mathewhe/aqua_rat huggingface dataset:
Question: An electric pump can fill a tank in 6 hours. Because of a leak in the tank, it took 12hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
(A) 10hours
(B) 12hours
(C) 8hours
(D) 5hours
(E) 15hours
Rationale: Work done by the leak in 1 hour = 1/6 - 1/12 = 1/12
The leak will empty the tank in 12hours
Answer is B
Answer: (B) 12hours
Question: During the months May through October, Teddy the bear quadruples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
(A) 16m - 1300
(B) 16m - 1200
(C) 4m - 1300
(D) 4m - 1200
(E) 4m
Rationale: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 4m - 300
April' 75 = 4m - 400
Oct' 75 = 16m - 1200
April'76 = 16m - 1300
Hence answer will be (A) 16m - 1300
Answer: (A) 16m - 1300
Question: Six boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
(A) A)4^30
(B) B)2^30
(C) C)1^30
(D) D)3^30
(E) E)6^30
Rationale: Each Mango can be given to any one of the six people or in other words..1 mango can be divided into 6 ways...so all 30 can be divided in 6^30 ways
ANS:E
Answer: (E) E)6^30
Question: What least number should be subtracted from 13604 such that the remainder is divisible by 87 ?
(A) 32
(B) 29
(C) 28
(D) 30
(E) 31
Rationale: 13604 ÷ 87 = 156, remainder = 32
Hence 32 is the least number which can be subtracted from 13604 such that the remainder
is divisible by 87
Answer is A
Answer: (A) 32
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3360. They completed the work in 3 days with the help of C. How much is to be paid to C?
(A) s. 380
(B) s. 600
(C) s. 420
(D) s. 400
(E) s. 480
Rationale: Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3360 × (1/8) = 420
Answer : Option C
Answer: (C) s. 420
Question: Rs. 5200 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
(A) 1600
(B) 1500
(C) 1200
(D) 600
(E) 100
Rationale: 1/2:1/3:1/4
= 6:4:3
3/13*5200
= 1200
Answer: C
Answer: (C) 1200
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 2 (1/9) km/h
(B) 2 (1/5) km/h
(C) 2 (3/2) km/h
(D) 2 (1/2) km/h
(E) 2 (1/1) km/h
Rationale: :100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer: D
Answer: (D) 2 (1/2) km/h
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 60% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A)  36%
(B)  60%
(C)  64%
(D)  80%
(E)  84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.6*0.6 = 0.36. So, the probability that he will be able to attend is 1 - 0.36 = 0.64.
Answer: C.
Answer: (C)  64%
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 187 m
(B) 278 m
(C) 876 m
(D) 150 m
(E) 267 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 9) m
= 150 m.
Answer: D
Answer: (D) 150 m
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 290 votes. The total number of votes polled was?
(A) votes
(B) votes
(C) votes
(D) votes
(E) votes
Rationale: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 290
40% = 40×7 = 290
100% =100×7 =700 votes
A)
Answer: (A) votes
Question: if a@b = a * b^(1/2) then 4@9 = ?
self made
(A) 2
(B) 12
(C) 3
(D) 8
(E) 4
Rationale: 4* (9)^1/2= 4*3= 12
B is the answer
Answer: (B) 12
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 280 sq cm. Find the area of the square?
(A) 482
(B) 268
(C) 260
(D) 480
(E) Cannot be determined
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 280
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: E
Answer: (E) Cannot be determined
Question: What is the next number of the following sequence
2,2,12,12,30,30,_?
(A) 54
(B) 55
(C) 56
(D) 57
(E) 58
Rationale: 1^2+1=2
2^2-2=2
3^2+3=12
4^2-4=12
5^2+5=30
6^2-6=30
next is (7^2+7)=56
ANSWER:C
Answer: (C) 56
Question: The smallest number which when diminished by 12, is divisible 12, 24, 36, 48 and 56 is:
(A) 1008
(B) 1015
(C) 1020
(D) 1032
(E) 1048
Rationale: Required number = (L.C.M. of 12, 24, 36, 48,56 ) + 12
= 1008 + 12
= 1020
Answer: Option C
Answer: (C) 1020
Question: A k-almost prime number is defined as a positive integer with exactly k prime factors that are not necessarily distinct. The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number is
(A) 6
(B) 8
(C) 16
(D) 24
(E) 28
Rationale: Solution: 3-almost prime numbers : 8(as 8 = 2*2*2) , 12 (2*2*3) , 18 (2*3*3) , 20 (2*2*5)....
4-almost prime numbers : 16(as 8 = 2*2*2*2) , 24 (2*2*2*3) , 36 (2*2*3*3)...
The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number = 36-20 = 16.
Option C.
Answer: (C) 16
Question: If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. Line L must passes through the first quadrant
2. Line L does pass the origin
3..The slope of L is negative
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: Slope of the given line= 3-n/n-3
Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.
1) n<3 (n=2)
3-2/2-3= -1
2) n<3 (n= 0)
3-0/0-3= -1
3) n<3 (n=-3)
3+3/ -3-3= -2/3
4) n>3
3-4/4-3= -1
NAswer C
Answer: (C) III only
Question: 2: 5 = 4/3: x. The value of x is?
(A) 10/3
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x * 2 = 5 * 4/3
x *2= 20/3
x=10/3
ANSWER:A
Answer: (A) 10/3
Question: A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?
(A) 420
(B) 700
(C) 220
(D) 400
(E) None of these
Rationale: Explanation :
He sells 40% of oranges and still there are 420 oranges remaining
=> 60% of oranges = 420
⇒ (60 × Total Oranges)/100 = 420
⇒ Total Oranges/100 = 7
⇒ Total Oranges = 7 × 100 = 700
Answer : Option B
Answer: (B) 700
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.140. Find the unknown rate of two blankets?
(A) 350
(B) 550
(C) 490
(D) 450
(E) 457
Rationale: 10 * 140 = 15=1400
3 * 100 + 5 * 150 = 1050
1400 – 1050 = 350
Answer:A
Answer: (A) 350
Question: 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is ?
(A) 1
(B) 7
(C) 3 years
(D) 9
(E) 2
Rationale: Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.
Total age of 4 members now = [96 + (10 x 4)] years = 136 years.
Total age of 6 members now = (24 x 6) years = 144 years.
Sum of the ages of 2 children = (144 - 136) years = 8 years.
Let the age of the younger child be years.
Then, age of the elder child = years.
So,
Age of younger child = 3 years.
Answer: C
Answer: (C) 3 years
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
(A) 15360
(B) 153600
(C) 30720
(D) 307200
(E) 308765
Rationale: Perimeter = Distance covered in 8 min. =(12000/60)x 8m = 1600 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m2. Answer: Option B
Answer: (B) 153600
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 8% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
(A) 2
(B) 5
(C) 200/27
(D) 110/20
(E) 9/4
Rationale: Let price be 10/ticket
then 220 tickets for this month's performance at its usual price=2200
which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000
now new revenue this month=200*10.8=2160
as per question asked 2000=2160(1-A/100)----->A=200/27%
Ans C
Answer: (C) 200/27
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 227 m
(B) 150 m
(C) 187 m
(D) 167 m
(E) 187 m
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer: B
Answer: (B) 150 m
Question: How many integers between 1 and 10^18 are such that the sum of their digits is 2?
(A) 161
(B) 171
(C) 181
(D) 191
(E) 201
Rationale: The integers with a sum of 2 are:
2, 20, 200,...,2*10^17 and there are 18 integers in this list.
Also, these integers have a sum of 2:
11
101, 110
1001, 1010, 1100
etc...
The number of integers in this list is 1 + 2 + ... + 17
Thus, the total number of integers is 1 + 2 + ... + 17 + 18 = 18*19/2 = 171
The answer is B.
Answer: (B) 171
Question: A cylindrical water filter is filled with water at a rate of 11 cubic meters per hour, the level of water in the filter rises at a rate of 0.4 meters per hour. Which of the following best approximates the radius of the filter in meters?
(A) √10/2
(B) √10
(C) 4.183
(D) 5
(E) 10
Rationale: Here's my re-worked solution:
volume = 11 = pi (r^2)(0.4)
22 = 22/7 (4/10)(r^2)
70/4 = r^2
r = sqrt(70/4)
Ans: C
Answer: (C) 4.183
Question: A train 132 m long passes a telegraph pole in 6 seconds. Find the speed of the train
(A) 70 km/hr
(B) 72 km/hr
(C) 79.2 kilometre per hour
(D) 80 km/hr
(E) None
Rationale: Solution
Speed	= (132 / 6) m/sec
= (22 x 18 /5) km/hr
= 79.2 km/hr
Answer C
Answer: (C) 79.2 kilometre per hour
Question: Company X provides bottled water to its employees in 1 liter bottles, $2 each. At least how many 1L bottles must Company X buy monthly, so that new contract with $50 fixed monthly rate and $1 for 10L bottle each paid off? (Assume that no other costs apply)
(A)  28
(B)  29
(C)  30
(D)  31
(E)  27
Rationale: let the no. of 1 liter bottles be x, so the no. of 10l bottles will be x/10 (to equate the vol.) since the total cost will be equal , 2x= 50+x/10 so x= 26.31 or 27. Answer is (E).
Answer: (E)  27
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 60 per kg. How much amount did he pay to the shopkeeper?
(A) A)1055
(B) B)1075
(C) C)1065
(D) D)1070
(E) E)1100
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 60 × 9 = 540.
Total cost he has to pay = 560 + 540 = 1100.
E)
Answer: (E) E)1100
Question: The units digit in the product 274 x 318 x 577 x 313 is
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Sol.
Required digit = Unit digit in (4 x 8 x 7 x 3) = 2.
Answer A
Answer: (A) 2
Question: For a journey the cost of a child ticket is 1/3rd of the cost of an adult ticket. If the cost of the ticket for 4 adults and 5 children is Rs. 85, what is the cost of a child ticket?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: cost of 1 child=C
cost of 1 adult=A
C=1/3 A =>A=3C
4A+5C=85
=> 12C+5C=85
=> 17C= 85
=>C=5
ANSWER:C
Answer: (C) 5
Question: This year, MBB Consulting fired 5% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction?
(A) 98.5%
(B) 100.0%
(C) 102.8%
(D) 104.5%
(E) 105.0%
Rationale: 100 employees, each earning 1$.
After the cut, 95 are left, each earning 1.1$.
1.1*95 = 104.5
100*1 = 100
This gives you the answer.
ANSWER:C
Answer: (C) 102.8%
Question: A farmer divided certain number of acres of land among 3 sons and 1 daughter in such a way that 1/3rd of the total land was given to elder son, 1/2 of the remaining was given to second son, 1/3rd of the remaining was given to his younger son, and the remaining to his daughter. As a result, the younger son and daughter received equal number of acres. Find the total number of acres divided, if daughter gets 12 acres land.
(A) 72
(B) 90
(C) 120
(D) 84
(E) 62
Rationale: Let total number of land Y acre
Elder son =
Y × 1/3 = 1/3 Y
Remaining = Y – 1/3 Y = 2/3 Y
Second son = 1/2 of 2/3 Y = 1/3 Y
Remaining = 1/3 Y = 24 acre [12 + 12 = 24, younger son + Daughter]
1/3 Y = 24, then Y = 24 × 3/1 = 72
Option A
Answer: (A) 72
Question: Margaret is 8 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages
(A) 10yrs
(B) 20yrs
(C) 30yrs
(D) 40yrs
(E) 50yrs
Rationale: Let, age of son x=12
Margaret is 8 years more than twice the age of his son, y = 8+2(x)
=8+2(12)
=8+24
=32yrs
Difference = 32 - 12
=20yrs
ANSWER:B
Answer: (B) 20yrs
Question: How many of the positive factors of 24 are not factors of 25
(A) 2
(B) 3
(C) 4
(D) 1
(E) 5
Rationale: factors of 24 - 1, 2, 3, 4, 6, 8, 12,24
factors of 25 -1,5, 25
Comparing both, we have 1 factor of 24 which are not factors of 25- 1
Answer: D
Answer: (D) 1
Question: If 2x + y + 3z = 10 ,-3x - 2y + 7z = 5 ,3x + 3y - 4z = 7 , what is the value of x ?
(A) 3
(B) 6
(C) 4
(D) 7
(E) 8
Rationale: Explanation:
2x + y + 3z = 10 â€“-------I
-3x - 2y + 7z = 5 â€“------ II
3x + 3y - 4z = 7 -------- III
add II and III
-3x - 2y + 7z =5
3x + 3y - 4z = 7
-------------------------------
0+y+3z = 12â€¦.......... IV
sub (IV)from 1, we get 2X= 8
x = 4
ANSWER: C
Answer: (C) 4
Question: If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers is :
(A) 2 :3
(B) 3 :4
(C) 3:20
(D) 20 : 3
(E) 30:7
Rationale: 0.4A = 0.06B
-> A/B = 0.06/0.40 = 6/40 = 3/20
:. A : B = 3 : 20
ANSWER:C
Answer: (C) 3:20
Question: A glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution. If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?
(A)  3.00
(B)  5.00
(C)  4.50
(D)  5.50
(E)  6.75
Rationale: We are given that a glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of glucose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution, we can set up a proportion.
We can say: “10 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 45 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.
10/100 = x/45
When we cross multiply we obtain:
(10)(45) = 100x
450 = 100x
4.50 = x
There are 4.5 grams of glucose in the solution in the container.
The answer is C.
Answer: (C)  4.50
Question: Tom has travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
(A) $1
(B) $1.84
(C) $1.98
(D) $2.34
(E) $2.56
Rationale: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Answer: (B) $1.84
Question: r=3^(n+3), then in terms of r, 9^n=
(A) r^2/81
(B) r^3/729
(C) r^2
(D) r/3
(E) r
Rationale: Questions in terms of variables can be easily solved by plugging in some values: Say n = 0
r = 3^2 = 27
and you need the value of 9^n which is 9^0 = 1
So when you put r = 27 in the options, you should get 1. Only option (A) satisfies.
Answer (B)
Answer: (B) r^3/729
Question: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive T difference between n and m?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0
third variant give us the mininal difference
n - m = 10 - 6 = 4
And there is some mistake in my way of thinking because we don't have such answer )
If we change the task and will seek for difference between m and n
than minimal result T will be 8 - 5 = 3
And answer B
Answer: (B) 3
Question: Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
(A) 75000
(B) 70000
(C) 72000
(D) 78000
(E) 76000
Rationale: Explanation:
Ratio of the profits of Kamal and Kiran
=25000×12:60000×8
=25×12:60×8
=5×3:12×2
=5:4×2
=5:8
Let the total profit =x
Then Kamal received 10x/100=x/10 as commission for managing the business.
Remaining profit =x−x10=9x10 which is shared in the ratio =5:8
Total amount received by Kamal =x/10+9x/10×5/13
⇒x/10+9x/10×5/13=58000
⇒x+9x ×5/13=580000
⇒x(1+45/13)=580000
⇒x(58/13)=580000
⇒x x 1/13=10000
⇒x=130000
Kiran's share = 130000−58000=72000
Answer: Option C
Answer: (C) 72000
Question: Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.
(A) 360
(B) 390
(C) 400
(D) 410
(E) 420
Rationale: A straight Q requiring direct formulae..
when compounded annually the final amount=P(1+ r/100)^n..
here P=1200, r=10 and n=3..
1200(1+ 10/100)^3..
1200*1.1^3=1597.2
interest =1597-1200=397, which is nearly 400 in the choices given
ANSWER:C
Answer: (C) 400
Question: Two pipes A and B can fill a cistern in 8 and 12 minutes respectively, and a third pipe C can empty it in 16 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/9 min
(B) 5 1/8 min
(C) 6 1/7 min
(D) 6 6/7 min
(E) 17 3/7 min
Rationale: 1/8 + 12 - 1/16
= 7/48
48/7 = 6 6/7
Answer:D
Answer: (D) 6 6/7 min
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
7 minutes more to walk to work than to ride his bicycle, then x equals
(A) 4
(B) 7
(C) 10.5
(D) 15
(E) 20
Rationale: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 7 mins or 7*60 secs in 7*60/40 =10.5 km
ANSWER:C
Answer: (C) 10.5
Question: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(6)?
(A) 2
(B) 3/2
(C) 5/3
(D) 8/5
(E) 13/8
Rationale: A(n+1)=1+(1/A(n))
A(1) = 1
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5
A(6) = 13/8
The answer is E.
Answer: (E) 13/8
Question: 100 is what percent of 40?
.
(A) 0.2%
(B) 250%
(C) 5%
(D) 20%
(E) 500%
Rationale: 100= x*40/100
x = 250%
Ans; B
Answer: (B) 250%
Question: a is an integer greater than 49 but less than 61, b is an integer greater than 59 but less than 71, what is the range of a/b?
(A) 2/7
(B) 1/2
(C) 3/4
(D) 1
(E) 5/4
Rationale: min value of a/b will be when b is highest and a is lowest ---> a=50 and b=70
So, a/b = 5/7
max value of a/b will be when b is lowest and a is highest ---> a=60 and b=60
So, a/b = 1
Range is 1-(5/7) = 2/7.
Answer should be A.
Answer: (A) 2/7
Question: During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold was 25,200, how many of them were sold at full price?
(A) 21,000
(B) 19,800
(C) 16,500
(D) 15,800
(E) 8,700
Rationale: 5400 + x = 25200 then x is 19800
our x = 19800 is 6/5 of a certain number X
so 19800 = 6/5 of X ---> 19800 * 5 / 6 -->
ANSWER:C
Answer: (C) 16,500
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 9. Which of the following is NOT a possible value for y + b?
(A) 24
(B) 21
(C) 20
(D) 17
(E) 15
Rationale: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>9 --> y+b>15.
Answer: E.
Answer: (E) 15
Question: 17 times a positive integer is more than its square by 60, then the positive integer is
(A) 13
(B) 10
(C) 11
(D) 5
(E) 14
Rationale: Explanation:
Let the number be x. Then,
17x = x2 + 60
=> x2 - 17x + 60= 0
=>(x - 12)(x - 5) = 0
=> x = 5 or 12
Answer: Option D
Answer: (D) 5
Question: Peter and Tom shared the driving on a certain trip. If Peter and Tom both drove for the same amount of time, but Peter only drove 2/5 of the total distance, what was the ratio of Tom's average speed to Peter's average speed?
(A) 1:5
(B) 2:5
(C) 1:2
(D) 3:2
(E) 2:3
Rationale: The answer is suppose to be D. 3:2. It's from the GMATPrep
option D is answer
Answer: (D) 3:2
Question: Mixture A is 30 percent alcohol, and mixture B is 60 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 40 percent alcohol, approximately how many gallons of mixture A are in the mixture?
(A) 0.8
(B) 0.7
(C) 0.6
(D) 0.5
(E) 0.4
Rationale: (60-50)/(50-30) = Qa/Qb
10/20= Qa/Qb
1/2 = Qa/Qb
Qa = (1/6) * 4 = 4/6 = 1/2 = 0.50
Answer : D
Answer: (D) 0.5
Question: The product of Tom's age in years, and half of Jerry's age in years, is 54. If Jerry is 3 years younger than Tom is, Jerry is how many years old?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: Let Tom's age be x & Jerry's age be y.
x * y/2 = 54
x * y = 108
Also, given y=x-3
Substituting x^2 - 3x = 108
Factoring, we get the ages to be 12 and -9.
Since age cannot be negative, Tom's age is 12.
Jerry's age therefore must be 9
Ans :(Option C)
Answer: (C) 9
Question: A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases?
(A) 500bc
(B) 500b/c
(C) 1000bc
(D) 1000b/c
(E) 1000/bc
Rationale: 2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips
The answer is C.
Answer: (C) 1000bc
Question: Chandigarh express of 100 m runs at a speed of 60 km/hr. What will be the time taken to cross a platform of 150 meters long?
(A) 11.00 sec
(B) 12.50 sec
(C) 15.00 sec
(D) 15.23 sec
(E) 5.23 sec
Rationale: EXPLANATION:
Given: Length of train = 100 m, speed of train = 60 km/hr, length of platform = 150 m
1) Always remember first step is the conversion of units.
Convert 60 km/hr into m/s by multiplying it with (5/18)
Speed of the train = 60 x	5/18=16.66 m/s
2) Distance covered by the train in passing the platform = (Length of train + Length of platform) = (100 + 150) = 250 m
Therefore,
The time taken =	Distance/Speed
= 250/16.66
= 15 sec
ANSWER IS C
Answer: (C) 15.00 sec