MU-NLPC/Calc-aqua_rat huggingface dataset:
The compound interest earned on a sum for the second and the third years are $1400 and $1540 respectively. What is the rate of interest?
Choose the correct choice from the following answers:  A) 2%  B) 4%  C) 6%  D) 8%  E) 10%

Solution: 1540 - 1400= 
1540 - 1400 = 140
140 is the rate of interest on $1400 for one year.   The rate of interest= (100 * 140) / (1400)= 
(100 * 140) / (1400) = 10
10%   The answer is 10%.
Answer: E
For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/19
Select the correct option:
A) a)22 B) b) 6 C) c) 10 D) d) 16 E) e) 32

Solution: It seems that the accepted answer is wrong, according to WolframAlpha. The answer should be 32, which isn't even listed as a selectable answer.   a)22
Answer: A
P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 30 days to complete the same work. then Q alone can do it in
Choose the correct choice from the following answers.
A) 10  B) 22  C) 25  D) 27  E) 30

Solution: Work done by P and Q in 1 day = 1/10   Work done by R in 1 day = 1/30   Work done by P, Q and R in 1 day = 1/10 + 1/30 = 4/30   But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 4/30   => Work done by P in 1 day = 4/60   => Work done by Q and R in 1 day = 4/60   Hence work done by Q in 1 day = 4/60 â€“ 1/30 =2/60 = 1/30   So Q alone can do the work in 30 days   Answer is 30.
Answer: E
what is the smallest integer that is multiple of 3,7 and 20  Choose the correct choice from the following options.
A) 141  B) 180  C) 130  D) 122  E) 420

Solution: Correct Answer :420   It is the lcm of 3,7 and 20 which is 420
Answer: E
If a: b :: 3 : 7, then what is (5a+6b): (a-4b)?	Pick.
A) 57:11 B) -57:11 C) 11 : 10 D) -57 : 25 E) -1 : 10

Solution: a/b= 3/7   -57 : 25ividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,   [5(a/b)+6]/[(a/b)-4]= [5*(3/7)+6]/[(3/7)-4]= -57/25   ANSWER:-57 : 25
Answer: D
The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).  Choose the correct choice from the following:
A) 178.27
B) 178.29
C) 178.21
D) 178.19
E) 178.55

Solution: Calculated average height of 35 boys = 180 cm.   Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm   = 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm   = 180 cm - 1.71 cm = 178.29 cm.Answer:178.29
Answer: B
If it takes a hrs for x to repair 1 machine and b hrs for y to repair 1 machine then how many hrs will they take to repair 750 machines if they work together? Choose the most appropriate option:
A) 750 × ab/(a+b)
B) 750 (a+b)/ab
C) 750 ab
D) 750/(a+b)
E) None of these

Solution: Explanation:   x repair machine in a hrs he work 1/a for 1 hr   y repairs machine in b hrs he works 1/b for 1 hr   (x+y) work per 1 hr = 1/a+1/b= (a+b)/ab   time = ab/(a+b)   for 750 machines time = 750 × ab/(a+b)   750 × ab/(a+b)nswer: Option 750 × ab/(a+b)
Answer: A
In a box of 11 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?  Choose the correct answer.
A) 5/11
B) 16/33
C) 28/55
D) 38/77
E) 45/88

Solution: # defective pens = 3   # good pens = 8   Probability of the 1st pen being good = 8/11   Probability of the 2nd pen being good = 7/10   Total probability = 8/11 * 7/10 = 28/55   The answer is 28/55.
Answer: C
After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?  Choose the correct choice from the following.
A) 2338  B) 2298  C) 5000  D) 2871  E) 1171

Solution: Explanation:   Given SP = Rs. 6800   Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000   If SP = Rs. 8000, profit = 60%   CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000   Answer:5000
Answer: C
A tradesman by means of his false balance defrauds to the extent of 30%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?	Options
A) 60%
B) 70%
C) 69%
D) 71%
E) 68%

Solution: g% = 30 + 30 + (30*30)/100= 
30 + 30 + (30*30)/100 = 69
69%   ANSWER:69%
Answer: C
If A earns 99/3% more than B,how much percent does B earn less then A ?	Choices:
A) 42%
B) 14%
C) 25%
D) 15%
E) 35%

Solution: Required Percentage = [((100/3)*100)/[100+(100/3)]]%   =[(100/400)*100= 
(100/400)*100 = 25
25%   Answer is 25%.
Answer: C
The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age?  Choose the correct choice from the following answers:
A) 100 B) 40 C) 80 D) 20 E) 10

Solution: Let the present age of the son =x   Then, present age of the father =(60−x)   Six years ago father's age was 5 times the age of the son   (60-X)-6=5(X-6)   84=6X   X=84/6= 
84/6 = 14
14   Son's age after 6 years=X+6=14+6= 
14+6 = 20
20   answer is 20.
Answer: D
From the word 'HEARTLESS', how many independent words can be made with-out changing the order of the letters and using each letter only once ? Select
A) 5	B) 8	C) 3	D) 2	E) 9

Solution: Explanation:   The words formed are   HE, 5RT, LESS, HE5RT and E5R   5nswer: 5) 5
Answer: A
By the how much is two-fifth of 150 greater than three -fifths of 25?
Pick.
A) 15	B) 3	C) 45	D) 30	E) None of these

Solution: Reqd no. = 2â„5 Ã— 150 - 3â„5 Ã— 25   = 60 - 15= 
60 - 15 = 45
45   Answer 45
Answer: C
A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 4 rows or 5 rows or 6 rows, then no tree will be left. Find the least number of trees required Choose the correct choice from the following.
A) 22  B) 60  C) 28  D) 76  E) 21

Solution: Explanation:   The least number of trees that are required = LCM(4, 5, 6) = 60.   Answer: 60
Answer: B
Baker Adam is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?	Pick:	A) 330	B) 300	C) 252	D) 225	E) 210

Solution: Baker Adam is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5.   To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210.   Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (210) 210.
Answer: E
During the second quarter of 1984, a total of 3,976,000 domestic cars were sold. If this was 32% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ? Choose the correct choice from the following answers
A) 714,240  B) 2,261,760  C) 2,400,000  D) 3,012,121  E) 3,915,790

Solution: Let number of cars sold in 1st quarter = x   Number of cars sold in 2nd quarter = 32% greater than the number sold during the first quarter = (1 + 32/100)= 
(1 + 32/100) = 33/25 = around 1.32
1.32 x   1.32 x= 3,976,000   => x = 3,012,121   So, answer will be 3,012,121
Answer: D
What is the difference between the place value and face value of 3 in the numeral 1375?	Pick one:
A) 287
B) 290
C) 297
D) 390
E) 398

Solution: place value of 3 = 3 * 100= 
3 * 100 = 300
300   face value of 3= 3   300 - 3= 
300 - 3 = 297
297   297
Answer: C
A certain sum of money doubles itself in 12 years in how much many years will it trible itself at the same rate?  Options:
A) 20 years  B) 76 years  C) 24 years  D) 44 years  E) 11 years

Solution: 100 ---- 100 --- 12   100 --- 12   --------------------   300 ---- 24 years   Answer: 24 years
Answer: C
Jerry, an electrician, worked 6 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 6? 12 months = 1 year  Select:
A) 58.33% B) 68.33% C) 78.33% D) 50.00% E) 98.33%

Solution: 1. Multiply the opposites   6 x 100 = 600   100=6/12   50% (rounded to hundredth)   correct answer 50.00%
Answer: D
A textile manufacturing firm employees 70 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 70 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:  Choose the correct choice from the following choices.
A) 13000	B) 7000	C) 10000	D) 5000	E) None of these

Solution: Explanation :   Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.   Since, such loom contributes equally to sales and manufacturing expenses.   But the monthly charges are fixed at Rs 75,000.   If one loan breaks down sales and expenses will decrease.   New profit :-   =>500000Ã—(69/70)âˆ’150000Ã—(69/70)âˆ’75000.   =>Rs 2,70,000.   Decrease in profit   =>2,75,000âˆ’2,70,000   =>Rs. 5,000.   Answer : 5000
Answer: D
Jeya invested an amount of Rs. 9,500 at the rate of 13% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?  Answers:	A) 15550	B) 18450	C) 13450	D) 14450	E) 14650

Solution: Let the second amount be Rs. x. Then,   (9500 * 13 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100   12350+ 15x= 16800 + 14x   x = 4450   Total investment = 10000 + 4450 = Rs. 14450 .Answer: 14450
Answer: D
In a classroom, 12 students brought apples and 8 students brought bananas. If exactly 10 students brought only one of the two types of fruits, how many students brought both types of fruits?
Choose the correct answer.
A) 5 B) 6 C) 7 D) 12 E) 14

Solution: Say x students brought both fruits.   (12 - x) + (8 - x) = 10 --> x = 5.   5nswer: 5.
Answer: A
Helen went to the stationers and bought things worth Euro 45, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Pick one:
A) Euro 15
B) Euro 15.7
C) Euro 19.7
D) Euro 39.7
E) None

Solution: Explanation: Let the amount taxable purchases be Euro x.   Then, 6% of x = 30/100   x = (30/100 x 100/6) = 5.   Cost of tax free items = Euro [45 - (5 + 0.30)= 
45 - (5 + 0.30) = 39.7
Euro 39.70   Answer: Option Euro 39.7
Answer: D
Find the value of 72519 x 9999 = m?
Select:
A) 434539873  B) 355797990  C) 435453490  D) m=725117481  E) 873430134

Solution: 72519 x 9999 = 72519 x (10000 - 1)   = 72519 x 10000 - 72519 x 1   = 725190000 - 72519= 
725190000 - 72519 = 725_117_481
725117481   m=725117481
Answer: D
At a certain university, 69% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?  Options:
A) 25  B) 37.5  C) 50  D) 52.5  E) 75

Solution: answer is 75%   total women = 69%   total men = 40%   total tenured = 70% (both men and women)   therefore, women tenured + women professors + men tenured = 90%   men tenured =21%   but question wants to know the percent of men that are tenured   21%/40% = 52.5%   52.5
Answer: D
Two trains of equal lengths take 12 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? Choose the correct choice:
A) 22	B) 13	C) 77	D) 99	E) 21

Solution: Speed of the first train = 120/12= 
120/12 = 10
10 m/sec.   Speed of the second train= 120/15= 
120/15 = 8
8 m/sec.   Relative speed= 10 + 8= 
10 + 8 = 18
18 m/sec.   Required time= (120 + 120)/18 = 13 sec.   Answer: 13
Answer: B
It's Valentine's day and Alan has promised to cook his girlfriend Alana her favorite meal: fish fingers and custard. Alana will be arriving in one hour exactly. Alan only has a microwave. The fish fingers take 13 minutes to defrost in the microwave and 6 minutes to cook in the microwave. The custard must be prepared after the fish fingers and takes 24 minutes to cook in the microwave and then 6 minutes to cool sufficiently so as not to burn someone's tongue. It will take Alan 1 minute to plate the food. However, Alan is on his Xbox and really wants to play one more game of his football video game before Alana arrives. What is the maximum length of each half of the match that Alan can play to ensure the meal is ready for Alana's arrival?
Choose the correct choice from the following options.
A) 5 min B) 6 minutes C) 7 minutes D) 8 minutes E) 10 minutes

Solution: Alana will arrive in 60 minutes.   The total meal preparation time is 13 (fish finger defrost) + 6 (fish finger cook) + 24 (custard cook) + 6 (custard cool) + 1 (plate time) = 50 minutes.   Alan therefore has 10 minutes (60-50 = 10) to play his football video game.   5 mins football matches have two halves, 5 minlan have select 5 minute halves (10/2 = 5)   5 minNSWER: 5 min
Answer: A
If X-Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?	Choose the correct choice from the following choices.
A) -4.5.
B) -2.
C) -1.7.
D) -0.667.
E) 2.5.

Solution: X-Y = 2X-2Z   Y= -X+2Z---------- 1   X-2Y = 4Z   X-4Z= 2Y--------- 2   Adding equation 1 from equation 2   -2Z= 3Y   Y/Z= -0.667   -0.667. is the answer
Answer: D
In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 400. Find the average mark scored by all the three boys?
Choose the correct choice from the following options.
A) 384
B) 192
C) 207
D) 269
E) 208

Solution: Average mark scored by all the three boys =   [64/100 (400) + 36/100 (400) + 44/100 (400)] / 3   = 192   Answer: 192
Answer: B
A man buys an song for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is:
Pick one
A) <25
B) <10
C) >20
D) >30
E) <30

Solution: C   >20   Let the song be worth $x.   C.P. 90% of $x = $9x/10   S.P. = 110% of $x = $11x/10   Gain = (11x/10 - 9x/10) = $x/5   Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%
Answer: C
An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time B will it take to fill the bucket to full capacity? Pick:	A) 7/18	B) 9/18	C) 2	D) 18/7	E) 18/5

Solution: Solution -   Work and Time are directly proportional. W1/W2=T1/T2   7/10 work in 6 mins   1 work in T mins   (7/10)/1 = 6/T -> T = 60/7 mins.   Remaining minutes to fill the tank B= 60/7 - 6 = 18/7 mins. ANS 18/7.
Answer: D
The probability that a number selected at random from the first 100 natural numbers is a composite number is ?
Choices:
A) 2/3  B) 3/5  C) 3/4  D) 3/2  E) 5/2

Solution: Explanation:   The number of exhaustive events = 100 C₁ = 100.   We have 25 primes from 1 to 100.   Number of favourable cases are 75.   Required probability = 75/50 = 3/2.   Answer is 3/2
Answer: D
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
Choose the correct option.
A) 17 years B) 19 years C) 29 years D) 10 years E) 12 years

Solution: Let C's age be x years.   Then, B's age = 2x years.   A's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25 => x = 5   Hence, B's age = 2x = 10 years.   Answer: 10 years
Answer: D
If N = 2^0.20 and N^b = 16, b must equal  Choose the correct choice from the following choices
A) 3/80 B) 3/5 C) 20 D) 5/3 E) 80/3

Solution: 20/100 = 1/5   N = 2 ^ 1/5   N^b = 2^4   (2^1/5)^b = 2^4   b = 20   Answer: 20
Answer: C
A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? Choose one:
A) 27
B) 29
C) 40
D) 89
E) 22

Solution: 1/8 - 1/x = 1/10   x = 40   Answer: 40
Answer: C
Cole drove from home to work at an average speed of 30 kmh. He then returned home at an average speed of 90 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
Choose the correct choice from the following:
A) 66  B) 70  C) 72  D) 75  E) 90

Solution: Let the distance one way be x   Time from home to work = x/30   Time from work to home = x/90   Total time = 2 hrs   (x/30) + (x/90)= 2   Solving for x, we get x = 45   Time from home to work in minutes= (45)*60/30= 
(45)*60/30 = 90
90 minutes   Ans= 90
Answer: E
Five years ago, John’s age was half of the age he will be in 6 years. How old is he now? Select:  A) 14years  B) 15years  C) 16years  D) 17years  E) 18years

Solution: Let John=j,j-5=(j+6)/2,then j=16years   ANSWER:16years
Answer: C
Two trains of length 180 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?	Choose the correct choice from the following answers
A) 28	B) 266	C) 990	D) 20	E) 23

Solution: Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 180 + 280= 
180 + 280 = 460
460 m.   The time required= d/s = 460/20= 
460/20 = 23
23 sec.   Answer: 23
Answer: E
A trader bought a car at 30% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?  Choose the correct choice from the following options:
A) 118
B) 110
C) 112
D) 113
E) 98

Solution: Original price = 100   CP = 70   S = 70*(140/100)= 
70*(140/100) = 98
98   100 - 112= 2%   Answer: 98
Answer: E
If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true?
i. s>v
ii. u is not equal to v
iii. s > u  Answers
A) None B) I only C) II only D) III only E) I and III

Solution: Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers.   Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I and III is always true. As for II: it's not necessarily true, for example 4=2+2.   Answer: I and III
Answer: E
A team of five entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score? Choose the most appropriate option.
A) 288  B) 413  C) 168  D) 127  E) 664

Solution: Explanation:   5 * 84= 
5 * 84 = 420
420 - 7= 
420 - 7 = 413
413   Answer:413
Answer: B
A box contains eight bulbs out of which three are defective. If three bulbs are chosen at random, find the probability that all the three bulbs are defective?  Options:
A) 1/56  B) 1/22  C) 1/29  D) 1/36  E) 1/12

Solution: Out of eight, five are good and three are defective. Required probability   = 3C3/8C3   = 1/56   1/56nswer:1/56
Answer: A
The weight of a glass of jar is 40% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar?  Choose the most appropriate option:
A) 1/5 B) 1/3 C) 2/5 D) 1/2 E) 2/3

Solution: Let weight of jar filled with beans = 100 g   Weight of jar = 40 g   Weight of coffee beans = 60 g   Weight of jar and remaining beans = 60 g   Weight of remaining beans = 20 g   Fraction remaining = 20/60 = 1/3   Answer is 1/3.
Answer: B
The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr the distance travelled downstream in 12 minutes is :	Choose the correct choice from the following:  A) 2 km  B) 2.6 km  C) 3.6 km  D) 4 km  E) None

Solution: Sol.   Speed downstream = (15 + 3)= 
(15 + 3) = 18
18 kmph.   Distance travelled= [18 * 12/60= 
18 * 12/60 = 18/5 = around 3.6
3.6 km.   Answer 3.6 km
Answer: C
In a 1000 m race, A beats B by 60 m and B beats C by 100 m. In the same race, by how many meters does A beat C?	Choose the most appropriate option:  A) 154 m  B) 176 m  C) 268 m  D) 129 m  E) 218 m

Solution: By the time A covers 1000 m, B covers  (1000 - 60)= 
 (1000 - 60) = 940
940 m.   By the time B covers 1000 m, C covers  (1000 - 100)= 
 (1000 - 100) = 900
900 m.   So, the ratio of speeds of A and C=   1000/940 * 1000/900 = 1000/846 So, by the time A covers 1000 m, C covers 846 m.   So in 1000 m race A beats C by 1000 - 846= 
1000 - 846 = 154
154 m.   154 mnswer:154 m
Answer: A
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?  Choose the correct option:
A) 20 years
B) 21 years
C) 22 years
D) 23 years
E) 24 years

Solution: Explanation:   Let the average age of the whole team by x years.   11x – (26 + 29) = 9(x -1)   11x – 9x = 46   2x = 46   x = 23.   So, average age of the team is 23 years.   Answer 23 years
Answer: D
A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?	Pick:
A) Rs.7 B) Rs.4 C) Rs.9 D) Rs.3 E) Rs.2

Solution: 40*(40/100)= 
40*(40/100) = 16
16 --- 64   ? --- 12=> Rs.3   Answer: Rs.3
Answer: D
If (A+B) = 5, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?	Choose the correct choice from the following choices
A) 16.
B) 8.
C) 7.
D) 2.
E) -1.

Solution: Given A+B =5   B+C = 9   C+D = 3   (A+B)-(B+C)+(C+D)=(A+D)   => 5 - 9+3 = -1.   Option -1....
Answer: E
A club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly A new members into the club. If B is the number of new members brought into the club during the twelfth week, which of the following could be B?	Choices:
A) 5^1/12
B) 3^11 * 5^11
C) 3^12 * 5^12
D) 3^11 * 5^12
E) 60^12

Solution: At the end of the first week, there are 5 new members;   At the end of the second week, there are 5A new members (since each 5 new members from the previous week brings A new members);   At the end of the third week, there are 5A^2 new members (since each 5A new members from the previous week brings A new members);   ...   At the end of the twelfth week, there are 5A^11 new members (since each 5A^10 new members from the previous week brings A new members).   We are given that 5A^11=B. Out of the answers only D yields integer value for A: 5A^11=3^11 * 5^12 --> A=3*5= 
3*5 = 15
15.   Answer: 3^11 * 5^12.
Answer: D
Rita was running on a 500 metre track at a rate of 100 metres per minute. One minute after Rita started, Liz started running from the same starting point on the track at 150 metres per minute. What is the shortest time that Liz could run on the track in order to meet up with Rita?
Select:  A) 4 minutes  B) 3 minutes  C) 2 minutes  D) 1.6 minutes  E) 1 minute

Solution: we don't need to assume here the direction.we need to find which will take less time   so there are 2 cases   1)both moving in same direction...then time would be 2 minutes   2)both moving in opposite direction then time would be 1.6 minutes   as we need the shortest time it would be the second case   Answer:1.6 minutes
Answer: D
If 20 liters of chemical X are added to 80 liters of a mixture that is 25% chemical X and 75% chemical Y, then what percentage of the resulting mixture is chemical X?  Choose the correct choice from the following:
A) 28%
B) 32%
C) 36%
D) 40%
E) 44%

Solution: The amount of chemical X in the solution is 20 +0.25(80) = 40 liters.   40 liters / 100 liters = 40%   The answer is 40%.
Answer: D