MU-NLPC/Calc-aqua_rat huggingface dataset:
In a group of 650 readers who read science fiction or literacy works or both, 250 read science fiction and 550 read literacy works. How many read both science fiction and literacy works?	Answers
A) 650 B) 250 C) 150 D) 100 E) 400

Solution: 150onsider total number of reader n(S U L) = 650   People who read science fiction n(S) = 250   People who read literacy works n(L) = 550   both science fiction and literacy n(S âˆ© L) = ?   n(S U L) = n(S)+ n(L) - n(S âˆ© L)   650 = 250 + 550 - n(S âˆ© L)   n(S âˆ© L) = 800 - 650   n(S âˆ© L) = 150   SO People read both science fiction and literacy works are 150   ANSWER:150
Answer: C
What percent of 60 is 120? Options:
A) 200  B) 75  C) 60  D) 33 1⁄3  E) 25

Solution: % of 60 is 120?   = 120/60 = 21 = 200%   Thus 200 is the correct answer.
Answer: A
If a certain number is divided by 5, the quotient, dividend, and divisor, added together, will amount to 65. What is the number?  Choose the correct answer.
A) 18	B) 28	C) 48	D) 38	E) 50

Solution: Let x = the number sought.   Then x/5 + x + 5 = 65.   x = 50.   50
Answer: E
A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 9 members, then what is the exact number of researchers required?	Select the correct option:
A) 25	B) 24	C) 23	D) 22	E) 21

Solution: alternatively, we have   9*3-2( because james is included in all the three teams)   =25   25
Answer: A
The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.7.2. The true discount is
Pick one:  A) Rs.72  B) Rs.36  C) Rs.54  D) Rs.60  E) none

Solution: Solution   T.D	= [B.G x 100 / R x T]   = Rs.(7.2 x 100 / 12 x 1)   = Rs.60.   Answer Rs.60
Answer: D
In the next Cricket World Cup T-20, Team A has decided to score 200 runs only through 4s and 6s. In how many ways can the Team A score these 200 runs?	Choose the most appropriate option
A) 13
B) 15
C) 16
D) 17
E) 18

Solution: Team A can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.   So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.   Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1= 
(50 - 2)/3 + 1 = 17
17   Answer: 17
Answer: D
A photo-mat shop charges $0.60 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $42 if each film contains 36 photos? Choose the correct choice from the following options: A) 3 films and 6 photos B) 5 films and 6 photos C) 5 films and 14 photos D) 6 films and 4 photos E) 6 films and 28 photos

Solution: 1st photo = 0.60   Subsequent = 0.6*0.6= 
0.6*0.6 = 0.36
0.36   Price of 1 full film=0.6+0.36*35= 
0.6+0.36*35 = 13.2
13.2   Price of 3 full film= 13.2*3= 
13.2*3 = 39.6
39.6   42-39.6= 
42-39.6 = 2.4
2.4   2.4=0.6+0.36x   x=5   42--->3 full films and  1+5= 
 1+5 = 6
6 photos   3 films and 6 photosnswer: 3 films and 6 photos
Answer: A
1000 men have provisions for 20 days. If 200 more men join them, for how many days will the provisions last now? Choices
A) 12.8	B) 12.6	C) 12.5	D) 12.2	E) 16.6

Solution: 1000*20 = 1200*x   x = 16.6.Answer: 16.6
Answer: E
The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 70 percent of the pollutant?
Choose the correct choice from the following options.
A) $200,000	B) $100,000	C) $50,000	D) $10,000	E) $5,000

Solution: To remove 90% of pollutant   C= 100,000(90)/(100-90) = 900,000   To remove 70% of pollutant   C' = 100,000(70)/(100-70) = 700,000   Difference = C - C' = 200,000   $200,000nswer - $200,000
Answer: A
A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?
A)
B)
C)
D)
E)
Choose the correct choice from the following answers:
A) 1/6 B) 7/216 C) 1/36 D) 9/216 E) 11/216

Solution: The sum of 16 is obtained if the dices show: (6, 5, 5) or (6, 6, 4).   Each can occur in 3!/2!=3 ways, for example we can get (6, 5, 5) in 3 ways: (6, 5, 5), (5, 6, 5), (5, 5, 6), permutation of three items (6, 6, 5) out of which 2 5's are identical.   So, # of favorable outcomes is  2*3= 
 2*3 = 6
6;   Total # of outcomes is 6*6*6= 
6*6*6 = 216
216;   P=favorable/total=6/216=1/36.   Answer: 1/36
Answer: C
How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/7!?  Select.
A) 1 B) 3 C) 5 D) 6 E) 9

Solution: 7! = 7*6*5*4*3*2*1= 
7*6*5*4*3*2*1 = 5_040
5040   1/7!= 1/5040   =[1/(5.04)] * 10^-3   1/(5.04) will be approximately lesser than .2   Number of leading zeros will be 3   Answer 3
Answer: B
How many 6's are there in the following number sequence which are immediately preceded by 9 but not immediately followed by 4 ?
5 6 4 3 2 9 6 3 1 6 4 9 6 4 2 1 5 9 6 7 2 1 4 7 4 9 6 4 2
Choices.
A) 1  B) 3  C) 2  D) 5  E) None

Solution: Answer: C . 2
Answer: C
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/7.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?	Select:
A) 27
B) 26
C) 24
D) 23
E) 21

Solution: answer of 1st   just add the given probabilities p(blue)+p(red)+p(green) i.e   1/8+1/5+1/7=35+56+40/280 =131/280   now we know p(blue)+p(red)+p(green)+p(yellow)=1   131/280+p(yellow)=1   p(yellow)= 149/280 =21/40   i.e why yellow balls are 21.   21
Answer: E
If after 200 grams of water were added to the 15%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 15%-solution was used? Choose the correct answer
A) 180 grams	B) 220 grams	C) 250 grams	D) 350 grams	E) 400 grams

Solution: The 15% alcohol solution decreases by 1/3 once the 200 grams of water is added so  200/.05= 
 200/.05 = 4_000
4000*.1% (2/3 of 15%) is 400 grams, thus answer is 400 grams.
Answer: E
Find the unknown term X,8,6,2,-4, -12
Select the correct option.
A) 2	B) 4	C) 6	D) 8	E) 9

Solution: X,8,6,2,-4, -12   i guess each differ in d range of 2   8 - 8= 
8 - 8 = 0
0   8 - 6= 
8 - 6 = 2
2   6 - 2= 
6 - 2 = 4
4   2 - 6= -4   -4 - 8 = -12   ANSWER:8
Answer: D
How many even integers n, such that 20<=n<=250 are of the form 3k+4, where k is any natural number?	Choose the correct choice from the following options
A) 33	B) 36	C) 39	D) 42	E) 45

Solution: The first number is 22 = 16+6(1).   We can continue adding 6 to make a list: 22, 28, 34,...   The last number is 250 = 16+6(39)   There are 39 numbers in the list.   The answer is 39.
Answer: C
If it takes 4 identical printing presses exactly 6 hours to print 8,000 newspapers, how long would it take 2 of these presses to print 6,000 newspapers? Choose one:
A) 5 hrs	B) 7 hrs	C) 8 hrs	D) 9 hrs 50 mins	E) 9 hrs

Solution: 4 presses - 8,000 newspapers - 6 hours ;   2 presses - 4,000 newspapers - 6 hours ; (360 mins)   2 presses - 6,000 newspapers - 360/4000*6000 = 540 mins = 9 hrs   Answer : 9 hrs
Answer: E
A girl swims downstream 48 km and upstream 16 km taking 8 hours each time; what is the speed of the current?
Answers
A) 2.0	B) 2.1	C) 2.2	D) 2.3	E) 2.4

Solution: 48 --- 8 DS = 6   ? ---- 1   16 ---- 8 US = 2   ? ---- 1 S = ?   S = (6 - 2)/2= 
(6 - 2)/2 = 2
2   2.0nswer:2.0
Answer: A
A reduction of 25% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg? Select the correct option
A) s.2.8  B) s.2.4  C) s.2.5  D) s.2.2  E) s.3.33

Solution: 100*(25/100)= 
100*(25/100) = 25
25 --- 10   ? --- 1=> Rs.2.5   100 --- 75   ? --- 2.5 => Rs.3.33   Answer:s.3.33
Answer: E
In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 2:3, If Rs 15,0000 was their profit, how much amount did B receive.
Choose the correct option.
A) 12653	B) 14587	C) 36975	D) 75000	E) 12874

Solution: Explanation:   A:B = 2:3= 2:3   => A:C = 2:1 = 2:1   => A:B:C = 2:3:1   B share = (3/6)*150000= 
(3/6)*150000 = 75_000
75000   Option 75000
Answer: D
What least number must be added to 1170, so that the sum is completely divisible by 23 ?  Choose the correct answer.
A) 3
B) 5
C) 7
D) 9
E) 11

Solution: 51*23= 
51*23 = 1_173
1173   1173 - 1170= 
1173 - 1170 = 3
3   3nswer : 3
Answer: A
Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side a in the following steps: the original square of side a is divided into n smaller squares, not necessarily of the same size, then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is	Select:
A) 1:1  B) sqrt 2 : 1  C) n(4-π) / (4n - π)  D) (4n − π) / n (4 - π)  E) None of these

Solution: Explanation :   Consider the square of side x, then its area will be x2.   The area of largest circle = π(x/2)2   which can be cut from square πx2/4 .   Therefore, area scrapped = x2 - πx2/4 = x2 (1 - π/4).   Hence,   => the area scrapped / Area of square   => x2 (1 - π/4) / x2   => 1 - π/4 =constant.   As this ratio is constant, whether we cut a circle from smaller square or larger square, scrapped area will be a fixed percentage of square. Therefore, in this case where two squares are pf the same size, the ratio will be 1 : 1.   1:1nswer : 1:1
Answer: A
If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 17 days. If he works at reduced efficiency, he can work without break and finish that same job in 17 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?	Choose the correct choice from the following answers:
A) 6/5  B) 1/5  C) 9/5  D) 12/5  E) 6/35

Solution: We're told that there are 2 ways for Dale to complete a job:   1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 17 days.   2) Reduced Efficiency: 17 straight days with no days off.   Working at Full Efficiency creates the following pattern:   2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2+1+2+1+2+1+2+1+2= 
2+1+2+1+2+1+2+1+2+1+2 = 17
17 days   Totals: 12 days on, 5 days off   Reduced Efficiency means that Dale will do 12 days of work in 17 days, thus those Reduceddaysare 12/5 of Full Efficiency.   Answer : 12/5
Answer: D
If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
Choose one.
A) 2 B) 3 C) 8 D) 5 E) None of these

Solution: Explanation: Clearly, 4864 is divisible by 4.   So, 9P2 must be divisible by 3.   So, (9 + P + 2) must be divisible by 3.   P = 1.   Answer: Option None of these
Answer: E
You collect coins. Suppose you start out with 11. Since his mother makes coins, Miguel decides to double your coins. Since you're nice, you give Mary 12 coins. How many coins do you have at the end?  Choose the correct choice from the following
A) 9	B) 10	C) 11	D) 12	E) 13

Solution: Solution   Start with 11 coins.   Miguel doubles the number of coins you have: 11 × 2 = 22 coins.   Mary takes 12 coins from you:   22 - 12= 
  22 - 12 = 10
10 coins.   So you have 10 at the end.   Correct answer: 10
Answer: B
From his monthly salary a man spends 10% of his salary for house rent, 20% on food, 25% for all other expenses and saves Rs 2520 per month. His monthly salary is?  Pick one
A) Rs 4400	B) Rs 5000	C) Rs 5600	D) Rs 6200	E) Rs 6300

Solution: Explanation: Total salary = 100%   His spending are on house rent 10%, on food 20% and for other expenses 25%.   Total expenditure = 10 % + 20% + 25% = 55%   His savings are => Income – Expenses   => 100% - 55% => 45% 100  - 55= 
100  - 55 = 45
> 45%= Rs 2520   Hi salary is 1005 => 2520 45   x 100   = Rs 5600   Rs 5600
Answer: C
The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.7.8. The true discount is
Choose the correct option: A) Rs.72 B) Rs.65 C) Rs.54 D) Rs.50 E) none

Solution: Solution   T.D	= [B.G x 100 / R x T]   = Rs.(7.8 x 100 / 12 x 1)   = Rs.65.   Answer Rs.65
Answer: B
A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?
Choose the correct choice from the following options:  A) 33m  B) 34m  C) 35m  D) 36m  E) 37m

Solution: A runs 25% as fast as B.   That is, if B runs 100m in a given time, then A will run 125m in the same time   In other words, if A runs 5m in a given time, then B will run 4m in the same time.   Therefore, if the length of a race is 5m, then A can give B a start of 1m so that they finish the race in a dead heat.   Start:length of race :: 1:5   we know that the start is 7m. length of the race will be 7/x=1/5. i.e.7*5=35m.   ANSWER:35m
Answer: C
If a wholesaler distributes items to several outlets (A, B, C and D) in the ratio of 1/10 : 1/11 : 1/15 : 1/16, then find the total number of items the wholesaler distributes? Choose the correct choice from the following options: A) 945 B) 745 C) 845 D) 145 E) 345

Solution: Here, A : B : C : D = 1/10 : 1/11 : 1/15 : 1/16   1) L.C.M of 10, 11, 15,16 is 2640   2) Find the number of books each friend received --------- (To find no. of books each friend has, multiply the ratio with the L.C.M. calculated)   A = (1/10) x 2640 = 264   B = (1/11) x 2640 = 240   C = (1/15) x 2640 = 176   D = (1/16) x 2640 = 165   3) Total number of toys = (264 x + 240 x + 176 x + 165 x) = 845 x   Minimum number of pens (x) = 1   Therefore, total number of items = 845 items.   845orrect option :845
Answer: C
A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?	Choose the correct choice
A) 20	B) 3	C) 6	D) 12	E) 2

Solution: B is 6 years younger to C.   B and D are twins.   Hence C is 6 years elder to D.   ANSWER:6
Answer: C
A man was born on January 1st, 23 B.C. and died January 2nd, 23 A.D. How old did he live to be?	Choose the correct choice.
A) 25 B) 35 C) 45 D) 55 E) 65

Solution: 45 years old.   There is no year 0 so you can add 23 to 23 but you must subtract one to take year 0 out of consideration:   23 + 23 - 1= 
  23 + 23 - 1 = 45
45 years old. In some cultures people are born 1 years old, in this case they would be 46 years old when they die.
Answer: C
Seven men and four boys can complete a work in 6 days. A man completes double the work than a boy. In how many days will 5 men and 4 boys complete the work?	Choose the correct choice from the following choices.
A) 5 B) 4 C) 6 D) Cannot be determined E) None of these

Solution: M = 2B   ∴ 7M + 4B = 14B + 4B = 18B   5M + 4B 14  + 4= 
14  + 4 = 18
18B   5M + 4B= 10B + 4B = 14B   ∴ 18 boys complete the work in 6 days.   ∴ 14 boys complete the work in   6×18/1410  + 4= 
10  + 4 = 14
14B   ∴ 18 boys complete the work in 6 days.   ∴ 14 boys complete the work in   6×18/14=7 5/7days   Note: 7 men and 4 boys complete the work in 6 days. We have to find out the no. of days in which 5 men and 4 boys complete the work. Here, we see that 4 boys are common in both the cases, therefore, 5 men will take more time to complete the work, i.e., more than 6 days, which is not given in any options. Therefore, without calculating we can say that our answer is(e).   Answer None of these
Answer: E
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years?  Choose the correct answer: A) 14300 B) 14400 C) 14500 D) 14600 E) 15400

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 × 120/100 × 120/100 = 14400   14400)
Answer: B
Pradeep has to obtain 20% of the total marks to pass. He got 160 marks and failed by 25 marks. The maximum marks are	Select:
A) 1925  B) 600  C) 925  D) 1325  E) 900

Solution: Explanation :   Let their maximum marks be x.   Then, 20% of x = 160 + 25   =>20/100x= 185   x = (18500/20)= 
(18500/20) = 925
925.   Answer : 925
Answer: C
There are 12 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?	Choose the correct choice from the following choices.
A) 15	B) 16	C) 28	D) 56	E) 132

Solution: Every team plays with 11 teams...so total no of matches = 12 x 11 = 132.   Now, each match is played twice => 132 x 2   But 2 teams play a match => 132 x 2 /2 = 132.   Answer: 132
Answer: E
The area of a sector of a circle of radius 5 cm formed by an arc of length 4.5 cm is?	Pick.
A) 8.78
B) 11.25
C) 8.75
D) 8.98
E) 8.28

Solution: (5 * 4.5)/2= 
(5 * 4.5)/2 = 11.25
11.25   Answer:11.25
Answer: B
Given that on 27th February 2003 is Thursday. What was the day on 27th February 1603?  Choose one:
A) Monday B) Thursday C) Sunday D) Tuesday E) None

Solution: Solution:   After every 400 years, the same day occurs.   Thus, if 27th February 2003 is Thursday, before 400 years i.e., on 27th February 1603 has to be Thursday.   Answer Thursday
Answer: B
If X is to be chosen at random from the integers between 1 to 6, inclusive, and Y is to be chosen at random from the integers between 7 and 11, inclusive, what is the probability that X + Y will be even?
Choices.
A) 1/2	B) 2/3	C) 3/4	D) 4/5	E) 5/6

Solution: X+Y will be even if X and Y are both even or both odd.   P(X and Y are both even) = 3/6*2/5 = 1/5   P(X and Y are both odd) = 3/6*3/5 = 3/10   P(X+Y is even) = 1/5 + 3/10 = 1/2   The answer is 1/2.
Answer: A
How many positive two-digit whole numbers are divisible by 7?	Choose one:
A) 11 B) 9 C) 15 D) 12 E) 13

Solution: The largest two-digit number that is a multiple of 7 is 7x14 = 98.   Thus, there are 14 positive multiples of 7 that are less than 100.   However, this includes 7x 1 = 7 which is not a two-digit number.   Therefore, there are   14 -1= 
  14 -1 = 13
13 positive two-digit numbers which are divisible by 7.   (Note that these 13 numbers are 14,21,28,35,42,49,56,63,70,77,84,91 and 98.)   correct answer 13
Answer: E
Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 24 seconds, the speed of each train (in km/hr) is Choose the correct choice from the following answers
A) 18  B) 36  C) 28  D) 20  E) 24

Solution: Explanation:   Distance covered = 120+120= 
120+120 = 240
240 m   Time= 24 s   Let the speed of each train = v. Then relative speed = v+v = 2v   2v = distance/time = 240/24= 
240/24 = 10
10 m/s   Speed of each train= v = 10/2= 
10/2 = 5
5 m/s= 5×36/10 km/hr = 18 km/hr   18nswer: Option 18
Answer: A
In a class of 25 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 4 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? Select the correct option:
A) 8  B) 9  C) 10  D) 11  E) 12

Solution: The total number of books the students borrowed is 25*2= 
25*2 = 50
50.   The students who borrowed zero, one, or two books borrowed   12*1+4*2= 
  12*1+4*2 = 20
20 books.   The 7 students who borrowed at least three books borrowed   50-20= 
  50-20 = 30
30 books.   If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is  30-18= 
 30-18 = 12
12 books.   The answer is 12.
Answer: E
3, 5, 7, 11, 13, 17, 19, ____  Select:
A) 25
B) 36
C) 23
D) 49
E) 27

Solution: The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23....   Answer : 23.
Answer: C
Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?  Choose the correct choice from the following answers:
A) 20 hours 30 min B) 25 hours 30 min C) 30 hours 30 min D) 40 hours 30 min E) 50 hours 30 min

Solution: 20 hours 30 min   20 hours 30 min   1/18 + 1/24 = 7/72   72/7 = 10 2/7   7/72 * 10 = 35/36 ----- 20 hours   WR = 1 – 35/36 = 1/36   1 h ----- 1/18   ? ----- 1/36 = 1/2 hours   => 20 1/2 hours
Answer: A
9548 + 7314 = 5362 + (?) Choose the correct option:
A) 8300
B) 8400
C) 11500
D) 8700
E) 9000

Solution: 9548 16862 = 5362 + x   + 7314 x = 16862 - 5362   ----- = 11500   16862   -----   11500)
Answer: C
Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many W minutes it takes John to reach the station? Choose the correct choice from the following
A) 5 min  B) 6 min  C) 7 and 1/2 min  D) 8 min  E) 10 min

Solution: Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minutes. As he has to travel 5/4km more, it is going to take him 6(5/4) minutes. Hence, W=6(5/4)=15/2 minutes. The correct answer is 7 and 1/2 min.
Answer: C
What is the least integer that is a sum of four different prime numbers each greater than 50?	Choices
A) 232 B) 234 C) 236 D) 238 E) 240

Solution: The sum of the four smallest primes greater than 53+59+61+67= 
53+59+61+67 = 240
240.   The answer is 240.
Answer: E
A milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is: Select:	A) 4%	B) 6(1/4)%	C) 20%	D) 25%	E) 30%

Solution: Explanation:   Let C.P. of 1 litre milk be Re. 1   Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.   C.P. of 1 litre mixture = Re. 100	x 1 =	4   125	5   By the rule of alligation, we have:   Ratio of milk to water =	4/5 : 1/5 =4:1.   Hence, percentage of water in the mixture =(1/5 x 100)%=20%   ANSWER IS 20%
Answer: C
If integers x and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. xb + b^2
II. (x + b)^2
III. x + b  Choose the correct choice:
A) I only	B) II only	C) III only	D) I and II only	E) I, II, and III

Solution: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.   I. xb + b^2 --> if x=1 and b=2 then xb + b^2=6, which is a factor of 30. OK;   II. (x + b)^2 --> (x + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;   III. x + b --> if x=1 and b=2 then x + b=3, which is a factor of 30. OK.   Answer: II only.
Answer: B
If r and s are negative integers, which of the following statements must be true?
I. (-r)^s is positive.
II. (-r)^(-s) is positive.
III. r^(-s) is positive.	Select the correct option
A) None B) II only C) I and II D) I and III E) I, II and III

Solution: Let's r = -2 and s = -3   I. (-r)^s = (2)^(-3) = 1/(2^3) --> Positive   II. (-r)^(-s) is positive. = 2^3 --> Positive   III. r^(-s) is positive. = -2^3 --> Negative   Answer: I and II
Answer: C
A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 168 km downstream	Choose the most appropriate option
A) 3 hours B) 4 hours C) 5 hours D) 6 hours E) 7 hours

Solution: Explanation:   Speed of the boat in still water = 24 km/hr   speed of the stream = 4 km/hr   Speed downstream = (22+5) = 28 km/hr   6 hoursistance travelled downstream = 168 km   Time taken = distance/speed = 168/28= 
168/28 = 6
6 hours   Answer: Option 6 hours
Answer: D
A portion of the 85% solution of chemicals was replaced with an equal amount of 30% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced?	Pick one.
A) 5/11 B) 6/11 C) 7/11 D) 9/11 E) 13/6

Solution: This is a weighted average question. Say x% of the solution was replaced --> equate the amount of chemicals: 0.85(1-x)+0.3*x=0.4 --> x=9/11.   Answer: 9/11.
Answer: D