MU-NLPC/Calc-aqua_rat huggingface dataset:
A cubical block of metal weighs 3 pounds. How much will another cube of the same metal weigh if its sides are twice as long?  Choose the correct choice from the following
A) 48	B) 32	C) 24	D) 18	E) 12

Solution: For example our cube have a side 1 meter, so we have 1 cubical meter in this cube   and this cubical meter weigth 3 pounds   If we take cube with side 2 meters we will have 8 cubical meters in this cube   8 meters * 3 pounds = 24 pounds   So answer is 24   And similar but more theoretical approach:   if we have sides a and b than they have equal ration with their areas:   a/b = a^2/b^2   and they have equal ration with their volumes:   a/b = a^3/b^3   we have two sides 1/2 so their volume will be in ratio 1/8   weight of one cube * volume of another cube     3 * 8= 
  3 * 8 = 24
24   So answer is 24
Answer: C
If a, b, t are integers, 33 = abt, and a < b < t, what is the smallest possible value of a? Options:
A) -33
B) -3
C) 1
D) 3
E) 11

Solution: Given : a * b * t = 33.   33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.   Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).   We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.   -33 * -1 * 1= 
-33 * -1 * 1 = 33
33.   Correct answer is -33
Answer: A
For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.
Choose the correct choice.
A) 9	B) 18	C) 27	D) 36	E) 45

Solution: f(x) = -3(x - 10)(x - 4) = -3x2*square* + 42x - 120 : expand and obtain a quadratic function   h = -b/2a = -42/-6= 
-42/-6 = 7
7 : h is the value of x for which f has a maximum value   f(h)= f(7) = 27 : maximum value of f.   correct answer 27
Answer: C
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 ? Options.
A) 1 : 1	B) 2 : 1	C) 2 : 3	D) 3 : 2	E) 1 : 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: D
The ratio between the speeds of two trains is 5: 6 If the second train runs 540 kms in 6 hours, then the speed of the first train is  Choose the most appropriate option:  A) 90 km/h  B) 60 km/h  C) 45 km/h  D) 80 km/h  E) 75km/h

Solution: 75km/h   75 km/h
Answer: E
If -1 < h < 3, which of the following has the greatest value?	Select.
A) a) 1-h
B) b) 1+h
C) c) 1+h^2
D) d) 1-1/h
E) e) 1-1/(h^2)

Solution: easiest way of solving this would be to substitute a value.   lets say h= - 1/2   a) 3/2   b) 1/2   c) 5/4   d) 3   e) - 3   the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.   Answer is b) 1+h.
Answer: B
A hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 18 kilometers per hour. The cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
Choose the correct choice:
A) 7.5	B) 12.5	C) 17.5	D) 22.5	E) 27.5

Solution: In 5 minutes, the cyclist travels a distance of   (5/60)*18= 
  (5/60)*18 = 3/2 = around 1.5
1.5 km.   The time it takes the hiker to complete this distance is 1.5/4 hours= 22.5 minutes   The cyclist needs to wait  22.5 - 5= 
 22.5 - 5 = 17.5
17.5 minutes   The answer is 17.5.
Answer: C
A bag holds 4 red marbles and 4 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?	Pick one:
A) 1/7
B) 1/5
C) 3/14
D) 2/7
E) 1/2

Solution: probability of selecting first red marble = 4/8   probability of selecting second red marble without replacement = 3/7   final probability = 4/8 * 3/7 = 3/14   The correct answer is 3/14.
Answer: C
If goods be purchased for $840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction? Choose the correct choice from the following answers.
A) 35 1/3%	B) 30 2/3%	C) 33 1/3%	D) 38 1/2%	E) 40 1/3%

Solution: 33 1/3%   33 1/3%   1/4 33 1/3%P = 210 SP = 21*(80/100) = 168   SP = 840*(120/100)= 
840*(120/100) = 1_008
1008   1008 - 168= 
1008 - 168 = 840
840   3/4 SP= 630   Gain = 210   630 --- 210   100 --- ? => 33 1/3%
Answer: C
Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after? Choose the correct choice from the following choices.
A) 7 min B) 9 min C) 4 min D) 9 min E) 1 min

Solution: Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.   x(2/75 + 1/45) + (30- x) 2/75 = 1   11x + 180 - 6x = 225 => x = 9   Answer:9 min
Answer: B
A 9% stock yields 8%.The market value of the stock is : Options:
A) Rs. 72  B) Rs. 92  C) Rs. 112.50  D) Rs. 116.50  E) None of these

Solution: solution   To obtain Rs. 8, investment = Rs. 100.   To obtain Rs. 9, investment = Rs.(100/8X9)= Rs. 112.50   ∴ Market value of Rs. 100 stock = Rs.112.50   Answer Rs. 112.50
Answer: C
A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the sixth hour?	Answers.
A) 38	B) 47	C) 50	D) 53	E) 62

Solution: Suppose food eaten in first hour : x   The AP is : x, x+3, x+6, .... [Number of terms 'n' = 9]   Therefore,   9/2[2 x + (9-1)*3] = 450.   Solving for x, x = 38.   Now, 6th term will be : x + (6-1)*d = 38 + 5*3= 
38 + 5*3 = 53
53.   Hence 53 !!
Answer: D
There is a 10% chance that Tigers will not win at all during the whole season. There is a 10% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?	Choose one
A) A)55%  B) B)60%  C) C)70%  D) D)72%  E) E)90%

Solution: There is a 10% chance that Tigers will not win at all during the whole season   We can infer that there is 90% chance Tigers will win .   Similarly There is a 10% chance that Federer will not play at all in the whole season   We can also infer that there is 90% chance that Federer will play.   Answer 90%
Answer: E
A man whose speed is 6 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey? Select
A) 7
B) 5.6
C) 6
D) 9
E) 3

Solution: M = 6.0   S = 1.5   DS = 7.5   US = 4.5   AS = (2 * 7.5 * 4.5) /12 = 5.6   Answer:5.6
Answer: B
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in?	Choose the correct choice from the following answers:  A) 8  B) 4  C) 6  D) 12  E) 10

Solution: (A + B + C)'s 1 day work = 1/6;   (A + B)'s 1 day work = 1/8   (B + C)'s 1 day work = 1/12   (A + C)'s 1 day work = (2 * 1/6) - (1/8 + 1/12)   = (1/3 - 5/24) = 1/8   So, A and C together will do the work in 8 days.   8NSWER 8
Answer: A
The contents of a bag of marbles consist of 12 green marbles and 20 blue marbles. How many blue marbles must be removed so that 40% of the marbles in the bag will be green?	Choose the correct choice from the following
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: We can use simple arithmetic to solve this problem by testing our answers.   Lets test B:   If we only remove 1 blue marble:   12 green marbles and 19 blue marbles for a total of 31 marbles   12/31=37.5% not quite our answer.   Lets test 2:   If we remove 2 blue marbles:   12 green marbles and 18 blue marbles for a total of 30 marbles   12/30=40%   2 is our answer!
Answer: C
What will come in place of the x in the following Number series? 25, 100, 400, X, 6400	Pick one
A) 6400 B) 6900 C) 1600 D) 7500 E) 7900

Solution: (1600)   25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Answer: C
A boat goes 150 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?	Choose the correct choice from the following options
A) 22 1/7	B) 22 1/4	C) 22 1/2	D) 22 1/1	E) 5

Solution: 150 --- 10 DS = 15   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (15 - 5)/2= 
(15 - 5)/2 = 5
5 kmp Answer: 5
Answer: E
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is -. Choose the correct choice from the following answers:
A) 1/26	B) 3/52	C) 15/26	D) 11/26	E) 1/13

Solution: Explanation:   Let E1 be the event of drawing a red card.   Let E2 be the event of drawing a king .   P(E1 ∩ E2) = P(E1) . P(E2)   (1/26s E1 and E2 are independent)   = 1/2 * 1/13 = 1/26   1/26NSWER IS 1/26
Answer: A
How many multiples of 10 are there between 100 and 10000 (both are inclusive)? Choices
A) 456  B) 789  C) 991  D) 1020  E) 1100

Solution: the answer is (10000-100)/10+1= 
(10000-100)/10+1 = 991
991   Answer is 991
Answer: C
A man can row upstream at 7 kmph and downstream at 10kmph.find man’s rate in still water and the rate of current.
Choose the correct choice from the following answers
A) 1.5 km/hr
B) 1 km/hr
C) 1.5 km/min
D) 0.5 km/hr
E) 1.75 km/hr

Solution: Rate in still water=1/2(10+7)km/hr=8.5 km/hr.   Rate of current=1/2(10-7)km/hr=1.5 km/hr.   1.5 km/hrnswer is 1.5 km/hr.
Answer: A
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is?
Choose the correct option
A) 35 B) 50 C) 88 D) 22 E) 12

Solution: Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x   = 35 km/hr.35nswer:35
Answer: A
11 persons are sittingin a row. how many ways can 11 persons be arranged in a row such that 3 persons should always be together?  Choices:	A) 7!×2!	B) 10!×1!	C) 9!×3!	D) 8!×2!	E) 6!×3!

Solution: Given that three particular persons should always be together. Hence, just group these three persons together and consider as a single person.   Therefore we can take total number of persons as 9. These 9 persons can be arranged in 9! ways.   We had grouped three persons together. These three persons can be arranged among themselves in 3! ways.   Hence, required number of ways   =9!×3!   9!×3!
Answer: C
The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.
Answers
A) 30	B) 40	C) 50	D) 70	E) 80

Solution: Let the price of gift pack be 'aa'   Then number of packs bought =a+1=a+1   Hence total cost is a(a+1)a(a+1)   It is given that 380<a(a+1)380<a(a+1)   If a=19a=19, the total cost =19×20=380=19×20=380   Dexter would not have fallen short, If:   a=20a=20, a(a+1)=420a(a+1)=420   So he would have fallen short by Rs 40.   This is the minimum amount by which he may have fallen short.   40)
Answer: B
The average age of 30 students in a class is 15 years. If the age of teacher is also included, the average becomes 16 years, find the age of the teacher.
Choose the correct option.
A) 46
B) 55
C) 43
D) 39
E) 54

Solution: Explanation:   If teacher's age is 15 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 16.   46ge of teacher = 46verage age of all + Total increase in age   = 16 + (1 x 30 ) = 46 years   46nswer:46
Answer: A
In a certain office 1/3 of the workers are women ½ of the women are married and 1/3 of the married women have children if ¾ of the men are married and 2/3 of the married men have children what part of workers are without children?  Choose one
A) 11/18  B) 12/18  C) 13/18  D) 10/18  E) None of them

Solution: Let the total no of workers be x   No of women =x/3   No of men =x-(x/3)=2x/3   No of women having children =1/3 of ½ ofx/3=x/18   No of men having children=2/3 of ¾ of2x/3=x/3   No of workers having children = x/8 +x/3=7x/18   Workers having no children=x-7x/18=11x/18=11/18 of all wprkers   11/18nswer is 11/18.
Answer: A
A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 5 miles per day and it will take them two days, how many miles long is the route down the mountain?  Choose the correct choice from the following options.
A) 4  B) 6  C) 8  D) 12  E) 15

Solution: On the way down, the rate is  1.5*5= 
 1.5*5 = 7.5
7.5 miles per day.   The distance of the route down the mountain is   2*7.5= 
  2*7.5 = 15
15 miles.   The answer is 15.
Answer: E
Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 16, 12, and 8 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?	Choose the correct choice from the following answers: A) 5/2 B) 7/4 C) 8/5 D) 10/3 E) 12/5

Solution: The time it takes printer X is 16 hours.   The combined rate of Y and Z is 1/12 + 1/8 = 5/24   The time it takes Y and Z is 24/5   The ratio of times is 16 / (24/5) = 5*16/24 = 10/3   The answer is 10/3.
Answer: D
A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?	Pick one
A) 22 1/6  B) 22 1/2  C) 22 1/0  D) 22 1/9  E) 22 1/1

Solution: 1/18 + 1/30 = 8/90 = 4/45   45/4 = 11 1/4 *2 = 22 1/2 days   Answer: 22 1/2
Answer: B
The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $800 per sq. metre.
Choose the correct answer:
A) $12500	B) $13500	C) $16500	D) $14500	E) $18500

Solution: C   $16500   Area =5.5×3.75 sq. metre.   Cost for 1 sq. metre. = $800   Hence, total cost   =5.5×3.75×800=5.5×3000= $16500
Answer: C
On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled?	Answers:
A) 80
B) 81
C) 82
D) 83
E) 84

Solution: Solution:   Mabel handled 90 transactions   Anthony handled 10% more transactions than Mabel   Anthony = 90 + 90 × 10%   = 90 + 90 × 0.10   = 90 + 9= 
90 + 9 = 99
99   Cal handled 2/3rds of the transactions than Anthony handled   Cal= 2/3 × 99   = 66   Jade handled 15 more transactions than Cal.   Jade = 66 + 15= 
66 + 15 = 81
81   Jade handled= 81 transactions.   Answer: 81
Answer: B
If the numbers 1 to 100 are written on 100 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
Choose the correct choice from the following answers:
A) 1/50 B) 1/25 C) 1/100 D) 1 E) 2

Solution: There are 25 primes, 74 composite numbers from 1 to 100. The number   which is neither prime nor composite is 1.   Therefore, required probability = 1/100.   ANSWER:1/100
Answer: C
Two trains are running in opposite directions with the same speed. If the length of each train is 300 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:  Pick:	A) 31 km/hr.	B) 32 km/hr.	C) 60 km/hr.	D) 35 km/hr.	E) 90 km/hr.

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (300 + 300)/12   2x = 50   x = 25.   Speed of each train = 25 m/sec = 25 x 18/5 km/hr = 90 km/hr.   answer :90 km/hr.
Answer: E
Uncle Bruce is baking chocolate chip cookies. He has 50 ounces of dough (with no chocolate) and 40 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 30% chocolate? Choose the correct choice from the following answers:	A) 22.86	B) 23.86	C) 25	D) 26	E) 27

Solution: First, you must find the total weight of the mixture given that 80% of it will be dough.   70%*Total = 40 => (7/10)Total=40 => Total=400/7 => Total=57.14 oz,   From there, you must find 30% of the total 57.14 oz of the mixture.   30%*Total => (3/10)(57.14)= 17.14 oz choclate used,   Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 40-17.14 = 22.86 oz chocolate left over.   22.86nswer : 22.86
Answer: A
A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?  Pick one
A) 109	B) 105	C) 129	D) 119	E) 113

Solution: x:y:z = 100:45:30   20:9:6   9 --- 27   35 --- ? => 105   Answer:105
Answer: B
In how many ways can a cricket 15 be chosen out of a batch of 20 players? Choose one:
A) 12500
B) 18250
C) 13250
D) 15504
E) 14520

Solution: Required number of ways = 20C15 = 20C (20-15) = 20C5   20C5 = (20*19*18*17*16)/(5*4*3*2*1)= 
(20*19*18*17*16)/(5*4*3*2*1) = 15_504
15504   Answer is 15504
Answer: D
The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 90 cents more than the commodity Y?  Select: A) 2010 B) 2011 C) 2012 D) 2013 E) 2014

Solution: The cost of commodity X increases by 10 cents per year relative to commodity Y.   The price of X must gain 20 + 90 = $1.10 cents on commodity Y, which will take 11 years.   The answer is 2012.
Answer: C
A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 70% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?	Options:	A) 1000	B) 1250	C) 1300	D) 1600	E) 1857.14

Solution: 300 gallons of water increases capacity by 30% that means   30% is 300 gallons, so 100% would be = 300*100/30= 
300*100/30 = 1_000
1000 gallons   Now 1000 +300 gallons is 70% capacity of tank.   so 100% capacity would be= 1300 *100/70= 1857.14   1857.14 is the answer
Answer: E
What is the present worth of Rs. 187 due in 2 years at 5% simple interest per annum? Options.
A) 288  B) 266  C) 120  D) 277  E) 170

Solution: Let the present worth be Rs. x. Then,   S.I. = (187 - x)   (x * 5 * 2) / 100 = (187 - x)   10x = 18700 - 100x   110x = 18700 => x = 170.   Answer: 170
Answer: E
If a real number x is chosen at random in the interval [0,5] and a real number y is chosen at random in the interval [0,6], what is the probability that x < y?
Answers.
A) 2/3  B) 3/5  C) 5/12  D) 7/12  E) 11/15

Solution: Since x is in [0,5] and y is in [0,6] we can draw a rectangle in the coordinate plane with vertices (0, 0), (5, 0), (0, 6), and (5, 6).   The points above the line y=x satisfy x < y.   The part of the rectangle below y=x has an area of 12.5   The whole rectangle has an area of 30.   P(x < y) = (30-12.5)/30 = 17.5/30 = 35/60 = 7/12   The answer is 7/12.
Answer: D
In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 49 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?  Choose the correct choice from the following answers
A) 70 B) 245 C) 150 D) 35 E) 350

Solution: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7= 
0.2*0.7 = 0.14
0.14, or 14% of the boys in the camp are from school A and do not study science.   We are told that this number equals to 49, so 0.14*{total}= 49 --> {total} = 350.   Answer: 350.
Answer: E
A merchant purchased a jacket for $54 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale? Options.
A) $0 B) $3 C) $4 D) $12 E) $18

Solution: Actual Cost = $54   SP = Actual Cost + Mark up   = Actual Cost + 40% SP   = 54*100/60   on sale SP = 80/100(54*100/60) = 72   Gross profit = $18   Answer is $18
Answer: E
On the xy co-ordinate plane, point C is (3,-2) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:  Choose the correct choice from the following options:	A) (1,-1)	B) (1,1)	C) (2,0.25)	D) (3,0.5)	E) (3,1)

Solution: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.   *It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:   Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)= 
5 - (-1) = 6
6   The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is  5-4= 
 5-4 = 1
1, or  (-1)+2= 
 (-1)+2 = 1
1.   Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5|= 4.5   The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is  (-2)+3= 
 (-2)+3 = 1
1, or  2.5-1.5= 
 2.5-1.5 = 1
1.   So now we have our coordinates of the point on the line that is twice as far from C as it is from (3,0.5): (3,0.5)   Answer: (3,0.5)
Answer: D
A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning. Options:
A) 24
B) 52
C) 39
D) 36
E) 85

Solution: Sol. Let the average after 17th inning = x.   Then, average after 16th inning = (x - 3).   16 (x - 3) + 87 = 17x or x = (87 - 48)= 
(87 - 48) = 39
39.   Ans: 39
Answer: C
There are 7 books on a shelf, of which 2 are paperbacks and 5 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?	Pick one
A) a) 30	B) b) 45	C) c) 50	D) d) 55	E) e) 60

Solution: approach 1   at-least 1 paper back = total - no paper back   7c4-5c4 = 30   approach 2   at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back   = 2c1*5c3+2c2*5c2 = 30   a) 30nswer is a) 30
Answer: A
If 4 men can color 48 m long cloth in 2 days, then 6 men can color 36 m long cloth in	Choose the correct choice from the following:
A) 2 days
B) 1 day
C) 3 days
D) 4 days
E) 5 days

Solution: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.   1 day
Answer: B