MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 60 km apart both 3 and 6 hours after start, then find the distance between the two stations. Choose the correct choice from the following:  A) 240 km  B) 200 km  C) 220km  D) 180km  E) 210km

Solution: In first 3 hours T1 travels R km and T2 travels S km.   After 6 hours they traveled R+S+60+ 60   2(R+S ) = R+S +120   R+S = 120   Hence distance between XY is R+S+ 60 = 120 +60 =200   Answer : 200 km
Answer: B
A boat can travel with a speed of 25km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 90km downstream. Choices.
A) 1 hr	B) 2 hrs	C) 3 hrs	D) 4 hrs	E) 5 hrs

Solution: Speed downstream = (25 + 5) km/hr = 30 km/hr.   Time taken to travel 90 km downstream = 90/30= 
90/30 = 3
3 hrs.   Answer : 3 hrs
Answer: C
An incredible punch is composed of mango, orange juice, and milk. How many pints of orange juice are required to make 9 gallons of punch containing twice as much mango as orange juice and three times as much orange juice as milk? (1 Gallon = 8 Pints )
Select the correct option
A) 13 pints  B) 7.2 pints  C) 5 pints  D) 12 pints  E) 6.5 pints

Solution: 1 gallon=8 pints   9 gallons=72   mango=2 orange   orange=3 milk   mango+orange+milk=72   2 orange+orange+1/3 orange=72   10 orange=72   orange=7.2pints   Answer 7.2 pints
Answer: B
If a man can cover 12 metres in 0ne second, how many kilometres can he cover in 3 hours 45 minutes?  Pick.
A) 132 km
B) 167 km
C) 143 km
D) 162 kilometres
E) 245 km

Solution: 162 kilometres   12 m/s = 12 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   162 kilometresistance = speed * time = 12 * 18/5 * 15/4= 
12 * 18/5 * 15/4 = 162
162 km.
Answer: D
John has on his shelf four books of poetry, two novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?	Pick
A) 1/2
B) 2/5
C) 4/45
D) 7/20
E) 8/45

Solution: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 2/10*2/9 + 2/10*2/9 = 4/45.   Answer: 4/45
Answer: C
Ajay can ride 50km in 1 hour. In how many hours he can ride 900km? Pick:	A) 10hrs	B) 15hrs	C) 20hrs	D) 25hrs	E) 18hrs

Solution: 1 hour he ride 50km   he ride 900km in = 900/50 * 1= 
900/50 * 1 = 18
18hours   Answer is 18hrs
Answer: E
A window 2 inches wide is placed on the back of a rectangular painted area with dimensions 8 inches by 12 inches. What is the area of the window, in square inches? Choose the correct option:
A) 44
B) 96
C) 128
D) 144
E) 168

Solution: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.   We're told that a window 2 inches wide is placed around a rectangular painted area with dimensions 8 inches by 12 inches. We're asked for the area of the window, in square inches.   Area of a rectangle = (length)(width)   So the area of the window is... (8)(12) = 96   The window 'adds' 2 inches to the top, bottom, left and right 'sides' of the painted area, so the area of EVERYTHING is...   (8+2+2)(12+2+2) = (12)(16) = 196   When we 'punch out' the area of the painted area, we'll be left with the area of the window:    192 - 96= 
 192 - 96 = 96
96   Final Answer:   96
Answer: B
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is: Select.
A) 50 m
B) 72 m
C) 80 m
D) 82 m
E) 84 m

Solution: Let the length of each train be x metres.   Then, distance covered = 2x metres.   Relative speed = (46 - 36) km/hr   (10 x (5/18) ) m/s = 25/9 m/s   2x/36 = 25/9   2x=100   x=50   50 mNSWER:50 m
Answer: A
X and Y invest Rs.12500 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?	Options:
A) Rs.14400
B) Rs.26400
C) Rs.11000
D) Rs.12500
E) Rs.13500

Solution: Ratio of the investment=12000:17500=5:7   Share of X in the profit=(26400×5)/12=11000   ANSWER:Rs.11000
Answer: C
The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 302 to 400 inclusive?
Options:  A) 11,550  B) 14,550  C) 17,550  D) 20,550  E) 23,550

Solution: 2 + 4 + 6 + 8 +...+ 100 = 2550   302 + 304 + ... + 400 = 50(300) + (2+4+...+100) = 15,000 + 2550 = 17,550   The answer is 17,550.
Answer: C
If Janice was 24 years old z years ago and Lisa will be 22 years old in p years, what was the average (arithmetic mean) of their ages 6 years ago?	Choose the correct option: A) (z + p)/2 B) (z - p + 34)/4 C) (z - p + 24)/4 D) (z + p + 44)/2 E) (z - p + 34)/2

Solution: Today, J = z+24 and L = 22-p   6 years ago, J = z+18 and L = 16-p   The average of their ages was (z-p+34) / 2   The answer is (z - p + 34)/2.
Answer: E
A train 225 m long passes a man, running at 10km/hr in the same direction in which the train is going, in10 seconds. The speed of the train is:
Pick:
A) 81	B) 90	C) 91	D) 85	E) 96

Solution: Speed of the train relative to man =225/10 m/sec   =45/2m/sec.   =45/2x18/5km/hr   = 81 km/hr.   Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.   x - 10 = 81 =91km/hr.   Answer:91
Answer: C
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 4 different offices? Choose one:
A) 52
B) 64
C) 32
D) 11
E) 12

Solution: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 4*4*4=4^3=64.   Answer: 64.
Answer: B
If Janice was 22 years old z years ago and Lisa will be 20 years old in p years, what was the average (arithmetic mean) of their ages 7 years ago?	Select the correct option.
A) (z + p)/2 B) (z - p + 28)/4 C) (z - p + 18)/4 D) (z + p + 38)/2 E) (z - p + 28)/2

Solution: Today, J = z+22 and L = 20-p   7 years ago, J = z+15 and L = 13-p   The average of their ages was (z-p+28) / 2   The answer is (z - p + 28)/2.
Answer: E
It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn	Answers.
A) 16  B) 45  C) 36  D) 20  E) 90

Solution: 1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min..   only A and B are left..   if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins..   ans 20 20
Answer: D
The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $2.00 in 1970 was 150 percent of its price in 1960, what was its price in 1980?  Choose the most appropriate option
A) a) $ 1.80
B) b) $ 2.00
C) c) $ 2.40
D) d) $ 2.70
E) e) $ 3.00

Solution: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).   Therefore the price in 1980 = $2.0*1.5 = $3.00.   Answer: e) $ 3.00.
Answer: E
What will come in place of the x in the following Number series? 12, 38, 116, 350, x
Choose the correct answer
A) 1052
B) 5464
C) 3456
D) 7554
E) 3158

Solution: 12   12 Ã— 3 + 2 = 38   38 Ã— 3 + 2 = 116   116 Ã— 3 + 2 = 350   350 Ã— 3 + 2 = 1052   1052
Answer: A
Machine A and machine G are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine G. Machine G produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?  Select the correct option.
A) 6
B) 6.6
C) 60
D) 100
E) 110

Solution: [Reveal]Spoiler:   TimeG: 660/x   Time6: [660/x+10]   660/x = [660/x+10] *110/100   660/x =66*11/x+10   660x+10= 66*11*x   660x +6600 = 66*11*x   x= 100   plug in back to time6   660/100+10 => 660/110= 
660/110 = 6
6
Answer: A
350 is increased by 50%. Find the final number.  Choose one.
A) 725  B) 625  C) 225  D) 525  E) 425

Solution: ExplanationFinal number = Initial number + 50%(original number) = 350 + 50%(350) = 350 + 175= 
350 + 175 = 525
525.Answer 525
Answer: D
If f(x) = 12 - x^2/2 and f(2k) = 5k, what is one possible value for k? Choose the correct choice from the following answers
A) 2 B) 3 C) 4 D) 5 E) 8

Solution: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.   We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be  12 - 4/2= 
 12 - 4/2 = 10
10.   So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:   f(2k)= 12 - (2k)^2/2 = 12 - 2k^2.   Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.   12 - 2k^2 = 2k --> k = -3 or k =5.   All the answers are positive, so we choose k = 5.   Answer =5
Answer: D
A card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart?  Choose the correct choice
A) 8/58  B) 9/25  C) 1/26  D) 6/25  E) 8/45

Solution: here n(s)=52   let E be the event of getting queen of the club or king of kings   n(E)=2   p(E)=n(E)/n(S)=2/52=1/26   Answer(1/26)
Answer: C
A reduction of 40% in the price of oil enables a house wife to obtain 8 kgs more for Rs.2400, what is the reduced price for kg?
Choose the correct choice from the following answers.
A) Rs.120  B) Rs.125  C) Rs.130  D) Rs.135  E) Rs.140

Solution: Explanation:   2400*(40/100)= 
2400*(40/100) = 960
960 ---- 8   ? ---- 1=> Rs.120   Rs.120nswer: Rs.120
Answer: A
Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1200. What is the gain or loss in percentage?	Choices.
A) 10%	B) 22%	C) 25%	D) 20%	E) None of these

Solution: Explanation:   As selling price is Rs.1200 for 10 bags, each bag is sold at Rs.120.   Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 120 = Rs.220.   %profit = 220/1000 *100= 
220/1000 *100 = 22
22%   ANSWER 22%
Answer: B
I. x + 2y + 3z = 2
II. x + y - z = 0
III. 2x + 2y - z = 1
What is the value of y in the system above? Choose the correct choice from the following options
A) -2  B) -1  C) 0  D) 1  E) 2

Solution: 1. from the given system of equations i can make equation II. to be x + y = z   2. now put that in III. :   2x + 2y - (x + y) = 1   = 2x + 2y - x - y = 1   = x + y = 1   that gives usz = 1!   3. put z = 1 in I. and solve:   x + 2y + 3 = 2; calculate minus 3   = x + 2y = -1; calculate minus x   =2y = -1 - x;   4. now put 2y = -1 - x in III. and solve:   2x + (-1 - x) - 1 = 1   = x - 2 = 1; calculate plus 2   that gives usx = 3   5. now solve for y with x = 3 and z = 1:   x + y = 1   = 3 + y = 1; calculate minus 3   that gives y = -2, and hence answer (-2) -2
Answer: A
Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 47 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 53 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?  Select the correct option:
A) 19 B) 28 C) 30 D) 33 E) 44

Solution: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 47 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 53 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?   40 floors/100 floors per minute=2/5 minutes   11+57/3=33   51-63/3=33   Answer : 33
Answer: D
A tap can fill the tank in 15 minutes and another can empty it in 8 minutes. If the tank is already half full and both the taps are opened together, the tank will be:
Choose the correct answer:
A) filled in 12 min  B) emptied in 12 min  C) filled in 8 min  D) will be empty in 8 min  E) emptied in 10 min

Solution: work done by both taps= 1/15+(-1/8)= -7/120 so tank will be emptied becoz of minus sign.   so time taken= 120/7   given the tank is already half filled   so another half will be emptied in 120/7*1/2   nearly 8 minutes   ANSWER:will be empty in 8 min
Answer: D
For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 231 books with me to gift her.
Can you calculate, on which day is our anniversary?  Options:
A) 31 B) 28 C) 23 D) 21 E) 25

Solution: D   21rd day   1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21= 
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 231
231   Thus our anniversary falls on the 21rd day of the month.   You can apply other formulas to shorten the process but that is the simplest way to do it.
Answer: D
After M students took a test, the average score was 56%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 60%? Answers.
A) M + 30 B) 0.56M + 30 C) M + 28 D) 2M + 28 E) 2M + 30

Solution: The total number of correct answers for M students is (0.56)*50*M=28*M   For an average of 75%: (total correct answers) / (M+1) = 0.6*50= 
0.6*50 = 30
30   Let x be the number of correct answers for the next student.   (x + 28M) / M+1= 30   x + 28M= 30M+30   x = 2M + 30   The answer is 2M + 30.
Answer: E
A company has two models of computers, model X and model Y. Operating at a constant rate, a model X computer can complete a certain task in 72 minutes and a model Y computer can complete the same task in 36 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model X computers were used?	Choose the correct choice
A) 22	B) 23	C) 24	D) 25	E) 26

Solution: Let's say 1 work is processing 72 gb of data.   Model X : 1 gb per min   Model Y : 2 gb per min   Working together, 1 X and 1 Y = 3 gb per min   So, 24 times as many computers would work at 72 gb per min.   So no. of X =24   Answer is 24
Answer: C
Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?	Choose the correct choice:
A) 1/4 B) 1/5 C) 5/26 D) 12/42 E) 13/42

Solution: Desired outcomes= 13   Total outcomes= 52   Probability of getting any card as the heart card= 13/52= 1/4   And the same probability will be for 10th card as well.   1/4 is the answer
Answer: A
Find the area of the sector whose are is making an angle of 90° at the center of a circle of radius 3.2 Cm.	Choose the correct choice:
A) 56.72 Sq.Cm
B) 56.22 Sq.Cm
C) 56.82 Sq.Cm
D) 56.42 Sq.Cm
E) 56.32 Sq.Cm

Solution: Area of the sector = 90/360 × πr(power)2   = 90/360 × 22/7 × 3.2 × 3.2   = (11 × 10.24)/2 = 112.64/2= 
112.64/2 = 56.32
56.32 Sq.Cm   Answer is 56.32 Sq.Cm.
Answer: E
If P = Q-R, -1 < R < 0 and Q=0, which of the following is correct?	Choose the correct option:  A) P < -1.  B) 0 < P <2  C) P > 0  D) 0 < P <4  E) P < -20

Solution: Q is 0 & R is -ve   For min. value max. numerator and minimize denominator   take Q=0 & R=-0.9   P=0-(-0.9)   P > 0   Ans P > 0
Answer: C
Approximately what percentage of the world’s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world’s 8.076 billion hectares of forested land.	Choose the most appropriate option.
A) 0.0066%  B) 0.066%  C) 0.66PERCENT  D) 6.6%  E) 66%

Solution: Approximation is a strategy that helps us arrive at less than an exact number and the inclusion in this problem of the word “approximately” is an obvious clue. First, 8.076 billion is 8,076 million. Next, 8,076 million rounds to 8,000 million and 53.42 million rounds to 53 million. Dividing 53 million by 8,000 million we arrive at 0.0066 (53M/8,000M). We convert this decimal figure to a percentage by multiplying by 100 (or moving the decimal point two places to the right) and adding a percent sign in order to obtain our answer of 0.66%. Note that the shortcut method involves comparing 53 million to 1% of 8,000 million or 80 million. Since 53 million is approximately two-thirds of 80 million then the answer is some two-thirds of 1% or 0.66%.   Answer: 0.66PERCENT.
Answer: C
Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers?	Choose the most appropriate option
A) 7 hours and 30 minutes. B) 8 hours and 30 minutes. C) 9 hours and 30 minutes. D) 3 hours and 30 minutes. E) 4 hrs and 30 min

Solution: The time it takes Kim to walk 18 kilometers is equal to     18 / 4= 
  18 / 4 = 9/2 = around 4.5
4.5 hours= 4 hours + 0.5 * 60 minutes   = 4 hours and 30 minutes.   correct answer 4 hrs and 30 min
Answer: E
If y = 2 + 2K and y≠0y≠0, then 2/y + 1/y + 1/y + 1/y = ? Pick one.
A) 1/(8+8k) B) 5/2(1+k) C) 1/(8+k) D) 4/(8+k) E) 4/(1+k)

Solution: 2/Y + 1/Y + 1/Y + 1/Y   = 5/Y   = 5/(2 + 2K)   = 5/2(1 + K)   ANSWER:5/2(1+k)
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train? Choose the correct choice from the following choices.
A) 27 7/9  B) 27 7/6  C) 27 7/2  D) 27 7/9  E) 27 7/1

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.   Answer:27 7/9
Answer: D
P, Q, R enter into a partnership. P initially invests 25 lakh and adds another 10 lakh after one year. Q initially invests 35 lakh and withdraws 10 lakh after 2 years. R's investment is Rs 30 lakh. In what ratio should the profit be divided at the end of 3 years?	Options: A) 19:18:19 B) 18:19:19 C) 19:17:18 D) 19:19:18 E) 17:18:19

Solution: P : Q : R   =(25×1+35×2):(35×2+25×1) :(30×3)   =95:95:90=19:19:18   Answer is 19:19:18.
Answer: D
The sale price of a trolley bag including the sale tax is Rs. 1232. The rate of sale tax is 10% . If the shopkeeper has made a profit of 12%, the cost price of the trolley bag is:	Choose the correct choice from the following answers:
A) Rs 1000 B) Rs 1515 C) Rs 1525 D) Rs 1250 E) None of these

Solution: Explanation :   110% of S.P. = 1232   S.P. = Rs.(1232 x 100/110) = Rs.1120.   C.P. = Rs (100/112 x 1120) = Rs 1000   Rs 1000nswer : Rs 1000
Answer: A
Vishal and Raghu jointly started a business. Vishal invested three times as Raghu did and invested his money for double time as compared to Raghu. Raghu earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?  Choose the correct choice from the following answers
A) 28,000 B) 28,129 C) 28,109 D) 28,009 E) 28,011

Solution: Investments ratio is = 3:1   Time period ratio is = 2:1   As they are proportional to gain   ------   Gain ratio of Vishal and raghu = 6:1   But given Raghu got Rs. 4000,   =? 1 ----- 4000   7 ----- ?   => Rs.28,000   The total gain = Rs.28,000   28,000nswer: 28,000
Answer: A
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a grey cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible? Options:
A) 150	B) 160	C) 200	D) 180	E) 240

Solution: # ways to distribute Blue marbels(3) is :   1 in each cup= 1   2 in one cup and 1 in other=6   all 3 in one cup = 3   total 1+6+3= 
1+6+3 = 10
10 possibilities   # ways to distribute Red marbels(2) is :   1 in each cup= 3 ways   all in one cup = 3ways   total 6ways.   # ways to distribute Green marbels(1) is :   3 ways   total number of ways = 10*6 *3= 
10*6 *3 = 180
180   180
Answer: D
The diameter of two circles are 18 cm and 8 cm. The distance between their centres is 13 cm. What is the number of common tangents?  Pick one.
A) 3 B) 2 C) 1 D) 5 E) 7

Solution: 3   3   Here, r1 = 9 cm and r 2 = 4 cm   r 1 + r 2 = 9 + 4= 
9 + 4 = 13
13 cm   and r 1 – r 2= 9 – 4 = 5cm   3lso, d = 13 cm   Here, d = r 1 + r 2   = 13 cm   Hence, two circles touch each other externally, so three total no of common tangents are three.
Answer: A
It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010? Choose the correct answer
A) Sunday B) Sarurday C) Friday D) Wednesday E) Monday

Solution: Explanation:   On 31st December, 2005 it was Saturday. Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1)= 
(1 + 1 + 2 + 1) = 5
5 days. On 31st December 2009, it was Thursday. Thus, on 1st Jan, 2010 it is Friday.   Answer: Friday
Answer: C
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Pick
A) 752	B) 799	C) 719	D) 750	E) 712

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 25 è x = 25 * 60 / 2= 
25 * 60 / 2 = 750
750   Answer: 750
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?  Pick one.
A) 100	B) 130	C) 150	D) 170	E) 160

Solution: Speed=(60x5/18)m/sec = (50/3) m/sec.   Length of the train = (Speed x Time).   Length of the train = (50/3 x 6)m = 100 m.   100nswer is 100.
Answer: A
Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 10 percent sulfuric acid, approximately how many liters of the 12 percent solution will be required?
Answers.
A) 18 B) 20 C) 48 D) 36 E) 42

Solution: let a=amount of 2% acid and b= amount of 12% acid.   Now, The equation translates to,   0.02a + .12b = .1(a+b)   but a+b= 60   therefore .02a + .12b = .1(60)   => 2a + 12b = 600   but b=60-a   therefore   2a+ 12(60-a) = 600   => 10a = 120   hence a = 12. b = 60 -12= 
60 -12 = 48
48.   Answer : 48
Answer: C
If after successive discounts of 20% and 25/4% on the marked price of an article, a trader gets 20% profit on the cost price,then by what percent is the marked price above the cost price?
Choose the correct option:
A) 50%	B) 60%	C) 70%	D) 80%	E) 90%

Solution: Let the market price be RS 100. Then after first discount S.P becomes 80 and after another discount it becomes Rs. 75.   so S.P = 75. now with this S.P he has made a profit of 20% and hence the   C.P = (75/120)*100= 
(75/120)*100 = 125/2 = around 62.5
62.5   so percentage change with respect to market price is= (37.5/62.5)*100   giving 60%   ANSWER:60%
Answer: B
When 30 is divided by the positive integer k, the remainder is 6, for how many different values of k is this true?  Pick one.
A) 2 B) 3 C) 5 D) 7 E) 8

Solution: When 30 is divided by k, remainder is 6 i.e. there are 6 balls leftover after grouping. so k must be greater than 6.   It also means that 30 is completely divisible by k.   Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24   Out of these, k can be 4, 6, 8, 12, 24.   Answer (5)
Answer: C