MU-NLPC/Calc-aqua_rat huggingface dataset:
In measuring the sides of a rectangle, one side is taken 20% in excess and the other 10% in deficit. Find the error per cent in area calculated from the measurement?  Pick
A) 12% deficit
B) 10% excess
C) 8% excess
D) 9% excess
E) none of these

Solution: Since Side1 x Side2 = Area   Therefore, error% in area   = ( x + y + xy/100) %   = [20 - 10 + ( -10 x 20)/100]% or 8%   i.e., 8% excess   ANSWER:8% excess
Answer: C
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15%, in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007	Pick one:
A) 3436521
B) 3546577
C) 3546546
D) 7565643
E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 1083875   1083875
Answer: E
Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 7 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?
Choose the correct choice from the following choices
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: if n =8   mark sold 1 box   and Ann sold 6 boxes   total 7 < 8   Answer:8
Answer: E
The sum of the present ages of father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be?
Choose the correct choice.
A) 11 years B) 17 years C) 18 years D) 20 years E) 58 years

Solution: Let the present ages of son and father be x and (60 - x) years respectively.   Then, (60 - x) - 6 = 5(x - 6)   6x = 84 => x = 14   Son's age after 6 years = (x + 6) = 20 years.   Answer:20 years
Answer: D
Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $2,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?  Choose the correct choice:
A) 19,500
B) 24,500
C) 25,500
D) 26,500
E) 27,500

Solution: OFFICIAL SOLUTION:   The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 2,000), and Isabella’s are 0.10x. Set up the equation and solve:   550 + (0.08)(x – 2,000) = 0.10x   Distribute the 0.08:   550 + 0.08x – 160 = 0.10x   Combine terms and subtract 0.08x from both sides:   390 = 0.02x   Divide both sides by 0.02:   19,500 = x   Your answer is 19,500.
Answer: A
6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.  Choose the correct choice from the following answers:
A) 4 days  B) 6 days  C) 2 days  D) 8 days  E) 10 DAYS

Solution: Explanation :   Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b   Work done by 6 men and 8 women in 1 day = 1/10   => 6m + 8b = 1/10   => 60m + 80b = 1 --- (1)   Work done by 26 men and 48 women in 1 day = 1/2   => 26m + 48b = ½   => 52m + 96b = 1--- (2)   Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200   Work done by 15 men and 20 women in 1 day   = 15/100 + 20/200 =1/4   => Time taken by 15 men and 20 women in doing the work = 4 days   4 daysnswer : Option 4 days
Answer: A
C and D are tying water balloons for a party. 5 out of every 8 balloons that C ties does not pop, and 2 out of every 3 balloons that D ties does not pop. If they each tie 120 balloons, what fraction of the 240-pack will pop?
Choose the correct option:
A) 85/240 B) 70/240 C) 155/240 D) 140/240 E) 60/240

Solution: Ratio of 85/240's balloons that do not pop: 5/8   Ratio of B's balloons that do not pop: 2/3   Ratio of 85/240 and B's balloons that do not pop: 5/8+2/3=31/24   Total number of 85/240's and B's balloons that do not pop: 120x(31/24)=155/240   Fraction of balloons that pop: 1-155/240=85/240   85/240nswer is 85/240
Answer: A
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform?	Choose the most appropriate option
A) 229  B) 240  C) 288  D) 277  E) 320

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Length of the train= 20 * 20= 
20 * 20 = 400
400 m.   Let the length of the platform be x m . Then,   (x + 400)/36= 20 => x = 320 m.   Answer: 320
Answer: E
20 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?  Pick.
A) 32 B) 87 C) 40 D) 99 E) 77

Solution: 3W = 2M   20M ------ 21 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   20 * 21 * 8 = 14 * x * 6   x = 40   Answer: 40
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? Options: A) 27 B) 50 C) 27 D) 29 E) 12

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.   Answer: 50
Answer: B
A bag contains 3 white balls, 3 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
Choose the correct choice from the following answers:
A) 0.25	B) 0.15	C) 0.35	D) 0.45	E) 0.4

Solution: Each ball has an equal probability of being the third ball drawn.   P(3rd ball is red) = 4/10= 
4/10 = 2/5 = around 0.4
0.4   The answer is 0.4.
Answer: E
An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference V between the highest and the lowest incentive received by the 5 salesmen in the month?
Choose the most appropriate option:
A) $4000
B) $5000
C) $9000
D) $11,000
E) $13,000

Solution: Break down the question in to steps:   Step #1: incentives received by 5 salesmen -->abcde   Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de   Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000   Step #4: What is the difference between the highest and the lowest incentive:   - The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.   - The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.   - Therefore the first two numbers( ab) must equal 4, 000   - There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b   if a = 1,000 b = 3,000 --> difference V between the highest and the lowest incentive = 12,000 - 1,000 =11, 000   no other options for a or b to fit the criteria   Final List:1,0003,0007,00012,00012,000   Answer $11,000
Answer: D
If a is an even integer and b is an even integer and a > b which of the following must be an odd integer :
Choose the correct choice from the following answers:
A) a/b	B) ab	C) 2a+b	D) 2(a+b)	E) none of these

Solution: a= even = e.g 4   b= even = e.g 2   A. even/even for example   4/2= 
  4/2 = 2
2==> even   B. even * even = 4 * 2= 
4 * 2 = 8
8== >even   C. 2*even + even = even + even ===> even   D. 2(even + even) = 2(even) ===> even   Hence none of these it is.
Answer: E
A farm is made up of brown and white goats. the number of male brown goats is 35% less than the total number of brown goats. The total number of female goats is 20 times more than the number of female brown goats. If the total population of male goats is half the population of the female goats, what percentage of male goats are brown? Choose the correct choice from the following.
A) 30.1
B) 20.5
C) 15.2
D) 10.2
E) 28.6

Solution: Since we are dealing in percentage let us pick 100 as the number of brown male goats.   That means that the total number of brown goats is= 135 (number of male brown goats is 35% less than the total number of brown goats),   therefore the number of brown female goats is 35.   The total number of female goats is 15x the number of brown female goats= 35*20= 
35*20 = 700
700 female goats.   Male goats total population is half the population of the female goats= 700/2= 
700/2 = 350
350   Therefore percentage of male horses goats that are brown= 100/350*100=28.6   Correct option is 28.6
Answer: E
When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of T?	Choose the correct choice from the following options
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: A simple and elegant solution.   As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1   39-15= 
39-15 = 24
24   24 divide by 3 is 8.   Meaning mean of the n terms is 15+8= 39-16= 
39-16 = 23
23   Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.   T*23 +39= 25*(T+1)   T = 7   Ans. (7)
Answer: A
A circular well with a diameter of 2 metres , is dug to a depth of 8 metres. What is the volume of the earth dug out?  Select the correct option:
A) 32 m3
B) 25.1 m3
C) 40 m3
D) 44 m3
E) None

Solution: Solution   Volume	= πr2h   ‹=› (22 /7 ×1×1×8)m3   ‹=›25.1 m3.   Answer 25.1 m3
Answer: B
0.0002152/0.000205 x 12.05=?  Choose the most appropriate option
A) 19.64	B) 14.64	C) 12.6	D) 15.64	E) 13.64

Solution: Explanation :   ? = 0.0002152/0.000205 x 12.05 = 12.6   Answer : Option 12.6
Answer: C
In how many ways can 22 books on English and 20 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?	Choose the correct choice from the following choices.
A) 4586
B) 5896
C) 2415
D) 1771
E) 1881

Solution: In order that two books on Hindi are never together, we must place all these books as under:   H E H E H E H….. H E H   Where H denotes the position of Hindi book and E that of English book.   Since there are 22 books on English, the number of places marked E are 23.   Now, 20 places out of 23 can be chosen in 23C20 = 23C3 = 23*22*21   3*2*1   = 1771 ways.   Hence the number of ways = 1771 ways   ANSWER:1771
Answer: D
A math teacher has 24 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
Choose the correct choice
A) 7 B) 10 C) 11 D) 12 E) 13

Solution: a square is a special kind of rhombus (sides are perpendicular)   a square is a special kind of rectangles (sides with same length)   Among the 24 cards with have:   15 rectangles   10 rhombus   8 squares   Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.   Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.   We have 8 squares.   So the minimum different cards that represent a square, a rhombus or a rectangle is   2 + 7 + 8= 
  2 + 7 + 8 = 17
17   Which means that the maximum number of circles that you could have is  24 - 17= 
 24 - 17 = 7
7   7nswer (7)
Answer: A
Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 54 meter head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him? Answers.
A) 15 seconds B) 18 seconds C) 25 seconds D) 27 seconds E) 45 seconds

Solution: used pluging in method   say t is the time for cristina to catch up with Nicky, the equation will be as under:   for Nicky=N=3*t+54   for Cristina=C=5*t   @t=27, N=135 C=135 right answer   ans:27 seconds
Answer: D
Shop Offered 30% offer for every Shirt, Smith bought a shirt at Rs. 560. and What was the shop's original selling Price?  Choose the correct choice from the following options:
A) 500	B) 800	C) 600	D) 700	E) 750

Solution: SP* (70/100) = 560   SP= 8 * 100 => CP = 800   Answer:800
Answer: B
Dimitri weighs x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of 3y-y pounds. Which of the following represents Allen’s weight? Choose the correct choice from the following:	A) y - x/2	B) 2x - y/2	C) (y - x)/2	D) y - 2x	E) 2x - y

Solution: These type of multi-variable story problems are usually perfect for TESTing VALUES.   Here, we're told that Dimitri weighs X pounds more than Allen weighs and that they weight a combined TOTAL of 3Y-2Y or Y pounds.   IF....   Dimitri = 30   Allen = 20   X = 10   Y = 50   We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.   Answer A:  50 - (10/2)= 
 50 - (10/2) = 45
45 NOT a match   Answer B: 20 - (50/2)= -5 NOT a match   Answer (y - x)/2: (50-10)/2 = 20 This IS a match   Answer D:   50 - 20= 
  50 - 20 = 30
30 NOT a match   Answer E: 20 - 50= -30 NOT a match   Final Answer:   (y - x)/2
Answer: C
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:	Choose the correct choice from the following answers.
A) Rs. 3900 B) Rs. 3990 C) Rs. 4000 D) Rs. 4100 E) Rs. 4200

Solution: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.   Then, 10x = 4y or y = 5 x.   2   15x + 2y = 4000   15x + 2 x 5 x = 4000   2   20x = 4000   x = 200.   So, y = 5 x 200 = 500.   2   Hence, the cost of 12 chairs and 3 tables = 12x + 3y   = Rs. (2400 + 1500)   = Rs. 3900.   Rs. 3900
Answer: A
24 oz of juice P and 25 oz of juice V are mixed to make smothies E and Y . The ratio of p to V in smothie E is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie E?
Choose the correct choice from the following answers.
A) 5 B) 10 C) 15 D) 20 E) 25

Solution: The ratio of p to V in smothie E is 4 is to 1 and that in Y is 1is to 5. p1 + p2 = 24   v1 + v2 = 25   p1 = 4v1   p2 = v2/5   4v1 + v2/5 = 24   v1 + v2 = 25   4v2 - v2/5 = 76   19v2/5 = 76 => v2 = 20   => v1 = 5   => p1 = 20   Answer - 20
Answer: D
Jane and Ashley take 20 days and 10 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?	Choose the correct choice from the following choices.
A) 12 Days B) 15 Days C) 16 Days D) 18 Days E) 20 Days

Solution: Let us assume that the work is laying 40 bricks.   Jane = 2 bricks per day   Ashley = 4 brick per day   Together = 6 bricks per day   Let's say first 8 days Ashley works alone,   No of bricks = 32   Last 4 days Jane works alone,   No. of bricks = 8   Remaining bricks = 40 - 40= 
40 - 40 = 0
0   So together, they would take   0/6= 
  0/6 = 0
0   Total no. of days= 8 + 4 + 0= 
8 + 4 + 0 = 12
12   12 Daysnswer is 12 Days
Answer: A
Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 50,000 after completion of one year. What will be Madhu's share of profit?  Options:	A) Rs. 27,000	B) Rs. 24,000	C) Rs. 25,000	D) Rs. 36,000	E) None of these

Solution: 30,000 *12=45,000*8   1:1   Madhu's share=1/2*50,000   i.e. Rs. 25,000   ANSWER:Rs. 25,000
Answer: C
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? Choose the correct option
A) 9:32	B) 9:31	C) 9:33	D) 9:39	E) 9:12

Solution: 1/4 : 3/4 = (1:3)5 = 5:15   1/5 : 4/5 = (1:4)4 = 4:16   ------   9:31   Answer: 9:31
Answer: B
In how many different number of ways 4 man and 2 woman can sit on a bench?  Pick.
A) 600	B) 620	C) 640	D) 660	E) 720

Solution: npn = n!   6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720   720)
Answer: E
A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $3.00, what total number of pens and pencils did the customer purchase?	Choose the correct choice from the following
A) 8  B) 9  C) 10  D) 11  E) 12

Solution: Answer: Algebraically, the question looks like this: 3.0 = 0.35x + 0.25y   There are six possible numbers of pens that fit that requirement:   1 pen: $0.35   2 pens: $0.70   3 pens: $1.05   4 pens: $1.40   5 pens: $1.75 balance 1.25   5 pencils cost $1.25   That's 5 pens and 5 pencils 10hoice (10) is correct.
Answer: C
A 240 meter long train crosses a man standing on the platform in 4 sec. What is the speed of the train?	Choose the correct option:
A) 176 kmph
B) 108 kmph
C) 216 kmph
D) 134 kmph
E) 161 kmph

Solution: S = 240/4 * 18/5= 
240/4 * 18/5 = 216
216 kmph   Answer: 216 kmph
Answer: C
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Choose the correct choice from the following answers
A) 59028  B) 27777  C) 29999  D) 59000  E) 27772

Solution: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.   Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (2500 + 18000 + P) = 2(P)   P = 20500   Total profit = 2P + 18000   = 2*20500 + 18000= 
2*20500 + 18000 = 59_000
59000.Answer:59000
Answer: D
If f(x) = 6x^4 - 4x^3 - 3x^2 + 6x , then f(-1) =
Pick one:
A) -2
B) -1
C) 0
D) 1
E) 2

Solution: f(-1) = 6(-1)^4 - 4(-1)^3 - 3(-1)^2 + 6(-1) = 6+4-3-6= 
6+4-3-6 = 1
1   The answer is 1.
Answer: D
You enter a weight loss challenge game and manage to lose 11% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in?  Choose the correct option:
A) 13% B) 9.22% C) 9% D) 14% E) 12%

Solution: (100%-11%)*(100%+2%) = 0.89*1.02 = 9.22%   The weigh in records your weight loss at 9.22%!   The Answer is 9.22%
Answer: B
Find the arithmetic mean A of all roots of the following equation- see an attachment.	Choose the correct answer: A) 2 B) 1 C) 0.5 D) -1/3 E) 0.3

Solution: Arithmetic mean A your answer C and E are same, can you correct one of them please. thanks.0.5
Answer: C
In an election, candidate Douglas won 58 percent of the total vote in Counties X and Y. He won 64 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y?  Choose the correct choice from the following answers
A) 15%	B) 18%	C) 25%	D) 36%	E) 46%

Solution: given voters in ratio 2:1   let X has 200 votersY has 100 voters   for X 64% voted means 64*200=128 votes   combined for XY has 300 voters and voted 58% so total votes =174   balance votes=174-128= 
174-128 = 46
46   As Y has 100 voters so 46 votes means 46% of votes required   Ans 46%
Answer: E
Evaluate: 40 - 10÷2×2 = Choices:
A) 20
B) 25
C) 10
D) 16
E) 30

Solution: According to order of operations, 10÷2×2 (division and multiplication) is done first from left to right   10÷2×2 = 5 × 2 = 10   Hence   40 - 10÷2×2 = 40 - 10= 
40 - 10 = 30
30   correct answer 30)30
Answer: E
Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $100 per month and Plan B costs $200 per month per customer. If the company’s average revenue per customer per month is $150, then what percent of the company's revenue comes from customers with Plan A?	Choose the most appropriate option:  A) 25%  B) 30%  C) 37.5%  D) 56.25%  E) 75%

Solution: We can show this algebraically:   If there are A customers with plan A, and B customers with plan B, then the total revenue is $100A + $200B.   Since the average customer pays $75, we know that   $150 = ($100A + $200B) / (A + B)   $150(A + B) = ($100A + $200B)   $150A + $150B = $100A + $200B   $50A = $50B   A = B.   Since there are Equal times as many $100 clients as $200 clients, for every $200 received from Plan B customers, $100 is received from Plan A customers, and the percent of revenue from customers with Plan A is:   $100/($100 + $200) = $100/$300 = 30%.   Answer 30%
Answer: B
Oil is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour. If the empty rectangular tank is 9 feet long, 8 feet wide, and 5 feet deep, approximately how many hours does it take to fill the tank? Choices.
A) 60 B) 70 C) 80 D) 90 E) 100

Solution: The volume the tank is: length*width*depth = 9*8*5= 
9*8*5 = 360
360 cubic feet.   360 cubic feet / 4 cubic feet per hour= 90 hours.   It will take 90 hours to fill the tank.   The answer is 90.
Answer: D
Divide 675 to A and B in ratio 5:4.  Choose the correct choice from the following choices:
A) 400,275  B) 300,375  C) 325,350  D) 375,300  E) 350,325

Solution: Addition of ratio no.=9   Part of A=[675×5/9]=375 and part of B=[675×4/9]=300   Answer 375,300
Answer: D
A teacher gave the same test to three history classes: K, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Choose the correct choice from the following:	A) 74	B) 75	C) 76	D) 77	E) 78

Solution: Ans : B (75)   lets say class K indeed has 4 children, B has 6 children and C has 5 children.   now, if the average of class K is 65, hence total marks awarded in the class = 65*4= 
65*4 = 260
260   Similarly,   class B= 80*6= 
80*6 = 480
480   class C= 77*5= 
77*5 = 385
385   total marks provided= K+B+C = 260+480+385= 
260+480+385 = 1_125
1125   avg. marks= 1125 / 15 (total no. of students) = 75=75
Answer: B
Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution Q in the liquid in the tank after 3 minutes?  Choose the correct choice from the following options
A) 1/11	B) 2/11	C) 3/11	D) 4/11	E) 5/11

Solution: Part filled by (A + B + 3/11) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20   Part filled by B in 3 minutes = 3/20   Required ratio = 3/20 * 20/11 = 3/11   Answer:3/11
Answer: C
If m is the average (arithmetic mean) of the first 10 positive multiples of 6 and if M is the median of the first 10 positive multiples of 6, what is the value of M – m ?
Choose the correct choice from the following options: A) –5 B) 10 C) 5 D) 0 E) 27.5

Solution: The first 10 positive multiples of 6 is an evenly spaced set. One of the most important properties of evenly spaced set (aka arithmetic progression) is:in any evenly spaced set the arithmetic mean (average) is equal to the median.   Hence M=m --> M-m=0.   Answer: 0.
Answer: D