MU-NLPC/Calc-aqua_rat huggingface dataset:
In how many ways can 10 people, A, B, C, D, E, F, G, H, I, J be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?	Choose the correct choice from the following answers:	A) 384	B) 396	C) 576	D) 3628704	E) 6960087

Solution: Number of total arrangements = 10!   Restriction 1= ABC3628704 not next to each other --> let say AB and C3628704 are considered as one unit, respectively   Restriction 2= AB is not the same as BA + C3628704 is not the same as 3628704C --> the number will increase by 2*2   Total number of arrangements - Number out of restrictions = Result   10! - (4!*2*2) = 3628800 - (24*2*2)= 
3628800 - (24*2*2) = 3_628_704
3628704   Answer 3628704
Answer: D
The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 20x + 25. If the sum of the perimeters of both squares is 36, what is the value of x?  Choose the correct choice from the following answers:	A) 3	B) 5	C) 7	D) 9	E) 11

Solution: The areas are (x+5)^2 and (2x-5)^2.   The lengths of the sides are x+5 and 2x-5.   If we add the two perimeters:   4(x+5) + 4(2x-5) = 36   12x = 36   x = 3   The answer is 3.
Answer: A
What is the rate percent when the simple interest on Rs.810 amount to Rs.155 in 4 Years?
Select the correct option
A) 4.78
B) 4.68
C) 4.58
D) 4.48
E) 4.38

Solution: 155 = (810*4*R)/100   R = 4.78%   4.78nswer: 4.78
Answer: A
In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 5 ounces of corn syrup, how many ounces of water does it contain?  Pick.
A) 45  B) 50  C) 55  D) 60  E) 75

Solution: F:C:W   1:12:30   Sport version:   F:C   3:12   F:W   1:60   OR 3:180   So C:F:W = 12:3:180   C/W = 12/180 = 3 ounces/x ounces   x = 5*180/12= 
5*180/12 = 75
75 ounces of water   75
Answer: E
In how many ways 5 different balls can be arranged in to 3 different boxes so that no box remains empty?  Select the correct option:
A) 125
B) 150
C) 175
D) 200
E) 225

Solution: 1. The total number of possibilities including empty boxes: 35=24335=243   2. Two of the boxes are empty: C32=3C23=3   3. One but not two of the boxes is empty: 3∗(25−2)=903∗(25−2)=90   4. the total number of possibilities excluding empty boxes:  243 - 3 - 90= 
 243 - 3 - 90 = 150
150   ANS:150
Answer: B
The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit?  Choices:
A) 1000
B) 3000
C) 2000
D) 4000
E) 5000

Solution: B   2000   Let C.P. be $x.   Then, (1920 - x)/x * 100 = (x - 1280)/x * 100   1920 - x = x - 1280   2x = 3200 => x = 1600   Required S.P. = 125 % of $1600 = 125/100 * 1600= 
125/100 * 1600 = 2_000
$2000.
Answer: C
Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 39.6. The difference between the unit digit and hundreds digit of that number is :
Choose the correct option
A) a) 4	B) b) 3	C) c) 2	D) d) 1	E) e) 0

Solution: Since the average increased by 39.6 and there were a total of 10 numbers, it means the incorrect number was 396 greater than the correct number.   Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)   Then the incorrect number was cba.   100c + 10b + a - (100a + 10b + c) = 396   99c - 99a = 99(c - a) = 396   396 = 99*4 = 99(c - a)   So c - a = 4   a) 4nswer (a) 4
Answer: A
In a University the average age in an arts class is 21 and average age in technical class is 18. What is the age average of University if there are 8 arts classes and 5 technical classes?	Select: A) 18.75 B) 19.85 C) 20.32 D) 20.9 E) 21.0

Solution: Average age of University= ((8x21)+(5x18))/13   =19.85   Answer: 19.85
Answer: B
In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 11 and 200, then the least and greatest integer on the card would be Choose the correct option
A) 3 and 15	B) 3 and 20	C) 4 and 13	D) 4 and 14	E) 5 and 14

Solution: Given: 11<x(x+1)<200.   Now, it's better to test the answer choices here rather than to solve:   If x=3 then x(x+1)=12>11 --> so, the least value is 4. Test for the largest value: if x=15 then   x(x+1)=15*16= 
15*16 = 240
240>200 --> discard B.   3 and 15nswer: 3 and 15.
Answer: A
In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 5 Ohms and y is 7 Ohms?  Select.
A) 3/5	B) 1/7	C) 12/35	D) 31/12	E) 35/12

Solution: 1/R = 1/x + 1/y   1/R = 1/5+1/7 = 12/35   R = 35/12   The answer is 35/12.
Answer: E
How many real roots does the equation x^2y+15xy+64y=0 have if y < 0? Choose the correct choice from the following answers:
A) 0
B) 1
C) 2
D) 3
E) Infinite

Solution: x^2y+15xy+64y=0   => y ( x^2 + 15x + 64) = 0   => y (x+8)^2 = 0   if y<0 , then x=-7   So although there are 2 factors , they are the same x=-7 .   The equations has 2 distinct real root .   Answer 2
Answer: C
A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:4, respectively, by weight. If 60 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
Choose the correct choice from the following choices
A) 15
B) 12
C) 8
D) 6
E) 4

Solution: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:4, respectively, by weight. Thus, we can say:   apples : peaches : grapes = 6x : 5x : 4x   We are given that 60 pounds of the mixture is prepared so we can set up the following question and determine a value for x:   6x + 5x + 4x = 60   15x = 60   x = 4   Now we can determine the number of pounds of apples and of grapes.   pounds of grapes = (4)(4) = 16   pounds of apples = (6)(4) = 24   Thus we know that there are  24 - 16= 
 24 - 16 = 8
8 more pounds of apples than grapes.   Answer is 8.
Answer: C
If the personal income tax rate is lowered from 40% to 33%, what is the differential savings for a tax payer having an annual income before tax to the tune of $45000?  Choose the correct choice from the following answers
A) $3500
B) $5000
C) $3150
D) $7000
E) $10000

Solution: Saving = (40-33)% of 45000 = 3150.   Answer:$3150
Answer: C
E is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in E?
I. 9
II. 15
III. 27 Choose the correct choice from the following answers
A) I only  B) II only  C) I and II only  D) I and III only  E) I, II, and III

Solution: Ans: C   E->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3   means x must contain 3^2 and 5^2   so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25   but 27 is not a divisor because it can't divide 9*25 fully.   so Ans : I and II only
Answer: C
The first three terms of a proportion are 2, 10 and 20. The fourth term is? Choose the correct option:  A) 105  B) 102  C) 190  D) 100  E) 134

Solution: (10*20)/2= 
(10*20)/2 = 100
100   Answer:100
Answer: D
A bag contains 6 black and 7 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? Choose the correct choice from the following options:
A) 3/4 B) 7/13 C) 1/7 D) 1/8 E) 4/3

Solution: Let number of balls = (6 + 7)= 
(6 + 7) = 13
13.   Number of white balls= 7.   P (drawing a white ball) =7/13   Option 7/13.
Answer: B
Apple Street begins at Peach Street and runs directly east for 3.2 kilometers until it ends when it meets Cherry Street. Apple Street is intersected every 200 meters by a perpendicular street, and each of those streets other than Peach Street and Cherry Street is given a number beginning at 1st Street (one block east of Peach Street) and continuing consecutively (2nd Street, 3rd Street, etc...) until the highest-numbered street one block west of Cherry Street. What is the highest-numbered street that intersects Apple Street? Choose the most appropriate option:
A) 14th	B) 15th	C) 16th	D) 17th	E) 18th

Solution: 3.2 km / 200 m = 16.   However, the street at the 3.2-km mark is not 16th Street; it is Cherry Street.   Therefore, the highest numbered street is 15th Street.   The answer is 15th.
Answer: B
When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 13. Which of the following is true?
Choices:
A) 23x + 17y =19  B) 17x –23y = 8  C) 17x +23y =19  D) 14x + 5y = 6  E) 5x – 14y = -6

Solution: From the problem it follows:   n=17x+5   n=23y+13   So, 17x+5=23y+13   17x-23y=8   The answer is 17x –23y = 8
Answer: B
f(x) = x! g(x)=x^10 h(x)= 10^x for large values of x which is greater?
Answers
A) f(x) B) g(x) C) h(x) D) both E) none

Solution: let x=100   then g(x)=100^10=10^20   h(x)=10^100   so h(x) is greater   ANSWER:h(x)
Answer: C
If (2^x)(3^y) = 108, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
Choose one:
A) 6  B) 24  C) 48  D) 96  E) 144

Solution: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=2, y=3. now quickly 2^1(3^1)=6. Than answer should be number 1.   6
Answer: A
Mr. Shah decided to walk down the escalator of a tube station. He found Â that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins Â to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?  Answers:
A) 44 B) 45 C) 46 D) 47 E) 48

Solution: (s1*t2~s2*t1)/(t2~t1)=(26*18~34*30)/(18~30)=46   ANSWER:46
Answer: C
If a certain sample of data has a mean of 35.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?  Choose the correct choice from the following options:
A) (14.0; 16.5)  B) (14.5; 21.0)  C) (14.0; 26.5)  D) (16.5; 26.0)  E) (28.0; 46.5)

Solution: 2.5 standard deviation equals to 2.5*2= 
2.5*2 = 5
5;   2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 30 40.   The correct answer choice must cover all this range: only answer choice E does this.   Answer:(28.0; 46.5).
Answer: E
Three people each took 3 tests. If the ranges of their scores in the 3 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?	Choose the correct choice from the following choices.
A) a 17
B) b) 28
C) c) 35
D) d) 45
E) e) 80

Solution: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:   A- 0 and 17   B- 0 and 28   therefore the minimum range is 35, it cant be any lower however you play with the numbers.   b) 28
Answer: B
If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)	Choose the correct choice
A) 0.5  B) 1.5  C) 2.5  D) 1.0  E) 2.0

Solution: (a-b)-(c-d)=6 and (c-d)-(a+b)=3   (a-c)-(b+d)=6 and (c-a)-(b+d)=3   (b+d)= (a-c)-6 and (b+d)=3-(c-a)   2(a-c)=3   (a-c)=1.5   ANSWER 1.5 1.5
Answer: B
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 72 kmph. After how much time will the trains meet?
Choose the correct choice from the following options.
A) 27/7 sec B) 20/9 sec C) 33/7 sec D) 21/7 sec E) 32/7 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (90 + 72)*5/18 = 9*5= 
9*5 = 45
45 mps.   The time required= d/s = 100/45 = 20/9 sec.   Answer : 20/9 sec
Answer: B
What will be the compound interest on a sum of Rs. 26000 after 3 years at the rate of 12% p.a.?  Select the correct option.
A) s.10123.22	B) s.10823.20	C) s.10123.20	D) s.10123.29	E) s.10528.13

Solution: Explanation:   Amount = [26000 * (1 + 12/100)3]   = 26000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20   C.I. = (36528.13 - 26000) = Rs.10528.13   Answer:s.10528.13
Answer: E
In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase?	Pick.
A) 45%
B) 125%
C) 145%
D) 150%
E) 180%

Solution: The percent increase is (24947-8902)/8902=16045/8902=1.80   So the approximate answer is 180%
Answer: E
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 ?
Select: A) 45 B) 60 C) 75 D) 80 E) 90

Solution: 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.   answer :90
Answer: E
In some quantity of ghee, 60% is pure ghee and 40% is vanaspati. If 10kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was?
Choose the correct choice from the following answers.
A) 10
B) 15
C) 20
D) 18
E) 22

Solution: Let the original quantity be x   then, vanaspati ghee in xkg = 40x/100 kg= 2x/5kg   (2x/5)/(x+10) = 20/100   2x/(5x+50) = 1/5   x = 10   10nswer is 10
Answer: A
What will come in place of the x in the following Number series? 25, 100, x, 1600, 6400
Choose the correct option
A) 2345 B) 3579 C) 6400 D) 6799 E) 8646

Solution: (6400)   25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Answer: C
If 6x = 8y = 10z, then what is a possible sum of positive integers x, y, and z?  Choose the correct choice: A) 52 B) 58 C) 84 D) 94 E) 168

Solution: 6x = 8y = 10z   3x = 4y = 5z   3(4*5) = 4(3*5) = 5(3*4)   Addition = 20+15+12= 
20+15+12 = 47
47   Answer would be multiple of 47 which is 94   Answer :94
Answer: D
2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =
Answers:
A) 2^24(2^(21)-1)
B) 2^24(2^(20)-1)
C) 2^24(2^(23)-1)
D) 2^21(2^(20)-1)
E) 2^21(2^(21)-1)

Solution: 2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =   2^(24)*(1+2+4+...+2^(20)) =   2^(24)*(2^(21) - 1)   The answer is 2^24(2^(21)-1).
Answer: A
David pays the simple interest on an amount he borrowed from his boss, if interest rate is halved, then simple interest is multiplied by Choose the correct choice from the following answers.
A) 2 B) 1 C) 1/4 D) 1/2 E) 4

Solution: Formula for SI = (P*T*R)/100   SI = Simple Interest   P = Principle Amount   T = Time   R = Interest Rate   Say r=2 => SI1 = 2*SI   when r=1; SI2 = SI   SI2 = 1/2*SI1.   Answer : 1/2
Answer: D
Three people have $30, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money? Choose the correct option:
A) $72
B) $85
C) $98
D) $100
E) $202

Solution: Solution -   Total money distributed is $200. In order to maximize median, one person has to accept $0 and remaining two people share $100 each. Hence median is $100.   ANS $100
Answer: D
If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?
Select:
A) 40%
B) 30%
C) 50%
D) 70%
E) 65%

Solution: C   50%   Length is halved.   i.e., length is decreased by 50%   Breadth is tripled   i.e., breadth is increased by 200%   50%hange in area   =(−50+200−(50×200/100))%=50%   i.e., area is increased by 50%
Answer: C
What is value of ((2^5)*(9^2))/((8^2)*(3^5))=?  Choose one.
A) 1/6	B) 1/3	C) 2/3	D) 1/4	E) 4

Solution: =>((2^5)*((3^2)^2)/((2^3)^2)*(3^5))   =>((2^5)*(3^4))/((2^6)*(3^5))   =>1/(2*3)   =>1/6   Option 1/6 is answer
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?  Choose the correct choice from the following answers:
A) 120 metres
B) 180 metres
C) 324 metres
D) 150 metres
E) 175 metres

Solution: Explanation:   Speed= 60 x	5/18	m/sec	= 50/3	m/sec.   Length of the train = (Speed x Time).   Length of the train = 50/3	x 9	m = 150 m.   ANSWER IS 150 metres
Answer: D
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?	Choose the correct choice from the following answers.
A) 1/19 B) 1/11 C) 1/12 D) 1/17 E) 1/14

Solution: A's 1 hour work = 1/4;   (B + C)'s 1 hour work = 1/3;   (A + C)'s 1 hour work = 1/2   (A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12   B's 1 hour work = (7/12 + 1/2) = 1/12   B alone will take 12 hours to do the work.   Answer: 1/12
Answer: C
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
Pick:  A) 1/37  B) 1/36  C) 1/31  D) 1/33  E) 1/32

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= 
6 * 6 * 6 = 216
216 ways.   Hence the probability is 6/216= 1/36.Answer: 1/36
Answer: B
There are three different hoses used to fill a pool: hose U, hose V, and hose W. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3 Choices:
A) I	B) III	C) I and II only	D) II & III	E) II

Solution: Name T = full pool   U fills a pool in a days ==> 1 day U fills: T/a   V fills a pool in b days ==> 1 day V fills: T/b   W fills a pool in c days ==> 1 day W fills: T/c   1 day (U+V+W) together fill: T(1/a + 1/b + 1/c)   d days (U+V+W) together fill: T   ==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)   ==>d = abc/(ab+bc+ca)   d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3   II
Answer: E
A man’s speed with the current is 14 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : Choose the correct choice from the following choices:	A) 9 km/hr	B) 8.5 km/hr	C) 10 km/hr	D) 12.5 km/hr	E) None of these

Solution: Solution   Man's rate in still water = (14-2.5) km/hr = 11.5 km/hr.   Man's rate against the current = (11.5-2.5) km/hr = 9 km/hr 9 km/hrnswer 9 km/hr
Answer: A
Two motor cycles A & B are started from one point at 4 Kmph & 6 Kmph; After 45 min B starts returning, at what time they will meet ?	Choices.
A) 54 mins	B) 55 mins	C) 56 mins	D) 57 mins	E) 58 mins

Solution: Distance covered by A in 45 mins= 3 kms.   Distance covered by B in 45 mins= 4.5 kms.   Distance between and B after 45 mins= 1.5 kms.   Relative speed when B is returning = 4+6= 
4+6 = 10
10 kmph   Distance between A and B is covered in   1.5/10= 
  1.5/10 = 0.15
0.15 hrs= 9 mins   so they will meet again after 54 mins from starting time.   54 minsNSWER:54 mins
Answer: A
Set A consists of all the prime numbers between 2 and 13. What is the range of set A?
Choose the correct option:
A) 12	B) 13	C) 16.6	D) 17	E) 8

Solution: The range of a set of data is the difference between the highest and lowest values in the set   In this set,   Highest number = 11   Lowest number = 3   Range = Highest - Lowest = 11 - 3= 
11 - 3 = 8
8   Option 8
Answer: E
How many shots of 1cm radius can be prepared from a sphere of 6cm radius?  Select:	A) 33	B) 88	C) 216	D) 288	E) 299

Solution: 4/3 Ï€ * 6 * 6 * 6 = 4/3 Ï€ * 1 * 1 * 1 * x   x = 216   Answer: 216
Answer: C
The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 3 and 5 slices per customer. How many slices cannot be bought?	Pick
A) 19.	B) 38.	C) 33.	D) 22.	E) 21.

Solution: Let X pizzas of 3 slices and Y pizzas of 5 slices.   3X + 5Y.   Lets check options wise.   A. 19 => 3(3) + 5(2)   B. 38 => 3(6) + 5(4)   C. 33 => 3(1) + 5(6)   D. 22 => 3(4) + 4(2)   E. 21 = we can't write anything with 3 and 5 series..Lets try 3(5) + 5(1) = 20 , 3(4) + 4(2) = 22 , nothing works out.   Answer: correct option is 21.
Answer: E
a=2, b=3, c=6 Find the value of c/(a+b)-(a+b)/c  Choose the correct choice from the following options
A) 8/30 B) 9/30 C) 10/30 D) 11/30 E) 12/30

Solution: c/(a+b)-(a+b)/c   = (c/(a+b))-((a+b)/c)   = (6/(2+3))-((2+3)/6)   = (6/5)-(5/6)   = 11/30   ANSWER:11/30
Answer: D
Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 10 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 10 minute mark.) Answers:
A) 41  B) 42  C) 43  D) 44  E) 45

Solution: 10 minutes is 600 seconds.   Lamp A and Lamp B will flash together every 24 seconds.   600/24= 
600/24 = 25
25.   In the time period, Lamp A and Lamp B will flash together 25 times.   Lamp A and Lamp C will flash together every 30 seconds.   600/30= 
600/30 = 20
20.   In the time period, Lamp A and Lamp C will flash together 20 times.   Lamp B and Lamp C will flash together every 40 seconds.   600/40= 
600/40 = 15
15.   In the time period, Lamp B and Lamp C will flash together 15 times.   All three lights will flash together every  2*2*2*3*5= 
 2*2*2*3*5 = 120
120 seconds.   600/120= 
600/120 = 5
5.   We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.   The number of times that exactly two lights flash together is   25+20+15-15= 
  25+20+15-15 = 45
45 times.   The answer is 45.
Answer: E
At the recent downhill mountain bike race 4 entrants entered a challenging slalom event. Prem came first. The entrant wearing no 2 wore red. whereas kian did not wear yellow. the loser wore blue and rahul wore no 1.Sanjay beat rahul and the person who came second wore no 3.te entrant in yellow beat the entrant in green. Only one of the entrant s wore the same number and the final position. Determine who finished 3rd, the no and the color they wore?	Choose the correct choice:
A) Rahul 1 green
B) rahul 2 red
C) Kiran 4 blue
D) Kiran 7 blue
E) none of these

Solution: the names are prem, sanjay, rahul, kian   colors are red,yellow,green,blue   since prem came 1st and sanjay beat rahul so, given that sanjay came 2nd, wore no 3, yellow color   and rahul wore no 1, green color, came 3rd   hence,   name position wore t-shirt no color   prem 1 2 red   sanjay 2 3 yellow   rahul 3 1 green   kian 4 (1,2,3) blue   Rahul 1 greenNSWER:Rahul 1 green
Answer: A
Find the area of a parallelogram with base 32 cm and height 18 cm?
Choices:	A) 576 cm2	B) 384 cm2	C) 672 cm2	D) 267 cm2	E) 286 cm2

Solution: 576 cm2rea of a parallelogram   = base * height   = 32 * 18= 
32 * 18 = 576
576 cm2   576 cm2nswer: 576 cm2
Answer: A
Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age?
Choose the most appropriate option:
A) 56 years	B) 72 years	C) 56 years	D) 66 years	E) 76 years

Solution: Let the age before 10 years =x. Then,   115x/100=x+10   ⇒115x=100x+1000   ⇒x=1000/15=66   Present age =x+10=66+10= 
66+10 = 76
76   ANSW76 yearsR:76 years
Answer: E