale: 20 + 28 + 8 * 2
= 64/2
= 32
Answer:C
Answer: (C) 32
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
(E) (–2)-a = –2-a
Rationale: If we put a = 1 then
A. -2
B. 2
D. -2
E. -3
Answer : C
Answer: (C) -2*a = -2-a
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
(E) 277789
Rationale: Explanation:
Let sum=Rs.x
C.I. when compounded half yearly =
C.I. when compounded annually =
=> x=20000
Answer: B) 20000
Answer: (B) 20000
Question: One-third less than 15% of 180 is equal to:
(A) 18
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: 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
Answer: (A) 18
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
(E) None of these
Rationale: 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
Answer: (D) (√15 - 3 ) / 2
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
(E) 7
Rationale: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
B
Answer: (B) 2
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
(E) 16
Rationale: Avg speed= 2xy/x+y
Hence Ans: 12
ANSWER:A
Answer: (A) 12
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
(E) 155 m
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
ANSWER:A
Answer: (A) 150 m
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
(E) Rs.38.08
Rationale: Average price per book = (1160 + 920) / (65 + 50) = 2080 / 115 = Rs.18.08
ANSWER:C
Answer: (C) Rs.18.08
Question: If an object travels 70 feet in 2 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
(A) 15.95
(B) 17.28
(C) 19.54
(D) 21.73
(E) 23.86
Rationale: 70 feet/2 seconds = 35 feet/second
(35 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 23.86 miles/hour (approximately)
The answer is E.
Answer: (E) 23.86
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
(E) 188,989
Rationale: 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.
Answer: (B) 138,889
Question: Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) A)7
(B) B)6
(C) C)8
(D) D)9
(E) E)4.74
Rationale: 1/5 + 1/15 - 1/x = 1/18
x = 4.74
Answer:E
Answer: (E) E)4.74
Question: Evaluate: 50 - 12*3*2 = ?
(A) 62
(B) 52
(C) 32
(D) 12
(E) 42
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
50 - 12*3*2 = 50 - 8 = 42
correct answer E
Answer: (E) 42
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
(E) 17
Rationale: 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.
Answer: (C) 7
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
(E) None of these
Rationale: 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
Answer: (B) 1/9
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
(E) 3912
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Answer: (D) 3900
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
(E) 45
Rationale: = 4x – (60 – x) = 130
= 5x = 190 x = 38
Answer: Option B
Answer: (B) 38
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
(E) 25
Rationale: 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
Answer: (B) 10
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
(E) n(p + 1) (p − 1)
Rationale: 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
Answer: (A) p(n + 1)
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
(E)  $60,000
Rationale: 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
Answer: (D)  $46,460.17
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
(E) 54
Rationale: 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
Answer: (D) 28
Question: Find a sum for first 4 prime no's from number series?
(A) 24
(B) 28
(C) 30
(D) 17
(E) 36
Rationale: Required sum = (2 + 3 + 5 + 7 ) = 17
Note: 1 is not a prime number
Option D
Answer: (D) 17
Question: After giving a discount of rs.45 the shopkeeper gets a loss of 10%,if the cost price is rs.180.find the markup %?
(A) 0.21
(B) 0.2
(C) 0.17
(D) 0.21
(E) 0.15
Rationale: cost price=180
s.p=180*90/100=162
disc=45
so...mark price=162+45=207......
mark up%=207-180/180=81/180=.15 or 15%
ANSWER:E
Answer: (E) 0.15
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
(E) s. 1204
Rationale: 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
Answer: (C) s. 1232
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
(E) None
Rationale: 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
Answer: (C) Rs.3150
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
(E) 64
Rationale: 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
Answer: (A) 59
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
(E) 115 seconds
Rationale: 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
Answer: (D) 188 seconds
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
(E) $1400
Rationale: 1.05*1.05*7000 = $7717.50
The answer is D.
Answer: (D) $717.50
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
(E) 362
Rationale: 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.
Answer: (B) 352
Question: 1,3,5,7,9,..50 find term of sequnce
(A) 1230
(B) 1300
(C) 1500
(D) 1679
(E) 2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: (E) 2500
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
(E) 176
Rationale: 80* 7: x* 3
= 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: (D) 280
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
(E) 14
Rationale: 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
Answer: (D) 12
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
(E) 58 hours
Rationale: 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
Answer: (D) 48 hours
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
(E) 722.7
Rationale: 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
Answer: (A) 756.7
Question: The instructions state that Cheryl needs 4/9 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 6/12 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
(A) 1/12
(B) 1/9
(C) 2/3
(D) 1 1/9
(E) 11/18
Rationale: total bought = 4/9+2/3
left part 6/12--->1/2
so used part 4/9+2/3-1/2=11/18
Ans E
Answer: (E) 11/18
Question: A woodworker normally makes a certain number of parts in 24 days. But he was able to increase his productivity by 5 parts per day, and so he not only finished the job in only 22 days but also he made 80 extra parts. How many parts does the woodworker normally makes per day and how many pieces does he make in 24 days?
(A) 240
(B) 420
(C) 560
(D) 190
(E) 360
Rationale: Let x be the number of parts the woodworker normally makes daily. In 24 days he makes 24⋅x pieces. His new daily production rate is x+5 pieces and in 22 days he made 22⋅(x+5) parts. This is 80 more than 24⋅x Therefore the equation is:
24⋅x+80=22(x+5)
30=2x
x=15
Normally he makes 15 parts a day and in 24 days he makes 15⋅24=360 parts.
Answer: (E) 360
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
(E) 3y
Rationale: 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)
Answer: (C) 3/2 y
Question: We run a business that rents out canoes and kayaks. A canoe rental costs $9 per day, and a kayak rental costs $12 dollars per day. One day, our business rents out 4 canoes for every 3 kayaks and receives a total of $432 in revenue. How many more canoes than kayaks were rented out?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
Rationale: Let x be the number of canoes.
Then 3x/4 is the number of kayaks.
9x+(3x/4)*12=432
9x+9x=432
18x=432
x=24 (canoes)
3x/4=18 (kayaks)
There were 24-18 = 6 more canoes rented out.
The answer is E.
Answer: (E) 6
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
(E) 8
Rationale: 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
Answer: (D) 7
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
(E) None of these
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 250
=> x = 50
Total students = 8x+5x = 13x = 13(50) = 650
Answer: D
Answer: (D) 650
Question: 1.45, 2.56, 4.78, 8.11, 12.55, (....)
(A) 17.3
(B) 16.2
(C) 15.3
(D) 19.5
(E) 18.1
Rationale: Explanation:
1.11, 2.22, 3.33, 4.44, 5.55,
Hence 5.55=18.1
Answer: E
Answer: (E) 18.1
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
(E) 43
Rationale: The sum of the six small smallest primes numbers is 2+3+5+7+11+13=41.
The answer is D.
Answer: (D) 41
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
(E) Four
Rationale: None is the answer. A.
Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.A
Answer: (A) None
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
(E) 12 meters
Rationale: 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
Answer: (A) 6 meters
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 17 more transactions than Cal. How much transactions did Jade handled?
(A) 80
(B) 81
(C) 82
(D) 83
(E) 84
Rationale: Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 16 more transactions than Cal.
Jade = 66 + 17
= 83
Jade handled = 83 transactions.
Answer: D
Answer: (D) 83