MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following fractions is greater than 1/6?	Choose the correct answer: A) 1. 12/50 B) 2. 3/11 C) 3. 2/9 D) 4. 4/17 E) 5. 6/24

Solution: 1. 12/50   12.5/50 = 1/4 thus 12/50 < 1/4   2. 3/11   3/12 = 1/4 thus 3/11 > 1/4   3. 2/9   2/8 = 1/4 thus 2/9 < 1/4   4. 4/17   4/16 = 1/4 thus 4/17 < 1/4   5. 6/24   6/24 = 1/4   5. 6/24
Answer: E
There are 20 balls in a box: 11 balls are green, 6 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a green ball is selected at random from the box?
Choose the correct choice from the following choices
A) 1/13	B) 10/18	C) 3/13	D) 5/13	E) 6/13

Solution: If 1 green and 1 blue ball are taken from the box, then there are 10 green, 5 blue and 3 white balls, a total of 18 balls. If one ball is selected at random, the probability that it is green is given by 10 / 18   Answer :10/18
Answer: B
Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $250, and the total cost is $16,000, what is the value of n?  Choose one:
A) 10 B) 24 C) 60 D) 70 E) 85

Solution: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $10,000 + n * $250 --> n = 24.   Answer: 24.
Answer: B
In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?
Choose the correct answer: A) $130 B) $220 C) $190 D) $200 E) $150

Solution: Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.   4x + 4y + 2z = 560 :   9x + 9y + 6z = 1,290   3x + 3y + 2z = 430 : divide all terms of equation C by 3   x + y = 130 : subtract equation D from equation B   3(x + y) + 2z = 430 : equation D with factored terms.   3*130 + 2z = 430   z = 20 : solve for z   x + y + z = 130 + 20= 
130 + 20 = 150
$150   correct answer $150
Answer: E
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? Choose the correct choice from the following answers: A) 07.30 p.m. B) 09.30 p.m. C) 08.30 p.m. D) 10.30 p.m. E) 11.30 p.m.

Solution: D   10.30 p.m.   10.30 p.m. = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     3.30 + 7= 
  3.30 + 7 = 10.3
10.30 p.m.
Answer: D
Solution X is 80% chemical A and 20% chemical B by volume. Solution Y is 50% chemical A and 50% chemical B by volume. If a mixture of X and Y is 68% chemical A, what percent of the mixture is Solution X?
Options:
A) 20%  B) 25%  C) 30%  D) 35%  E) 40%

Solution: The volume of the mixture be X+Y.   0.8X +0.5Y=0.68(X+Y)   0.12X=0.18Y   X=3Y/2   X/(X+Y)=(3Y/2) / (5Y/2)=3/5=40%.   The answer is 40%.
Answer: E
If x^2=2x+2, then x^3 = ?  Choices.
A) 3x+2
B) 4x-2
C) 2x+1
D) 2x-3
E) 6x+4

Solution: x^2 = 2x+2   x^3 = x*x^2 = x*(2x+2) = 2x^2 + 2x = 2(2x+2)+2x = 6x+4   The answer is 6x+4.
Answer: E
Sakshi can do a piece of work in 20 days .Tanya is 25% more efficient than Sakshi. the number of days taken by tanya to do the same piece of work is?  Select the correct option:	A) 25days	B) 45days	C) 24days	D) 16days	E) 36days

Solution: The ratio of times taken by Sakshi and Tanya=125:100=5:4.   suppose Tanya takes x days to do the work.   5:4::20:x   x=(4*20)/5= 
(4*20)/5 = 16
16 days   Tanya can do work in 16 days   Answer(16days)
Answer: D
What is the sum of the different positive prime factors of 620?
Pick
A) 17
B) 24
C) 38
D) 47
E) 62

Solution: The prime factorization of 620   = 62 * 10   = 2*31 * 2*5   The sum of the different positive prime factors = 2+5+31= 
2+5+31 = 38
38   The answer is 38.
Answer: C
A right triangle is inscribed in a circle. The legs of the triangle have lengths 6 and 8. What is the diameter of the circle?  Choose the correct option:	A) 8	B) 8π	C) 9√3	D) 10	E) 12

Solution: Property of a right triangle inscribed in a circle is that when an angle is made from diameter of the circle, it is a right triangle. Or if a right triangle is made inscribed in a circle, its its longest side is the diameter of the circle.   Hence diameter= (6^2+8^2)^1/2= 10   10 is the answer
Answer: D
1000 men have provisions for 21 days. If 800 more men join them, for how many days will the provisions last now? Choose the correct choice from the following answers.
A) 12.9 B) 12.5 C) 12.6 D) 11.6 E) 12.1

Solution: 1000*21 = 1800*x   x = 11.6   Answer: 11.6
Answer: D
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 3 flips but not on the last 3 flips? Choose the most appropriate option:
A) 1/8
B) 1/16
C) 1/32
D) 1/64
E) 1/128

Solution: P(HHHTTT) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64   The answer is 1/64.
Answer: D
If a jar contains 25 percent red candies, 10 percent blue candies, and 55 white candies, what fraction of candies are of another color? Answers:	A) 4/5	B) 3/5	C) 3/10	D) 1/5	E) 1/10

Solution: 100%-(25%+10%+55%)=10% of candies are another color --> 10% 100 -(25 +10 +55 )= 
100 -(25 +10 +55 ) = 10
10% of candies are another color --> 10% = 10/100  --  10= 
 --  10 = 10
10/100= 1/10.   Answer: 1/10.
Answer: E
Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of a gamma raised to the seventh power and a delta raised to the seventh power?
Choose the correct answer
A) alpha
B) beta
C) gamma
D) delta
E) epsilon

Solution: Solution : 2 is gamma and 3 is a delta. 2^7 + 3^7 will have a units digit as 8+7=5. So, label is alpha.   or   alpha : 5k   beta : 5k +1   gamma : 5K+2   delta : 5k+3   epsilon : 5K+4   (5k + 2)^7 has unit digit as 8 or 3   (5k + 3)^7 has unit digit as 7 or 2   In any case (5k + 2)^7 + (5k + 3)^7 will have units digit as 0 or 5 which is a alpha.   Option alpha
Answer: A
Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have	Choose the correct choice from the following:	A) 4	B) 6	C) 9	D) 10	E) 12

Solution: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides   4
Answer: A
If a person sells a wooden furniture at 8% profit against 8% loss, then he could had earned Rs12 more. What is the cost price of furniture? Choose the correct choice from the following answers
A) 72	B) 70	C) 80	D) 75	E) None

Solution: Answer   Let Cost Price (CP) = x   Then Selling Price(SP) if he sells at profit = x(1+8%) = 1.08x   and SP, if he sells at loss = x(1-8%) = 0.92%   Given, 1.08%-0.92% = Rs12   0.16x = Rs.12   ⇒x = Rs.75   Correct Option: 75
Answer: D
A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance? Choose the correct choice from the following options:	A) 21 (1/8)	B) 21 (1/3)	C) 21 (7/3)	D) 22 (1/3)	E) 31 (1/3)

Solution: Let the total distance be x km   total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64   Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.   Answer: 21 (1/3)
Answer: B
Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1395 as rent for parking his cars, what is the total rent paid by all the four agencies?
Choose the correct choice from the following answers:  A) Rs. 4500  B) Rs. 4800  C) Rs. 5250  D) Rs. 7626  E) None of these

Solution: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15   = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60   Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.   The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k   It is given that A paid Rs. 1395   45k 45  + 60  + 81  + 60= 
45  + 60  + 81  + 60 = 246
246k   It is given that A paid Rs. 1395   45k= 1395 => k = 31   246k = 246(31) = Rs. 7626   Thus the total rent paid by all the four agencies is Rs. 7626.   ANSWER:Rs. 7626
Answer: D
A person purchased a TV set for Rs. 14000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Choose the correct choice:
A) 16.82%
B) 87.82%
C) 53.82%
D) 17.82%
E) 18.82%

Solution: The total CP = Rs. 14000 + Rs. 6250 = Rs. 20250 and SP   = Rs. 31150   Profit(%) = (31150 - 20250)/20250 * 100   = 53.82%   Answer:53.82%
Answer: C
Lilly has 10 fish and Rosy has 12 fish. In total, how many fish do they have in all?	Choose the correct answer
A) 18
B) 20
C) 22
D) 24
E) 26

Solution: 10+12= 
10+12 = 22
22   The answer is 22.
Answer: C
33 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Choose one:
A) 10	B) 11	C) 13	D) 18	E) 19

Solution: Let the required number of days be x.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   Persons 30 : 33 :: 12 : x   Working hours/day 6 : 5   30 x 6 x x = 33 x 5 x 12   x = (33 x 5 x 12)/(30 x 6)   x = 11   ANSWER 11
Answer: B
If x+y=-4, and x=6/y, what is the value of x^2+y^2? Choices.
A) 10
B) 15
C) 6
D) 4
E) 5

Solution: x^2 + y^2 should make you think of these formulas:   (x+y)(x+y) = x^2+y^2+2xy   We already know (x+y) = -4 and x*y = 6   (x+y)(x+y) = (-4)(-4) = x^2+y^2+2*(6)   x^2+y^2 = 16 - 12= 
16 - 12 = 4
4   Answer : 4
Answer: D
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?	Choose the correct choice from the following options:
A) 3/6
B) 3/2
C) 3/3
D) 3/5
E) 5/2

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train   = 27 x meters, and length of the second train   = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y   ==> 4 x = 6 y ==> x/y   = 3/2.   Answer:3/2
Answer: B
During the last 5 days, John ran 5 miles per day on average. How many miles must he run tomorrow to increase his daily average to 7 miles per day.	Choose the correct choice from the following answers.
A) 2 B) 7 C) 17 D) 30 E) 32

Solution: Solution   Average after 6 days = 7   âˆ´ Required miles to run= (6 days x 7 miles/day)-(5 days x 5 miles/day)   = 42 - 25= 
42 - 25 = 17
17.   Answer 17
Answer: C
A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares?  Answers: A) $37.5 B) $40 C) $50 D) $48 E) $52

Solution: Dividend on 1 share = $(10/100*50)= 
(10/100*50) = 5
$5   $12.5 is an income on an investment of $100   $5 is an income on an investment of $  (100*2/25*5)= 
  (100*2/25*5) = 40
40   Thus, cost of 1 share=$40   option $40
Answer: B
If m > 1 and n = 2^(m+3), then 4^m =
Answers:
A) 16n^2	B) 4n^2	C) 8n^2	D) n^2/64	E) n^2/16

Solution: n = 2^(m+3) = 2^m*8   2^m = n/8   4^m = (2^m)^2 = (n/8)^2 = n^2/64   The answer is n^2/64.
Answer: D
A party supply store sells noisemakers arranged on display such that each of the three different colors of noisemakers, red, blue, and purple are consecutive in a repeating pattern. If four consecutively displayed noisemakers are purchased, what is the probability that two of the noisemakers are purple?  Choose the correct choice from the following.
A) 2/3
B) 1/9
C) 2/9
D) 1/3
E) 2/7

Solution: After red, blue, and purple, the next noisemakers can be of any given three colours, therefore we have total three possibilites, out of which we need purple i.e. 1 therefore prob is 1/3. Correct answer is 1/3.
Answer: D
if A fills a tank in 30mins,and B fills the same tank in 20mins,and C emptys it in 40min ,if A,B,C works together how much time will the tank take to fill?  Options
A) 15.14mins
B) 16.14mins
C) 17.14mins
D) 18.14mins
E) 19.14mins

Solution: 1/30+1/20-1/40=7/120   so total time=120/7   =17.14mins   ANSWER:17.14mins
Answer: C
In how many ways can 5 men & 4 women can be made from a gang of 6 men & 6 women ?	Choose the correct answer:
A) 10
B) 21
C) 24
D) 27
E) 29

Solution: Explanation:   6C5* 6C4 = 21   21
Answer: B
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the sixth digit of p, counting right to left from the units digit?
Choose the correct choice: A) 1 B) 2 C) 4 D) 5 E) 9

Solution: C   Sum of unit digits of first 30 terms = 60   Sum of tens digits of first 30 terms = 58   Sum of thousands digits of first 30 terms = 56   and so on..   p1 = 0   p2 = (6+58) = 4   p3 = (6+56) = 2   p4 = (6+54) = 0   p5 = (6+52) = 8   p6 = (5+50) = 5   ANSWER :5
Answer: D
A train sets off at 2 p.m. at the speed of 80 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Choices
A) 3.30 p.m.	B) 4.30 p.m.	C) 3.50 p.m.	D) 9.30 p.m.	E) 8.30 p.m.

Solution: D = 80 * 1 ½ = 120 km   RS = 85 – 80 = 5   T = 120/5= 
120/5 = 24
24 h   3.30 + 24 h=3.30 p.m.   3.30 p.m.NSWER:3.30 p.m.
Answer: A
A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets  Choose the correct choice from the following options:
A) 40%  B) 50%  C) 55%  D) 60%  E) 70%

Solution: Number of runs made by running = 110 - (3 x 4 + 8 x 6)   = 120 - (60)= 
120 - (60) = 60
60   Now, we need to calculate 60 is what percent of 120.=> 60/120 * 100= 
60/120 * 100 = 50
50%   50%
Answer: B
Carrie likes to buy t-shirts at the local clothing store. They cost $9.95 each. One day, she bought 25 t-shirts. How much money did she spend?	Select the correct option:
A) $150 B) $248.75 C) $200 D) $171.6 E) $190

Solution: $9.95*25=$248.75. Answer is $248.75.
Answer: B
The value of land increases by a% during June and decreases by b% during July. If the value of the land is the same at the end of July as at the beginning of June, what is b in terms of a?	Choose the correct choice from the following answers: A) 200a/(100+2a) B) 100a/(100+a) C) a(2+a)/(1+a)2 D) a(200+a)/10000 E) 2a/a+2a

Solution: let the value of land be : x   it is increased by a%, new value= (x)+(ax/100)   now, it is decreased by b%, such that it equals the initial value   hence final value of land= x(1+a/100) - x(1+a/100)(b/100)= x(1+a/100)(1-b/100)=x   solving for b you get b=100a/(100+a)   ANSWER:100a/(100+a)
Answer: B
A certain car can travel 20 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 60 mph?  Choose one.
A) 16.67%
B) 20%
C) 25%
D) 30%
E) 40%

Solution: Let, Tank capacity = T gallon   Used Fuel = (T-8) gallons   Distance Travelled (@60 miles/hr) = 80 miles   Distance travelled in 1 gallon = Distance travelled in 20 mins (@60 miles/hr) = (60/60)*20= 
(60/60)*20 = 20
20 miles   Fuel used to travel 80 miles= (80/20)= 
(80/20) = 4
4 gallon   i.e. Used fuel= (T-8) = 4 gallon   i.e. T = 12 Gallons   i.e. Used Fuel = (2/12)*100 =16,67%   16.67%
Answer: A
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Choose the correct choice from the following answers:
A) 52  B) 24  C) 27  D) 26  E) 28

Solution: Let the ten's and unit digit be x and	8/x	respectively.   Then, 10x +	8/x + 18 = 10 x	8/x	+ x   10x2 + 8 + 18x = 80 + x2   9x2 + 18x - 72 = 0   x2 + 2x - 8 = 0   (x + 4)(x - 2) = 0   x = 2.   Answer:24
Answer: B
Average age of students of an adult school is 46 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.  Select:
A) 1200  B) 120  C) 360  D) 168  E) None of these

Solution: Explanation :   Let the original no. of students be x.   According to situation, 46x + 120*32 = (x + 120)36 ⇒ x = 48   So, Required no. of students after joining the new students   = x + 120 = 168.   Answer : 168
Answer: D
A man can row three - quarters of a kilometer against the stream in 11¼minutes. The speed(in km/hr) of the man in still water is Choose the correct choice.
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: Solution   Rate upstream	= (750 / 675)m/sec   = (10 / 9) m/ sec.   Rate downstream	= (750 / 450)   =(5 / 3) m/sec   Rate in still water	= 1/2(10 /9 + 5/3)   = (25/18x18/5)km/hr   = 5 km/hr.   Answer 5
Answer: D
In Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?	Choose the correct option
A) 86.5 kg  B) 66.5 kg  C) 46.5 kg  D) 26.5 kg  E) 16.5 kg

Solution: Let Arun's weight be X kg.   According to Arun, 65 < X < 72.   According to Arun's brother, 60 < X < 70.   According to Arun's mother, X < 68.   The values satisfying all the above conditions are 66 and 67.   Required average = (66 + 67) / 2= 
(66 + 67) / 2 = 133/2 = around 66.5
66.5 kg   Answer: 66.5 kg
Answer: B
For any positive integer n, the length of n is defined as number of prime factors whose product is n, For example, the length of 75 is 3, since 75=3*5*5. How many two-digit positive integers have length 6?  Select
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Length of a number = Total number of prime factors of the number.   Any composite number can be represented as a product of prime numbers as shown below:   N= 2^x * 3^y * 5^z * 7^a ...so on   Since our requirement is a two digit number, we shall raise maximum power for smallest prime factor.   N= 2^6 = 64 has Length 6   N= 2^5 * 3 = 96 has length 6   N=2^4 * 3^2 = 144 is a three digit number and so on the other combinations would reveal 3 digit numbers.   Hence there are only 2 numbers   ANSWER:2
Answer: C
Which of the following best approximates the value of q if 20^50+20^11=20^q ? Select the correct option:
A) 61 B) 52 C) 51 D) 50 E) 39

Solution: We have: 20^50+20^11=20^q   ==> because 20^11 > 0 --> 20^q MUST be equal or greater than 20^50 ==>q MUST be equal or greater than 50   ==> Option E is out immediately.   Divide both sides by 20^q and q >= 50   We have:   20^(50-q) + 20^11/20^q = 1   Because q >= 50 ==>20^11/20^q = 0.0000xyz, that is very small,we can ignore it.   Thus, 20^(50-q) must be approximately 1   ==> 50-q = 0 ==> q is approximately 50   50 is the answer.
Answer: D
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:	Answers
A) 2600
B) 2700
C) 2900
D) 3900
E) 4000

Solution: 10c=4t   15c+2t=4000   take the cost of c & t is 2000 b'coz 10c + 4t cost is same. and divid 2000 by 10 as well as 4 and get c & t cost as,   1t-500   1c-200   therefore,   12c-2400 + 3t-1500 = 3900.   answer -3900
Answer: D
Two trains travelling in the same direction at 90 and 36 kmph completely pass off another in 1 minute. If the length of the first train is 300 m, what is the length of the second train?  Choices.
A) 228
B) 266
C) 175
D) 99
E) 600

Solution: RS = 90 â€“ 36 = 54 * 5/18= 
54 * 5/18 = 15
15 mps   T= 60 sec   D = 15 * 60= 
15 * 60 = 900
900 m   300   --------   600 m   Answer: 600
Answer: E
The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is? Pick one:
A) 2.4% B) 2.6% C) 0.3% D) 2.0% E) 1.3%

Solution: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100 = 13.50 4500(R1 - R2) = 1350   R1 - R2 = 0.3%   Answer:0.3%
Answer: C
Find the slope of the line perpendicular to the line y = (1/3)x - 7	Choose the correct option
A) -1  B) -2  C) -3  D) -4  E) -5

Solution: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 3. If m is the slope of the line perpendicular to the given line, then   m × (1/3) = -1   Solve for m   m = - 3   correct answer -3) -3
Answer: C
A and B started a business investing Rs. 92,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
Choose the correct choice.
A) 9:2  B) 3:2  C) 23:5  D) 18:4  E) 17:4

Solution: A: B = 92000 : 20000   = 92 : 20   = 46 : 10   = 23 : 5   ANSWER:23:5
Answer: C
On decreasing the price of a colour TV by 20%, its sale is increased by 30%. The effect on the revenue is?  Select:  A) 4% decrease  B) 4% increase  C) 16% decrease  D) 16% increase  E) none of these

Solution: Net% change in revenue   = ( x + y + xy/100) %   = [-20 + 30 + ( -20 x 30)/100]% or 4%   ANSWER:4% increase
Answer: B
If p shirts can be purchased for q dollars, how many shirts can be purchased for r dollars? Select:
A) q/pr B) q/p C) pr/q D) p/(qr) E) r/(pq)

Solution: Ans = pr/q
Answer: C
How many of the positive divisors of 360 are also multiples of 4 not including 360?
Choose the correct option.
A) 8 B) 11 C) 12 D) 15 E) 16

Solution: 360 = 2^5 * 3 * 5 = (4) * 2 * 3^2 * 5   Besides (4), the exponents of 2, 3, and 5 are 1, 2, and 1.   There are (1+1)(2+1)(1+1) = 12 ways to make multiples of 4.   We must subtract 1 because one of these multiples is 360.   The answer is 11.
Answer: B
If (A+B) = 14, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?	Select the correct option:
A) 16.	B) 8.	C) 7.	D) 2.	E) -2.

Solution: Given A+B = 14 => A = 14 - B --> Eq 1   B+C = 9   C+D = 3 => D = 3 - C --> Eq 2   Then Eqs 1 + 2 => A + D = 14 - B + 3 - C   => 17 - (B+C)   => 17 - 9= 
17 - 9 = 8
8.   Option 8....
Answer: B
On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 210,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?  Choose the correct choice:
A) 77,500  B) 1,860,000  C) 2,480,000  D) 3,360,000  E) 4,960,000

Solution: 210,000 × 2 × 2×2×2 = 210,000 × 16 = 3,360,000
Answer: D
Nine men went to a hotel. Eight of them spent Rs.1 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them? Choose the correct choice from the following options
A) 19.28	B) 10.28	C) 11.28	D) 14.28	E) 17.28

Solution: Average of 9 = x   9x = 8 * 1 + x * 2   x = 1.14   Total = 9 * 3.25 = 10.28   ANSWER:10.28
Answer: B
TheOG 13thed page 193 #77 says
If n = 90! + 87, then n is divisible by which of the
following?
I. 15
II. 17
III. 19  Choose the correct choice from the following options.
A) None	B) I only	C) II only	D) I and II	E) II and III

Solution: The example you have taken   n = 4! + 4 = 4(3!+1)   The equation gets further simplified to deviate the expected results   Try some other examples   7! + 4   9! + 5   4! + 3   Answer:I only
Answer: B
A1B, D4F, H9K,then find next term ?  Choose the correct choice from the following options.
A) M16Q  B) L25P  C) N36P  D) N25S  E) M9K

Solution: By giving the number to alphabets, we get   M16Q - B = 1-2 = -1 --> -1^2 = 1   D - F = 4-6 = -2 --> -2^2 = 4   H - K = 8-11= -3 -->-3^2 = 9   : :   : :   M - Q = 13-17=-4 --->-4^2 = 16   M16QNSWER:M16Q
Answer: A