MU-NLPC/Calc-aqua_rat huggingface dataset:
If x is a positive integer with fewer than 3 digits, what is the probability W that x*(x + 1) is a multiple of either 4 or 5?  Choose one.
A) 4/99
B) 2/25
C) 8/99
D) 49/100
E) 86/99

Solution: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.   We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability W that x(x+1) is a multiple of either 4 or 5.   When will this happen? If either x OR (x+1) is a multiple of 4 or 5.   Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.   Out of the numbers from 1 to 20:   4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20   So, 14 out of the first 20 numbers match our criteria. Since:   probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (86/99) is the only answer greater than 1/2, we go with (86/99).
Answer: E
Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?	Select the correct option.
A) 20% B) 42% C) 44% D) 66% E) 84%

Solution: You are correct. People who cover local politics are a subset of people who cover politics.   25% of reporters who cover politics do not cover local politics so 75% DO cover local politics.   Reporters covering local politics= 75% of reporters covering politics= 25% of all reporters   Reporters covering politics/All Reporters = 25/75 = 1/3   Reporters not covering politics/All Reporters = 2/3 = 66%=66%
Answer: D
What least number must be subtracted from 2000 to get a number exactly divisible by 17 ? Pick one
A) 11  B) 12  C) 13  D) 14  E) 15

Solution: Sol. On dividing 2000 by 17, we get 11 as remainder.   Required number to be subtracted = 11.   Option 11
Answer: A
The least number which should be added to 1920 so that the sum is exactly divisible by 5,6,4 and 3 is :	Choose the correct option:
A) 3  B) 13  C) 23  D) 33  E) 28

Solution: Solution   L.C.M. of 5,6,4 and 3 = 60. on dividing 1920 by 60, the remainder is 32.   ∴ Number to be added = (60-32)= 
(60-32) = 28
28. Answer 28
Answer: E
Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 40mph, what was his average speed over the three hour portion of his ride?  Choose one:
A) 14 mph
B) 40 mph
C) 70/3 mph
D) 80/3 mph
E) 34 mph

Solution: Average speed for first two hours, S1 = 40 mph   Distance travelled in these two hours, D1 = 80 miles   Average speed for the entire 5 hour ride, S = 40 mph   Total Distance traveller in the entire 5 hour ride, D = 40 x 5 = 200 miles.   Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 200 - 80= 
200 - 80 = 120
120   Average speed for the latter 3 hour period S2= D2/3 = 120/3= 
120/3 = 40
40   Hence, the correct answer is 40 mph
Answer: B
Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?  Choose the correct choice from the following:
A) 5040
B) 2520
C) 360
D) 120
E) 42

Solution: 6! = 720   720/2= 
720/2 = 360
360 half the time carmelo is in front, vice versa   Answer:   (360) 360
Answer: C
60 % of 2 is equal to	Answers
A) 1.2  B) 0.4  C) 0.6  D) 0.7  E) 0.9

Solution: 60 % of 2 = (60 / 100) * 2= 
(60 / 100) * 2 = 6/5 = around 1.2
1.2   1.2nswer: Option 1.2
Answer: A
Find the cost price of an item if by selling at Rs.320, a profit of 6% is made? Select the correct option
A) Rs.300	B) Rs.200	C) Rs.500	D) Rs.100	E) Rs.310

Solution: SP = 320   CP = (SP)*[100/(100+P)]   = 320 * [100/(100+6)]   = Rs.300   Rs.300nswer: Rs.300
Answer: A
The speed at which a man can row a boat in still water is 6 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 80 meters?
Choose the correct choice:
A) 28	B) 32	C) 36	D) 40	E) 44

Solution: The speed of the boat downstream = 6 + 3= 
6 + 3 = 9
9 km/hr   9 km/hr * 5/18= 2.5 m/s   The time taken to cover 80 meters = 80/2.5= 
80/2.5 = 32
32 seconds.   The answer is 32.
Answer: B
A shopkeeper sold an article at $100 with 15% profit. Then find its cost price?	Choose the correct choice from the following options.
A) $120  B) $100  C) $91  D) $87  E) $69

Solution: cost price = selling price *100/(100+profit)   C.P. = 100*100/115 = $87(approximately)   Answer is $87
Answer: D
Bill is golfing with three friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome, if he will buy no more than 3 packages of the generic golf tees? Choose the correct choice from the following answers
A) 16 B) 10 C) 8 D) 22 E) 2

Solution: At least 20 golf tees for each member of his foursome = total of at least 4*20= 
4*20 = 80
80 tees.   3 packages of the generic golf tees, that are packaged by the dozen= 3*12= 
3*12 = 36
36 tees.   So, Bill must by at least 44 Aero tees. They come by the pair, hence he must by at least 44/2= 
44/2 = 22
22 packages of Aero flight tees.   Answer: 22
Answer: D
The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child? Choose one:
A) 2 years
B) 8 years
C) 3 years
D) 4 years
E) 1 years

Solution: 28 * 2= 
28 * 2 = 56
56   20 * 3= 
20 * 3 = 60
60   -----------   4 years   Answer:4 years
Answer: D
There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
Choose the correct choice from the following answers:  A) 3  B) 6  C) 9  D) 15  E) 21

Solution: List down possibilities: From only 1 box all the way to all 6   If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.   If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.   If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.   If all 6 boxes have green balls, there is just 1 possibility.   Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1= 
6 + 5 + 4 + 3 + 2 + 1 = 21
21.   Option 21
Answer: E
In a kilo meter race, if A gives B a 40 m start, A wins by 19 s. But if A gives B a 30 s start, B wins by 40 m. Find the time taken by B to run 5,000 m?	Choose the correct answer:
A) 150 s  B) 450 s  C) 750 s  D) 825 s  E) 925 s

Solution: When B is given a 40 m start then B runs 960m in T secs and A runs 1000m in T-19 secs.   When B is given a 30 second start then B runs 1000m in t secs and A runs 960m in t - 30 secs.   Assume that the speed of A (Va) and B (Vb) is constant in both situations.   Then Vb = 960 ÷ T = 1000 ÷ t, and Va = 1000 ÷ (T - 19) = 960 ÷ (t - 30)   So 960t = 1000T, and 1000t - 30000 = 960T - 18240. Then 40t = -40T + 11760, t = -T + 294.   Substituting for t in 960t = 1000T   gives : -960T + 282240 = 1000T   1960T = 282240   T = 144   B 's speed is 960 / T = 960 / 144 = 6.67 metres per second.   Assuming the same constant speed to run 5000 metres then the time taken is   5000 / 6.67 = 750 seconds   ANSWER:750 s
Answer: C
The average weight of 4 person's increases by 3 kg when a new person comes in place of one of them weighing 70 kg. What might be the weight of the new person?
Choose one
A) 75 kg B) 82 kg C) 86 kg D) Data inadequate E) None of these

Solution: Total weight increased = (4 x 3) kg = 12 kg.   Weight of new person = (70 + 12)= 
(70 + 12) = 82
82 kg.   Answer: Option 82 kg
Answer: B
When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? Choose the correct answer:
A) 4.5 B) 5 C) 5.6 D) 7 E) 7.2

Solution: if $x$ is the number, x/6 * 12 = 9   => 2x = 9   => x = 4.5   4.5
Answer: A
Trapezoid ABCD has AB parallel to CD, with \ADC = 90o. Given that AD = 5, BC = 13
and DC = 18, compute the area of the trapezoid.	Pick:
A) 30 B) 40 C) 50 D) 60 E) 70

Solution: The trapezoid can be divided into a right triangle with legs of length 5 and 12, and   a rectangle with side lengths 5 and 6. This gives an area of 60 .   correct answer 60
Answer: D
The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?	Choose the correct choice from the following choices.
A) 221
B) 240
C) 388
D) 288
E) 113

Solution: Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)   Their sum = 10x = 440   x = 44 => 2(x - 2) = 84   Second least number of the other set = 2(84) - 121 = 47   This set has its least number as 46.   Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50   = 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240   Answer: 240
Answer: B
Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 90 players took part in that tournament.
How many matches were played? Choose the correct choice from the following answers:
A) 99 matches.	B) 89 matches.	C) 77 matches.	D) 66 matches.	E) 55 matches.

Solution: Solution:   89 matches.   The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 89 matches were played.   Answer 89 matches.
Answer: B
If a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 30 minutes? Select.
A) 165km B) 170km C) 176.4km D) 180km E) 190km

Solution: 14 m/s = 14 * 18/5 kmph   3 hours 30 minutes = 3 1/2 hours = 7/2 hours   Distance = speed * time = 14 * 18/5 * 7/2= 
14 * 18/5 * 7/2 = 882/5 = around 176.4
176.4 km.   Answer:176.4km
Answer: C
If 20m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options
A) 2m −1 B) 4m C) 6m D) 7m E) 6m/5

Solution: 20m - n = p   Add n to both sides:   20m = n + p   Add m to both sides:   21m = n + p + m   Now, divide both sides by 3   7m = (n + p + m)/3 = the average of n, p, and m   7m
Answer: D
3 men or 6 women can do a piece of work in 21 days. In how many days will 12 men and 8 women do the same work? Choose the correct option
A) 63/16 days
B) 15/4 days
C) 18/4 days
D) 11/4 days
E) 35/4 days

Solution: 3M = 6W ---- 21 days   12M + 8W -----?   24W + 8 W = 32W ---?   6W ---- 21 32 -----?   6 * 21  24  + 8= 
 24  + 8 = 32
32W ---?   6W ---- 21 32 -----?   6 * 21= 32 * x => x = 63/16 days   63/16 daysnswer:63/16 days
Answer: A
An outlet pipe can empty 1/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
Choose the correct choice from the following options.
A) 4/9 B) 4/3 C) 2/9 D) 4/8 E) 4/1

Solution: 1/3 ---- 12   ? ----- 8 ==> 2/9   Answer: 2/9
Answer: C
Which one the following fractions has the Highest value?	Pick.
A) A)120/847	B) B)120/849	C) C)120/874	D) D)120/877	E) E)240/1700

Solution: 240/1700 = 120/850.   Now, all options have the same numerator 123.   If numerator is same, the fraction with the Highest value will be the one with the Lowest denominator.   120/847nswer (120/847).
Answer: A
How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
Choose one
A) 20.0 kgs  B) 12.5  C) 16.0 kgs  D) 200.0 kgs  E) None of these

Solution: Explanation :   Given, there is 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg.   C.P of 1 kg of rice of 1st kind = Rs. 42.   C.P of 1 kg of rice of 2nd kind = Rs. 24.   Mean price = Rs. 40   By the rule of alligation, we have:   C.P. of 1kg of C.P. of 1kg of   rice of 1st rice of 2nd   kind (Rs. 42/kg) kind (Rs. 24/kg)   \ /   Mean Price   (Rs. 32/kg)   / \   40 - 24 : 42 - 32   (8) (10)   Let the amount of Basmati rice being mixed be x kgs.   =>8/10=x/25.   =>x=20.   Hence, amount is 20.0 kgs.   20.0 kgsnswer : 20.0 kgs
Answer: A
The difference between the place values of 9 and 4 in the number 529435 is Choose one:	A) 8500	B) 8900	C) 8600	D) 6970	E) None

Solution: Sol.= (Place value of 9) – (place Value of 4)= (9000 - 400)= 
(9000 - 400) = 8_600
8600 Answer 8600
Answer: C
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 38 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?  Choose the correct option:	A) 405	B) 420	C) 440	D) 447	E) 490

Solution: Car Y began travelling after 72 minutes or 1.2 hours.   Let t be the time for which car Y travelled before it stopped.   Both cars stop when they have travelled the same distance.   So,   35(t+1.2) = 38t   t=14   Distance traveled by car X from the time car Y began traveling until both cars stopped is   35 x 14   = 490 miles   Answer:- 490
Answer: E
A and B started a business with their capitals Rs. 24,000 and 48,000 respectively. Annual profit will be distributed between them in the ratio  Choose the correct choice from the following choices
A) 1:4	B) 2:3	C) 1:2	D) 1:5	E) 2:5

Solution: 24,000:48,000   Ans. 1:2   ANSWER:1:2
Answer: C
An article when sold for 200 fetches 25 per cent profit. What would be the percentage profit/loss if 6 such articles are sold for 1,056?  Select the correct option.
A) 10 per cent loss
B) 10 per cent profit
C) 5 per cent loss
D) 5 per cent profit
E) None of these

Solution: CP = 200⁄125 × 100 = 160   ∴ CP of 6 articles = 6 × 160 = 960   ∴ profit = 1056 – 960 = 96   Percentage profit = 96⁄960 × 100 = 10%   Answer 10 per cent profit
Answer: B
There are 4 girls and 4 boys. If they are to be seated in a row, what is the probability that no two girls sit together? Choose the correct choice from the following answers.
A) A)1/8!  B) B)6!5!/8!  C) C)2*4!4!/8!  D) D)2∗6!6!/12!  E) E)6!7!/12!

Solution: If girls are alternate, then only no 2 girls can be together.   So among 8 places, girls can be seated in 4 alternate places in 4! ways.   And boys can be seated in the remaining 4 places in 4! ways.   Therefore total number of ways = 4! * 4!   But there could be 2 such arrangements-->   1. When first place is filled by a girl   2. When first place is filled by a boy   Therefore total number of ways = 2*4! * 4!   Also total number of ways to fill 8 places = 8!   Hence probability =2∗4!4!/8!   Answer:2*4!4!/8!
Answer: C
In a village they organize 4 programs for an festival. The festival occurs in 2 days. In how many ways that the 4 programs can be divided for 2 days festival? Choose the correct choice from the following:
A) 12	B) 10	C) 6	D) 4	E) 2

Solution: Here 4 programs organize for 2 day festival. So, 4C2 ways to solve this problem.   4C2=4!/2!*2!   4C2=4*3*2!/2!*2*1=6   There are 6 ways to divided the programs.   Answer:option 6
Answer: C
Which of the following inequalities is equivalent to –2 < x < 4 ?  Select
A) | x – 2 | < 4	B) | x – 1 | < 3	C) | x + 1 | < 3	D) | x + 2 | < 4	E) None of the above

Solution: First remove the mod   then set the expression to 0   then get a value of X   then add and subtract the value from the given number on the RHS   Lets try with an example (| x – 1 | < 3) --------------> | x – 1 | < 3   First remove the mod -------------------> x-1   then set the expression to 0--------------> x-1=0   then get a value of x---------------------> x=1   then add and subtract the value from the given number on the RHS   1+3= 
  1+3 = 4
4 and 1-3= -2   the range become -2 to 4 correct answer   Now try its with an incorrect option (C) | ----------> |x + 1 | < 3   First remove the mod --------------------------> x+1   then set the expression to 0----------------------> x+1=0   then get a value of x------------------------------> x=-1   then add and subtract the value from the given number on the RHS   -1+3= 
  -1+3 = 2
2 and -1-3= -4   the range become -4 to 2 Incorrect   THE CORRECT ANSWER IS | x – 1 | < 3
Answer: B
The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 2500?  Select
A) 7  B) 9  C) 11  D) 13  E) 15

Solution: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^11 = 2048 < 2500, then the greatest possible length of integer z is 11.   The answer is 11.
Answer: C
A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 69 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 Choices:
A) 2000
B) 2100
C) 2200
D) 2300
E) 2400

Solution: 1 percent for 3 years= 69   1 percent for 1 year = 23   => 100 percent = 2300   ANSWER:2300
Answer: D
It takes Avery 2 hours to build a brick wall while Tom can do it in 5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own? Select the correct option:
A) 25 minutes.	B) 30 minutes.	C) 40 minutes.	D) 1 hour and 30 minutes	E) 1 hour and 20 minutes

Solution: Avery's efficiency is 100/2= 
100/2 = 50
50%   Tom's= 100/5= 
100/5 = 20
20%   they worked together for 1 hour and finished 70% of the job   remaining= 30 %   Tom will complete 20% in 60 minutes , and   10% in   60*10/20= 
  60*10/20 = 30
30 minutes   Time taken by Tom to finish the remaining on his own= 60+30= 
60+30 = 90
90 minutes   ANSWER:1 hour and 30 minutes
Answer: D
T is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can T be?	Choose the correct choice from the following choices: A) 300,000 B) 349,999 C) 350,000 D) 399,999 E) 400,000

Solution: T 1,000,000-300,000=700,000 integers   700,000/2= 350,000 even integers.   350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.   350,001-2=349,999   349,999
Answer: B
A box of paper clips contains 100 clips. If an office uses paper clips at the rate of 15 per 100 pieces of outgoing mail, how many boxes will be required for the 4000 pieces of outgoing mail? Choose one: A) 4 boxes B) 5 boxes C) 6 boxes D) 7 boxes E) 8 boxes

Solution: 15clips --- 100 pieces   x clips --- 4000 pieces   x = 4000/100 * 15= 
4000/100 * 15 = 600
600 clips   1 box -- 100 clips   y box -- 600= 
-- 600 = 600
600/100= 
600/100 = 6
6 boxes   ANSWER:6 boxes
Answer: C
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 3 is
Choose the correct choice from the following:
A) 3
B) 189
C) 221
D) 227
E) 230

Solution: In that case, the Sophie prime numbers greater than 5 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9   Product would be 1 x 3 x 7x9 =189 Answer should be 189.
Answer: B
A camera lens filter kit containing 5 filters sells for $52.50. If the filters are purchased individually, 2 of them are priced at $6.45 each, 2 at $11.05 each, 1 at $15.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?  Choose one:
A) 3.76%  B) 4.76%  C) 5.76%  D) 6.76%  E) 7.76%

Solution: Cost of kit = $52.50   If filters are purchased individually - $6.45*2 + $11.05*2 + $15.50 = $50.50   Amount saved = $52.50 - $50.50 = $2.50   Required %age = ($2.50/$52.50)*100 = 4.76%   So, the correct answer is 4.76%.
Answer: B
In an objective competitive exam, a correct answer score 4 marks and on a wrong answer 2 marks are negatively added. A student scores 420 marks from 150 question. How many answers were correct ?  Choose the correct choice from the following options
A) 150
B) 155
C) 140
D) 120
E) 165

Solution: let x be the correct answer and y be the wrong answer   so the total number of questions is (x + y) = 150.....(1)   => 4x - 2y = 420.....(2)   By solving (1) & (2), we get   => 6x = 720   hence x = 120   Therefore, number of correct answers are 120.   Answer 120
Answer: D
Kim is taking a math class, and the teacher gives a multiple choice test consisting of 8 questions. If each question has 4 answer choices, and Kim answers every question, in how many different ways can she complete the test?  Choose the correct choice from the following answers:
A) a 4^8
B) b 400
C) c 5^8
D) d 8^5
E) e 40^40

Solution: different ways to solve each question is 4.   So, 4*4*4*4.. 8 times ----> 4^8   a 4^8nswer will be a 4^8
Answer: A
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?	Pick one.
A) 5/2  B) 5/2  C) 5/3  D) 5/6  E) 5/8

Solution: P(at least one graduate)   = 1 - P(no graduates)   = 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8)   = 5/6   Answer:5/6
Answer: D
Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir? Pick
A) 33  B) 88  C) 20  D) 72  E) 27

Solution: 1/x + 1/(x + 10) = 1/12   x = 20   Answer: 20
Answer: C
Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 16000, then find his savings?  Pick:  A) 6769  B) 3200  C) 3201  D) 2319  E) 7591

Solution: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.   Income, 5x = 16000 => x = 3200   Savings = Income - expenditure = 5x - 4x = x   So, savings = Rs. 3200.   Answer:3200
Answer: B
The average age of 15 students of a class is 16 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is?	Select:
A) 11 years
B) 17 years
C) 26 years
D) 14 years
E) 12 years

Solution: Age of the 15th student   =[15 * 16 - (14 * 5 + 16 * 9)]   = (240 - 214)= 
(240 - 214) = 26
26 years.   Answer:26 years
Answer: C
A 6-liter solution is 25% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?  Choose one
A) 2.1 B) 2.4 C) 2.7 D) 3.0 E) 3.3

Solution: Let x be the amount of pure alcohol required.   0.25(6) + x = 0.5(x+6)   0.5x = 3 - 1.5   x = 3 liters   The answer is 3.0.
Answer: D
How many integers are divisible by 3 between 10! and 10! + 20 inclusive?
Choose the correct choice:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: 0! is divisible by 3 - The way I look Factorials is that any number included will also be divisible by the product. 10,9,8,7,6,5,4,3,2,1 are all divisors of 10!   There are 6 numbers between 10! and 10!+20 that are divisible by 3.   Hence 7: 7
Answer: B
A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
Options:
A) 297	B) 278	C) 287	D) 140	E) 272

Solution: A+B+C = 675   A = 3B   3B+B+B-25 = 675   5B = 700   B = 140   Answer: 140
Answer: D
A can do double work of B.so,A take 15 days less than B in doing a work.then both together in how much days will finish that work?
Choose the correct answer:  A) 10  B) 12  C) 15  D) 8  E) 16

Solution: let alone finish a work in x days.,then B will take 2x days   2x-x=15,x=15.   so,10 alone finish this work in 15 days and B alone finish this work in 30 days   work of 10 in 1 days=1/15,work of B in 1 days=1/30   (10+B) work in 1 days=1/10   so, together they finish the work in 10 days   answer 10
Answer: A