mathewhe/aqua_rat huggingface dataset:
Question: At a certain amateur bands rock show the ratio of freaks to nerds to geeks( G) is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yells rock on!will be a geek?
(A) 1/8
(B) 1/3
(C) 1/2
(D) 1/4
(E) 1/6
Rationale: Another approach is toassign some nice valuesfor the number of freaks, nerds and geeks.
Given: the ratio of freaks to nerds to geeks is 1:2:3
So, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people.
P(next person who yellsrock on!is a geek) = (# of geeks in the crowd)/(TOTAL # of people in the crowd)
=3/6
= 1/2
Answer:
C
Answer: (C) 1/2
Question: A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $1000 or doubled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $50,000 in property taxes, but did not pay until October 15th?
(A) $1,400
(B) $1,800
(C) $4,000
(D) $21,400
(E) $22,800
Rationale: Original amount = 50,000
Fine for July = 50,000 * 1% = 500
Fine for August = lesser of the 2 , 500+1000= 1500 or 500*2=1000 . Pick 1000
Fine for September = 1000+1000=2000 or 1000*2 = 2000. Pick 2000
Fine for October = 2000+1000=3000 or 2000*2 = 4000. Pick 4000.
The wording of the question should be have been clearer as total fines should be = 4000+2000+1000+500 = 7500 and NOT 4000.
4000 is the fine ONLY for the month of October!
C
Answer: (C) $4,000
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8900. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) s.2900
(B) s.3570
(C) s.4500
(D) s.4550
(E) s.2500
Rationale: Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8900
= 35600 ----(2)
(2)-(1) i.e. May - Jan =3600
Salary of May is Rs.6500
Salary of January = Rs.2900
Answer:A
Answer: (A) s.2900
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer W that must divide n is?
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer W that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Answer: (B) 12
Question: The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 58, then 1/m + 1/n is equal to
(A) 1/35
(B) 3/35
(C) 5/37
(D) 2/35
(E) None
Rationale: Answer
We have, m x n = 6 x 210 = 1260
âˆ´ 1/m + 1/n = (m + n)/mn = 58/1260 = 17/620
Correct Option: E
Answer: (E) None
Question: A straight fence is to be constructed from posts 9 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)
(A) 17
(B) 28
(C) 35
(D) 39
(E) 40
Rationale: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}
The minimum length is with 2 posts = 0.5 + 5 + 0.5 = 6 feet. To increase the fence, each time we should add{post = 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:
9 feet;
9 + 5.5 = 14.5 feet;
11.5 + 5.5 = 20 feet;
17 + 5.5 = 25.5 feet;
22.5 + 5.5 = 31 feet;
28 + 5.5 = 34.5 feet;
33.5 + 5.5 = 41 feet.
...
We skipped 40 feet.
Answer: E.
Answer: (E) 40
Question: Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.530. If Sanoop returned 3 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts?
(A) 560
(B) 561
(C) 562
(D) 571.6
(E) 564
Rationale: Total price of 8 t-shirts= 8*530=4240
Total price of 5 t-shirts=5*505=2525
Total price of 3 t-shirts=4240-2525=1715
Average price of 3 t-shirts=1715/3=571.6
Correct option Answer:D
Answer: (D) 571.6
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 94
(C) 96
(D) 97
(E) 99
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
A
Answer: (A) 90
Question: If $15,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years?
(A)  compounding annually
(B)  compounding quarterly
(C)  compounding monthly
(D)  All four of these would produce the same total
(E)  compounding daily
Rationale: This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest.
This process will be repeated every day till the amount matures
Compounding annually will give least returns
Answer = E
Answer: (E)  compounding daily
Question: The ration of the number of boys and girls in a college is 2:3. If the percentage is increase in the number of boys and girls be 10% and 20% respectively. What will be the new ration?
(A) 21:22
(B) 13:17
(C) 15:43
(D) 11:18
(E) 15:23
Rationale: Let the number of boys and girls be 2x and 3x
their increased number is 110% of 2x and 120% of 3x
2x*110/100 and 3x*120/100
11x/5 and 18x/5
Required ratio = 11x/5 : 18x/5 = 11:18
Answer is D
Answer: (D) 11:18
Question: Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 36 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
(A) 542
(B) 540
(C) 514
(D) 829
(E) 432
Rationale: 1/12 + 1/15 - 1/x = 1/15
x = 12
12 * 36 = 432
Answer: E
Answer: (E) 432
Question: A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
(A) 56
(B) 48
(C) 30
(D) 40
(E) 50
Rationale: B = 1/16 â€“ 1/24 = 1/48 => 48 days
ANSWER B
Answer: (B) 48
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum?
(A) 2999
(B) 2770
(C) 2708
(D) 2000
(E) 2791
Rationale: P(11/10)4 - P(6/5)2 = 482
P = 2000
Answer: D
Answer: (D) 2000
Question: Find the average of the first 19 natural numbers?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Average of the first 'n' natural numbers = (n + 1)/2
We get (19 + 1)/2 = 10
ANSWER:C
Answer: (C) 10
Question: Alice and Bob contributed $8 and $4 respectively to the price of a $12 lottery ticket. The ticket won fourth prize, worth $24,000. How much money should they each receive from the prize?
(A) Alice should get $13,000; Bob should get $11,000
(B) Alice should get $16,000; Bob should get $8,000
(C) Alice should get $17,000; Bob should get $7,000
(D) Alice should get $17,500; Bob should get $6,500
(E) Alice should get $18,000; Bob should get $6,000
Rationale: A = $8
B = $4
A share 8 parts & B share 4 parts
Total 12 parts -----> $24000
----> 1 part -------> $2000
A share = 8 parts -----> $12000
B
Answer: (B) Alice should get $16,000; Bob should get $8,000
Question: The sum of the mean, the median, and the range of the set {1, 2, 9} equals which one of the following values?
(A) 12
(B) 14
(C) 16
(D) 8
(E) 10
Rationale: set {1, 2, 9}
Mean = (1+2+9)/3 = 4
Meadian = Middle term = 2
Range = Highest - Lowest = 9-1 = 8
Mean+Median+Range = 4+2+8 = 14
Answer: Option B
Answer: (B) 14
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 16 seconds, the speed of each train (in km/hr) is
(A) 42
(B) 27
(C) 28
(D) 20
(E) 24
Rationale: Explanation:
Distance covered = 120+120 = 240 m
Time = 16 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/16 = 15 m/s
Speed of each train = v = 15/2 = 7.5 m/s
= 7.5×36/10 km/hr = 27 km/hr
Answer: Option B
Answer: (B) 27
Question: Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?
(A) 24.
(B) 28.
(C) 36.
(D) 42.
(E) 48
Rationale: Diameter of tube= 5 inches
Height of wooden tube= 15 inches
Two tubes can stand in 31 inches height
Two tubes can fit in 11 inches length
Two tubes can fit in 10 inches width
So, one box can hold 8 tubes
Three boxes can hold= 8*3= 24 tubes
A is the answer
Answer: (A) 24.
Question: What is 2 2/3 - 1 1/4 divided by 1/4 - 1/6 ?
(A) 17/36
(B) 36/17
(C) 17/6
(D) 17/1
(E) 51/4
Rationale: 2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12
1/4 - 1/6 = (6-4)/24 = 2/24 = 1/12
So 17/12/1/12 = 17/12 * 12 = 17/1
Answer - D
Answer: (D) 17/1
Question: X and Y started a business in partnership investing Rs. 8,000 and Rs. 12,000 respectively. After nine months, Z joined them with Rs. 20,000. What will be Z's share in total profit of Rs. 20,000 earned at the end of 3 years from the starting of the business?
(A) Rs. 8,751
(B) Rs. 8,571
(C) Rs. 9,751
(D) Rs. 9,571
(E) None
Rationale: Solution: X : Y : Z = (8,000 * 36) : (12,000 * 36) : (20,000 * 27) = 8 : 12 : 15.
So B's share = Rs. (20000 * 15/35) = Rs. 8,571.
Answer: Option B
Answer: (B) Rs. 8,571
Question: In Kaya's teacher's desk there are 24 pink highlighters, 28 yellow highlighters, and 25 blue highlighters. How many highlighters are there in all?
(A) 11
(B) 22
(C) 77
(D) 33
(E) 88
Rationale: Add the numbers of highlighters.
24 + 28 + 25 =77.
Answer is C.
Answer: (C) 77
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 48
(B) 9
(C) 7
(D) 67
(E) 15
Rationale: :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125
= 48 sec.
Answer: A
Answer: (A) 48
Question: A train running at the speed of 54 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 140
(B) 135
(C) 150
(D) 170
(E) 160
Rationale: Speed=(54x5/18)m/sec = 15 m/sec.
Length of the train = (Speed x Time).
Length of the train = (15 x 9)m = 135 m.
Answer is B.
Answer: (B) 135
Question: The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places?
(A) Rs.20043.94
(B) Rs.20043.99
(C) Rs.20043.91
(D) Rs.20043.92
(E) Rs.20044.94
Rationale: Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer:A
Answer: (A) Rs.20043.94
Question: Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers?
(A) 2 hours and 30 minutes.
(B) 6 hours and 30 minutes.
(C) 5 hours and 30 minutes.
(D) 3 hours and 30 minutes.
(E) 4 hours and 30 minutes.
Rationale: The time it takes Kim to walk 18 kilometers is equal to
18 / 4 = 4.5 hours = 4 hours + 0.5 ? 60 minutes
= 4 hours and 30 minutes.
correct answer E
Answer: (E) 4 hours and 30 minutes.
Question: If T is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, T, 0, 1, 3, K, 7}?
I. -1.5
II. -2
III. 0
(A)  I only
(B)  II only
(C)  III only
(D)  I and III only
(E)  None
Rationale: The answer should be T (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either..E
Answer: (E)  None
Question: The average of five integers is 60, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers?
(A) 5
(B) 15
(C) 20
(D) 21
(E) 30
Rationale: When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 60
So, the sum of ALL 5 integers = (60)(5) =300
The average of three of the integers is 65
So, the sum of the 3 integers = (65)(3) =195
So, the sum of the 2 REMAINING integers =300-195=105
If the sum of the 2 REMAINING integers =105, and we want to minimize one value, we must MAXIMIZE the other value.
100 is the maximum value so let 1 integer = 100, which means the other must equal 5
Answer: A
Answer: (A) 5
Question: At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour?
(A) $1.40
(B) $2.40
(C) $3.40
(D) $4.40
(E) $5.40
Rationale: Manager wages per hour = $8.50
Dishwasher wages per hour = half of manager's wages. = 1/2($8.50) ==> $4.25
Chef wages per hour = 20% greater than Dishwasher wages
--> 20% of $4.25 = (20*($4.25)) /100
--> ($85)/100
--> $0.85
Therefore,
Chef wages per hour = $4.25 + $0.85 ==> $5.10
Difference of wages between manager and chef = $8.50 - $5.10 ==> $3.40
ANSWER:C
Answer: (C) $3.40
Question: If y exceeds x by 25%, then x is less than y by?
(A) 21%
(B) 29%
(C) 20%
(D) 80%
(E) 24%
Rationale: X=100	y=125
125--------25
100--------? => 20%
Answer:C
Answer: (C) 20%
Question: A group of 7 friends are having lunch together. Each person eats at least 3/4 of a pizza. What is the smallest number of whole pizzas needed for lunch?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If each person eats at least 3/4 of a pizza, then the 7 will eat at least.
7 * (3 / 4) = 21 / 4 = 5 + 1/4
At least 6 pizzas are needed for lunch
correct answer E
Answer: (E) 6
Question: In a survey, 60 percent of the people surveyed admitted to being smokers, while 25 percent of the people surveyed who were smokers declined to include that information in the survey. What percent of the people surveyed were actually smokers?
(A) 20%
(B) 80%
(C) 90%
(D) 75%
(E) 85%
Rationale: Statement: 60% of People Surveyed (PS) Admitted to being Smokers (AS). Of the people who took the survey who were Smokers (S), 25% declined to admit to being smokers (notAS). [Note: A Venn Diagram is useful to visualize the problem.]
Solution: Sample space is 100%.
PS = 100%
AS/PS = 60%
notAS/S = 25% => 100% - 25% => AS/S = 75%
S/PS = (60)/(75)% = 80%
Answer: B
Answer: (B) 80%
Question: The tax on a commodity is diminished by 25% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
(A) 12%
(B) 14%
(C) 16%
(D) 20%
(E) 17.5%
Rationale: Explanation:
100 * 100 = 10000
75 * 110 = 8250
10000------- 1750
100 ------- ? = 17.5%
E)
Answer: (E) 17.5%
Question: Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
(A) 65 hrs
(B) 16 hrs
(C) 88 hrs
(D) 55 hrs
(E) 41 hrs
Rationale: 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
Answer:B
Answer: (B) 16 hrs
Question: Ben is driving on the highway at y miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of z feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?
(A) 5,280(x/y)
(B) 5,280(y/z)
(C) 5,280(xy)
(D) 5,280/(xy)
(E) (xy)/5,280
Rationale: In one hour, at the rate of y miles per hour, Ben covers y miles, so 5,280y feet.
The number of revolutions = distance/circumference = 5,280y/z.
Answer: B.
Answer: (B) 5,280(y/z)
Question: If there is exactly one root of the equation x^2 + 2ax + b, where a and b are positive constants, what is b in terms of a?
(A) a/2
(B) a
(C) 3a/2
(D) a^2
(E) a^2/4
Rationale: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here b = 2a
c= b
a = 1
substituting these values in 1, we have
2^2*a^2 = 4b => b =a^2
Answer is D.
Answer: (D) a^2
Question: If x is a positive integer with fewer than 3 digits, what is the probability that Z x*(x + 1) is a multiple of either 4 or 5?
(A) 4/99
(B) 2/25
(C) 8/99
(D) 49/100
(E) 86/99
Rationale: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.
We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability Z that x(x+1) is a multiple of either 4 or 5.
When will this happen? If either x OR (x+1) is a multiple of 4 or 5.
Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.
Out of the numbers from 1 to 20:
4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20
So, 14 out of the first 20 numbers match our criteria. Since:
probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (E) is the only answer greater than 1/2, we go with (E).
Answer: (E) 86/99
Question: A man sells a horse for Rs.620 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 587
(B) 679
(C) 740
(D) 860
(E) 898
Rationale: CP = SP + 1CP = SP - g
620 + x = 980 - 2x
3x = 360 => x
= 120
CP = 620 + 120
= 740
Answer:C
Answer: (C) 740
Question: Type the missing number.
-95,-90,-85,x, -75,-70
(A) -82
(B) -86
(C) -76
(D) -60
(E) -80
Rationale: Added with +5 Previous Number get next number
-85+5 =-80
answer :E
Answer: (E) -80
Question: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 13 multiples of 14, how many multiples of 7 are there in Q?
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 13+12 = 25.
The answer is C.
Answer: (C) 25
Question: A and B start a business with Rs.6500 and Rs.8500 respectively. Hoe should they share their profits at the end of one year?
(A) 3:5
(B) 3:4
(C) 3:1
(D) 3:2
(E) 13:17
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6500 : 8500 => 13:17
Answer:E
Answer: (E) 13:17
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 27 seconds
(B) 29 seconds
(C) 40 seconds
(D) 11 seconds
(E) 12 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C
Answer: (C) 40 seconds
Question: If A^4 + B^4 = 100, then the greatest possible value of B is between
(A) 0 and 1
(B) 1 and 2
(C) 2 and 3
(D) 3 and 4
(E) 4 and 5
Rationale: for the greatest possible value of B^4, we must minimize the value of B^4 i.e. lets say A^4 = 0
then we need to find a number B such that B^4 < 100. 3^4 = 81 and 4^4 = 256 so we can say that the maximum possible value of B can be a little more than 3 hence answer = between 3 and 4
hence D
Answer: (D) 3 and 4
Question: Set A contains all the even numbers between 4 and 50 inclusive. Set B contains all the even numbers between 104 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
(A) 2400
(B) 2550
(C) 5050
(D) 6275
(E) 11325
Rationale: Set A contains 4 , 6 ... 50
Set B contains 104 , 106 ... 150
Number of terms in each set = 24
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*24 = 2400
Answer A
Answer: (A) 2400
Question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 3
Rationale: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9
Answer: A
Answer: (A) 9
Question: A shopkeeper sells sugar in such a way that the selling price of 950g of sugar is the same s the cost price of 1 kg of sugar. What is his gain percent?
(A) 5(5/19)
(B) 5(1/5)
(C) 5
(D) 4(1/19)
(E) None
Rationale: Solution: Sell sugar = 950g instead of 1000g.
Profit in Sugar = 1000 - 950 = 50g.
Now, % profit = (50*100)/950 = 5(5/19)%.
Short-Cut
% profit = (Goods left/Goods sold)*100.
= (50/950)*100 = 5(5/19)%.
Answer: Option A
Answer: (A) 5(5/19)
Question: A collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 15 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?
(A) 28%
(B) 32%
(C) 36%
(D) 40%
(E) 44%
Rationale: Let x be the number of stamps in the original collection.
The percentage of the collection given away is:
0.2x + 0.15(0.8x) = 0.2x + 0.12x = 0.32x = 32%
The answer is B.
Answer: (B) 32%
Question: The average age of a family of 6 members is 40 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member?
(A) 33
(B) 18
(C) 21
(D) 12
(E) 19
Rationale: Present age of total members = 6 X 40 = 240
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 240 - 42 = 198
Therefore, avg age at the birth of youngest member = 198/6 = 33.
ANSWER:A
Answer: (A) 33
Question: If the sum of two numbers is 16 and the sum of their squares is 200, then the product of the numbers is
(A) 40
(B) 44
(C) 80
(D) 88
(E) 28
Rationale: according to the given conditions x+y = 16
and x^2+y^2 = 200
now (x+y)^2 = x^2+y^2+2xy
so 16^2 = 200+ 2xy
so xy = 56/2 =28
ANSWER:E
Answer: (E) 28
Question: If x is an integer, which of the following is a possible value of H=(x^2 +2x – 7)/9?
(A) -2.4
(B) 0.268
(C) 1.166 repeating
(D) 4.555 repeating
(E) 8.125
Rationale: x is an integer, which of the following is a possible value of H=(x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer
Answer choice D seems to fit
Answer: (D) 4.555 repeating
Question: A 35 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 10
(B) 20
(C) 88
(D) 77
(E) 14
Rationale: 1: 2/5 = 5: 2
2/7 * 35 = 10
Answer: A
Answer: (A) 10