MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1344?  Choose the correct choice from the following:
A) 1200  B) 2777  C) 2889  D) 27670  E) 2771

Solution: 1344 = P [1 + (5*12/5)/100]   P= 1200.1200nswer:1200
Answer: A
If the average marks of two sections of 40 and 45 students respectively is 75 and 60, then the average marks of all the students is:
Options:
A) 53.33
B) 67.05
C) 75
D) None of these
E) Cannot be determined

Solution: Explanation :   Required average = (40 x 75 + 45 x 60)/(40 + 45)   = (3000 + 2700)/85   = 5700/85   = 67.05   Answer : 67.05
Answer: B
A rectangular field has a length 10 meters more than it is width. If the area of the field is 231, what is the length (in meters) of the rectangular field?
Choose the correct answer:
A) 21  B) 23  C) 25  D) 27  E) 29

Solution: area = l * w = (L) * (L-10) = 231   trial and error:    20*10= 
 20*10 = 200
200 (too low)   21*11= 
21*11 = 231
231   The length is 21 meters.   The answer is 21.
Answer: A
A manufacturing plant produces 2 products (hats and gloves). 25% of all products are colored red, the remaining products are colored blue. If the ratio of products made is 3:4, respectively, and the percentage of hats colored red is 55%, what percentage of gloves are colored blue? Choose the correct choice from the following options: A) 87% B) 90.5% C) 97.5% D) 55.5% E) 96%

Solution: Let H and G be number hats and gloves, and r and b represent red and blue, respectively.   H + G = total products.   H:G = 3:4   Hr/H = 55%   Gb/G = 100% - Gr/G = ?   [(3)(Hr/H) + (4)(Gr/G)]/(3 + 4) = 25%   [(3)(55%) + (4)(Gr/G)]/7 = 25%   Gb/G = 100% - 2.5% = 97.5%   Answer: 97.5%100  - 2.5= 
100  - 2.5 = 97.5
97.5%   Answer: 97.5%
Answer: C
Let a, b, c, d and e be distinct integers such that (6-a)(6-b)(6-c)(6-d)(6-e) = 45. What is a+b+c+d+e?	Choices.
A) 5  B) 17  C) 25  D) 27  E) 30

Solution: Since the prime factorization is 3*3*5   The constraint in the question is that they are distinct so the only possible way is 3,-3,5,1,-1   6-a = 3 => a=3   6-b = -3 => b=9   6-c = 5 => c=1   6-d = 1 => c=5   6-e = -1 => e = 7   Answer is 25 = 25
Answer: C
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? Select.
A) 2.5
B) 2.6
C) 2.9
D) 2.1
E) 2.2

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5nswer: 2.5
Answer: A
Lisa plays a dice game in which she rolls two, fair, six-sided dice two times. If her second roll matches her first roll, she wins. What is the probability that she wins if her first roll was 10?
Choose the correct answer.
A) 1/6	B) 5/36	C) 1/9	D) 1/12	E) 1/18

Solution: There are 3 ways to roll a 10 with two six-sided dice: 4 and 6, 6 and 4, 5 and 5. You only count 5 and 5 once.   There are  6*6= 
 6*6 = 36
36 ways to roll two six-sided dice. Thus the probability of rolling a 10 is 3/36= 1/12.   1/12
Answer: D
Car A leaves the airport at 9:00 am and travels at a constant rate of 30 km per hour. Car B leaves the airport at 9:30 am and travels in the same direction along the same highway at a constant rate of 35 km per hour. At what time will Car B be 20 km ahead of Car A?
Choose the correct choice from the following answers:
A) 4:00 pm  B) 4:30 pm  C) 5:00 pm  D) 5:30 pm  E) 6:00 pm

Solution: At 9:30 am, Car A will be 15 km ahead of Car B.   Car B travels at a rate 5 km per hour faster than Car A.   Car B needs to travel 35 km more than Car A in order to be 20 km ahead.   This will take 35 km/5 km per hour=7 hours.   Car B will be 20 km ahead at 4:30 pm.   The answer is 4:30 pm.
Answer: B
A single letter is drawn at random from the word."ASPIRATION", the probability that it is a vowel is? Choose the correct choice from the following answers
A) 1/2 B) 1/3 C) 1/4 D) 1/5 E) 1/6

Solution: 1/2SPIR1/2TION   vowels= 1/2I1/2IO= 5   total alphabets = 10   so the probability is 5/10 = 1/2   1/2NSWER:1/2
Answer: A
If a 4-member subcommittee is to be formed from a certain 9-member committee, how many different such subcommittee are possible?	Choose the correct choice.
A) 6  B) 18  C) 20  D) 126  E) 216

Solution: Another way:   1st member can be selected in 9 ways   2nd can be selected in 8 ways   3rd can be selected in 7 ways   4th can be selected in 6 ways   So total ways : 3024   But to avoid the similar scenarios 3024/4!=126   126
Answer: D
There are 408 boys and 264 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
Choose the correct choice from the following answers:
A) 28 B) 32 C) 35 D) 30 E) 45

Solution: Explanation:   HCF (408, 264) = 24   The number of boys or girls that can be placed in a section = 24.   Thus the total number of sections is given by   408/24+264/24 =17+11= 
17+11 = 28
28   28nswer: 28
Answer: A
A 5 litre jug contains 4 litres of a salt water solution that is 15 percent salt. If 1.5 litres of the solution spills out of the jug, and the jug is then filled to capacity with water,approximately what percent of the resulting solution in the jug is salt? Choose the correct choice from the following answers
A) 7.5%	B) 8.5%	C) 9.5%	D) 10.5%	E) 11.5%

Solution: A 5 litre jug contains 4 litres of a salt water solution that is 15 percent salt. If 1.5 litres of the solution spills out of the jug,then 2.5 ltrs of solution with 15% salt is left in jug.   If solution is now increased to 5 ltrs, the volume is doubled, then salt percentage is halved to 7.5%.   7.5%NSWER:7.5%
Answer: A
Diya finished 2/3 of a book. She calculated that she finished 70 more pages than she has yet to read. How long is her book?  Choose the correct option
A) A)210
B) B)150
C) C)130
D) D)90
E) E)280

Solution: Let x be the total number of pages in the book, then she finished 2/3*x pages.   Then she has x−2/3*x=1/3*x pages left.   2/3*x−1/3*x=70   1/3*x=70   x=210   So the book is 210 pages long.   210nswer is 210.
Answer: A
Four cups of water are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of water should be poured into the 4-cup bottle?
Choose the correct choice.
A) 2/3
B) 8/3
C) 5/2
D) 7/3
E) 3

Solution: Let x be the # of cups going into the 4 cup bottle.   so.... x/4 = ((4-x)/2)   16 - 4x = 2x   16 = 6x   x = 8/3.   Answer : 8/3
Answer: B
A lion chases a pony 7 hours after the pony runs. lion takes 8 hours to reach the pony. If the average speed of the lion is 49 kmph, what s the average speed of the pony?
Select.
A) 28.3kmph  B) 29.8kmph  C) 28.4kmph  D) 29.5kmph  E) 29.4kmph

Solution: pony take 15 hours and lion take 8 hours...then Distance chased by them is 49*8.so speed of pony is (49*8)/15=29.4kmph.   ANSW29.4kmphR IS 29.4kmph
Answer: E
Of the 5 numbers, whose average is 200, the first is one-fourth of the sum of the last 4. The first number is?  Pick one.
A) 200 B) 80 C) 78.63 D) 56.98 E) 67.85

Solution: Total of 5 numbers = 5 * 200= 
5 * 200 = 1_000
1000   Let total of last 4 numbers= x   1st number = x/4   x+ x/4 = 1000   5x = 4000 => x = 800   1st number = 800/ 4= 
800/ 4 = 200
200   200nswer : 200
Answer: A
P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?
Choose the correct choice from the following answers:
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: Explanation :   Let P takes x days to complete the work   Then Q takes x/2 days and R takes x/3 days to finish the work   Amount of work P does in 1 day = 1/x   Amount of work Q does in 1 day = 2/x   Amount of work R does in 1 day = 3/x   Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x   6/x = 2   => x = 12   => Q takes 12/2= 
12/2 = 6
6 days to complete the work   Answer : Option 6
Answer: C
A boat has to travel upstream 20 km distance from point X of a river to point Y. The total time taken by boat in travelling from point X to Y and Y to X is 41 minutes 40 seconds. What is the speed of the boat? Pick one:  A) 66 km/hr  B) 72 km/hr  C) 48 km/hr  D) Data inadequate  E) None of these

Solution: Let x be the speed of the boat.   and y the speed of the current.   20/x−y+20/x+y=25/36   In this equation there are two variables, but only one equation, so, the value of ‘x’ cannot be determined.   Answer Data inadequate
Answer: D
In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital? Choose the correct answer.
A) 11750	B) 28882	C) 27789	D) 11750	E) 28978

Solution: 200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 5000   470 ---- ?=> 11750   Answer: 11750
Answer: D
The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ? Pick:
A) 20 years	B) 21 years	C) 22 years	D) 34 years	E) 24 years

Solution: The average age of the 5 members is 20 years   => The sum of the ages of the 5 members is 20*5= 
20*5 = 100
100 years   Once the new member joins, the average age becomes 24 years.   Let the age of the new member be x.   Then (110+x)/6= 24   => x = 34 years   Answer 34 years
Answer: D
The residents of the town O participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town O, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? Select
A) - 30
B) - 20
C) - 18
D) - 12
E) - 6

Solution: (21-6*2)<number of hours that Pat watched television last week <(21-6*1)   =9<L<15   Only option - 6 (12) satisfies this condition.
Answer: E
What percent of a day is 20 hours? Pick:  A) 12Ã—1/2%  B) 16Ã—1/2%  C) 18Ã—2/3%  D) 22Ã—1/2%  E) None

Solution: Solution   Required percentage	= (20/24Ã—100)%   = (250 / 3)%.   = 83Ã—1/3%.   Answer None
Answer: E
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?  Choose the correct choice from the following answers.
A) 38	B) 40	C) 42	D) 44	E) 46

Solution: 2:3   2x + 10 : 3x + 10 = 5 : 7   7[2x + 10] = 5[3x + 10]   14x + 70 = 15x + 50   15x - 14x = 70 - 50= 
70 - 50 = 20
20   Then the first number is= 2   2x = 40   40
Answer: B
how many such letters pairs are in word SERVANT having same no. of letters left between them in the word as they have in the series
Choose the correct choice from the following options:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 2 pairs.S-V,S-N   ANSWER:2
Answer: B
A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 105 km downstream.  Select.
A) 4 hours
B) 5 hours
C) 6 hours
D) 7 hours
E) 8 hours

Solution: Explanation:   It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.   Lets see the question now.   Speed downstream = (16 + 5)= 
(16 + 5) = 21
21 kmph   Time= distance/speed = 105/21= 
105/21 = 5
5 hours   Option 5 hours
Answer: B
The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
Choose the correct choice from the following answers:  A) Rs.10577  B) Rs.10528  C) Rs.10560  D) Rs.10512  E) Rs.11292

Solution: Let the rate of interest be R% p.a.   4400{[1 + R/100]2 - 1} = 11193.60   [1 + R/100]2 = (44000 + 11193.60)/44000   [1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625   [1 + R/100]2 = 784/625 = (28/25)2   1 + R/100 = 28/25   R/100 = 3/25   Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100   =Rs.10560   Answer:Rs.10560
Answer: C
On 7th Nov, 2003 Friday falls. What day of the week was it on 7th Nov, 2002?	Pick:
A) Tuesday B) Wednesday C) Thursday D) Friday E) Saturday

Solution: Explanation:   7th Nov 2003 – 7th Nov 2002 = 52 weeks 1 day. So Nov 7th 2002 is behind one day = Thursday   Answer: Thursday
Answer: C
If x = 3 - t and y = 4t + 13, then for what value of t are x and y equal?	Choose the correct choice:
A) -1	B) -2	C) -(1/2)	D) -(1/4)	E) None of these

Solution: Explanation:   If x = y   => 3 - t = 4t + 13   => 5t = -10 => t = -2   Answer: Option -2
Answer: B
Each of the integers from 1 to 16 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?	Choose the correct answer
A) 9  B) 12  C) 11  D) 10  E) 3

Solution: Out of the 16 integers: 8 are odd and 8 are even.   If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:   1. we will end up picking odd numbers one by one, so we will pick all 8 odd numbers first   2. 9th number will be the first even number   So we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even.   So, answer will be 9. (9)
Answer: A
Which of the following is the Highest Common Factor of 25, 40 and 20? Choose the correct choice from the following answers
A) 8 B) 5 C) 6 D) 14 E) 12

Solution: COMMON FACTOR IS 5Ans is :5
Answer: B
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A?
Pick one
A) 240  B) 209  C) 279  D) 270  E) 272

Solution: (3*8 + 2*4):(4*8 + 5*4)   8:13   8/21 * 630= 
8/21 * 630 = 240
240   240nswer: 240
Answer: A
Daniel went to a shop and bought things worth Rs. 50, out of which 90 Paise went on sales tax on taxable purchases. If the tax rate was 15%, then what was the cost of the tax free items?  Pick.
A) A)19.7 B) B)20 C) C)43.1 D) D)21.5 E) E)22

Solution: Total cost of the items he purchased = Rs.50   Given that out of this Rs.50, 90 Paise is given as tax   => Total tax incurred = 90 Paise = Rs.90/100   Let the cost of the tax free items = x   Given that tax rate = 15%   ∴ (50−90/100−x)15/100 = 90/100   ⇒ 15(50 −0.9 −x) = 90   ⇒ (50 − 0.9 − x) = 6   ⇒ x = 50 − 0.9 − 6   = 43.1   43.1
Answer: C
Look at this series: 0.15, 0.3, ____, 1.2, 2.4, ... What number should fill the blank?
Choose the correct choice from the following options: A) 0.7 B) 0.2 C) 0.4 D) 0.1 E) 0.6

Solution: E   0.6   This is a simple multiplication series. 0.6ach number is 2 times greater than the previous number.
Answer: E
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?	Select the correct option
A) 17 cm
B) 18 cm
C) 20 cm
D) 21 cm
E) 22 cm

Solution: 2(l + b)	=	5   b	1   2l + 2b = 5b   3b = 2l   b =	2	l   3   Then, Area = 216 cm2   l x b = 216   l x	2	l	= 216   3   l2 = 324   l = 18 cm.   18 cm
Answer: B
An empty fuel tank is filled with brand Z gasoline. When the tank is 1/4 empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent of the gasoline in the tank is brand Z?
Pick one
A) 31.25%
B) 30%
C) 40%
D) 50%
E) 45%

Solution: Work with fraction of brand Z in the tank.   1st step: brand Z is 1   2nd step: brand Z is 1/4   3rd step: brand Z is (1/2)*(1/4) + 1/2 =5/8   4th step: brand Z is (1/2)*(5/8) = 5/16   31.25%nswer (31.25%)
Answer: A
A soccer store typically sells replica jerseys at a discount of 30 percent to 40 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?  Choose the correct choice from the following answers:
A) 20
B) 25
C) 30
D) 40
E) 50

Solution: Let the list price be 2x   for min sale price, the first discount given should be 50%, 2x becomes x here   now, during summer sale additional 20% off is given ie sale price becomes 0.8x   it is given lise price is $80   => 2x = 80   => x = 30   and 0.8x = 32   so lowest sale price is 32, which is 40% of 80   hence, 30 is the answer
Answer: C
A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 40-sided polygon have? Choose the correct choice from the following answers:
A) 875  B) 740  C) 1425  D) 2025  E) 2500

Solution: There's a direct formula for this.   Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.   Here, n = 40.   Plugging it in, we get 740 diagonals!   Answer (740).
Answer: B
The bankers discount of a certain sum of money is Rs. 18 and the true discount on the same sum for the same time is Rs. 15. The sum due is:  Options:  A) 89  B) 90  C) 91  D) 92  E) 93

Solution: Sum = (90.D*T.D)/(90.D-T.D)   (18*15)/18-15;   90   ANSWER:90
Answer: B
A 2member committee comprising of one male & one female member is to be constitute out of 5 males and 3females. Among st the females. Ms.A refuses to be a member of the committee in which Mr.B is taken as the member. In how many different ways can the committee be constituted ?
Select.
A) 12	B) 14	C) 16	D) 18	E) 19

Solution: 5C1 * 3C1 -1   = 15-1= 
15-1 = 14
14   14
Answer: B
Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A and B combined. Machine D processes work three times as fast as Machine C; Machine D’s work rate is also exactly four times Machine B’s rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 6 hours and 20 minutes. If all four machines work together on the same job simultaneously, how many minutes will it take all of them to complete it? Select:	A) 15	B) 17	C) 19	D) 21	E) 24

Solution: C = A + B   D = 3C = 3(A+B) = 4B   Then B = 3A and C = 4A   The combined rate of the four machines is A + 3A + 4A + 12A = 20A   Machine A can complete the work in 380 minutes, so its rate is 1/380 of the work per minute.   The combined rate is 20/380 = 1/19 so the work will be completed in 19 minutes.   The answer is 19.
Answer: C
At what percent age above the C.P. must an article be marked so as to gain 33% after allowing a customer a discount of 5%?  Choose the correct choice from the following options.
A) 10% B) 15% C) 20% D) 25% E) 40%

Solution: Let C.P. = $100   Then, S.P. = $133   Let marked price be $x   Then, 95% of x = 133   95x/100 = 133   x = 133*100/95= 
133*100/95 = 140
140   Marked price= 40% above the C.P.   Answer is 40%
Answer: E
A student has to obtain 40% of the total marks to pass. He got 150 marks and failed by 50 marks. The maximum marks are? Pick one:
A) 500
B) 650
C) 400
D) 575
E) 610

Solution: Let the maximum marks be x   Then, 40% of x = 150+50   40x/100 = 200   x = 500   500nswer is 500
Answer: A
In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 225 and the slope of line segment AC is 4/3, what is the length of AB?  Choose the correct choice from the following choices
A) 12 B) 180 C) 24 D) 28 E) 40

Solution: Slope = Change in Vertical Direction/Change in Horizontal Direction = 4/3   Change in Vertical Direction = 4x = A180   Change in Horizontal Direction = 3x = 180C   A180^2 + 180C^2 = 225^2   16x^2 + 9x^2 = 225^2   25x^2 = 225^2   x^2 = 25*9^2   x = 45   Therefore A180 = 45*4= 
45*4 = 180
180   Answer: 180
Answer: B
In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?	Pick.
A) 1 : 2
B) 2 : 1
C) 1 : 3
D) 3 : 1
E) 2 : 3

Solution: Explanatory Answer   Let there be 1 litre of the solution after mixing 20% methyl alcohol and 50% methyl alcohol..   If the concentration of methyl alcohol in it is 40%, then 0.4 litres of the resultant mixture is methyl alcohol.   Let x litres of the solution containing 20% methyl alcohol be mixed with (1 - x) litres of the solution containing 50% methyl alcohol to get 1 litre of the solution containing 40% methyl alcohol.   X litres of 20% methyl alcohol solution will contain 20% of x = 0.2x litres of methyl alcohol in it.   (1 - x) litres of 50% methyl alcohol solution will contain 50% of (1- x) = 0.5(1 - x) litres of methyl alcohol.   The sum of these quantities of methyl alcohols added up to the total of 0.4 litres in the resultant mixture.   Therefore, 0.2x + 0.5(1 - x) = 0.4 litres   0.2x + 0.5 - 0.5x = 0.4   0.5 - 0.4 = 0.5x - 0.2x   x = 0.1/0.3 = 1/3 litres   And 1 - x = 1 - 1/3 = 2/3 litres.   So, the two solutions are mixed in the ratio of 1 : 2.   correct choice is (1 : 2)
Answer: A
A call center has two teams. Each member of Team A was able to process 7/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B? Choose the correct choice from the following answers
A) 3/2  B) 3/4  C) 8/15  D) 1/2  E) 1/5

Solution: Let team B has 8 agents, so team A has 5 agents   Let each agent of team B picked up 5 calls, so total calls by team B = 40   So, each agent in Team A picked up 7 calls, so total calls for team A = 35   Fraction for team B = 40/(40+35) = 8/15 = Answer = 8/15
Answer: C
Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?  Choose one
A) Rs.547	B) Rs.548	C) Rs.527	D) Rs.540	E) Rs.522

Solution: A+B+C = 1170   4A = 3B = 2C = x   A:B:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1170 = Rs.540   Answer: Rs.540
Answer: D
A man goes downstream at 13 kmph, and upstream8 kmph. The speed of the stream is
Choices:	A) 0kmph	B) 4kmph	C) 16kmph	D) 2.5kmph	E) 26kmph

Solution: Speed of the stream = 1/2(13-8)kmph   =2.5kmph.   correct option :2.5kmph
Answer: D
A student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
Choose the correct choice from the following:
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: xC1 * (x-1)C1=72   x^2 -x -72 =0   (X-9) (X+8) = 0   X= 9 , -8   -8 can't possible.   9
Answer: C
If x is equal to the sum of the integers from 20 to 30, inclusive, and y is the number of EVEN integers from 20 to 30, inclusive, what is the value of x+y ?  Choose the correct choice from the following options
A) 171 B) 281 C) 361 D) 461 E) 561

Solution: sum s= n/2{2a+(n-1)d} = 11/2{2*20+ (11-1)*1} =11*25= 
11*25 = 275
275=X   number of even number =( 30-20)/2 +1= 
( 30-20)/2 +1 = 6
6= Y   X+Y = 275+6= 
275+6 = 281
281   281
Answer: B
Pipes P and Q can fill a tank in 10 and 20 hours respectively. Pipe Q can empty it in 24 hours. If all the three pipes are opened together, then the tank will be filled in what time? Pick one:
A) 9 3/7 B) 5 2/7 C) 5 6/7 D) 9 3/13 E) 3

Solution: Pipe----------P---------Q--------R--------------(P+Q-R)--   Time--------10--------20-------24----------------x   *   Rate---------12--------6---------5---------------13   Work--------120------120------120--------------120   Time required to fill the tank if all the 3 pipes are open = 120/13   = 9 3/13   Ans -9 3/13
Answer: D