MU-NLPC/Calc-aqua_rat huggingface dataset:
In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is eleven years older than Ellen, how old is Aaron? Answers
A) 1–5	B) 3–5	C) 11–15	D) 16–20	E) 21–25

Solution: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'   In ten years, David will be four times as old as Aaron --> d+10 = 4(a+10)   Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)   David is seven years older than Ellen --> d = e + 11   e+11-20 = 2e-40   e-9 = 2e-40   e = 31   d = 42   52 = 4a + 40   a = 3   Answer: 3–5
Answer: B
A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the amount of money that the student earned per day for the 16th day?
Amounts earned per day : $96 $84 $80 $70 $48
Number of days : 4 7 4 3 2  Choose the correct option:
A) (1) $96  B) (2) $84  C) (3) $80  D) (4) $70  E) (5) $48

Solution: 4+7+4+3+2= 
4+7+4+3+2 = 20
20   The series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount.   1st to 2nd term= 48 (2 days)   3rd to 5th term = 70 (3 days)   6th to 9th term = 80 (4 days)   10th to 16th term = 84 (7 days)   Pick (2) $84
Answer: B
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/4 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
Choose one:
A) 0 B) 1/15 C) 2/15 D) 1/8 E) 2/10

Solution: Suppose the water in each jug is L liters   CX x (1/4) = L   CX = 4L liters   CX is capacity of X   CY x (2/3) = L   CY = 3L/2 liters   CY is capacity of Y   Now, Y is 3L/2 - L empty = L/2 empty   So, we can put only L/2 water in jug Y from Jug X   Jug X's remaining water = L - L/2 = L/2   Fraction of X which contains water = water / CX   = (L/2)/ 4L   = 1/8   Answer will be 1/8
Answer: D
Ten coins are tossed simultaneously. In how many of the outcomes will the first coin turn up a head? Choose the correct choice from the following choices:
A) 2^7
B) 2^10
C) 3 * 2^8
D) 2^9
E) 3 * 2^10

Solution: Fix the third coin as H. The remaining 9 coins have 2^9 outcomes.   Ans:2^9
Answer: D
Bill and Jane play a simple game involving two fair dice, each of which has six sides numbered from 1 to 6 (with an equal chance of landing on any side). Bill rolls the dice and his score is the total of the two dice. Jane then rolls the dice and her score is the total of her two dice. If Jane’s score is higher than Bill’s, she wins the game. What is the probability the Jane will win the game?	Choose the correct choice from the following options:  A) 15/36  B) 175/432  C) 575/1296  D) 583/1296  E) 1/2

Solution: There are three possible outcomes in the game:   1. B Wins   2. J Wins   3. Draw   So, 1=P(J)+P(B)+P(Draw)1=P(J)+P(B)+P(Draw)   The probability of B winning or J winning the game is same.   so, 1=2∗P(J)+P(Draw)1=2∗P(J)+P(Draw)   So, we need to calculate the probability of a draw.   A draw can happen when both will have the same sum.   The possible sums are - 2,3,4,5,6,7,8,9,10,11,12   Prob. of each sum is -   2 - 1,1 - 1/36   3 - 1 2, 2 1 - 2/36   4 - 1 3, 2 2, 3 1 - 3/36   5 - 1 4, 2 3, 3 2, 41 - 4/36   6 - 1 5, 2 4, 3 3, 4 2, 5 1 - 5/36   7 - 1 6, 2 5, 3 4, 4 3, 5 2, 61 - 6/36   8 - 2 6, 3 5, 4 4, 5 3, 6 2, - 5/36   9 - 3 6, 4 5, 5 4, 63 - 4/36   10 - 4 6, 5 5, 6 4 - 3/36   11 - 5 6, 6 5 - 2/36   12 - 6 6 - 1/36   Now, since both have to get the same sum, the probability will be same for both and the combined probability will be the square of the probabilities   i.e. 2 - (1/36)^2   3 - (2/36)^2   etc.   Squaring the probabilities and adding them will give 146/1296   So, P(D) = 146/1296   1 = 2*P(J) + P(D)   2*P(J) = 1150/1296   P(J) = 575 / 1296   Ans. 575/1296
Answer: C
A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets?
Choose the correct choice from the following answers.
A) 5 B) 6 C) 8 D) None of these E) Cannot determined

Solution: 7 + 4 + 0 + 3 + 1 + 5 + 1 + x = 26   21 + x = 26   x = 5 patrons have none of these animals   5)
Answer: A
Two trains of equal are running on parallel lines in the same direction at 18 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Choose the correct choice from the following options.
A) 25	B) 26	C) 27	D) 28	E) 21

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/18 = 25/9 => x = 25.   25nswer: 25
Answer: A
The tax on a commodity is diminished by 10% and its consumption increased by 25%. The effect on revenue is? Choose the correct choice from the following choices
A) 12% decrease	B) 18% decrease	C) 19% decrease	D) 13% decrease	E) 12.5% increase

Solution: 100 * 100= 
100 * 100 = 10_000
10000   90 * 125= 
90 * 125 = 11_250
11250   -----------   10000-----------1250   100-----------?=> 12.5% decrease   Answer: 12.5% increase
Answer: E
Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 2 times before stopping? Choose the correct choice from the following choices:
A) 11/180
B) 125/216
C) 25/216
D) 91/216
E) 1/6

Solution: The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:   The probability that Molly will roll the die once: P=1/6 (she gets 1on the first roll)   P = 1/6   Answer: 1/6
Answer: E
Wendy begins sanding a kitchen floor by herself and works for 7 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?
Select: A) 9/80 hours B) 3/20 hours C) 20/3 hours D) 80/9 hours E) 10 hours

Solution: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.   Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.   If wendy works for 7 hours and is then joined by Bruce to finish the work in 2 more hours,   7/W + 2/W+2/B = 1 (1 denotes the total amount of work)   9/W + 2/B =1 and given B =20 hours.   Thus W = 10 hours , 10 hours is the correct answer.
Answer: E
Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 7 hours. How long would it take Taimour to paint the fence alone?	Answers.
A) 6 hours	B) 8 hours	C) 14 hours	D) 21 hours	E) 32 hours

Solution: I believe the answer is D. Please see below for explanation.   if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T   if working together they can do the job in 8 hours we can infer 1 = 2T+T * 7 => 1/21   Working alone Taimour can do the job in 1 = 1/21 * hours => 21   Answer 21 hours
Answer: D
A bat is bought for Rs.800 and sold at a gain of 20% find its selling price	Choose the correct choice from the following answers.
A) Rs.920/- B) Rs.950/- C) Rs.860/- D) Rs.960/- E) None of these

Solution: Explanation:   100 % ------> 800 (100 * 8 = 800)   120 % ------> 960 (120 * 8 = 960)   Selling price = Rs. 960/-   Answer: Option Rs.960/-
Answer: D
A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?	Pick one.
A) 7 km	B) 3 km	C) 6 km	D) 9 km	E) 2 km

Solution: Average speed = (2 * 3 * 2) / (3 + 2)   = 12/5 km/hr.   Distance traveled = 12/5 * 5= 
12/5 * 5 = 12
12 km.   Distance between house and school= 12/2= 
12/2 = 6
6 km.   Answer: 6 km
Answer: C
If the mode of Set F is equal to the median of Set F, Set F could be
Choose the correct answer
A) [0, 1, 2, 2, 3, 4, 5, 6]	B) [2, 2, 5, 7, 9]	C) [x, x+1, x+2, x+2, x+3, x+3]	D) [10, 102, 105, 105]	E) [4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]

Solution: Correct Answer: (C)   Set F could be The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set [x, x+1, x+2, x+2, x+3, x+3] is equal to the median of set [x, x+1, x+2, x+2, x+3, x+3].
Answer: C
Three numbers are in the ratio 3:4:5 and their L.C.M. is 2400. Their H.C.F is?  Pick one
A) 20	B) 30	C) 40	D) 50	E) 60

Solution: Let the numbers be 3x,4x and 5x   their L.C.M. = 60x   60x = 2400   x = 40   The numbers are 3*40 , 4*40 , 5*40   Hence required H.C.F. = 40   Answer is 40
Answer: C
There are a total of 12 students in Mr. Sri's gym class. Over the course of a badminton unit, each of the 12 students will compete exactly once against every other student in the class. How many total games of badminton will be played?	Select.
A) 68
B) 67
C) 69
D) 60
E) 66

Solution: there are 19 students , if each play with all other members .   then total games can be calculated as 11+10....+1 = 66.   alternate approach is to choose 2 distinct out of 12 = 12c2 = 66   Answer is 66.
Answer: E
Which of the following is the sum of all the even numbers between 1 and 97, inclusive?	Answers.
A) 2550	B) 2450	C) 2600	D) 2449	E) 2652

Solution: This question can be solved withbunching.   We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 4, 6, 8.....96.   If you take the next smallest and next biggest numbers, you have...   4+96= 
4+96 = 100
100   This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...   44+56= 
44+56 = 100
100   46+54= 
46+54 = 100
100   48+52= 
48+52 = 100
100   There IS a middle number: 50; this number does NOT get paired up.   Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50-1= 2449   Final Answer:   2449
Answer: D
An article is bought for Rs.900 and sold for Rs.1000, find the gain percent?  Select:
A) 11 2/5%	B) 11 2/9%	C) 11 1/9%	D) 11 2/3%	E) 11 3/3%

Solution: 900 ---- 100   100 ---- ? => 11 1/9%   Answer: 11 1/9%
Answer: C
In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling price was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $5,100. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June? Answers.
A) 1. $15,600 B) 2. $15,750 C) 3. $17,100 D) 4. $18,100 E) 5. $19,200

Solution: Edited the question as there was a typo.   Range = Highest Value - Lowest Value.   Range in May was 15,000 and the lowest price in May was 4,500, thus the highest price in May was 15,000+4,500=19,500.   Range in June was 16,500 and the lowest price in June was 5,100, thus the highest price in June was 16,500+5,100=21,600.   Lowest price of a car in May-June was 4,500 (May) and the highest price of a car in May-June was 21,600, thus the range for May-June is 21,600-4,500=17,100.   Answer: 3. $17,100.
Answer: C
A tour group of 25 people paid a total of $945 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices  Answers:
A) $22  B) $23.94  C) $36  D) $25.20  E) $30

Solution: Soln:-   945/25=x+0.05x   945/25=1.05x   x=36   ANSWER:$36
Answer: C
A parking garage rents parking spaces for $10 per week or $40 per month. How much does a person save in a year by renting by the month rather than by the week?  Choose the correct option.
A) $140	B) $160	C) $220	D) $40	E) $260

Solution: 10$ per week!   An year has 52 weeks.   Annual charges per year = 52* 10= 
52* 10 = 520
520$   30$ per month!   An year has 12 months.   Annual charges per year= 12 * 40= 
12 * 40 = 480
480$    520 - 480= 
 520 - 480 = 40
40   Ans $40
Answer: D
Which of the following fractions W has a decimal equivalent that is a terminating decimal?  Select the correct option
A) 10/189	B) 15/196	C) 16/225	D) 25/144	E) 39/128

Solution: The fraction W will terminate if and only if the denominator has prime divisors only 2 and 5 or both.   A. 10/189 = 10/(3*3*3*7) Non-term.   B. 15/196 = 15/(2*2*7*7) Non-term.   C. 16/225 = 16/(5*5*3*3) Non-term.   D. 25/144 = 25/(2*2*2*7) Non-term.   E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: E
A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference?	Choose one
A) 9 feet
B) 12 feet
C) 13 feet
D) 15 feet
E) 18 feet

Solution: total circuit=12/4= 
12/4 = 3
3   total feet squirrel travels=3*3= 
3*3 = 9
9 feet   9 feetNSWER:9 feet
Answer: A
James and David work at a grocery shop with 12 other workers. For an internal review, 2 of the 12 workers will be randomly chosen to be interviewed. What is the probability that James and David will both be chosen?  Choices
A) 1/26	B) 1/36	C) 1/46	D) 1/66	E) 1/56

Solution: Probability that James and 1/66avid will both be chosen out of 12 workers   = (2/12)*(1/11)   = 1/66   Answer 1/66
Answer: D
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Choose the correct choice from the following choices
A) 140 sq.units B) 149 C) 148 D) 17 E) 143

Solution: Given that the area of the square = 1225 sq.units   => Side of square = √1225 = 35 units   The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35= 
2/5 * 35 = 14
14 units   Given that breadth= 10 units   140 sq.unitsrea of the rectangle = lb = 14 * 10= 
14 * 10 = 140
140 sq.units   140 sq.unitsnswer: Option 140 sq.units
Answer: A
Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $7 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ? Choose the correct choice
A) 8n + 2  B) 8n + 4  C) 9n + 2  D) 9n + 3  E) 9n + 6

Solution: its C   n items for $8 each   total price $8n   postage and handling of $3 for 1st item and $1 for the rest   total postage and handling = $ [7+ (n-1)]   = $ n+6   total cost   8n+n+6 = 9n+6   9n + 6
Answer: E
What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle.  Select:
A) 1 : 2
B) 2 : 1
C) 3 : 1
D) Data inadequate
E) None of these

Solution: Area of ΔEBC = 1⁄2 × BC × EF   = 1⁄2 × BC × AB[Since, EF = AB]   Area of ΔEBC = 1⁄2 × area of ΔABCD   \ Required ratio = 2 : 1.   Answer 2 : 1
Answer: B
Winners will be announced the following day at 12 AM Pacific/1 PM Eastern Time.
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ?	Pick:  A) 13  B) 21  C) 23  D) 24  E) 25

Solution: The reasoning is as follows:-   B) can't be answer because Y<x 3="" 4="" a)="" answer="" be="" because="" but="" c)="" can't="" correct="" d)="" digit="" e)="" equal="" give="" is="" it="" middle="" not="" number="" number.="" the="" thus="" to="" will="" wrong="" x="" xy="" y="" y.="" yx="">xwill give 5 digit numbermiddle digit is Y   25</x>
Answer: E
The cost price of a radio is Rs.2300 and it was sold for Rs.1800, find the loss %?  Choose the correct choice from the following:
A) 18
B) 99
C) 27
D) 26
E) 21

Solution: 2300 ---- 500   100 ---- ? => 21%   Answer: 21
Answer: E
The mean of 20 observations was 36. It was found later that an observation 25 was wrongly taken as 40. The corrected new mean is Options:	A) 30	B) 25.4	C) 40	D) 35.25	E) 26.55

Solution: Explanation:   Correct Sum = (36 * 20 + 25 - 40)= 
(36 * 20 + 25 - 40) = 705
705   Correct mean= = 705/20= 
705/20 = 141/4 = around 35.25
35.25   Answer: 35.25
Answer: D
For integers x and y, if (x+2)(y+3) is even then 4xy must be divisible by: Select:
A) 4
B) 8
C) 9
D) 10
E) 12

Solution: Just looking at the question, (x+2)(y+3) could be even*even, odd*even, or even*odd in order for the whole expression to be even.   However, just looking at 4xy, since x*y will always be an integer, it will always be divisible by 4. 4 divided by 4 is 1, hence preserving x*y.   Answer: A. 4
Answer: A
How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Choose the correct answer:  A) 12 sec  B) 30 sec  C) 36 sec  D) 16 sec  E) 18 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 600 * 3/50= 
600 * 3/50 = 36
36 sec.   Answer: 36 sec
Answer: C
It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible? Choose the correct choice from the following options:
A) 142	B) 144	C) 3680	D) 3280	E) 3680

Solution: Total number of candidates = 4 + 3= 
4 + 3 = 7
7. In the row of 7 positions, the even places are 2nd, 4th, 6th .   Now, number of even places= 3.   Number of girls to occupy the even places = 3.   Even places can be filled = P (3, 3) ways.   Number of boys = 4.   The remaining 4 places can be filled by 4 boys = P (4, 4) ways   144y the fundamental principle of counting:   The required number of seating arrangements   P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144   ANSWER:144
Answer: B
Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores 1/4, what is the value of Y/X ?  Choose the correct choice from the following answers:
A) 3.
B) 2.
C) 1/5
D) 1/3.
E) There isn't enough data to answer the question.

Solution: Answer is 1/5 : 1/5   X - Y = (X + Y)/4   Solving for Y/X = 1/5
Answer: C
A bowl was filled with 10 ounces of water, and 0.010 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?	Choose the correct answer.
A) 0.004%
B) 0.04%
C) 0.40%
D) 5%
E) 40%

Solution: Total amount of water evaporated each day during a 50-day period = .008 * 50   =.010 * 100/2   = 1.0/2= 
1.0/2 = 0.5
.5   percent of the original amount of water evaporated during this period= (.5/10) * 100= 
(.5/10) * 100 = 5
5 %   Answer 5%
Answer: D
The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number?
Answers:
A) 3  B) 6  C) 9  D) 12  E) 15

Solution: Sol.   Let the numbers be x, x + 2 and x + 4.   Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7.   ∴ Middle number = x + 2 = 9.   Answer 9
Answer: C
If cyclist is covering a circular distance of diameter 15 inches at the speed of x inches/min, and another cyclist is covering a circular distance of diameter 25 inches at the speed of y inches/min then what is the value of y in terms of x if both the cyclists cover the distance at the same time?  Pick one.
A) 2x/4	B) 6x/2	C) 7x/3	D) 5x/3	E) 4x/3

Solution: t=S1/V1=S2/V2   or 15/x=25/y   or y=25x/15=5x/3   Answer is 5x/3
Answer: D
The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of? Answers
A) 6:6  B) 6:9  C) 6:5  D) 6:2  E) 6:1

Solution: 4:5   3:2   -------   12:15:10   12:10   6:5   Answer:6:5
Answer: C
Zeeshan having a certain number of one rupee,fifty paise and twenty
five paise coins are in the ratio of 3:2:4, add up to
Rs 75. Then how many 1 rupee coins he have? Select the correct option:
A) 10	B) 20	C) 45	D) 128	E) 49

Solution: Explanation :   Given ratio = 3:2:4.   Let us assume that there are 3 one rupee coins,2   fifty paise coins and 4 twenty-five paise coins in all.   Their value=(3*1)+(2*.50)+(4*.25)=3+1+1= 
3+1+1 = 5
Rs 5   If the total is Rs 5, number of 1 rupee coins are 3.   If the total is Rs 75, number of 1 rupee coins would be  75*3/5= 
 75*3/5 = 45
45.   Answer : 45
Answer: C
Yesterday i noticed that in my clock , there is time when the hour needle and the minute needle are exactly between 1 and 2.
Also both the needles lie on top of each other.
What time i and talking about ?  Select the correct option: A) 10:00 B) 11:00 C) 09:00 D) 12:00 E) 07:00

Solution: 12:00   12:00   both minute and hour clock lie exactly between the number one and two in the number.
Answer: D
Simple interest on a certain sum at a certain annual rate of interest is 1/4 of the sum. If the numbers representing rate percent is 5time of years , then the Time is:  Choices:
A) 6 1/2 years.
B) 5 1/2 years.
C) 4 1/2 years.
D) 2 1/2 years.
E) 3 1/2 years.

Solution: Explanation :   Let sum = x. Then, S.I. = x/4   Let Time =N and R = 4 N.   [x * N * 4N / 100] = x / 4? N^2 = 25/4   N = 5/2 = 2 1/2 years.   Hence,n = 2 1/2 years.   Answer : 2 1/2 years.
Answer: D
If m is a positive integer, and m/15 = 8.2, what is the remainder Y when m is divided by 15?
Choose the correct choice.
A) A.1  B) B.2  C) C.3  D) D.4  E) E.8

Solution: If m were a multiple of 15, the quotient m/15 would be an integer. The fact that it's a decimal tells us that 15 goes into m eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let Y be the remainder.   Y/15 = 0.2 = 1/5   Y = (15)*(1/5)= 
(15)*(1/5) = 3
3   Answer=(C.3)
Answer: C
The sum of two number is 25 and their difference is 13. Find their product. Pick.
A) 114	B) 104	C) 315	D) 350	E) 400

Solution: Let the numbers be x and y.   Then, x + y = 25 and x - y = 13.   4xy = (x + y)2 - (x- y)2=(25)2 - (13)2   = (625 - 169) = = 456 =>114   114NSWER 114
Answer: A
Kim is taking a math class, and the teacher gives a multiple choice test consisting of 6 questions. If each question has 5 answer choices, and Kim answers every question, in how many different ways can she complete the test? Choose the correct choice.
A) a 40 B) b 400 C) c 5^8 D) d 5^6 E) e 40^40

Solution: different ways to solve each question is 5.   So, 5*5*5*5.. 6 times ----> 5^6   Answer will be d 5^6.
Answer: D
In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ? Choose one:  A) 33  B) 28  C) 76  D) 54  E) 912

Solution: Explanation:   Let R, G and B represent the number of balls in red, green and blue boxes respectively.   Then,   R + G + B = 108 ...(i),   G + R = 2B ...(ii)   B = 2R ...(iii)   From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.   Putting G = 3R and B = 2R in (i), we get:   R + 3R + 2R = 108 {\color{Blue} \Rightarrow } 6R = 108 {\color{Blue} \Rightarrow } R = 18.   Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.   Answer: 54
Answer: D