MU-NLPC/Calc-aqua_rat huggingface dataset:
A deer is standing 50 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 35 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?	Select the correct option:
A) 91
B) 97
C) 103
D) 109
E) 115

Solution: Let x be the length of the tunnel.   When the deer runs 50 meters west, the train goes 500 meters to a point 35 meters from the west entrance of the tunnel.   When the deer runs east, the deer runs x-50 meters while the train goes x + 500 + 35 meters.   x + 500 + 35 = 10(x-50)   9x = 1035   x = 115 meters   The answer is 115.
Answer: E
In the biology lab of "Jefferson" High School there are 0.037*10^5 germs, equally divided among 74000*10^(-3) Petri dishes. How many germs live happily in a single dish?	Choose the correct choice from the following: A) 10 B) 20 C) 30 D) 40 E) 50

Solution: 0.037*10^5 can be written as 3700   74000*10^(-3) can be written as 74   Required= 3700/74= 
3700/74 = 50
50   ANSW50R:50
Answer: E
A question paper has 2 parts, A & B, each containing 6 questions. If a student has to choose 4 from part A &3 from part B, in how many ways can he choose the questions?  Choose the correct answer.
A) 100
B) 200
C) 350
D) 150
E) 140

Solution: There 6 questions in part A out of which 4 question can be chosen as = 6C4.   Similarly, 3 questions can be chosen from 6 questions of Part B as = 6C3.   Hence, total number of ways,   =6C4*6C3   =[6!/(2!4!)]*[6!/(3!*3!)]   = {15}*{6*5*4*3/(3*2*1)}   = 300.   150
Answer: D
Anand starts from a point P towards point Q, where PQ = 50 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.	Choose the correct choice from the following.
A) (45/7) kmph B) (100/21) kmph C) (40/7) kmph D) (30/7) kmph E) (65/7) kmph

Solution: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (50-x) km   Anand traveled this x kms in 3 hours, making his speed x/3 kmph   Ram traveled the same x kms in 2 hours, making his speed x/2 kmph   So, in 6 hours:   Anand will cover=6x/3=2x km   Ram will cover6 /3= 
6 /3 = 2
2x km   Ram will cover=6x/2=3x km   And between their first meeting point and second, they both together covered a distance of 2(90-x) km.   2x+3x6 /2= 
6 /2 = 3
3x km   And between their first meeting point and second, they both together covered a distance of 2(90-x) km.   2x+3x=2(50-x)   5x=100-2x   7x=100   x=100/7 km   Anand's speed=x/3=100/(3*7)=100/21 kmph   Ans:(100/21) kmph
Answer: B
Two identical machines have the ability to produce both nuts and bolts. However, it takes 2 second to produce a bolt but 1 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?  Choices
A) 1,250 seconds
B) 1,500 seconds
C) 1,750 seconds
D) 2,000 seconds
E) 3,000 seconds

Solution: To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.   Two machines to produce 1,000 bolts will need (1,000*2)/2 = 1,000 seconds.   Two machines to produce 1,000 nuts will need (1,000*1)/2 = 500 seconds.   Total = 1,000 + 500 = 1,500.   Answer: 1,500 seconds.
Answer: B
An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?  Choose one
A) 10.29  B) 10.25  C) 10.27  D) 10.24  E) 10.21

Solution: Let the sum be Rs. 100. Then,   S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5   S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25   So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25   Effective rate = (110.25 - 100) = %.   Answer: 10.25
Answer: B
total num of pupiles in 3 grades of scholl is 333 . the no of pupiles in grades 1 and 2 are un 3:5 ratio and 2 and 3 grades are 7:11 ratio .what is the strength of class that has highest no of pupils	Choose the correct choice from the following
A) 145  B) 155  C) 165  D) 175  E) 185

Solution: Ratio G1:G2=3:5 and G2:G3=7:11   So G1:G2:G3=21 : 35 : 55   Let the strength of three classes are 21x, 35x and 55x respectively, then 21x+35x+55x= 333   => 111x= 333 or x=3   So strength of the class with highest number of pupils=55x=55*3= 
55*3 = 165
165   ANSWER:165
Answer: C
On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 2 is how many times as great as the frequency corresponding to a reading of 8?
Choose the correct choice from the following choices.
A) 40 B) 50 C) 10^4 D) 10^5 E) 10^6

Solution: If Richter scale reading goes from X-1 to X it will be 10   if Richter scale reading goes from 2 to 3 it will be 10   if Richter scale reading goes from 3 to 4 it will be 10   if Richter scale reading goes from 4 to 5 it will be 10   if Richter scale reading goes from 5 to 6 it will be 10   Similarly if Richter scale reading goes from 6 to 7 it will be 10   and if Richter scale reading goes from 7 to 8 it will be 10   so it will from 2 to 8 i.e 3,4,5,6,7,8 = 10*10*10*10*10*10 = 10^6   Answer is 10^6
Answer: E
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 9 years, son's age will be:	Choose one
A) 12 years	B) 14 years	C) 18 years	D) 20 years	E) 23 years

Solution: Explanation:   Let the present ages of son and father be x and (60 -x) years respectively.   Then, (60 - x) - 6 = 5(x - 6)   54 - x = 5x - 30   6x = 84   x = 14.   Son's age after 9 years = (x+ 9) = 23 years..   Answer: 23 years
Answer: E
What is the CP of Rs 100 stock at 4 discount, with 1/5% brokerage? Answers:	A) 96.9	B) 96.3	C) 96.2	D) 96.7	E) 96.21

Solution: Explanation:   Use the formula,   CP= 100 – discount + brokerage%   CP= 100-4+1/5   96.2   Thus the CP is Rs 96.2.   ANSWER: 96.2
Answer: C
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many F cents does a liter of kerosene cost? [One dollar has 100 cents.]	Choices.
A) 0.33	B) 0.44	C) 0.55	D) 44	E) 55

Solution: Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $   Just multiply by 100, Answer F= 44.44
Answer: D
Dana borrows 4000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after four years of college? Choose the correct choice from the following choices:
A) 11100 B) 11260 C) 12050 D) 12156 E) 12160

Solution: dana borrows 4000 and returns 2% per month.   so returns 80 per month. and 960 per year.   so dana owes  4000-960= 
 4000-960 = 3_040
3040 per year.   after 4 years she will owe 12160.   Ans (12160)
Answer: E
If 60% of 3/5 of a number is 18, then the number is? Choices:
A) 80 B) 100 C) 75 D) 50 E) None of these

Solution: Let the number be x. Then 60% of 3/5 of x=18   60/100*3/5*x=18   x=(18*25/9)= 
(18*25/9) = 50
50   Required number=50.   Correct Option: 50
Answer: D
A diner is having lunch at a salad bar. There are two types of lettuce to choose from, as well as four types of tomatoes, and five types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad? Choose the most appropriate option:
A) 10
B) 20
C) 30
D) 40
E) 50

Solution: 2*4*5= 
2*4*5 = 40
40   The answer is 40.
Answer: D
A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?	Select the correct option:
A) $150.000	B) $160.000	C) $132.000	D) $148.000	E) $176.000

Solution: 6% x = 8,880 : x = selling price of house.   x = $148,000 : solve for x.
Answer: D
With an average speed of 40 km/hr a car takes 7 hrs to reach a certain distance. With what speed will it be able to cover the same distance in 5 hours ?  Options.
A) 46 km/hr B) 56 km/hr C) 58 km/hr D) 48 km/hr E) 54 km/hr

Solution: 40:x= 5:7, x being the speed of the car. ie) 5x =40*7/5= 
40*7/5 = 56
56 The speed of the car=56 km/hr Answer : 56 km/hr
Answer: B
What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected? Choose the correct choice from the following options
A) 22 B) 66 C) 30 D) 77 E) 12

Solution: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women   == (4 * 3)/(2 * 1) * 5= 
(4 * 3)/(2 * 1) * 5 = 30
30 ways.   Answer: 30
Answer: C
A box contains 2 red, 3 yellow. 2 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours? Choose one
A) 2/3	B) 3/5	C) 2/5	D) 1/3	E) 2/7

Solution: Total number of balls = 3+2= 
3+2 = 5
5   n(S)= 5C2 = 5*4 / 2= 
5*4 / 2 = 10
10   n(E)= 2C1 * 3C1 = 2*3= 
2*3 = 6
6   Probability= 6/10 = 3/5   Answer is 3/5
Answer: B
If 6 boys can color 48 m long cloth in 2 days, then 6 boys can color 36 m long cloth in  Pick one: A) day B) days C) days D) days E) days

Solution: The length of cloth painted by one boy in one day = 48 / 6 × 2 = 4 m   No. of days required to paint 36 m cloth by 6 boys = 36/ 4 × 6 = 3/2 day.   day)
Answer: A
A certain amount earns simple interest of Rs. 1750 after 7 years.Had the interest been 2% more,how much more interest would it have earned ?
Pick:
A) Rs. 35  B) Rs. 245  C) Rs. 350  D) Cannot be determined  E) None

Solution: Solution   We need to know the S.I. , Principal and time to find the rate.Since the principal is not given,so, data is inadequate.   Answer Cannot be determined
Answer: D
A boy wants to go abroad by boat and return by flight. He has a choice of 2 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey? Answers
A) 20 B) 30 C) 43 D) 45 E) 10

Solution: Ans.(E)   Sol. Number of choices to go by ship = 2 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 2 x 5 = 10 ways
Answer: E
Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 57.2 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?  Answers
A) 1.3 B) 1.0 C) 1.1 D) 10.5 E) 41.8

Solution: Change in production of motor vehicles = 57.2 - 3.9= 
57.2 - 3.9 = 53.3
53.3 million in 41 years (1987 - 1946)   average increase per year= 53.3/41= 
53.3/41 = 1.3
1.3 million (apporx.)   1.3nswer (1.3)
Answer: A
At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 28.9 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?  Select the correct option: A) 16.2 B) 16.4 C) 16.6 D) 16.8 E) 17.0

Solution: Let x be the factor by which the bacteria increases every three hours.   At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.   10x^2 = 28.9   x^2=2.89   x=1.7   At 4:00 pm, the amount of bacteria was 10(1.7)=17 grams.   The answer is 17.0.
Answer: E
3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
Pick:
A) 11/4 days	B) 16/4 days	C) 18/4 days	D) 15/4 days	E) 13/4 days

Solution: 15/4 days   15/4 days   3M = 6W ---- 20 days   12M + 8W -----?   24W + 8 W = 32W ---?   6W ---- 20 32 -----?   6 * 20  24  + 8= 
 24  + 8 = 32
32W ---?   6W ---- 20 32 -----?   6 * 20= 32 * x => x = 15/4 days
Answer: D
The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit H on the height of vehicles that are allowed to use the tunnel?
Choose the correct choice.
A) 5½ ft B) 7½ ft C) 8 ½ ft D) 9½ ft E) 10 ft

Solution: Let's label the midpoint of the circle O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10.   We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Let's call the leftmost point on the base of the traffic lane A. So, the distance OA is 6.   Now draw a line straight up from A to the top of the tunnel. Let's label the point at which the line intersects the circle B. The answer to the question will, therefore, be the height AB - .5 feet (we need to leave .5 feet of clearance).   Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).   Finally: AB=8, so the correct answer H is 8 - .5 = 7.5... choose (7½ ft)!   From a strategic guessing point of view, as soon as we realize that the height of the tunnel is 10 in the middle, we should quickly eliminate (D) and (E) as too big; worse case you have a 1/3 shot at picking up the points.7½ ft
Answer: B
Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners.
Conclusions:
1) 80% of the team consists of spinners.
2) The opening batsmen were spinners.	Choose the correct choice from the following.
A) Only conclusion I follows	B) Only conclusion II follows	C) Either I or II follows	D) Neither I nor II follows	E) Both I and II follow

Solution: According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow.   Neither I nor II follows
Answer: D
At 3.40, the hour hand and the minute hand of a clock form an angle of
Choose the correct choice from the following options:  A) 378  B) 277  C) 297  D) 267  E) 130

Solution: Sol:   Use formula θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|   Angle = 30×3 – 11/2 × 40 = 90 – 220 = 130°   Answer:130
Answer: E
In 1982 and 1983, Company B’s operating expenses were $13.0 million and $15.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ? Choose the correct choice
A) 3%
B) 46 1/6%
C) 25%
D) 33 1/3%
E) 60%

Solution: Profit in 1982 = 15.6 - 13= 
15.6 - 13 = 2.6
2.6 million $   Profit in 1983= 18.8 - 15= 
18.8 - 15 = 3.8
3.8 million $   Percentage increase in profit= (3.8-2.6)/2.6 * 100 %   = 46 1/6 %   Answer 46 1/6%
Answer: B
In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.815 per pound? Select the correct option.
A) 1:3	B) 1:2	C) 6:1	D) 2:1	E) 3:1

Solution: Using weighted average method:   Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.   Thus 0.8*x + 0.9*(1-x) = 0.815   0.9 – 0.1x = 0.815   x = 0.85   Thus ratio of both flours is 6:1   6:1
Answer: C
A tradesman by means of his false balance defrauds to the extent of 15%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?	Select
A) 37.5 B) 32.25 C) 24.45 D) 26.46 E) 27.35

Solution: Explanation:   g% = 15 + 15 + (15*15)/100= 
15 + 15 + (15*15)/100 = 129/4 = around 32.25
32.25%   Answer: 32.25
Answer: B
Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 600 kms and City A and City C is 460 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) Choose the correct choice from the following answers:
A) 8/3
B) 3/8
C) 8/5
D) 5/8
E) 40/23

Solution: Distance traveled by 40/23ddy = 600 km   Time taken by 40/23ddy = 3 hours   Average speed of 40/23ddy = 600/3= 
600/3 = 200
200 km/hour   Distance traveled by Freddy= 460 km   Time taken by Freddy = 4 hours   Average speed of Freddy = 460/4= 
460/4 = 115
115 km/hour   Ratio of average speed of 40/23ddy to Freddy= 200/115 = 40/23   Answer 40/23
Answer: E
The odds against ram solving the problem are 4 to 5 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try?
Choose the correct choice from the following options:  A) 1/4  B) 5/21  C) 16/21  D) 23/28  E) 22/27

Solution: Odds against Ram are 4:5 so probability that he will solve the problem is 5/9.   Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12   It will be solved means that either Ram or Krishna or both will be able to solve it.   P(A or B) = P(A) + P(B) - P(A and B) = 5/9 + 7/12 - (5/9)*(7/12) = 22/27   22/27
Answer: E
Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 450 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day?  Select.
A) $ 1.50	B) $ 1.88	C) $ 2.25	D) $ 2.50	E) $ 3.25

Solution: 7 regular days --> sales = 7*32*x = 224x;   3 hot days --> sales = 3*32*(1.25x) = 120x;   Total sales 3*32*(1.25 )= 
3*32*(1.25 ) = 120
120x;   Total sales= 224x+120x = 344x.   Total cost 224 +120= 
224 +120 = 344
344x.   Total cost= 10*32*0.75= 
10*32*0.75 = 240
240.   Profit= 344x - 240 = 450 --> x=2.   1.25x=~2.50.   Answer: $ 2.50.
Answer: D
In a 2 digit no unit's place is halved and tens place is doubled. diff bet the nos is 37.digit in unit's place is 2 more than tens place. Select the correct option:
A) 36	B) 46	C) 56	D) 66	E) 76

Solution: let tenth place digit be x & unit place be y   then no. is = 10x + y   if unit place is halved and tens place is doubled   then no. is = 10*2x + y/2   10*2x + y/2 -(10x+y)=37   => 10x - y/2 = 37 .....(1)   and, y-x=2 ....(2)   solving, x=4,y=6   no. is 46   ANSWER:46
Answer: B
The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 294 square centimeters, what is the length of the rectangle in centimeters?  Choose one: A) 19 B) 20 C) 21 D) 22 E) 23

Solution: Perimeter = 2(W+L) = 5W   3W = 2L   W = 2L/3   WL = 294   2L^2/3 = 294   L^2 = 441   L = 21 cm   The answer is 21.
Answer: C
Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I?
Select the correct option.
A) 111
B) 145
C) 110
D) 119
E) 120

Solution: There are five letters in the given word.   Consider 7 blanks ....   The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways.   The number of words = 5! = 120.   Answer:120
Answer: E
Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 7 books, how many shelves does the bookcase have?  Select the correct option
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Let x be the number of shelves.   12x - 21 = 8(x-1) + 7   4x = 20   x= 5   The answer is 5.
Answer: A
If a 3-digit integer is selected at random from the integers 700 through 899, inclusive, what is the probability that the second digit is one greater then the first digit, and the third digit is one greater than the second digit?
Options:
A) 2/225	B) 2/200	C) 8/700	D) 1/50	E) 1/200

Solution: Hundreds digit can be 7 or 8   If the hundreds digit is 7, then the tens digit has to be 8 and the units digit has to be 9   If the hundreds digit is 8, then the tens digit has to be 9 and the units digit has to be 10   A digit has to fall between 0 and 9, so 10 cannot be a digit   The number is 789   Total numbers between 700 and 899 = (899-700)+1= 
(899-700)+1 = 200
200   Probability= 1/200   Answer 1/200
Answer: E
In the first M games of a team's season, the ratio of the team's wins to its losses was 3:1. In the subsequent N games, the ratio of the team´s wins to losses was 1:4. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games?
Choose the correct choice from the following answers: A) 1:2 B) 2:3 C) 3:4 D) 4:5 E) 5:6

Solution: M = 4/9 of total games   N = 5/9 of total games   Wins = 3/4*4/9 + 1/5*5/9 = 3/9 + 1/9 = 4/9   Losses = 1 - 4/9 = 5/9   The ratio of wins to losses is 4:5.   The answer is 4:5.
Answer: D
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?  Options.
A) 1500
B) 2000
C) 300
D) 8000
E) 500

Solution: State A and State B had an equal number of candidates appeared.   In state A, 6% candidates got selected from the total appeared candidates   In state B, 7% candidates got selected from the total appeared candidates   But in State B, 80 more candidates got selected than State A   From these, it is clear that 1% of the total appeared candidates in State B = 80   => total appeared candidates in State B = 80 x 100 = 8000   => total appeared candidates in State A = total appeared candidates in State B = 8000   Answer : 8000
Answer: D
The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?	Choose the correct choice from the following answers:	A) 75 Kg	B) 50 Kg	C) 85 Kg	D) 90 Kg	E) 60 KG

Solution: Explanation:   Total increase in weight = 10 Ã— 2.5 = 25   If x is the weight of the new person, total increase in weight = xâˆ’65   => 25 = x - 65   => x = 25 + 65= 
25 + 65 = 90
90   Answer: Option 90 Kg
Answer: D
Each of the following numbers has a remainder of 2 when divided by 13 except:  Choose the correct choice:
A) 15	B) 28	C) 42	D) 54	E) 67

Solution: It's 42   42 = 13*3+3
Answer: C
8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged?
Choices: A) A.1296 B) B.1850 C) C.2880 D) D.3546 E) E.4200

Solution: Glue milk and water bottlestogether: {AB}, {CD}.   6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways.   Therefore the final answer is 6!*2!*2!=2,880.   Answer: C.2880.
Answer: C
What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.? Choose the correct choice from the following answers.
A) Rs. 14705.24	B) Rs. 14602.25	C) Rs. 14822.26	D) Rs. 14322.10	E) Rs. 15350.23

Solution: Explanation:   Amount after 3 years = P(1+R/100)T=40000(1+11/100)3   =40000(111/100)3=40000×111×111×111/100×100×100   =4×111×111×111/100=54705.24   Compound Interest = 54705.24 - 40000 = Rs. 14705.24   Rs. 14705.24nswer : Option Rs. 14705.24
Answer: A