MU-NLPC/Calc-aqua_rat huggingface dataset:
A dishonest milkman sells a 50 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?	Pick.
A) 2:5 B) 13:12 C) 2:3 D) 3:2 E) 5:3

Solution: ............................... Milk ............... Water ....................... Total   Initial ...................... 30 .................... 20 .............................. 50   20 Lts mix. taken out 30-12 ............... 20-8 ........................... 50-20   20 Lts milk added..... 18+20 ................ 12 ..............................50   20 Lts mix. taken out 38-12 ............... 12-8 ........................... 50-20   20 Lts water added..... 26 ................ 4+20 .............................. 50   New ratio = 26:24 = 13:12   13:12
Answer: B
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?	Answers:
A) 420	B) 840	C) 1260	D) 2520	E) 5040

Solution: The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.   420nswer: 420.
Answer: A
John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 3 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?  Choose one: A) 4y B) 17y/3 C) 6y D) 8y E) 9y

Solution: Let $x be the advance that both receive = 3x   Amount earned per hour by John and Mary = x/10 and x/7   Mary gives $y to John to make the wages earned equal   Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/7   Solve (x+y)10 = (x-y)/7   7x + 7y = 10x -10y   3x = 17y   x = 9y   Ans. 17y/3
Answer: B
In a function they are distributing noble prize. In how many ways can 2 prizes be distributed among 9 boys when a boy gets any no. of prizes?  Choose the correct choice from the following answers:
A) 36  B) 42  C) 81  D) 69  E) 70

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the 2 prizes can be given in 9 ways, i.e. (9 x 9) ways = 92 ways = 81 ways Or nr ways = 92 ways = 81 ways
Answer: C
Allen and Drake were born on consecutive years on the same date. What could be their ages if teh sum of their age is 23 years?
Choose the most appropriate option.
A) 11 and 12 years B) 9 and 10 years C) 8 and 9 years D) 12 and 13 years E) All of these

Solution: Let the age of Allen and Drake be x and x+1   x + x+1 + 23   x = 11   The age of Allen and Drake is 11 and 12 years.   11 and 12 yearsnswer : 11 and 12 years
Answer: A
Which number is the odd one out under the list of numbers?	Choose the correct choice from the following:
A) 84129	B) 47232	C) 84123	D) 67626	E) 72927

Solution: B   47632   All the others are three digit numbers followed by their square root, eg 361 followed by its square root, 19.   Answer is 47232
Answer: B
Two trains 250 m and 500 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?	Select.
A) 10.6 B) 10.9 C) 10.4 D) 27 E) 10.1

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 250 + 500= 
250 + 500 = 750
750 m.   Required time= 750 * 9/250= 
750 * 9/250 = 27
27 sec   Answer: 27
Answer: D
A package contains 8 black and 11 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?	Options:
A) 3/5  B) 11/19  C) 6/8  D) 7/9  E) 1/3

Solution: Let number of balls = (8+11)= 
(8+11) = 19
19.   Number of white balls= 11.   P (drawing a white ball) =	11/19   11/19
Answer: B
A train running at the speed of 110 km/hr crosses a pole in 9 sec. What is the length of the train?
Choose the correct answer.
A) 298 m  B) 275m  C) 208 m  D) 988 m  E) 299 m

Solution: Speed = 110 * 5/18 = 275/9 m/sec   Length of the train = speed * time =275/9 * 9= 
275/9 * 9 = 275
275 m   Answer:275m
Answer: B
How many seconds will a 600 m long train take to cross a man walking with a speed of 2 km/hr in the direction of the moving train if the speed of the train is 56 km/hr?	Answers
A) 30  B) 54  C) 40  D) 36  E) 31

Solution: Speed of train relative to man = 56 - 2= 
56 - 2 = 54
54 km/hr.=54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Time taken to pass the man= 600 *1/15= 
600 *1/15 = 40
40 sec.   Answer: 40
Answer: C
If x and y are integers and 3^(x+4) = 3^(y+2), what is y in terms of x?	Answers:
A) x - 6 B) x - 5 C) x - 2 D) x + 2 E) x + 6

Solution: Answer: A   3^(x+4) = 3^(y+2)   Since the base is the same, I isolated the equations and solved for y.   x+4 = y+2   y=x+2   Ans : x + 2
Answer: D
23 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence. Choose the most appropriate option
A) 19
B) 20
C) 21
D) 22
E) 23

Solution: in case of cycle no of handshakes = no of persons   hence ans = 23   ANSW23R:23
Answer: E
How many integers from 101 to 600, inclusive, remains the value unchanged when the digits were reversed?	Choose the correct answer:
A) 50	B) 60	C) 70	D) 80	E) 90

Solution: question is asking for palindrome   first digit possibilities - 1 through 5 = 5   6 is not possible here because it would result in a number greater than 6 (i.e 606 , 616..)   second digit possibilities - 0 though 9 = 10   third digit is same as first digit   =>total possible number meeting the given conditions = 5 *10= 
5 *10 = 50
50   50nswer is 50.
Answer: A
If k^3 is divisible by 162, what is the least possible value of integer k?
Choose one
A) 12	B) 15	C) 18	D) 24	E) 36

Solution: k^3 = 162*x = 2*3^4*x   The factors of k must at minimum include 2*3^2 = 18.   The answer is 18.
Answer: C
My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age of my father when my brother was born? Options
A) 35years  B) 34years  C) 33years  D) 32years  E) 31years

Solution: Let my age =x   My brother's age =x+3   My mother's age =x+26   My sister's age =(x+3)+4=x+7   =(x+3)+4=x+7   My father's age =(x+7)+28=x+35   Age of my father when my brother was born   =x+35−(x+3)=32 Answer: Option 32years
Answer: D
A store sold cherries in the afternoon twice as many as in the morning. Throughout the day were sold 360 kg. How many kilograms were sold in the afternoon? Choose the correct choice
A) 140 kg.
B) 240 kg.
C) 340 kg.
D) 440 kg.
E) None

Solution: Solution:   Let's suppose that х kg. were sold in the morning then 2x were sold in the afternoon. x + 2x = 360 <=>   3x = 360 <=> x = 120. In the afternoon were sold 2x = 240 kg.   Answer 240 kg.
Answer: B
How many ways can 5 different colored marbles be placed in 3 distinct pockets such that any pocket contains at least 1 marble?  Pick one
A) 60  B) 90  C) 120  D) 150  E) 180

Solution: With 3,1,1 distribution:   # of ways to select 3 from 5   5!/3!2! = 10   # of ways to select 1 ball from 2   2!/1! = 2   # of ways to select 1 ball from 1   1!/1! 2 /1= 
2 /1 = 2
2   # of ways to select 1 ball from 1   1!/1! = 1   How many ways to distribute 3,1 and 1 to 3 boxes? 3!/2! 1 /1= 
1 /1 = 1
1   How many ways to distribute 3,1 and 1 to 3 boxes? 3!/2!= 3   10*2*3= 
10*2*3 = 60
60   With 2,2,1 distribution:   How many ways to select 2 from 5?   5!/2!3!= 10   # of ways to select 2 from 3   3!/2!1! = 3   # of ways to select 1 from 1   1   How many ways to distribute 2,2,1 to 3 boxes? 3!/2! = 3   10*3*3= 
10*3*3 = 90
90   90+60= 
90+60 = 150
150   Answer: 150. 150
Answer: D
Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an odd number?  Choose one:  A) 3/7  B) 4/7  C) 3/10  D) 7/10  E) 2/5

Solution: There are 7 numbers higher than 3 and 3 of them are odd.   The probability is 3/7.   The answer is 3/7.
Answer: A
What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 160° each? Choose the correct answer:  A) 96 cm  B) 108 cm  C) 120 cm  D) 132 cm  E) 270 cm

Solution: Sum of all interior angles is given by:   180(n-2) = n is number of sides   180(n-2) = 160*n   from here   n = 18   So perimeter becomes 15*18= 
15*18 = 270
270   Answer :270 cm
Answer: E
How many times in a day the hands of a clock are straight?  Choose the correct choice.
A) 12
B) 322
C) 87
D) 22
E) 771

Solution: In 12 hours, the hands coincide or are in oppesite direction 22 times.   In 24 hours, they are at right angles 22 times.   Answer: Option '22'
Answer: D
Of all the homes on Gotham Street, 1/3 are termite-ridden, and 2/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?	Choose the correct answer
A) a) 2/15
B) b) 3/15
C) c) 4/5
D) d) 2/5
E) e)1/5

Solution: let total homes be 15   termite ridden= 1/3(15)= 5   termite ridden and collapsing = 2/5(5)=2   thus homes that are termite ridden, but not collapsing = 5-2= 
5-2 = 3
3   thus required ratio= 3/15=1/5   Answer e)1/5
Answer: E
what is the maximum possible remainder when a number 104^n is divided by 51 ? (Assume n be any positive integer)
Choose one:
A) 29	B) 32	C) 96	D) 85	E) 78

Solution: let n=1 then 104/51= 2(rem)   for getting a max rem put n=5, because rem(2)*5= 32 which is less than 51   ANSWER:32
Answer: B
A lady took loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was :  Pick:
A) Rs. 15,000
B) Rs. 1,50,000
C) Rs. 1500
D) Rs. 1,62,000
E) None of these

Solution: Explanation:   Principal = Rs.(100 x 5400)/(12 x 3)= Rs. 15000.   Rs. 15,000nswer IS Rs. 15,000
Answer: A
5 20 380 144020 ?
Pick.
A) 20741616380	B) 20841616380	C) 21741616380	D) 22741616380	E) 20791616380

Solution: If number=N, then next number=N*(N-1)   So 5, (5*4=20), (20*19=380), (380*379=144020), (144020*144019=20741616380)   20741616380NSWER:20741616380
Answer: A
Three people have $26, $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?  Select the correct option.
A) $72	B) $85	C) $98	D) $101	E) $202

Solution: Solution -   Total money distributed is $196. In order to maximize median, one person has to accept $0 and remaining two people share $98 each. Hence median is $98.   ANS $98
Answer: C
The difference between a number and its two-fifth is 510. What is 10% of that number?  Pick one.
A) 58
B) 85
C) 76
D) 68
E) 86

Solution: Let the number be x. Then,   x - 2/5 x = 510   x = (510 * 5)/3= 
(510 * 5)/3 = 850
850   10% of 850= 85.   Answer:85
Answer: B
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 11?  Choose the correct choice from the following answers:
A) 7  B) 5  C) 9  D) 4  E) 1

Solution: You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4, and 5 then no two numbers out of these 6 add up to 10.   Now, the next, 7th number whatever it'll be (6, 7, 8, or 9) will guarantee that two number WILL add up to 11. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 11.   7nswer: 7
Answer: A
A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price D per t-shirt that the vendor paid for these purchases?
Options.
A) $12.20	B) $12.50	C) $12.55	D) $12.70	E) $13.00

Solution: Correct Answer: A   Explanation: The relevant formula for this problem is Average D= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.   NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice $12.20 is a possibility.
Answer: A
The length of the longest tape in cm which can be used to measure exactly, the length 8m; 5m 60cm; and 15m is:
Choose the correct choice from the following answers:	A) 37	B) 35	C) 34	D) 36	E) 20

Solution: The three lengths in cm are 800, 560 & 1500.   HCF of 800, 560 & 1500 is 20   Hence, the answer is 20 cm.   ANSW20R:20
Answer: E
Set A: 3, w, 8, 10
Set B: 4, y, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – w?	Pick: A) -2 B) -1 C) 0 D) 1 E) 2

Solution: So we have even no. of elements in the Set   So median is the average of Middle two numbers   (w+8)/2= (y+9)/2   y - w= -1   Answer -1
Answer: B
The curved surface of a sphere is 64 π cm2. Find its radius?  Select the correct option:
A) 8
B) 6
C) 4
D) 2
E) 5

Solution: 4 πr2   = 64   => r = 4   Answer: 4
Answer: C
H is a positive integer and 225 and 216 are both divisors of H. If H=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?  Pick
A) 4  B) 8  C) 6  D) 7  E) 5

Solution: Lets make factorization of 225 and 216 ..   225 = 5 X 5 X 3 X 3 X 3   216 = 2 X 2 X 2 X 3 X 3 X 3   H would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2= 
3 + 3 + 2 = 8
8(8) (answer) ...
Answer: B
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 36 years now, the son's age five years back was Pick:
A) 13years	B) 15years	C) 17years	D) 19years	E) 20years

Solution: Let the son's present age be x years. Then, (36 - x) = x   2x = 36.   x = 18.   Son's age 5 years back (18 - 5)= 
(18 - 5) = 13
13 years.   13years)
Answer: A
Two cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 114 km apart?  Choices:
A) 1 1/4 hours B) 3 hours C) 4hours D) 3 3/4 hours E) 6hours

Solution: To be (18+20) km apart, they take 1 hour   To be 114 km apart, they take   1/38 * 114= 
  1/38 * 114 = 3
3 hrs   Answer is 3 hours
Answer: B
A certain list of 301 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d? Choose the correct answer.
A) 75 and 80  B) 75 and 75  C) 70 and 75  D) 74 and 75  E) 70 and 80

Solution: Deviation means spreading of the numbers from one median point value..   as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.   so 75 and 75 are the most close numbers and they will increase the number of elements in the set without changing the median value.   75 and 75
Answer: B
Find the one which does not belong to that group ? Choose the correct choice from the following options.
A) 30  B) 82  C) 27  D) 62  E) 11

Solution: Explanation:   27, 36, 72 and 45 are divisible by 9, but not 30.   30nswer: 30
Answer: A
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Pick:  A) m  B) m  C) m  D) m  E) of these

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.   ANSWER:m
Answer: B
A train 450 m long running at 126 kmph crosses a platform in 20 sec. What is the length of the platform? Options
A) 271 B) 250 C) 350 D) 277 E) 232

Solution: Length of the platform = 126 * 5/18 * 20= 
126 * 5/18 * 20 = 700
700 – 450= 250   Answer:250
Answer: B
An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?
Pick one.
A) 12.50 %
B) 13.50 %
C) 14 %
D) 14.50 %
E) None

Solution: Sol.   Let C.P. = Rs. 100. Then, marked price = Rs. 150.   S.P. = 75% of Rs. 150 = Rs. 112.50.   ∴ Gain% = 12.50%.   12.50 %nswer 12.50 %
Answer: A
I bought two books; for Rs.600. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? Answers:
A) 197
B) 280
C) 189
D) 278
E) 350

Solution: x*(85/100)   = (600 - x)119/100   x = 350   Answer: 350
Answer: E
If the growth in production of company A from 1994 to 1995 was 25% and that from 1995 to 1996 was 60%, then what percentage growth took place from 1994 to 1996?	Choose the correct choice
A) 85%  B) 75%  C) 200%  D) 100%  E) None of these

Solution: Percentage growth from 1994 to 1996   = +25 + 60 + 25×60/100= +100%   Answer 100%
Answer: D
Jack bought 150 packets of chocolate. He was able to sell 1/3 of them at a 20% profit, another 1/3 of them at zero profit and the remainder was sold at a 10% loss. Find the total profit or loss made by the person after selling those 150 packets. A packet sold at a loss had a price of $9.
Please provide an intuitive answer if possible. Thanks!!  Pick:  A) Profit of $50  B) Profit of $20  C) Loss of $25  D) Profit of $30  E) Loss of $35

Solution: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.   50 packets was sold at a 20% profit --> gives profit of 10*0.2*50= 
10*0.2*50 = 100
$100.   50 packets was sold at a 10% loss --> gives loss of  10*0.1*50= 
 10*0.1*50 = 50
$50.   The overall Profit is $100 - $50 = $50.   Profit of $50nswer: Profit of $50.  100 -  50= 
  100 -  50 = 50
$50.   Profit of $50nswer: Profit of $50.
Answer: A
A sum of money is borrowed and paid back in two annual installments of Rs. 882 each allowing 5% C.I. The sum borrowed was? Choose the correct choice from the following.
A) 1647	B) 1640	C) 2888	D) 2298	E) 2709

Solution: Principal = (P.W. of Rs. 882 due 1 year hence) + (P.W. of Rs. 882 due 2 years hence)   = [882/(1 + 5/100) + 882/(1 + 5/100)2]   = (882 * 20)/21 + (882 * 400)/441 = Rs. 1640.Answer: 1640
Answer: B
Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes. Each inlet pipe can fill the tank in 9 hours and each outlet pipe can empty the tank in 6 hours. On opening all the pipes, an empty tank is filled in 9 hours. How many inlet pipes are there? Answers.
A) 2 B) 4 C) 3 D) 5 E) 6

Solution: x / 9 – y / 6 = 1/9; 2x – 3y + 2   We can compute that x = 4 and y = 2.   Thus, Inlet pipe = x = 4.   Answer: 4
Answer: B
There are 9 executives, including the CEO and CFO, that are asked to form a small team of 5 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
Choose the correct option.
A) 85  B) 87  C) 89  D) 91  E) 93

Solution: The total number of ways to form a team of 5 is 9C5=126.   We need to subtract the number of teams that have both the CEO and the CFO.   The number of teams with both the CEO and CFO is 7C3=35.   The number of ways to form an acceptable team is  126-35= 
 126-35 = 91
91.   The answer is 91.
Answer: D
The Guests at a football banquet consumed a total of 337 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
Choose the correct choice:	A) 160	B) 161	C) 162	D) 163	E) 169

Solution: To minimize one quantity maximize other.   168*2 (max possible amount of food a guest could consume) = 336 pounds, so there must be more than 168 guests, next integer is 169.   Answer: 169.
Answer: E
The grade point average of the entire class is 87. If the average of one third of the class is 95, what is the average of the rest of the class?	Choose the correct option.
A) 81
B) 82
C) 83
D) 84
E) 85

Solution: Let x be the number of students in the class.   Let P be the average of the rest of the class.   87x = (1/3)95x + (2/3)(P)x   261 = 95 + 2P   2P = 166   P = 83.   The answer is 83.
Answer: C
The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?  Choose the correct answer
A) 25
B) 35
C) 38
D) 29
E) 22

Solution: excluded number = (27 x 5) - (25 x 4)   = 135 - 100= 
135 - 100 = 35
35.   Answer: 35
Answer: B
Find the odd man out
1, 2, 5, 14, 41, 120 Pick one: A) 2 B) 14 C) 124 D) 120 E) 21

Solution: 1*3-1= 
1*3-1 = 2
2   2*3-1= 
2*3-1 = 5
5   5*3-1= 
5*3-1 = 14
14   14*3-1= 
14*3-1 = 41
41   41*3 -1= 
41*3 -1 = 122
122   ANSWER:120
Answer: D
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required? Pick one:
A) 34
B) 40
C) 68
D) 88
E) 78

Solution: We have: l = 20 ft and lb = 680 sq. ft.   So, b = 34 ft.   Length of fencing = (l + 2b) = (20 + 68)= 
(20 + 68) = 88
88 ft.   ANSWER:88
Answer: D
In a class,7 students like to play Basketball and 5 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?  Select the correct option
A) 12 B) 15 C) 16 D) 9 E) 22

Solution: 9raw a Venn 9iagram yourself !   B + C - BC = Number of students that play either Basketball or Cricket   7 +5 - 3= 
7 +5 - 3 = 9
9   9)
Answer: D
If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost?
Choose the correct choice
A) 24 paise	B) 65 paise	C) 56 paise	D) 87 paise	E) 15 paise

Solution: Explanation:   Let the required cost be x paise.   Less weight, Less cost (Direct proportion)   250 : 100 : : 60 : x   250 * x = (100 * 60)   x = (100 * 60) / 250= 
(100 * 60) / 250 = 24
24   24 paiseNSWER: 24 paise
Answer: A
In assembling a Bluetooth device, a factory uses one of two kinds of modules. One module costs $10 and the other one, that is cheaper, costs $6. The factory holds a $80 worth stock of 12 modules. How many of the modules in the stock are of the cheaper kind?  Choose the correct choice from the following options:
A) 20
B) 25
C) 10
D) 30
E) 35

Solution: So the number of $6 modules must be 10 so that the leftover 2 modules are of $10 which will give a total value $80. 10*6+2*10 = 60+20= 
60+20 = 80
80   Answer : 10
Answer: C
If x/y = 9/8, Then (8x + 7y) / (8x â€“ 7y) = ?  Options
A) 8  B) 7  C) 10  D) 9  E) 6

Solution: Answer   Dividing numerator as well as denominator by y, we get   Given Exp. = (8x + 7y) / (8x â€“ 7y) = (8x/y + 7) / (8x/y â€“ 7)   Since x/y = 9/8   this implies that   =[(8*9)/8 +7]/[(8*9)/8 -7)]   = (9+ 7) / (9 - 7)= 
(9+ 7) / (9 - 7) = 8
8   Option: 8
Answer: A
There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? Choose the correct option
A) 1023  B) 6000  C) 1980  D) 1800  E) 1450

Solution: 5 subjects can be arranged in 6 periods in 6P5 ways.   Any of the 5 subjects can be organized in the remaining period (5C1 ways).   Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.   Total number of arrangements   = 6P5× 5C1 /2!=1800   ANSWER 1800 1800
Answer: D