MU-NLPC/Calc-aqua_rat huggingface dataset:
It takes 2 team of farm workers 12 days to completely prepare a piece of land for planting. if both team of workers were to work separately, one of them can complete the work 10 days earlier than the other, how many days will it take each of them to separately complete the work? Select the correct option:
A) 12 and 22
B) 11 and 21
C) 15 and 25
D) 9 and 19
E) 20 and 30

Solution: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.   Here, we're told that (working together) the two team of workers would complete a job in 12 days. This means that (individually) each of team would take MORE than 12 days to do the job.   Answers D, A and B are illogical, since the individual times must both be greater than 12 days.   so we can TEST the values for Answers C and E.   Using the values for Answers B and D...   Answer B: (15)(25)/(15+25) = 375/40 = 9.4 This is a match   Answer 20 and 30: (20)(30)/(20+30) = 12   Final Answer:   20 and 30
Answer: E
The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $7.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?  Answers:
A) $4.50 B) $5.10 C) $5.30 D) $7.50 E) $5.60

Solution: I Tried using Time/Rate approach:-   Initial Price $7.50ifference = 7.80 - 3.20= 
7.80 - 3.20 = 4.6
4.60   Price of Corn increasing by 5x   Price of Wheat decreasing by x(1.4)-x= .4x   Since both the quantities are moving towards reducing the Price Gap hence:-   Relative Increase = 5x +.4x   Let T be the Time by which GAP is filled so,   4.6 = T(5.4x) -> T= (4.6)/5.4X   Final Price = 3.20 + 5X * T -> 3.20 + 5*4.6/5.4 = 7.5   Answer $7.50.
Answer: D
If f(x)= 5x^3- 4x+8 and g(y)= 6y-4, then g(f(x)) =	Pick one:  A) 11x^2+4x+4  B) 11x^2-12x+44  C) 30x^3-24x+44  D) 30x^3+4x+4  E) 30x^3-12x+44

Solution: g(f(x)) = 6(f(x)) -4 = 6(5x^3- 4x+8) - 4 = 30x^3-24x+44 =>30x^3-24x+44
Answer: C
By selling an article for $195, a person gains $45. What is the gain %?
Choose the correct choice from the following answers:
A) 25% B) 30% C) 50% D) 20% E) 10%

Solution: S.P. = $195   Gain = $45   C.P. = 195-45= 
195-45 = 150
150   Gain%= 45/150 * 100= 
45/150 * 100 = 30
30%   Answer is 30%
Answer: B
Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/5 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?	Choose one:
A) 1/2 B) 2/3 C) 3/4 D) 11/30 E) 5/6

Solution: Because we see H willbring 1/3 of his booksto the new home --> try to pick a number that isdivisible by 3.   Before:   Assume H = 30 books   H = 1/2 M --> M = 60 books   After:   H' = 1/3H = 10 books   M' = 1/5M =12 books   Total = 22 books   M' = 22 = 11/30*60   Ratio: 11/30   Ans:11/30
Answer: D
A herd of goats consists of A males and B females. In that herd, half of the goats that have horns are females. If C goats of the herd do not have horns, then the total number of male goats in the herd that do NOT have horns, in terms of A, B and C is - Choose the correct choice from the following options
A) (A−B+C)/2  B) (A−B−C)/2  C) (A+B+C)/2  D) (A+B−C)/2  E) (2A−B+C)/2

Solution: Male Goats = A   Female Goats = B   1/2 of Horn Goats = Females = x (say)   Therefore, other half will be Male = x   Now, Male Goats without horn = A -x -- (1)   Also, Total Goats without horn = C = (A -x) + (B-x)   or x = (A+B - C)/2   Substituting the value of x in equation (1)   We will have A - x =(A−B+C)/2.   (A−B+C)/2nswer (A−B+C)/2.
Answer: A
In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
Choose the correct option.
A) 40 kg  B) 50 kg  C) 65 kg  D) 66.5 kg  E) 80 kg

Solution: Let Mike's weight be X kg.   According to Mike, 65 < X < 72.   According to Mike's brother, 60 < X < 70.   According to Mike's mother, X < 68.   The values satisfying all the above conditions are 66 and 67.   Required average = (66 + 67) / 2= 
(66 + 67) / 2 = 133/2 = around 66.5
66.5 kg   66.5 kg
Answer: D
Find the value of 3 + 2 • (8 – 3)	Pick
A) 25 B) 13 C) 17 D) 24 E) 15

Solution: 3 + 2 • (8 – 3)   = 3 + 2 (5)   = 3 + 2 * 5   = 3 + 10= 
3 + 10 = 13
13   correct answer 13
Answer: B
If T = 5/9 * (K - 32), and if T = 35, then what is the value of K?	Choose the correct answer:
A) 92  B) 95  C) 98  D) 101  E) 104

Solution: K-32=9T/5   K=9T/5 + 32   K=9(35)/5 + 32 = 95   The answer is 95.
Answer: B
A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 1/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 10% less than the price each head sold for on the day before. What was the total gross profit on this shipment.	Choose the correct choice from the following:
A) $105	B) b $100	C) c $125	D) d $130	E) e $135

Solution: Purchase cost = 600/1500= 
600/1500 = 2/5 = around 0.4
$ 0.4   25% above the cost per head= (125/100)*0.4= 
(125/100)*0.4 = 0.5
$ 0.5   2/3 of the heads were sold means 1/3*1500= 
1/3*1500 = 500
500 ,Selling amount for 500 cabbage= 500 * 0.5= 
500 * 0.5 = 250
$ 250   Remaining were sold at a price equal to 10% less than the price each head sold for on the day before i.e , (90/100)*0.5= $ 0.45   Hence selling cost for the remaining cabbage = 1000 * 0.45= 
1000 * 0.45 = 450
$ 450   Total selling cost= 450 + 250= 
450 + 250 = 700
$ 700   Gross profit= $ 700 - $ 600 = $ 100   Hence Answer is b $100
Answer: B
If 200 lb of a mixture contain 80% husk and 20% sand. Then how much husk needs to be extracted in order to have 75% concentration of Husk? Choose one.
A) 1/4  B) 20/3  C) 1/2  D) 40  E) 60

Solution: We need to extract 40 lb of husk.   80 % of 200 = 160   20 % of 200 = 40   Now we have t remove husk to have 75 % of Husk ( key point sand is not supposed to be removed)   Let X be the new quantity after removing husk   So, 40 = 25 % of X   X = 160   Husk will 120 lbs , hence we need to remove 1/4 of the total husk or 40 lbs   ANSWER:40
Answer: D
The rational number for recurring decimal 0.125125.... is: Select the correct option
A) 119/999  B) 125/999  C) 125/1000  D) 125/999  E) None of them

Solution: 0.125125...   = 0.125   = 125/999   Answer is 125/999.
Answer: B
John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true? Pick.
A) 201
B) 301
C) 401
D) 101
E) 501

Solution: The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1. For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.
Answer: B
While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 3° east of north, in what direction was it originally flying?
Choose the correct choice from the following:
A) (a) 30° west of north B) (b) 30° east of north C) (c) 22° west of north D) (d) 22° east of north E) (e) 5° west of north

Solution: If after a turn of 25° you are 3°NEast, with a 22° turn you would be perfectly pointing at north. So you were, before the turn, 22° to the other side (West).   Answer (c) 22° west of north)
Answer: C
Triangle ATriangle B are similar triangles with areas 1536 units square and 2166 units square respectively. The ratio of there corresponding height would be  Choose the correct choice from the following options
A) 9:10
B) 17:19
C) 23:27
D) 13:17
E) 16:19

Solution: Let x be the height of triangle A and y be the height of triangle of B.   since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2   Therefore, (x^2/y^2)=1536/2166   (x^2/y^2)=(16*16*6)/(19*19*6)   (x^2/y^2)=17^2/19^2   x/y=16/19   Ans=16:19
Answer: E
A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?	Choose one
A) 2 / 3	B) 1 / 3	C) 3 / 3	D) 4 / 5	E) 2 / 4

Solution: Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by   (number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3   correct answer 1 / 3
Answer: B
You collect balls. Suppose you start out with 7. John takes half of one more than the number of balls you have. Since his mother makes balls, Peter decides to triple your balls. How many balls do you have at the end?
Choose the correct choice.
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: Solution   Start with 7 balls.   John takes half of one more than the number of balls you have. So John takes half of 7 + 1 which is 4,   so you're left with   7 - 4= 
  7 - 4 = 3
3.   Peter triples the number of balls you have: 3 × 3= 9 balls.   So you have 9 at the end.   Correct answer : 9
Answer: D
A circular rim 21 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?	Choose the correct choice from the following options
A) 48pi/x B) 75x C) 48x D) 45x E) x/75

Solution: Let's try the explanation. We have two wheels. One with 21pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 21pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).   Anyway, we have 21pi*x=35pi*a.   (21pi*x)/(35pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 45x.   Ans:45x
Answer: D
A group of men decided to do a work in 20 days, but 10 of them became absent. If the rest of the group did the work in 40 days, Find the original number of men?  Select:	A) 20	B) 50	C) 40	D) 100	E) 25

Solution: Original number of men = 10*40 / (40-20)= 
10*40 / (40-20) = 20
20   20nswer is 20
Answer: A
Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas.
Choose the most appropriate option:
A) 1:9 B) 2:9 C) 3:9 D) 5:9 E) None of them

Solution: Let their edges be a and b. Then,   =a^3/b^3 = 1/27 (or) (a/b)^3 3/  3= 
3/  3 = 1
1/27 (or) (a/b)^3= (1/3)3 (or) (a/b) = (1/3).   Therefore, Ratio of their surface area = 6a^2/6b^2 = a^2/b^2 = (a/b)^2 = 1/9, i.e. 1:9.   1:9nswer is 1:9.
Answer: A
In a normal 5-day work week, each of 12 employees produces 300 items per day-last week, 1/3 of the employees were absent from work for 2/5 of the days in the week. how many total items were produced last week?  Choose the correct option
A) 18000 B) 14400 C) 6000 D) 15600 E) 16,200

Solution: 1 employee produces 300 items per day   1/3 of the employees were absent for 2/5 days of last week.   ==> 4 employees were absent for 2 days.   Items produced by them in 3 days   = 300*3*4= 
300*3*4 = 3_600
3600   Items produced by other employees=8*5*300= 
8*5*300 = 12_000
12000   Total items produced= 12000+3600= 
12000+3600 = 15_600
15600   ANSWER:15600
Answer: D
A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 men?  Choose the most appropriate option:
A) 5/7  B) 1/7  C) 2/7  D) 3/7  E) 1/2

Solution: Total ways to choose 4 employees from 8 employees = 8C3   Two men = 5C2   Two women = 3C1   P = (5C2 * 3C1)/8C2 = 5/7 hence 5/7.
Answer: A
The average age of 15 students of a class is 15 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 Choose the correct option
A) 11  B) 12  C) 13  D) 14  E) 15

Solution: Explanation:   Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214)= 
(225-214) = 11
11 years. 11nswer: 11
Answer: A
If f is a number such that –2 ≤ f ≤ 2, which of the following has the largest possible absolute value?  Choose the correct choice from the following options.
A) 3f – 1	B) x^2 + 1	C) 3 – x	D) x – 3	E) x^2 – x

Solution: Ans is A .. leads to the max value of 7 for f = -2
Answer: A
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?	Choose the correct choice from the following answers:
A) 24
B) 35
C) 13
D) 61
E) 45

Solution: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.   Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.   Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.   Therefore, the total number of ways the 5 letters can be posted in 3 boxes is   3 * 3 * 3 * 3 * 3 = 35   Ans: 35
Answer: B
The length of an edge of a hollow cube open at one face is √3 metres. What is the length of the largest pole that it can accommodate?  Select the correct option: A) 2 metres B) 3 metres C) 4 metres D) 3√3metres E) None

Solution: Solution   Required length	= Diagonal   ‹=›√3 a   ‹=›(√3×√3) m   ‹=›3 m.   Answer 3 metres
Answer: B
The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube?
Select: A) 7 B) 10 C) 4 D) 6 E) 8

Solution: Cube volume = a(power)3 cubic units   Surface area = 6 a(power)2 sq.units   a(power)3 = 6 a(power)2   a = 6 m   Answer is 6.
Answer: D
The cost price of 40 articles is the same as the selling price of x articles. If the profit is 25%, what is x?  Choose the correct choice from the following answers.
A) 26 B) 28 C) 30 D) 32 E) 34

Solution: Let the cost price = y   The cost price of 40 articles = 40y   The selling price of x articles = 1.25y*x   1.25y*x = 40y   x = 40 / 1.25= 
40 / 1.25 = 32
32   The answer is 32.
Answer: D
How long does a train 120 m long running at the speed of 70 km/hr takes to cross a bridge 145 m length?
Answers
A) 13.9 sec  B) 12.1 sec  C) 17.9 sec  D) 13.9 sec  E) 47.98 sec

Solution: Speed = 70 * 5/18 = 19 m/sec   Total distance covered = 120 + 145= 
120 + 145 = 265
265 m.   Required time= 265/19 = 13.9 sec.   Answer:13.9 sec
Answer: D
If a and b are integers and a≠0 which of the following cannot equal 0?	Pick one:
A) ab B) a-b C) a+b D) ab-b^2 E) a^2+b^2

Solution: (A) ab   If b=0 , then ab=0   (B) a - b   If a=b , then a-b= =0   (C) a + b   If b=-a , then a+b=0   (D) ab - b^2   If a=b , then ab-b^2= 0   (E) a^2 + b^2   Can't be equal to zero .   If a=0 , then a^2 + b^2	=b^2   if a=-ve , then a^2 + b^2 not equal to 0   Answer a^2+b^2
Answer: E
A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?  Choices:
A) 11  B) 45  C) 66  D) 72  E) 32

Solution: Let the distance to be travelled to catch the bus be x km   x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km   By traavelling 30 kmph time taken = 60/30= 
60/30 = 2
2 hours   By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed= 60/(4/3)= 
60/(4/3) = 45
45 kmph.   Answer: 45
Answer: B
Which of the following is NOT a factor of 10! ? Choose the correct answer:  A) 1440  B) 625  C) 160  D) 80  E) 50

Solution: 625=5*5*5*5 and we dont have four 5 in 10! answer is 625
Answer: B
If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?	Select.
A) 1,20,000 B) 1,20,080 C) 1,20,900 D) 1,29,000 E) 1,20,070

Solution: X * (105/100) * (105/100) * (105/100) = 138915   X = 138915/1.157625= 
138915/1.157625 = 120_000
120000   1,20,000nswer:1,20,000
Answer: A
A circular mat with diameter 22 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Choose the correct option:
A) 5/12
B) 2/5
C) 3/2
D) 3/4
E) 5/8

Solution: SO we are looking for the area of the cloth over the area of the table   Area of the Cloth = (pi)(r)^2 which is about (3)(11)(11)   Area of the Table = (24)(24)   So the quick way to estimate is looking at the fraction like this: (3/24)(121/24)   I hope this is easy to follow, so with some simplification i get (1/8)(5) = (5/8) Answer is 5/8
Answer: E
There are 28 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?  Choose one:
A) 800	B) 820	C) 850	D) 870	E) 900

Solution: The total number of stations= 30   From 30 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 30P2 ways.   30P2= 30*29= 
30*29 = 870
870   ANSWER:870
Answer: D
The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Pick: A) 75 B) 267 C) 299 D) 266 E) 21

Solution: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.   P + C + M = 150 + P   C + M = 150   75verage mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.75nswer: 75
Answer: A
If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 240 responses are needed, what is the minimum number of questionnaires that should be mailed? Choose the correct choice from the following answers.
A) 400	B) 500	C) 600	D) 700	E) 800

Solution: Let x be the minimum number of questionnaires to be mailed.   0.6x = 240   x = 400   The answer is 400.
Answer: A
How many words can be formed by using all letters of the word 'PIG' ?  Answers:
A) 6
B) 8
C) 9
D) 5
E) 7

Solution: The word PIG contains 3 different letters   Required number of words = 3P3 = 3! = 3*2*1= 
3*2*1 = 6
6   6nswer is 6
Answer: A
If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Choose the correct choice from the following answers:
A) 132 km
B) 167 km
C) 143 km
D) 162 kilometres
E) 245 km

Solution: 162 kilometres   12 m/s = 12 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   162 kilometresistance = speed * time = 12 * 18/5 * 15/4= 
12 * 18/5 * 15/4 = 162
162 km.
Answer: D
If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value R of the product xy?  Pick:
A) -12
B) -3
C) 0
D) 2
E) None of the above

Solution: How to deal with inequalities involving absolute values? First example shows us the so callednumber case   In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:   y + 3 ≤ 3   y ≤ 0   So y is 0 or negative   Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:   y + 3 >= -3   y >= -6   Therefore we have a possible range for y: -6=<y<=0   Ok, so far so good, we're half way through. What about x?   Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.   You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value R.   Hence, Answer 0hoice 0 is the one to go.
Answer: C
A cube is divided into 512 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour? Choose the correct option
A) 216	B) 264	C) 296	D) 312	E) 324

Solution: Each face of the cube has 8 x 8 = 64 cubelets.   On each face, only the interior cubelets are painted one colour.   On each side, 6 x 6 = 36 cubelets are painted one colour.   Since the cube has six sides, the number of cubes with one colour is  6*36= 
 6*36 = 216
216   The answer is 216.
Answer: A
The population of a town is 10000. It increases annually at the rate of 30% p.a. What will be its population after 2 years?  Select the correct option.
A) 14000	B) 14400	C) 14500	D) 14600	E) 16900

Solution: Formula :   10000 × 130/100 × 130/100 = 16900   Answer : 16900
Answer: E
John has $2500 in his bank account that earns 10% interest every year. How much will be in John's bank account after one year?
Select the correct option:
A) $2600 B) $3000 C) $2250 D) $2750 E) $3500

Solution: Final number = Initial number + 20%(original number) = 2500 + 10%(2500) = 2500 + 250= 
2500 + 250 = 2_750
2750.   Answer $2750
Answer: D
Mary works in a restaurant a maximum of 45 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
Select:
A) 300	B) 420	C) 410	D) 320	E) 400

Solution: Mary receives $8(20)=$160 for the first 20 hours.   For the 25 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(25)=$250.   The total amount is $160+$250 = $410   Answer 410 410.160+ 250= 
160+ 250 = 410
$410   Answer 410 410.
Answer: C
What is the probability W of randomly selecting an arrangement of the letters of the wordMEDITERRANEANin which the first letter is E and the last letter is R?	Pick one.
A) 1/13 B) 1/20 C) 1/26 D) 1/50 E) 1/100

Solution: Why do you calculate the total combinations and everything, it is much easier to calculate as follows:   3/13 * 1 * 1 * 1 * 1 ..... * 2/12 = 6/156 = 1/26   This is because 3/13 = Probability that first letter will be E and 2/12 = probability that thefirstletter will be R. Between everything else cuts down to 1*1*1... e.g. probability W of the second letter is 11/11= 
11/11 = 1
1, > we do not care what's in between.1/26
Answer: C
A sum of Rs 12,500 amounts to Rs. 15,500 in the 4 years at the rate of simple interest. Find the rate percent  Choose the correct choice from the following options:
A) 6 %
B) 7 %
C) 8 %
D) 9 %
E) 10 %

Solution: Explanation:   S.I.=P∗R∗T/100=>R=S.I.∗100/P∗T   So, S.I = 15500 - 12500= 
15500 - 12500 = 3_000
3000.=>R=3000∗100/12500∗4=6%   Option 6 %
Answer: A
Chlorination is used in industry for the purification of water; 1gm solution of chlorine will remove half of the germs in 1 liter of water. If water containing less than 0.09% of germs is considered clean, what is the minimum amount of chlorine required to purify 150 liter of water containing 0.3 liter of harmful substances? Pick:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Assuming that it's SUPPOSED to state "0.3" liters of harmful substances, here's how you can answer this question.   First, we have to figure out what .09% of 150 liters is...   1% = .01   .1% = .001   .09% = .0009   So, .0009(150) = .135 liters   We need enough doses of chlorine to get the 0.3 liters down to LESS than .135 liters. Each "dose" of chlorine will remove HALF of the harmful substances...   Start = 0.3 liters   After 1st dose = .15 liters   After 2nd dose = .075 liters   We're now below the .135 liters that we need to be less than.   Final Answer:2
Answer: B