MU-NLPC/Calc-aqua_rat huggingface dataset:
In how many ways can the letters of the word MANIFOLD be arranged so that the vowels are separated ?	Choose one:  A) 14400  B) 36000  C) 18000  D) 24000  E) 22200

Solution: We have 3 vowels: AIO and 5 consonants: MNFLD.   Consider the following case: *M*N*F*L*D* If we place vowels in any 3 empty slots (*) then all vowels will be separated by at least one consonant:   The # of ways to choose 3 empty slots out of 6 for 3 vowels = C36=20C63=20;   The # of ways to arrange the vowels: 3! (or instead of these two steps we could use P36)P63);   The # of ways to arrange MNFLD = 5!.   Total = 20*3!*5! = 14,400.   14400nswer: 14400
Answer: A
There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 28 possible combinations in which Michael is not selected, what is the value of n?	Pick:
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: The combinations of two people, in which Michael was not selected = 28   The number of ways two people can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael.   Then m*(m-1) = 56 = 8*7   Thus, n = m + 1(Michael) = 9   The answer is 9.
Answer: C
A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.  Choose the correct choice from the following.
A) 6/7 B) 15/7 C) 8/9 D) 7/15 E) 4/3

Solution: .let S be the sample space   Then n(S)=no of ways of drawing 2 balls out of   (6+4)= 
  (6+4) = 10
10c2=(10*9)/(2*1)= 
(10*9)/(2*1) = 45
45   Let E=event of getting both balls of same colour   Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)   =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6= 
15+6 = 21
21   P(E)=n(E)/n(S)=21/45=7/15   Ans: 7/15
Answer: D
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. Choices
A) 179 B) 367 C) 269 D) 177 E) 191

Solution: Explanation:   Total runs scored by the batsman = 60*46= 
60*46 = 2_760
2760 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2760 – 2552 = 208 runs.   Let the highest score be x, hence the lowest score = x – 150   x + (x - 150) = 208   2x = 358   x = 179 runs   179NSWER: 179
Answer: A
In a coconut grove, (x + 1) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 1) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x. Select:
A) 2 B) 4 C) 5 D) 6 E) None of the above

Solution: (x+1)×60+x×120+(x−1)×180/(x+1)+x+(x−1)=100   ⇒ 360x−120/3x = 100   ⇒ 60x = 120 ⇒ x = 2   2nswer 2
Answer: A
The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Pick
A) 75	B) 66	C) 55	D) 44	E) 12

Solution: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.   P + C + M = 150 + P   C + M = 150   Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2= 
150/2 = 75
75.   75nswer:75
Answer: A
a box contain 4 small bos, each small box again contain 3 box,again these box contain 2 box . total how many boxes
Choose the correct choice from the following.
A) 38
B) 39
C) 40
D) 42
E) 41

Solution: a box contain 4 small box means   1+4= 
  1+4 = 5
5 Boxes   each small box again contain 3 box means   4*3= 
  4*3 = 12
12 boxes   Again these 12 boxes contain 2 boxes each... means  12*2= 
 12*2 = 24
24   Total Boxes till now are  5 + 12 + 24= 
 5 + 12 + 24 = 41
41   ANSW41R:41
Answer: E
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?	Pick one
A) 50  B) 100  C) 200  D) 1,000  E) 2,000

Solution: y = 50% of 50% 0f x   = x/4   and   y/100 of x = 100   y /100 *4y =100   y = 50   and x= 200   Answer - 200
Answer: C
Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is:
Answers
A) 53 B) 108 C) 77 D) 107 E) 109

Solution: Explanation:   Let the present ages of the father and son be 2x and x years respectively.   Then, (2x - 18) = 3(x - 18) => x = 36   Required sum = (2x + x) = 108 years.   Answer: Option 107
Answer: D
An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets liquid in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank. Choose the most appropriate option:
A) 8600 litres
B) 12800 litres
C) 12100 litres
D) 11200 litres
E) 13200 litres

Solution: Let the rate of outlet pipe be x liters/hour;   Rate of inlet pipe is 8 litres/min, or  8*60= 
 8*60 = 480
480 liters/hour;   Net outflow rate when both pipes operate would be x-480 liters/hour.   Capacity of the tank= x*10 hours = (x-480)*(10+6) hours   10x=(x-480)*16 --> x=1280 --> capacity = 10x = 12800 liters.   Answer: 12800 litres
Answer: B
Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?
Choose the correct choice from the following: A) Rs. 4000 B) Rs. 4500 C) Rs. 5500 D) Rs. 6000 E) Rs. 7000

Solution: Let investment in 12% stock be Rs. x.   Then, investment in 15% stock = Rs. (12000 - x).   12	x x +	15	x (12000 - x) = 1360.   120	125   x	+	3	(12000 - x) = 1360.   10	25   5x + 72000 - 6x = 1360 x 50   x = 4000.   Rs. 4000NSWER:Rs. 4000
Answer: A
If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a + b + c > a^3
II. a × b × c < a^3
III. 5b < bc	Choose the most appropriate option.
A) I only  B) II only  C) III only  D) II and III  E) I, II, and III

Solution: Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4   Putting the values in the answers only 'I only' seems valid.
Answer: A
If a real number x is chosen at random in the interval [0,3] and a real number y is chosen at random in the interval [0,5], what is the probability that x < y?  Choices
A) 23/30 B) 7/12 C) 11/15 D) 7/10 E) 3/4

Solution: Since x is in [0,3] and y is in [0,5] we can draw a rectangle in the coordinate plane with vertices (0, 0), (3, 0), (0, 5), and (3, 5).   The points above the line y=x satisfy x < y.   The part of the rectangle below y=x has an area of 4.5.   The whole rectangle has an area of 15.   P(x < y) = (15-4.5)/15 = 21/30 = 7/10   The answer is 7/10.
Answer: D
There are 3 sections with 4 questions each. If three questions are selected from each section, the chance of getting different questions is________  Choose the correct choice from the following answers:
A) 10
B) 78
C) 89
D) 64
E) 56

Solution: we have to select three questions from each section so the chances are 4C3.4C3.4C3=64   ANSWER:64
Answer: D
By weight, liquid X makes up 1.5 percent of solution P and 6.5 percent of solution Q. If 400 grams of solution P are mixed with 600 grams of solution Q, then liquid X accounts for what percent of the weight of the resulting solution? Pick one
A) 3.6% B) 3.9% C) 4.2% D) 4.5% E) 4.8%

Solution: The number of grams of liquid X is 1.5(400)/100 + 6.5(600)/100 = 6 + 39= 
6 + 39 = 45
45 grams.   45 / 1000= 4.5%   The answer is 4.5%.
Answer: D
Given distinct positive integers 1, 11,4, x, 2, and 10, which of the following could be the median? Choose the correct answer
A) 3 B) 4 C) 7 D) 8 E) 9

Solution: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.   Arrange numbers in ascending order: 1, 2, 4, 9, 11, and x.   Now, x can not possibly be less than 4 as given that all integers are positive and distinct (and we already have 1, 2, and 4).   Next, if x is 4<x<10 then the median will be the average of 4 and x. As all answers for the median are integers, then try odd values for x:   If x=4, then median=(4+4)/2= 
(4+4)/2 = 4
4 --> OK;   Answer: B.   P.S. If x is more than 9 so 10 or more then the median will be the average of 4 and 9 so  (4+10)/2= 
 (4+10)/2 = 7
7 (the maximum median possible).
Answer: B
Two numbers are in the ratio of 5:7. If 33 is subtracted from each number, they are in the ratio of 1:2. What are the two numbers?	Choose the most appropriate option
A) 45, 63
B) 50, 70
C) 55, 77
D) 60, 84
E) 65, 91

Solution: (5x-33):(7x-33) = 1y:2y   5x - 33 = y   7x - 33 = 2y   231-165 = 10y - 7y   66 = 3y   y = 22   5x-33 = 22   x = 11   The two numbers are 5x and 7x which are 55 and 77.   The answer is 55, 77.
Answer: C
7 people sit at the round table. In how many ways can we sit them so that ALI and BillI don't sit opposing each other?  Options:
A) A)400  B) B)420  C) C)440  D) D)460  E) E)480

Solution: 7 People: ALI,BillI,Red, Blue,White,Pink,Purple   Round Table: T   7 Chairs: 1,2,3,4,5,6,7   Let chairs 1 and 4 be opposite each other;   ALI is sitting on 1 and Bill is sitting on 4;   The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways   Now, BillI and ALI swap their positions;   ALI is sitting on 4 and BILLI is sitting on 1;   The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways   Thus total number of ways in which ALI and BillI are sitting opposite each other = 2*5! = 120*2= 
120*2 = 240
240   We have to find in how many ways they are NOT sitting opposite; subtract 240 from the total number of possible arrangements;   In circular permutation, Total number of arrangements of n people= (n-1)!   Here number of people = 7   Arrangements = (7-1)= 
(7-1) = 6
6!= 720   Number of ways ALI and BillI are NOT sitting opposite = 720-240= 
720-240 = 480
480.   Answer: 480
Answer: E
In the first 10 overs of a cricket game, the run rate was only 6.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Choices.
A) 6.25	B) 5.5	C) 6.75	D) 7	E) 8

Solution: 10 overs - run rate = 6.2   runs scored in first 10 overs = 62   remaining overs 40   total runs to be scored= 282   62 runs already scored 282-62= 
282-62 = 220
220   220 runs to be scored in 40 overs   let required runrate be x   40*x=220   x=220/40= 
220/40 = 11/2 = around 5.5
5.5   the required runrate is 5.5   ANSWER:5.5
Answer: B
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is: Pick.
A) 1520 m2  B) 2420 m2  C) 2480 m2  D) 2520 m2  E) 2645 m2

Solution: Explanation:   We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.   Solving the two equations, we get: l = 63 and b = 40.   Area = (l x b) = (63 x 40) m2 = 2520 m2.   Answer: 2520 m2
Answer: D
What least number should be subtracted from 13603 such that the remainder is divisible by 87 ?
Pick.
A) 27
B) 29
C) 28
D) 30
E) 31

Solution: 13603 ÷ 87 = 156, remainder = 31   Hence 31 is the least number which can be subtracted from 13603 such that the remainder   is divisible by 87   Answer is 31
Answer: E
In Kaya's teacher's desk there are 6 pink highlighters, 2 yellow highlighters, and 4 blue highlighters. How many highlighters are there in all?  Choices
A) 11  B) 12  C) 77  D) 33  E) 88

Solution: Add the numbers of highlighters.   6 + 2 + 4= 
6 + 2 + 4 = 12
12.   Answer is 12.
Answer: B
If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD? Choose the correct option.
A) 62	B) 55	C) 48	D) 31	E) 25

Solution: I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square.   25 is a perfect square.   Ans:25
Answer: E
Vijay sells a cupboard at 14% below cost price. Had he got Rs.2086 more, he would have made a profit of 14%. What is the cost price of the cupboard?
Choose the most appropriate option.
A) 7450	B) 14900	C) 7400	D) 7500	E) None of these

Solution: Explanation:   Cost price = 2086/(0.14 + 0.14) = 2086/0.28   = Rs.7450   7450NSWER 7450
Answer: A
There are two bags A and B. A contains 6 red flowers and 3 pink flowers. where as bag B contains 2 red flowers and 7 pink flowers. One flower is chosen from a bag randomly. What is the probability that the flower chosen is pink?  Answers.
A) 5/8
B) 5/6
C) 5/1
D) 5/9
E) 5/2

Solution: Bag A 6 red + 3 pink   Bag B 2 red + 7 pink   Probability of picking 1 pink from bag A is 3/9   Probability of picking 1 pink from bag B is 7/9   Total = 3/9 + 7/9 = 10/9   And probability of selecting a bag is 1/2   So finally probability of choosing a pink flower = 1/2(10/9) = 5/9   Answer : 5/9
Answer: D
The average weight of 6 person's increases by 1.8 kg when a new person comes in place of one of them weighing 69 kg. What might be the weight of the new person?  Answers:
A) 73 kg
B) 79.8 kg
C) 86 kg
D) Data inadequate
E) None of these

Solution: Total weight increased = (6 x 1.8) kg = 10.8 kg.   Weight of new person = (69 + 10.8)= 
(69 + 10.8) = 79.8
79.8 kg.   Answer: Option 79.8 kg
Answer: B
John and David work at a hospital with 8 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen?	Choose the correct choice from the following answers.
A) 1/30 B) 1/25 C) 1/20 D) 1/28 E) 1/30

Solution: Probability that John and 1/28avid will both be chosen out of 8 workers   = (2/8)*(1/7)   = 1/28   Answer 1/28
Answer: D
Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $5,200 less if they could find two more equal investors. How much is the total investment in the new business? Choose the correct choice from the following options:
A) $64,000
B) $78,000
C) $39,000
D) $ 5,200
E) $ 3,800

Solution: Total Investment between 5: (x/5)   Total investment including 5200 less between 3 people(x-(5200*3))/3   Set both eq. equal to eachother.   $39,000   Answer $39,000)
Answer: C
Given that G and H are events such that
G(Y)= 0.02
G(Z)=0.4
G(YnZ)=0.4
find G (Y|Z) and G(Y|Z) Choose the correct option:
A) 1/22	B) 1/20	C) 1/25	D) 1/10	E) 1/50

Solution: Here, Y and Z are events   G(Y|Z) = G(YnZ)/G(Z) = 0.4/0.4= 
0.4/0.4 = 1
1   Q(G|H)= G(YnZ)/G(Y) = 0.4/0.20 = 1/20   Answer is 1/20
Answer: B
The product Z of two prime numbers is between 20 and 56. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 14 but less than 30 then what is Z?	Choices:
A) 26 B) 35 C) 39 D) 51 E) 55

Solution: The smallest possible product is 51 which is 3*17.   All other products are too big.   The answer is 51.
Answer: D
A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.09. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the fourth day it is overdue? Choices:
A) $0.66
B) $0.70
C) $0.80
D) $0.90
E) $1.00

Solution: 1st day fine - 0.09   2nd day fine - 0.09*2 = 0.18 (as doubling gives lower value)   3rd day fine - 0.18*2 = 0.36 (as doubling gives lower value)   4th day fine - 0.36 + 0.3 = 0.66 (as doubling gives higher value we add 0.3 this time)   $0.66nswer: $0.66.
Answer: A
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?	Choose the correct choice
A) 18 B) 99 C) 77 D) 66 E) 43

Solution: S:E = 1:3   E:M = 3:5   ------------   S:E:M = 3:9:15   3/27 * 162= 
3/27 * 162 = 18
18   18nswer:18
Answer: A
Grace has 18 jellybeans in her pocket. She has 9 red ones, 5 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?  Choose the correct choice from the following options
A) 4 B) 8 C) 12 D) 13 E) 15

Solution: The worst scenario is when she takes 9 red and 5 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.   Answer: 15.
Answer: E
If two of the four expressions x + y , x + 6y , x - y , and 6x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?  Choices
A) 1/5  B) 1/8  C) 1/6  D) 1/7  E) 1/3

Solution: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6   now we have to find the expressions that are in form of x^2 - (by)^2   one is (x+y)(x-y) = x^2 - (1y)^2   If you see any other combination we are always going to have one term of xy since 6x and 6y are there, so there can be only one type of combination like this.   therefore, probablity is 1/6   Answer : 1/6
Answer: C
A wheel of a car of radius 21 cms is rotating at 500 RPM. What is the speed of the car in km/hr?
Choose the correct choice from the following choices:
A) 79.2 km/hr  B) 47.52 km/hr  C) 7.92 km/hr  D) 39.6 km/hr  E) 3.96 km/hr

Solution: Explanatory Answer   The radius of the wheel measures 21 cm.   In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.   ∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.   In a minute, the distance covered by the wheel = circumference of the wheel * rpm   ∴ this wheel will cover a distance of 132 * 500= 
132 * 500 = 66_000
66000 cm in a minute.   In an hour, the wheel will cover a distance of 66000 * 60= 
66000 * 60 = 3_960_000
3960000 cm.   Therefore, the speed of the car= 3960000 cm/hr = 39.6 km/hr   Choice 39.6 km/hr is the correct answer.
Answer: D
The sum of two numbers is 44. Five times one number is equal to 6 times the other. The bigger of the two numbers is Pick
A) 10 B) 12 C) 16 D) 22 E) 24

Solution: Sol.   Let the numbers be x and (44 - x).   Then, 5x = 6(44 - x)   ⇔ 11x = 264⇔ x = 24.   So, the numbers are 24 and 20.   Answer 24
Answer: E
I have a huge bed-sheet of 1 meter long.
I want to cuts this role into pieces of 20 centimeter long cloth.
How long will it take me to cut the bed sheet if each 20 centimeter cut took me 5 minutes ?
Choose one: A) 245 minutes B) 345 minutes C) 445 minutes D) 545 minutes E) None

Solution: Solution:   245 minutes   It will take 49 cuts not 50.   so 49*5= 
49*5 = 245
> 245 minutes   245 minutesnswer 245 minutes
Answer: A
In a forest 100 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest? Choose the correct choice from the following choices: A) 150 B) 750 C) 1,250 D) 1,000 E) 2,500

Solution: The percentage of tagged deer in the second sample = 5/50*100= 
5/50*100 = 10
10%.   So, 100 tagged deers comprise 10% of total # of deers --> total # of deers= 100*10 = 1,000.   Answer: 1,000.
Answer: D
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Choose the correct choice from the following
A) 11 B) 27 C) 20 D) 21 E) 24

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer: 20
Answer: C
A man while returning from his factory, travels 2/3 of the distance by bus, 3/4 of the rest partly by car and partly by foot. If he travels 2 km on foot, find the distance covered by him.	Choose the correct choice from the following options.
A) 24 km B) 22 km C) 28 km D) 26 km E) None of these

Solution: D=2/3D+1/3x3/4D+2,   Therefore D = 24km   24 kmnswer: 24 km
Answer: A
A bag contains 6 red, 3 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?	Choose the correct option:	A) 2/7	B) 3/5	C) 3/11	D) 1/4	E) 7/16

Solution: Total number of balls = 6+3+4= 
6+3+4 = 13
13   n(S)= 13C3 = 286   n(E) = 6C1 * 3C1 * 4C1 = 72   Probability = 72/286 = 1/4   Answer is 1/4
Answer: D
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?  Choose one:	A) 299	B) 2767	C) 120	D) 287	E) 261

Solution: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40   Volume of 1/40 part = 3 gallons\   Volume of whole = 3 * 40= 
3 * 40 = 120
120 gallons.   Answer: 120
Answer: C
Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Choose the correct choice:
A) 7/8
B) 1/8
C) 1/3
D) 1/5
E) 1/9

Solution: Original share of 1 person =1/6   New share of 1 person =1/5   Increase =1/5 -	1/6	=1/30   Required fraction =	(1/30)/(1/6)=1/5   Answer is 1/5.
Answer: D
In a triangle, one side is 6 Cm and another side is 12 Cm. which of the following can be the perimeter of the triangle? Choose the correct choice from the following options:	A) 18.	B) 25.	C) 30.	D) 32.	E) 34.

Solution: Given : one side is 6 Cm and another side is 9 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 32. Hence 32..
Answer: D
a,d,i,p,? what is next term
Choose the correct answer.
A) q B) t C) r D) s E) y

Solution: a=1*1   d=2*2   i=3*3   p=4*4   next will be   5*5= 
5*5 = 25
25=Y   ANSWyR:y
Answer: E
1850 men have provisions for 15 days. If 150 more men join them, for how many days will the provisions last now?	Select the correct option.
A) 12.9	B) 12.0	C) 13.9	D) 13.5	E) 12.1

Solution: 1850*15 = 2000*x   x = 13.9   Answer:13.9
Answer: C
If grapes are 91% water and raisins are 19% water, then how many kilograms did a quantity of raisins, which currently weighs 9 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)  Select.
A) 63
B) 72
C) 81
D) 90
E) 99

Solution: Let x be the original weight.   The weight of the grape pulp was 0.09x.   Since the grape pulp is 81% of the raisins, 0.09x = 0.81(9 kg).   Then x = 9*9= 
9*9 = 81
81 kg.   The answer is 81.
Answer: C
How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 40% salt?
Pick
A) 16.67 B) 30 C) 50 D) 60.33 E) 70

Solution: For 60% salt solution (X) and 20% salt solution (Y) to give 40%=(60+20)/2 salt solution, we should mix equal amounts of X and Y.   Answer: 50.
Answer: C
The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time? Choose one.
A) 3 months B) 4 months C) 5 months D) 6 months E) None of these

Solution: Explanation :   Bankers Discount, BD = Simple Interest on the face value of the bill for unexpired time.   True Discount, TD = Simple Interest on the present value for unexpired time.   Simple Interest on Rs. 1600 = True Discount on Rs.1680   => Rs. 1600 is the Present Worth (PW) of Rs. 1680   => Rs. 80 is the Simple Interest of Rs.1600 at 15%   ⇒80=(1600×T×15)/100   ⇒ 80 = 16 × T × 15   ⇒ 5 = T × 15   ⇒ 1 = T × 3   => T = 1/3 year = 12/3= 
12/3 = 4
4 months Answer : Option 4 months
Answer: B
An object thrown directly upward is at a height of h feet after t seconds, where h = -15 (t-2)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?  Choose the correct choice from the following options:
A) 72	B) 90	C) 124	D) 132	E) 140

Solution: We see that h will be a maximum h=150 when t-2=0, that is when t=2.   At t=4, h = -15(4-2)^2 + 150 = -15(4) + 150 = 90   The answer is 90.
Answer: B