MU-NLPC/Calc-aqua_rat huggingface dataset:
An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?
Pick one:
A) 194 seconds
B) 195 seconds
C) 196 seconds
D) 197 seconds
E) None of these

Solution: Explanation:   Let the time required by x seconds.   Then, More cloth means More time (Direct Proportion)   So,   0.128:1::25:x=>x=25∗1 /0.128   =>x=195.31   So time will be approx 195 seconds   Option 195 seconds
Answer: B
A train 150 m long can cross an electric pole in 3 sec and then find the speed of the train?
Choose the correct option.
A) 180	B) 120	C) 72	D) 27	E) 28

Solution: Length = Speed * time   Speed = L/T   S = 150/3= 
150/3 = 50
50 M/Sec   Speed= 50*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 180 Kmph   180nswer:180
Answer: A
A certain deck of cards contains 2 white cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not white?	Choose the correct choice from the following options
A) 15/28
B) 1/4
C) 9/16
D) 1/32
E) 1/16

Solution: The question asks they will both be not white. Considering that these are draws without replacement there are following possibilities :   draw 1, draw 2   ===== =====   1) Not white, white;   2) white, Not white;   3) white, white;   4) Not white, not white;   The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are white   P(4) = 6/8*5/7=15/28   1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28   15/28
Answer: A
A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Choose the correct choice from the following options
A) 1 kmph	B) 6 kmph	C) 5 kmph	D) 8 kmph	E) 7 kmph

Solution: Speed downstream = d/t = 85/(2 1/2) = 34 kmph   Speed upstream = d/t = 45/(2 1/2) = 18 kmph   The speed of the stream = (34 - 18)/2= 
(34 - 18)/2 = 8
8 kmph   Answer:8 kmph
Answer: D
A box contains 3red, 5yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours? Pick
A) 2/7
B) 3/11
C) 1/4
D) 3/7
E) 2/9

Solution: Total number of balls = 3+5+4= 
3+5+4 = 12
12   n(S)= 12C3 = 12*11*10/3*2 = 220 n(E) = 3C1*5C1*4C1 = 3*5*4= 
3*5*4 = 60
60 P(E)= 60/220 = 3/11 Answer is 3/11
Answer: B
If you roll a fair-sided die twice, what is the probability of getting a double (5,5)?  Choose one: A) 1/24 B) 1/36 C) 1/12 D) 1/18 E) 1/3!

Solution: total no. in two dice (1,1) ,(2,2) .....(6,)   Total number of events= 6*6   Total events of getting same pair(5,5) = 6   Probability= 6/6*6= 1/6=1/3!   1/3!
Answer: E
The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Choose one:
A) 46 B) 28 C) 25 D) 22 E) 29

Solution: Sum of all the 13 numbers = 13 * 60= 
13 * 60 = 780
780   Sum of the first 7 of them= 7 * 57= 
7 * 57 = 399
399   Sum of the last 7 of them= 7 * 61= 
7 * 61 = 427
427   So, the 8th number= 427 + 399 - 780= 
427 + 399 - 780 = 46
46.   46nswer: 46
Answer: A
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.84. How much was lent at 5%? Choose the correct choice from the following answers.
A) 299	B) 466	C) 578	D) 600	E) 677

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 84   5x/100 + 90 – 6x/100 = 84   x/100 = 6   => x = 600   Answer:600
Answer: D
A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent?
Select:  A) 25%  B) 5%  C) 10%  D) 15%  E) 20%

Solution: 3000 --- 600   100 --- ? => 20%   Answer: 20%
Answer: E
Tough and Tricky questions: Probability.
Medical analysts predict that a quarter of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?
Choose the most appropriate option:	A) 16/81	B) 37/64	C) 2/3	D) 19/27	E) 65/81

Solution: At the end of each day we will have 3/4 alive. So after 3 days we will have (3/4)^3 people alive. Therefore, fraction of dead people will be 1-(3/4)^3=37/64.   The correct answer is 37/64.
Answer: B
If r and s are positive integers and r-s=6, which of the following has the greatest value Q?
Select the correct option
A) 2r
B) 2s
C) r +s
D) 2r-s
E) 2s-r

Solution: The simplest way to do this is to assume values.   We are told that r and s are positive integers Q.   Also, r-s = 6 => r = 6+s   Hence r is 6 more than s.   Let s be 10. Hence r = 16.   Option 2r: 2r = 2*16= 
2*16 = 32
32   Option B: 2s= 2 * 10= 
2 * 10 = 20
20   Option C: r + s= 16 + 10= 
16 + 10 = 26
26   Option D: 2r - s= 2(16) - 10 = 32 - 10= 
32 - 10 = 22
22   Option E: 2s - r= 2(10) - 16 = 20 - 16= 
20 - 16 = 4
4   Hence option 2r is the greatest.
Answer: A
How many pieces of 75 cm can be cut from a rope 54 meters long?  Select.
A) 30 B) 40 C) 60 D) 72 E) Cannot be determined

Solution: Explanation :   Total pieces of 75 cm that can be cut from a rope of 54 meters long is   = (54 meters)/(75 cm)   = (54 meters)/(0.75 meters)   = 72   Answer : 72
Answer: D
If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?	Choose one
A) 2288  B) 1000  C) 2877  D) 2667  E) 1311

Solution: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x   1 = 1/10 * 1/10 * 1/10 * x => x = 1000   Answer: 1000
Answer: B
Ravi jogs 7 km at a speed of 5 kmph. at what speed would she need to jog during the next 2.5 hour to have an average of 7 km per hr at the entire jogging session?  Select the correct option
A) 17.8 kmph
B) 8.9kmph
C) 5.8kmph
D) 5.8kmph
E) 4.9kmph

Solution: let speed of the jogging be xkmph   total time taken=(7/5+2.5)= 
(7/5+2.5) = 3.9
3.9hrs   total distance covered=(7+2.5x)   7+2.5x/3.9=9   x=17.8kmph   17.8 kmphnswer(17.8 kmph)
Answer: A
An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 3 but were was no change in its perimeter. What is the ratio of the areas of the carpets?  Choose the correct choice from the following answers
A) 9:10
B) 19:20
C) 29:30
D) 39:40
E) 49:50

Solution: Let the length and width of one carpet be 3x and 2x.   Let the length and width of the other carpet be 4y and 3y.   2(3x + 2x) = 2(4y + 3y)   5x = 7y   (5/7) * x = y   The ratio of the areas of the carpet in both cases:   = 3x * 2x : 4y * 3y   = 6x^2 : 12y^2   = x^2 : 2y^2   = x^2 : 2*(25/49) * x^2   = 49 : 50   The answer is 49:50.
Answer: E
8^100 is divisible by 17. Find the remainder? Choose the correct answer:	A) 10	B) 12	C) 16	D) 18	E) 20

Solution: This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.   So divide 100 by 16 and find the remainder. Remainder = 4   Therefore, 100 = (16 × 6) + 4   Now this problem can be written as 810017 = 816×6+417 = (816)6×8417   Now this problem simply boils down to (1)6×8417 = 8417   84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.   16
Answer: C
If a survey shows that 26 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
Select
A) 56% B) 64% C) 72% D) 87% E) 86%

Solution: 26 out of 200 supports the bill and we are asked to find the percent who the does not support the bill.   26 out of 200 supports the bill = 13 out of 100 supports the bill ( taking in % terms )   14 out of 100 supports the bill = 87 (100-13) doesn't support the bill   So, answer is (87%) 87%
Answer: D
There are 16 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?	Choose the correct option
A) 288  B) 267  C) 261  D) 211  E) 306

Solution: The total number of stations = 18   From 18stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 18P₂ ways.   18P₂ = 18* 17= 
18* 17 = 306
306.   Answer: 306
Answer: E
Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?  Answers:
A) 45 m
B) 60 m
C) 50 m
D) 67 m
E) 78 m

Solution: Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 20) + x] = 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m   60 m
Answer: B
The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE.
If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE?  Select.
A) 80 yards	B) 82 yards	C) 84 yards	D) 85 yards	E) 90 yards

Solution: The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question.   1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle.   2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus.   3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle.   4) From (1), we know that x = 202+y2−−−−−−−√202+y2.   5) From (3), we know x = 25 - y.   6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y   7) Solving for y, we get 4.5.   8) 25 - 4.5 = 20.5 = x   9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2= 
41 * 2 = 82
82.   The answer is 82 yards, 82
Answer: B
There are 5 boxes in a cargo. The weight of the 1st box is 200 KG, the weight of the 2nd box is 20% higher than the third box, whose weight is 25% higher than the 1st box weight. The 4th box which weighs 350 KG is 30% lighter than the 5th box. Find the difference in average weight of the 4 heaviest boxes and the four lightest boxes. Select.
A) 22 B) 75 C) 25 D) 70 E) 11

Solution: weight of 1st box=200   weight of 3rd box=(125/100)*200= 
(125/100)*200 = 250
250   weight of 2nd box=(120/100)*250= 
(120/100)*250 = 300
300   weight of 4th box=350   weight of 5th box=(10/7)*350= 
(10/7)*350 = 500
500   average of 4 highest weighted boxes=(500+350+300+250)/4= 
(500+350+300+250)/4 = 350
350   average of 4 lightest boxes=(350+300+250+200)/4= 
(350+300+250+200)/4 = 275
275   therefore difference=350-275= 
350-275 = 75
75   Answer:75
Answer: B
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race? Choose the correct choice from the following choices:
A) 290 sec B) 190 sec C) 199 sec D) 192 sec E) 193 sec

Solution: Time taken by B run 1000 meters   = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   Answer: 190 sec
Answer: B
A wooden cube whose edge length is 7 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?	Choose the correct choice from the following:	A) 59.8%	B) 63.6%	C) 67.2%	D) 70.5%	E) 73.6%

Solution: There are a total of 7*7*7= 
7*7*7 = 343
343 cubes.   All the exterior cubes will have at least one face painted red.   The interior is formed by   5*5*5= 
  5*5*5 = 125
125 cubes.   The number of cubes with at least one side painted red is  343 - 125= 
 343 - 125 = 218
218 cubes   The probability that a cube has at least one side painted red is 218/343 which is about 63.6%   The answer is 63.6%.
Answer: B
A school has received 80% of the amount it needs for a new building by receiving a donation of $600 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? Choose the most appropriate option
A) $200 B) 100 C) $105 D) $250 E) $300

Solution: Let us suppose there are 100 people. 40% of them donated $ 24000 ( 600 * 40 )   $24000 is 80% of total amount.   So total amount = 24000 * 100/80   Remaining amount is 20% of total amount.   20% of total amount = 24000 * (100/80) * (20/100)= 
24000 * (100/80) * (20/100) = 6_000
6000   This amount has to be divided by 60 ( remaining people are 60 )   So per head amount is  6000/ 60= 
 6000/ 60 = 100
$100   ANSWER:100
Answer: B
A mixture contains alcohol and water in the ratio 4 : 3. If 6 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture  Choose the correct choice.
A) 15 litres
B) 10 litres
C) 30 litres
D) 12 litres
E) 8 litres

Solution: Let the quantity of alcohol and water be 4x litres and 3x litres respectively   4x/(3x+6)=4/5   20x=4(3x+6)   8x=24   x=3   Quantity of alcohol = (4 x 3) litres = 12 litres.   Answer is 12 litres
Answer: D
In what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way?	Choose the correct option.
A) 3 B) 5.4 C) 4.3 D) 6.5 E) 7

Solution: T = 75/50 * 18/5= 
75/50 * 18/5 = 27/5 = around 5.4
5.4 sec   Answer:5.4
Answer: B
A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
Options:  A) 32  B) 36  C) 33  D) 37  E) None of them

Solution: Let the speed of the goods train be x kmph.   Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours   10x = 4 x 90 or x =36.   So, speed of goods train = 36kmph.   Answer is 36.
Answer: B
Tim came second in Math. When his mother asked him how much he had scored, he answered that he got the sum of the first 8 even numbers. His mother immediately worked out the answer. How much had he scored in Math?	Answers.
A) 80  B) 90  C) 30  D) 72  E) 60

Solution: 72   72   Sum = (n x n) + n   Hence, 8 x 8 = 64 + 8= 
64 + 8 = 72
72
Answer: D
A basketball coach is choosing her starting lineup from a team of 11 girls. 7 of the girls are post players and 4 are guards. If she chooses 3 post players and 2 guards, how many different lineups can be made?  Select the correct option:	A) 210	B) 220	C) 240	D) 260	E) 270

Solution: (7c3)*(4c2)   [7!/(3!*4!)]*[4!/(2!*2!)]   35*6   210   210
Answer: A
A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?	Choose the correct choice.
A) 87 Kmph	B) 97 Kmph	C) 72 Kmph	D) 90 Kmph	E) 19 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 500/20= 
500/20 = 25
25 M/Sec   Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 90 Kmph   Answer: 90 Kmph
Answer: D
A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.12 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?  Choose the correct choice from the following:  A) 1440  B) 1200  C) 2832  D) 1299  E) 1236

Solution: Explanation:   l * 30 = 1200 è l = 40   40 + 30 + 50= 
40 + 30 + 50 = 120
120   120 * 12= 
120 * 12 = 1_440
1440   1440nswer: Option 1440
Answer: A
Bill has d animals, 28 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?
Choose the correct answer:
A) 6  B) 12  C) 18  D) 24  E) 42

Solution: Total d animals, suppose each has price of x - total price = dx   now 28 were sold at profit of 10%, making equation - - 28*1.1x   now d-28 were sold at loss of 20%, making eqn --- (d-28)*0.8x   Now he made no profit or loss so,   dx = 28*1.1x + (d-28)*0.8x   solving for d, we get d=42   Ans 42
Answer: E
A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 303 test scores with a standard deviation less than d? Choose the most appropriate option.
A) 75 and 80	B) 75 and 75	C) 70 and 75	D) 75 and 70	E) 70 and 80

Solution: Deviation means spreading of the numbers from one median point value..   as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.   so 75 and 75 are the most close numbers and they will increase the number of elements in the set without changing the median value.   75 and 75
Answer: B
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
Choose the correct choice:
A) 900
B) 950
C) 1000
D) 975
E) 870

Solution: Explanation:   X * (110/100) * (95/100) = 1045   X * (11/10) * (1/100) = 11   X = 1000   ANSWER IS 1000
Answer: C
Speed of a boat in standing water is 10kmph and speed of the stream is 2.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is?  Choose the correct choice from the following answers.
A) 23.4hours
B) 22.4hours
C) 21.4hours
D) 20.4hours
E) 19.4hours

Solution: Speed upstream = 7.5kmph   Speed downstream = 12.5kmph   Total time taken = 105/7.5 + 105/12.5= 
105/7.5 + 105/12.5 = 22.4
22.4 hours   Answer is 22.4hours
Answer: B
A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
Choose the correct answer:
A) 400
B) 798
C) 452
D) 635
E) 432

Solution: 2000 ---- 50   2000 ---- 40   x ----- 50   x*50 = 2000*40   x=1600   2000   -------   400   400nswer:400
Answer: A
Henry answered 1/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?	Choose the correct choice from the following.
A) x B) (85/48)*x C) (85/36)*x D) (17/5)*x E) (85/18)*x

Solution: Let Q be the number of homework questions.   Q = Q/5 + (5/17)(4Q/5) + x   Q = 17Q/85 + 20Q/85 + x   48Q/85 = x   Q = (85/48)*x   The answer is (85/48)*x.
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train? Choose the correct choice:
A) 356  B) 278  C) 127  D) 100  E) 150

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 6= 
50/3 * 6 = 100
100 m   Answer: 100
Answer: D
In how many ways can 3 men & 2 women can be made from a gang of 5 men & 5 women ?	Choose the correct choice.
A) 100
B) 150
C) 200
D) 250
E) 260

Solution: Explanation:   5C3 * 5C2 = 100   100
Answer: A
If the sum and difference of two numbers are 15 and 10 respectively, then the difference of their square is:  Choose the correct choice:
A) 12
B) 150
C) 160
D) 180
E) 18

Solution: Let the numbers be x and y.   Then, x + y = 15 and x - y = 10   x2 - y2 = (x + y)(x - y) = 15 * 10= 
15 * 10 = 150
150.   ANSWER:150
Answer: B
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 3 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad? Pick one.
A) 16	B) 18	C) 20	D) 33.3	E) 30

Solution: Time taken = Total Distance / Relative Speed   Total Distance = 50 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 3= 
6+ 3 = 9
9 kms/hr   Time taken= 50 / 9 = 5.55 hrs   Distance traveled by Brad = Brad's speed * time taken = 6 * 5.55= 
6 * 5.55 = 33.3
33.3 kms... Answer - 33.3
Answer: D
How many miles is 150KM?	Options:
A) 91.5miles
B) 92.75miles
C) 93.75miles
D) 94.5miles
E) 95.75miles

Solution: 93.75miles   150/1.6   Answer:93.75miles
Answer: C
Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 1:2. The first number is:  Answers
A) A)27 B) B)98 C) C)34 D) D)35 E) E)62

Solution: (3x-9):(5x-9) = 9:17   x = 9 => 3x = 27   27nswer:27
Answer: A
Glen and Hannah drive at constant speeds toward each other on a highway. Glen drives at a constant speed of 37 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Glen is 130 km away from Hannah at 6 am, and also 130 km away from Hannah at 11 am, then how fast is Hannah driving (in kilometers per hour)?
Choose the correct choice from the following.
A) 12  B) 13  C) 14  D) 15  E) 16

Solution: Glen and Hannah complete 260 km / 5 hours = 52 km/hour   Hannah's speed is  52-37= 
 52-37 = 15
15 km/hour   The answer is 15.
Answer: D
Four persons enter the lift of a six storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor Choose the correct choice from the following
A) 625
B) 1296
C) 1540
D) 1478
E) 360

Solution: Each person out of 4 has 5 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 5*5*5*5=5^4=625.   625nswer: 625.
Answer: A
P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last?
Choose one:	A) 5 days	B) 10 days	C) 14 days	D) 22 days	E) 26 days

Solution: Explanation :   Work done by P in 1 day = 1/10   Work done by Q in 1 day = 1/6   Work done by P in 2 days = 2 Ã— (1/10) = 1/5   Remaining work = 1 â€“ 1/5 = 4/5   Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15   Number of days P and Q take to complete the remaining work = (4/5) / (4/15)= 
(4/5) / (4/15) = 3
3   Total days= 2 + 3= 
2 + 3 = 5
5   5 daysnswer : Option 5 days
Answer: A
A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $237 for it, the cost price of the Cricket Bat for A is:	Pick:
A) 150  B) 120  C) 158  D) 160  E) 210

Solution: 125% of 120% of A = 237   125/100 * 120/100 * A = 237   A = 237 * 2/3= 
237 * 2/3 = 158
158.   ANSWER 158
Answer: C
The integers 1, 2, … , 40 are written on a blackboard. The following operation is then repeated 39
times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new
number a + b – 1 is written. What will be the number left on the board at the end?	Choose the correct choice from the following answers
A) 23  B) 122  C) 781  D) 377  E) 272

Solution: Initial sum of the number 1 to 40 = n(n+1)2=40×412=840n(n+1)2=40×412=840   After erasing two numbers a and b, and replacing with (a + b − 1), the new sum of the terms of the   sequence = 820 − 1   Similarly, after every operation, the sum of the terms of the sequence reduces by 1.   ∴ The last number left (i.e. final sum) = 820 − 39 = 781   Answer:781
Answer: C
Shekar scored 76, 65, 82, 62 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?	Choose the correct choice from the following answers
A) 74
B) 69
C) 75
D) 85
E) 90

Solution: Explanation :   74verage= (76+65+82+62+85)/5 = 370/5= 
370/5 = 74
74   Hence average=74   74nswer : 74
Answer: A