MU-NLPC/Calc-aqua_rat huggingface dataset:
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 ?	Choose the correct option
A) 240  B) 388  C) 208  D) 112  E) 102

Solution: The ratio of A & B investments = (3x8 + 2x4):(4x8 + 5x4)   => 8:13   => 8/21 x 630 = 240.   240nswer: 240
Answer: A
How many three letter words are formed using the letters of the word TIME?	Choose the most appropriate option: A) 20 B) 24 C) 26 D) 28 E) 32

Solution: Explanation:   The number of letters in the given word is four.   The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2= 
4 * 3 * 2 = 24
24.   Answer: Option 24
Answer: B
How many of the following numbers are divisible by 132?
264,396,462,792,968,2178,5184,6336  Choose the correct choice from the following answers:
A) 4
B) 5
C) 6
D) 7
E) 89

Solution: Explanation:   132 = 4 x 3 x 11, So if the number is divisible by all three numbers 4,3 and 11,then the number is divisible by 132 also.   264 => 4,3,11(/)   396 => 4,3,11(/)   462 => 11,3   792 => 4,3,11(/)   968 => 11,4   2178 => 11,3   5184 => 3,4   6336 => 4,3,11(/)   Required number of numbers=4.   4nswer: 4) 4
Answer: A
If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is:	Answers
A) 80%	B) 90%	C) 33%	D) 40%	E) 10%

Solution: Explanation:   Let C.P. of each pen be Re. 1.   Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12.   Gain % = 3/9 * 100 = 33%   Answer:33%
Answer: C
The sum of the heights of two high-rises is x feet. If the first high rise is 36 feet taller than the second, how tall will the second high rise be after they add an antenna with a height of z feet to the top?  Choose the correct choice from the following answers.
A) (x+z)/2 + 36	B) 2x−(37+z)	C) (x−36)/2 + z	D) x/2 - 37 + z	E) (2x−37)/z

Solution: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:   h1 + h2 = x   and h1 = h2 + 36 =>   Q: h2 + z = ?   h2 + h2 + 36 = x => 2h2 = x-376=? h2 = (x-36)/2   => h2 + z = (x-36)/2 + z, (x−36)/2 + zORRE(x−36)/2 + zT ANSWER (x−36)/2 + z
Answer: C
The cost of 2 liters of lube oil is $7. What is the cost of 5 liters of lube oil?	Select.
A) 17.5
B) 20.5
C) 24.0
D) 28.5
E) 30.0

Solution: The cost of one liter of oil=7/2= 
7/2 = 7/2 = around 3.5
3.5   The cost of five liters of oil= 3.5x5= $ 17.5   17.5nswer: 17.5
Answer: A
What is the greatest prime factor of 2^8 - 1?  Choices:
A) 11  B) 13  C) 17  D) 19  E) 23

Solution: 2^8-1 = (2^4-1)(2^4+1) = 15*17   The answer is 17.
Answer: C
There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.84 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?	Choose the correct choice.
A) Rs 450	B) Rs 920	C) Rs 550	D) Rs.630	E) None of these

Solution: Explanation :   Let the original average expenditure be Rs.x then,   42(x - 1) - 35x = 84 ? 7x = 126 ? x = 18   Therefore original expenditure = Rs.(35 18)=Rs.630.   Answer : Rs.630
Answer: D
The sum of the first 50 positive even integers is 2550. What is the sum T of even integers from 102 to 200 inclusive?
Select
A) 5100  B) 7550  C) 10100  D) 15500  E) 20100

Solution: My solution is:   First 50 even integers:   2   4   6   8   <...>   Integers from 102 to 200   102   104   106   108   <...>   We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:   T=2550+(100*50)=7550.7550
Answer: B
What is the sum of the odd integers from 35 to 65, inclusive? Pick one:
A) 800
B) 550
C) 555
D) 600
E) 605

Solution: The mean is 50.   Sum=Mean(# of elements)   There are 16 odd numbers between 35-65 inclusive. 16*50=800   800
Answer: A
10% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3213, how much was it in the beginning?  Choose the correct choice from the following answers:
A) A)3800
B) B)4200
C) C)4400
D) D)4500
E) E)4600

Solution: X * (90/100) * (85/100) = 3213   X = 4200   ANSWER:4200
Answer: B
Two employees X and Y are paid a total of Rs. 528 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?	Choose one.
A) s.250 B) s.280 C) s.290 D) s.299 E) s.240

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 528   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 528   ⇒ y[12/10 + 1] = 528   ⇒ 22y/10 = 528   ⇒ 22y = 5280   ⇒ y = 5280/22 = 480/2 = Rs.240   s.240
Answer: E
A flamboyant comic book villain has abducted a bystander! Captain Valiant is alerted to the crime and reaches the start of the villain's trail 30 minutes later. The villain is in a getaway car going 40 kmph, and Captain Valiant can fly at 50 kmph. How long will the bystander have to wait for rescue?
Choose the correct choice from the following answers.
A) 1 hour  B) 1 1/2 hours  C) 2 hours  D) 2 1/2 hours  E) 3 hours

Solution: Distance covered by the villain in 1/2 hour = 20 km   Now, 10 km is compensated in 1 hour   Therefore 20 km will be compensated in 2 hours   Added to the half hour head start, the bystander has been kidnapped for 2 1/2 hours.   Correct Answer: 2 1/2 hours
Answer: D
Find the middle one when The sum of three consecutive even numbers is 36?	Select:
A) 11	B) 12	C) 14	D) 16	E) 17

Solution: 3 consecutive numbers can be a - 1, a, a + 1   So sum of numbers = 3a = 36.   Hence a = 12.   12
Answer: B
What is the are of an equilateral triangle of side 18 cm?	Choose the correct choice:
A) 66âˆš3 cm2	B) 74âˆš3 cm2	C) 81âˆš3 cm2	D) 64âˆš5 cm2	E) 14âˆš3 cm2

Solution: Area of an equilateral triangle = âˆš3/4 S2   If S = 18, Area of triangle = âˆš3/4 * 18 * 18 = 81âˆš3 cm2;   Answer:81âˆš3 cm2
Answer: C
A man is 26 years older than his studen. In two years, his age will be twice the age of his student. The present age of his student is:
Choose the correct answer
A) 20
B) 21
C) 22
D) 23
E) 24

Solution: Let the student's present age be x years. Then, man's present age = (x + 26) years.   (x + 26) + 2 = 2(x + 2)   x + 28 = 2x + 4   x = 24.   Answer:24
Answer: E
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
Pick:	A) 3630	B) 2899	C) 277	D) 2870	E) 2787

Solution: 6300:4200:10500   3:2:5   3/10 * 12100= 
3/10 * 12100 = 3_630
3630   3630nswer:3630
Answer: A
Find the value of X, Y by solving the below equations
X + Y = 15
X - Y = 5 Choose the correct choice from the following options.
A) 10, 5	B) 8, 7	C) 9, 6	D) 11, 4	E) 12, 3

Solution: X + Y = 15 ---(I)   X - Y = 5 -----(II) by adding (I) and (II)   ------------   2X = 20 ==> X = 20/2= 
20/2 = 10
10   By Replacing the value of X in (I) we get 10 + Y= 15 ==>   Y = 15 -10= 
15 -10 = 5
5.   So, X= 10, Y = 5   10, 5nswer 10, 5) 10, 5
Answer: A
A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 64 chose brand C. Which of the following could be the number of customers who preferred brand D?	Select the correct option
A) 1  B) 8  C) 14  D) 20  E) 27

Solution: I get D, but I'm not sure that my method is sound.   You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.   x = total number of testers   A + B + C + D   .61x + (.5)(.61x) + 65 + D = x   .61x + .305x + 65 + D = x   I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.   x = 400   A = 244, B = 122, C = 65..also over 400   x = 600   A = 366, B = 183 C = 65....also over 600   x = 800   A = 488, B = 244, C = 65...D = 3...not an option on the list.   x = 1000   A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.   27
Answer: E
John had a stock of 1400 books in his bookshop. He sold 62 on Monday, 62 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold?
Select:  A) 81.57%  B) 36.5%  C) 80.67%  D) 56.5%  E) 80.57%

Solution: Let N be the total number of books sold. Hence   N = 62 + 62 + 60 + 48 + 40= 
62 + 62 + 60 + 48 + 40 = 272
272   Let M be the books NOT sold   M= 1400 - N = 1400- 272= 
1400- 272 = 1_128
1128   Percentage   Books not sold / total number of books= 1128/1200 = 0.81 = 80.57%   correct answer 80.57%
Answer: E
Find the maximum value of the function f(x)=x−5 if x is a number between -5 and 13. Select the correct option
A) 6
B) 7
C) 8
D) 9
E) None

Solution: Solution:   Since f(x) is a linear function whose slope is 1, a positive number, it is strictly increasing for all x. Therefore its maximal value is reached for the largest value of x, x=13 and f(x)=13-5= 
13-5 = 8
8.   Answer 8
Answer: C
A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet? Choose the correct choice from the following options:
A) 6
B) 5
C) 4
D) 9
E) 6

Solution: 9 a.m.   Answer: 4
Answer: C
Tough and Tricky questions: Percents.
Over the course of a year, a certain microbrewery increased its beer output by 60 percent. At the same time, it decreased its total working hours by 30 percent. By what percent did this factory increase its output per hour?  Pick one.
A) 228.5
B) 228
C) 229.5
D) 220
E) 229

Solution: Lets assume the initial production was 100 litres of beer for 100 hr.   With the 60% increase the total amount of beer production will be 160 litres and with 30 % decrease in total hours will be reduced to 70 hr.   100hr ----> 100 lts   1hr -----> 1 lts   70hr -----> 160 lts   1hr -----> 2.28 lts   Total Increase in production for 1 hr = 228%   Answer 228
Answer: B
A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 25% impurities to the product. Find the net profit percentage of the dealer?
Pick one
A) 44%	B) 40%	C) 50%	D) 56.25%	E) 36.25%

Solution: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.   It means that he is selling $4 worth of product for $5.   The dealer then further added 25% impurities to the product.   It means that he is selling $5 worth of product for $6.25.   So his profit is $6.25-$4 = $2.25   and his profit percent is   (2.25/4)*100 6.25- 4= 
6.25- 4 = 2.25
$2.25   and his profit percent is    (2.25/4)*100= 
 (2.25/4)*100 = 56.25
56.25%   Answer:- 56.25%
Answer: D
The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?  Choose one:
A) 16 2/7%	B) 16 2/6%	C) 16 2/3%	D) 16 7/3%	E) 12 2/3%

Solution: 10 16 2/3%P = 12 SP   12 --- 2 16 2/3%P loss   100 --- ? => 16 2/3%   Answer: 16 2/3%
Answer: C
At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 4 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?
Choose the correct option:
A) 7  B) 14  C) 25  D) 27  E) 30

Solution: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -   8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)   20 + 3*14 -8 * 4 = 27   27
Answer: D
There are 10 balls in a box: 5 balls are green, 3 are blue and 2 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a white ball is selected at random from the box?
Choose the correct choice from the following answers:	A) 1/13	B) 4/13	C) 3/13	D) 5/13	E) 2/8

Solution: If 1 green and 1 blue ball are taken from the box, then there are 4 green, 2 blue and 2 white balls, a total of 8 balls. If one ball is selected at random, the probability that it is white is given by 2 / 8   Answer : 2/8
Answer: E
Each of the 43 points is placed either inside or on the surface of a perfect sphere. If 16% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?  Choose the correct option:  A) 3  B) 11  C) 13  D) 23  E) 38

Solution: Maximum number of points on the surface is 16%*43 = 6.88 ... or 6 since it has to be an integer   Now note that if two points form a diameter, they cannot be part of any other diameter.   So in the best case we can pair up the points   We have 6 points, so at best we can form 3 pairs (6).   So, answer is (3)
Answer: A
On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 160 is how many times an intensity corresponding to a magnitude of 125?  Options.
A) 40  B) 100  C) 400  D) 1000  E) 10 000

Solution: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:   If intensity for 125 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 160 it'll be 10*10*10*10*x=10^3*x.   Answer: 1000.
Answer: D
Working together, printer M and printer N would finish the task in 24 minutes. Printer M alone would finish the task in 60 minutes. How many pages does the task contain if printer N prints 5 pages a minute more than printer M?  Choose the correct option.
A) 400
B) 450
C) 600
D) 1200
E) 1500

Solution: 24*M + 24*N = x pages   in 24 mins printer M will print = 24/60 * x pages = 2/5*x pages   thus in 24 mins printer printer N will print x - 2/5*x = 3/5*x pages   Also it is given that printer N prints 5 more pages per min that printer M. In 24 mins printer N will print 120 more pages than printer M   thus 3/5*x - 2/5*x = 120 => x = 600 pages   600)
Answer: C
If 'a' and 'b' are non-zero numbers such that their sum is ten times the product, what is the value of 1/a + 1/b?
Pick.
A) 2 B) 5 C) 10 D) 15 E) 20

Solution: a+b = 10ab   1/a + 1/b = (b + a)/(ab) = 10.   The answer is 10.
Answer: C
Two friends plan to walk along a 22-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 20% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other? Choose the correct choice from the following answers:
A) 10	B) 11	C) 12	D) 13	E) 14

Solution: If Q complete x kilometers, then P completes 1.2x kilometers.   x + 1.2x = 22   2.2x=22   x = 10   Then P will have have walked   1.2*10= 
  1.2*10 = 12
12 km.   The answer is 12.
Answer: C
1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of the girls pass. The percentage of the total who failed is ?
Choose the correct choice from the following answers:
A) 63.3%
B) 52.4%
C) 81.2%
D) 75.4%
E) 69.1%

Solution: Total number of students = 1100+700= 
1100+700 = 1_800
1800   Number of students passed= (42% of 1100+30% of 700) = 462+210= 
462+210 = 672
672   number of failures= 1128*100/1800 = 190/3%= 63.3%   63.3%nswer is 63.3%
Answer: A
The average of 10 numbers is 23. If each number is increased by 4, what will the new average be? Choose the correct choice from the following options:
A) 36
B) 27
C) 72
D) 29
E) 22

Solution: Sum of the 10 numbers = 230   If each number is increased by 4, the total increase =   4 * 10= 
4 * 10 = 40
40   The new sum= 230 + 40= 
230 + 40 = 270
270 The new average= 270/10= 
270/10 = 27
27.   Answer:27
Answer: B
Find the odd man out. 18, 16, 12, 24, 11, 34, 46  Select
A) 16
B) 46
C) 16
D) 11
E) 12

Solution: Explanation :   11 is the only odd number in the given series. Answer : Option 11
Answer: D
Out of a world population of approximately 6.6 billion, 1.2 billion people live in the richer countries of Europe, North America, Japan and Oceania and is growing at the rate of 0.25% per year, while the other 5.4 billion people live in the lees developed countries and is growing at the rate of 1.5%. What will be the world population in 5 years if we assume that these rates of increase will stay constant for the next 5 years. (round answer to 3 significant digits) Choose the correct choice from the following answers:
A) 7.02 billion.	B) 7.03 billion.	C) 7.04 billion.	D) 7.05 billion.	E) 7.06 billion.

Solution: Solution to Problem 12:   Let us first calculate the population PR in 5 years in the richer countries   PR = (1.2 + 0.25% * 1.2) = 1.2(1 + 0.25%) after one year   PR = 1.2(1 + 0.25%) + 0.25% * 1.2(1 + 0.25%)   = 1.2(1 + 0.25%) 2after two years   Continue with the above and after 5 years, PR will be   PR = 1.2(1 + 0.25%) 5 after 5 years   Similar calculations can be used to find the population PL in less developed countries after 5 years.   PL = 5.4(1 + 1.5%) 5 after 5 years   The world population P after 5 years will be   P = PR + PL = 1.2(1 + 0.25%) 5 + 5.4(1 + 1.5%) 5 = 7.03 billion.   Answer 7.03 billion.
Answer: B
A right triangle AWC has to be constructed in the xy-plane so that the right angle is at A and AW is parallel to x axis. The coordinates of A, W and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
Choose the correct option:
A) 63 B) 336 C) 567 D) 3024 E) 5040

Solution: All the cordinates are integer hence,   possible AW values are   {-1,0}, {-1,1} ....{-1,7}: 8 ways   ....   {7,-1}, {7,0} ......{7,6}: 8 ways     9*8= 
  9*8 = 72
72   for AC values can be   {1,2}, {1,3} .... {1,7} : 6ways   ......   {7,1}, {7,2} ..... {7,6} : 6 ways     7*6= 
  7*6 = 42
42   Total= 72 * 42= 
72 * 42 = 3_024
3024 hence 3024
Answer: D
At a wedding reception, 125 guests ate chicken and 75 guests ate beef. If exactly 100 guests ate only one of the two types of meat, how many guests ate both types of meat?
Choices:
A) 5  B) 100  C) 7  D) 4  E) 50

Solution: Say x guests ate both types of meat.   (125 - x) + (75 - x) = 100 --> x = 50.   Answer: 50.
Answer: E
After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago.What is the difference between the ages of the replaced and the new member? Select
A) 2 years  B) 4 years  C) 8 years  D) 15 years  E) 25 years

Solution: the age 5 members will be 13,14,15,16 and 17   3 years before there age was 10,11,12,13 and 14 hence the average is 12(10+11+12+13+14/5=60/5= 
60/5 = 12
12).   now if the oldest man 17 is replaced by 2 the the average is become same as three years ago the are .   as (13+14+15+16+2)/5= 60/5= 
60/5 = 12
12.   hence the difference between the ages of the replaced and the new member is  17-2= 
 17-2 = 15
15.   ANSWER:15 years
Answer: D
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:	Choose the correct choice from the following choices.
A) 50
B) 874
C) 168
D) 578
E) 120

Solution: 120xplanation:   Let speed of the car be x kmph   hen, speed of the train =150/100X=3/2X kmph   75/x-75/(3/2)x=125/(10*60)   75/x-50/x=5/24   x=25*24/5= 
25*24/5 = 120
120 kmph   Answer 120
Answer: E
70 students are required to paint a picture. 52 use green color and some children use red, 38 students use both the colors. How many students use red color?  Pick:
A) 53
B) 54
C) 55
D) 56
E) 57

Solution: 70 = red +green -both   Red = 70-green+both = 70-52+38= 
70-52+38 = 56
56   ANSWER:56
Answer: D
A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?  Choose the correct option
A) 500  B) 560  C) 670  D) 800  E) 900

Solution: science books sold = 2x × 0.2 = 0.4x   science books unsold = 2x – 0.4x = 1.6x   art books sold = 5x × 0.2 = x   art books unsold = 5x – x = 4x   total books unsold = 1.6x + 4x = 5.6x   5.6x 1.6  + 4= 
1.6  + 4 = 5.6
5.6x   5.6x= 2240   x = 400   2x science = 800   800
Answer: D
A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is
Select the correct option:
A) 22030
B) 220030
C) 23030
D) 24030
E) 20303

Solution: Explanation:   (555 + 445) * 2 * 110 + 30 = 220000 + 30= 
220000 + 30 = 220_030
220030   Option 220030
Answer: B
The Racing magic takes 40 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?  Select the correct option:
A) 3	B) 6	C) 9	D) 12	E) 15

Solution: Time taken by Racing magic to make one circle = 40 seconds   Time taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds   LCM of 90 and 40 seconds = 360 seconds = 6 mins   Time taken for them to meet at the starting point for the second time = 6 mins *2 = 12 mins   Answer 12
Answer: D
Balls are bought at 11 for Rs.10/- and sold at 10 for Rs.11/-. Find the gain or loss percentage?	Choose the correct option:
A) 21 % Profit
B) 22 % Profit
C) 24 % Profit
D) 31 % Profit
E) 32 % Profit

Solution: 11 balls -----> Rs.10/-   10 balls -----> Rs.11/-   Note: Number of articles bought is must equal to number of articles sold.   10(11 10) ==> 110 100 = Cost price   11(10 11) ==> 110 121 = Selling price   Then, 21/100 × 100 = 21 % Profit   21 % Profit)
Answer: A
if there is one larger cube with surface area 600 and no. of smaller cubes with surface area 24.then how many small cubes are required to make a larger cube with surface area of 600? Choose the correct choice from the following options:
A) 5
B) 125
C) 4
D) 100
E) 24

Solution: the ratio between larger and smaller is   6a12:6a22=600:24   a12:a22=100:4   a1:a2=10:2   then length of cube is 10 and 2   so make a cube with length 10, we have to 5 small cubes each in length, breadth and height. so total 125 cubes are required.   then the answer is 125
Answer: B
In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is?  Select
A) 11
B) 20
C) 28
D) 17
E) 13

Solution: Explanation:   It is the same as a person with 20 years more age replaces an existing person of the group ( or village)   Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.   Alternatively : ( n x 42 ) + 20 = ( n x 43 )   => n=20   Answer: 20
Answer: B
Harry started a 7-mile hike with a full 11-cup canteen of water and finished the hike in 3 hours with 2 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 3 cups of water during the last mile, how many cups did he drink per mile during the first 6 miles of the hike? Choose the correct choice from the following answers.
A) 2/6 B) 3/6 C) 4/6 D) 6/4 E) 5/6

Solution: No of cups leaked during the trip = 3 cups.   No of cups Harry drank = 6 cups.   No of cups harry drank during the first 6 miles = 3.   drink / mile = 3/6   Answer: 3/6
Answer: B
A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 55000. What is the share of C?
Pick one
A) Rs. 12250
B) Rs. 13375
C) Rs. 16750
D) Rs. 15000
E) None of these

Solution: Explanation:   Let the investment of C be Rs. x.   The inverstment of B = Rs.(2x/3)   The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)   Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3   C's share = Rs. [(3/11) × 55000] = Rs. 15000   Answer: Option Rs. 15000
Answer: D