MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 760 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?  Answers:
A) 320 B) 345 C) 425 D) 475 E) 400

Solution: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 760. Hence   3x + 5x = 760   Solve for x   8x = 760   x = 95   Number of boys   3x = 3 × 95 = 285   Number of girls   5x = 5 × 95 = 475   475
Answer: D
a boatman selling a boat along river flow.if he sell boat in steal water at 3m/sec and flow of river is 2m/sec.how much time he will take to sell 100m.
Choose the correct answer: A) 30 B) 10 C) 15 D) 20 E) 25

Solution: net speed = 3+2= 
3+2 = 5
5 m/sec   distance= 100m   time=100/5= 
100/5 = 20
20sec   answer 20
Answer: D
If a and b are multiples of 9 then which are all the multiples of 9
1) a*b
2) a/b
3) a+b
4) a-b
5) a^b Choose the correct choice from the following choices:
A) 1,2,5  B) all of these  C) 1,3,4,5  D) 2,3,4,5  E) 1,3

Solution: a*b a^b a+b a-b are multiples of 6 except a/b   ANSWER:1,3,4,5
Answer: C
Mark has a rectangular driveway with a line painted diagonally across. The length of the driveway is 6 feet longer than its width. If the total area of the driveway is 40 square feet, what is the length of the painted line (in feet)?	Choose the correct choice from the following options: A) Between 9 and 10 B) Between 10 and 11 C) Between 11 and 12 D) Between 12 and 13 E) Between 13 and 14

Solution: To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have   x(x + 6) = 40. By putting the equation in standard form, we get x^2+6x-40=0. By using the quadratic formula, we get roots of 4 and -10. We know that x is the width, and x+6 is the length, so by using the roots, we get 4 as the width (x), and 10 as the length (x+5).   Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=4^2+10^2   =16+100= 
16+100 = 116
116   The square root of 97 is more than 10, since 10^2= 100. Going up a number, we can compute 11^2 = 121 >116. Therefore, the length of the diagonal must be between 10 and 11.   The correct answer is Between 10 and 11.
Answer: B
Which greatest possible length can be used to measure exactly 15 meter 20 cm, 12 meter 20 cm and 14 meter 20 cm
Answers.
A) 20cm	B) 25cm	C) 24cm	D) 55cm	E) 30cm

Solution: Explanation:   Convert first all terms into cm.   i.e. 1520 cm, 1220cm, 1420cm.   Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 20.   Option 20cm
Answer: A
The sum of five numbers is 100. The average of the first two numbers is 10 and the third number is 30. Find the average of the two numbers?
Choose the correct option.
A) 25	B) 20	C) 23	D) 22	E) 30

Solution: Let the five numbers be P, Q, R, S and T.   => P + Q + R + S + T = 100   (P + Q)/2 = 10 and R = 30   P + Q = 20 and R = 30   P + Q + R = 50   S + T = 100 - (P + Q + R) = 50   25verage of the last two numbers   = (S + T)/2 = 25   25nswer:25
Answer: A
Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?	Choose the correct choice from the following answers
A) 75	B) 150	C) 300	D) 500	E) 2400

Solution: I'd use backsolving for this question.   Check E:   2400 lenses = 1200 usable lenses = 600 tubes = 600 eyepieces. We CAN buy 600 tubes and 600 eyepieces, so that not to have leftovers.   Answer: 2400.
Answer: E
A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?  Choose the most appropriate option.
A) 88% B) 50% C) 87% D) 66% E) 54%

Solution: L.C.M of 15 and 12 = 60   CP of 60 articles = Rs. 100 (25 * 4)   SP of 60 articles = Rs. 150 (30 * 5)   Profit percentage = (150 - 100)/100 * 100= 
(150 - 100)/100 * 100 = 50
50%   Answer: 50%
Answer: B
A FIVE DIGIT NUMBER DIVISIBLE BY 3 IS TO BE FORMED USING THE DIGITS 0, 1, 2, 3, 4 and 5 WITHOUT REPETITIONS. THAT TOTAL NO OF WAYS IT CAN BE DONE IS?
Select.
A) 122  B) 210  C) 216  D) 217  E) 220

Solution: First step:   We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.   We have six digits: 0,1,2,3,4,5. Their sum=15.   For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0=(1,2,3,4,5) and 15-3=(0,1,2,4,5). Meaning that no other 5 from given six will total the number divisible by 3.   Second step:   We have two set of numbers:   1,2,3,4,5 and 0,1,2,4,5. How many 5 digit numbers can be formed using this two sets:   1,2,3,4,5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.   0,1,2,4,5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=96   120+96= 
120+96 = 216
216   Answer: 216.
Answer: C
A grocer has a sale of Rs. 2500, Rs. 4000, Rs. 3540 for 3 consecutive months. How much sale must he have in the fourth month so that he gets an average sale of Rs. 2890?
Choose the correct option:
A) Rs.3500  B) Rs. 1520  C) Rs. 4996  D) Rs. 4000  E) Rs. 900

Solution: Total sale for 5 months = Rs. ( 2500 + 4000 + 3540) = Rs. 10040.   Required sale = Rs. [ (2890 x 4) -10040 ]   = Rs. (11560 - 10040)   = Rs. 1520.   Rs. 1520)
Answer: B
A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house ?	Choose the most appropriate option.
A) 50 km B) 80 km C) 20 km D) 10 km E) 30 km

Solution: Explanation:   Let distance = x km.   Time taken at 3 kmph : dist/speed = x/3 = 20 min late.   time taken at 4 kmph : x/4 = 30 min earlier   difference between time taken :   30-(-20)= 
  30-(-20) = 50
50 mins= 50/60 hours.   x/3- x/4 = 50/60   x/12 = 5/6   x = 10 km.   Answer: 10 km
Answer: D
Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 350 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 4 of the days were hot, then what was the price of 1 cup on a hot day? Pick one:
A) $ 1.50
B) $ 1.88
C) $ 2.09
D) $ 2.50
E) $ 3.25

Solution: 6 regular days --> sales = 6*32*x = 192x;   4 hot days --> sales = 4*32*(1.25x) = 160x;   Total sales 4*32*(1.25 )= 
4*32*(1.25 ) = 160
160x;   Total sales= 192x+160x = 352x.   Total cost 192 +160= 
192 +160 = 352
352x.   Total cost= 10*32*0.75= 
10*32*0.75 = 240
240.   Profit= 352x - 240 = 350 --> x=1.676.   1.25x=~2.09.   Answer: $ 2.09.
Answer: C
A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?  Pick: A) 1788 B) 1200 C) 2789 D) 1776 E) 1999

Solution: l * 30 = 1200 è l = 40   40 + 30 + 50= 
40 + 30 + 50 = 120
120   120 * 10= 
120 * 10 = 1_200
1200   Answer: 1200
Answer: B
A reduction of 40% in the price of bananas would enable a man to obtain 65 more for Rs.40, what is reduced price per dozen?	Choose the correct choice from the following options
A) 1.95 B) 2.95 C) 4.95 D) 3.95 E) 5.95

Solution: 40*(40/100)= 
40*(40/100) = 16
16 --- 65   ? --- 12=> Rs.2.95   Answer: 2.95
Answer: B
A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is?	Options:
A) 72 kmph B) 88 kmph C) 54 kmph D) 18 kmph E) 19 kmph

Solution: S = 120/6 * 18/5= 
120/6 * 18/5 = 72
72 kmph   72 kmphnswer: 72 kmph
Answer: A
A and B together can complete work in 5 days. A alone starts working and leaves it after working for 3 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?	Choose the correct choice from the following
A) 4  B) 8  C) 15  D) 6  E) 7

Solution: Explanation:   (A+B) one day work =1/5   now A does half of the work in 3 days so A can complete the whole work in 6 days   A’s one day work =1/6   B’s one day work=1/5 - 1/6= 1/30   B alone can complete the work in 30 days so half of the work in 15 days   Answer: Option 15
Answer: C
A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?	Choose the correct option
A) 337	B) 278	C) 221	D) 860	E) 121

Solution: Explanation:   CP = SP + 1CP = SP - g   800 + x = 980 - 2x   3x = 180 => x = 60   CP = 800 + 60= 
800 + 60 = 860
860   Answer:860
Answer: D
Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?  Choose the most appropriate option:  A) 600  B) 620  C) 670  D) 690  E) 700

Solution: Suppose Anju is allotted bed number 1.   Then, Parvin cannot be allotted bed number 2.   So Parvin can be allotted a bed in 5 ways.   After allotting a bed to Parvin, the remaining 5 students can be allotted beds in 5! ways.   So, in this case the beds can be allotted in 5×5!=6005×5!=600 ways.   Option is 600
Answer: A
A man is 22 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son? Choose the correct choice from the following answers:  A) 23 years  B) 22 years  C) 21 years  D) 20 years  E) 19 years

Solution: Let present age of the son =x years   Then, present age the man =(x+22) years   Given that, in 2 years, man's age will be twice the age of his son   â‡’(x+22)+2=2(x+2)   â‡’x=20   ANSWER:20 years
Answer: D
Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.	Select:
A) 121	B) 124	C) 127	D) 122	E) 129

Solution: Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032   _______   1651 ) 2032 ( 1 1651   1651_______   381 ) 1651 ( 4   1524_________   127 ) 381 ( 3   381   0   Required number = 127.   Answer is 127.
Answer: C
Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 30% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of Choose the correct option.
A) 18%
B) 20%
C) 21%
D) 23%
E) Cannot be determined

Solution: Answer: 23%.
Answer: D
If a and b are two-digit integers such that a > 20 and b<60, which of the following is closest to the maximum possible value of ab ?
Choose the most appropriate option
A) 700	B) 2,800	C) 5,841	D) 7,000	E) 28,000

Solution: To get the maximum possible value of ab, we need maximize the value of both a and b   max a can be = 99 (given a is a two-digit integer > 20)   max b can be = 59 (given b is a two-digit integer < 60)   xy = 99*59= 
99*59 = 5_841
5841   Answer (5,841)
Answer: C
A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 4, what is the smallest possible total number of tokens in the jar?  Answers:	A) 9	B) 12	C) 15	D) 18	E) 21

Solution: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)   i.e. Red*White = Blue*Total Coins   Let, Red = 3a   White = 3b   Blue = 3c   Total Coins = 3(a+b+c)   i.e. 3a * 3b = 3c*3(a+b+c)   i.e. a*b = c*(a+b+c)   For smallest values of a, b and c   2*3 = 1*(1+2+3)   i.e. Minimum Total 15oins = 3*(1+2+3)= 
3*(1+2+3) = 18
18   Answer: Option 15
Answer: C
Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (12,2). What is the slope of line m? Select:
A) -2	B) -1	C) 0	D) 1	E) 2

Solution: The midpoint of (2,8) and (12,2) is (7,5).   The slope of a line through (0,-2) and (7,5) is (5-(-2))/(7-0) = 7/7= 
7/7 = 1
1   The answer is 1.
Answer: D
A straight pipe 7 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?  Choose the correct answer
A) 1/6 and 1/4 only B) 1/4 and 1/3 only C) 1/6, 1/4, and 1/3 D) 1/12, 1/6 and 1/4 E) 1/12, 1/6, and 1/3

Solution: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.   In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).   Distinct lengths would be: 3=3/12=1/3, 4-3=1=1/12and  6-4= 
 6-4 = 2
2=2/12=1/6meters long pieces.   Answer: 1/12, 1/6, and 1/3.
Answer: E
A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 32 now, the son age 5 years back was  Options
A) 11
B) 17
C) 11
D) 19
E) 99

Solution: Let the son's present age be x years .Then, (32 - x) = x x= 16.   Son's age 5 years back = (16 - 5)= 
(16 - 5) = 11
11 years   11nswer: 11
Answer: A
How many integers k greater than 100 and less than 1100 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?  Pick
A) 50  B) 60  C) 70  D) 80  E) 90

Solution: Not sure if this is the shortest.. But this is how I did this   There are 9 sets of integers with hundreds and units digits exchanged that satisfies k + 99.   1. 102 | 201 (satisfies k+99, where k = 102)   2. 203 | 302 (satisfies k+99, where k = 203)   3. ...   4. ...   5. ...   6. ...   7. 708 | 807   8. 809 | 908   9. 910 | 1001   Each set has 10 such numbers.   1. 102 | 201 (still k+99 holds good)   2. 112 | 211   3. 122 | 221   4. 132 | 231   5. ...   6. ...   7. ...   8. ...   9. 182 | 281   10. 192 | 291   Therefore, 9 sets with 10 such number in each set will give 9 x 10 = 90 integers.   90
Answer: E
Compound interest of Rs.6000 at 10% per annum for 1 1/2years will be (interest compounded half yearly). Choose the correct option:
A) Rs.473  B) Rs.374  C) Rs.495  D) Rs.945  E) None of the above

Solution: 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)   So compound interest=6000[1+(5/100)]^3 - 6000=6000[(21/20)^3 -1]   =6000(9261-8000)/8000   =6*1261/8   =945   ANSWER:Rs.945
Answer: D
The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
Choose the correct choice from the following options.
A) 10	B) 40	C) 88	D) 66	E) 23

Solution: Speed of the boat in still water = (50+90)/2= 
(50+90)/2 = 70
70 kmph. Speed of the stream= (90-50)/2= 
(90-50)/2 = 20
20 kmph. Answer:40
Answer: B
On a map the distance between two mountains is 312 inches. The actual distance between the mountains is 140 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain? Choices:
A) 14.83  B) 14.81  C) 14.8  D) 15.25  E) 14.12

Solution: Explanation:   Since 312 inch = 140 km   So 1 inch = 140/312 km   So 34 inch = (140 Ã— 34)/ 312 = 15.25 km   Answer: 15.25
Answer: D
If the simple interest on Rs. 8010 amount to Rs $3364.20 in 6 Years, calculate the rate percent?	Select the correct option
A) 5% B) 6% C) 7% D) 3% E) 9%

Solution: 3364.20 = (8010*6*R)/100   R = 7%   Answer: 7%
Answer: C
During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold Q was 25,200, how many of them were sold at full price? Select the correct option:
A) 21,000	B) 19,800	C) 16,500	D) 15,800	E) 8,700

Solution: Given:   The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.   Approach:   The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.   Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e.   Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold   We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.   Working Out:   Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold   Substituting values in the equation, we get   5,400 + 5x + x = 25,200   x= 3,300   Tickets sold at full price = 5x = 16,500   Answer: Option 16,500
Answer: C
When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 38, what is the remainder when k is divided by 7?  Choose the most appropriate option.
A) 2 B) 4 C) 3 D) 5 E) 6

Solution: Cant think of a straight approach but here is how I solved it:   K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)   so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 38)   Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5   so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 38)   17 is the only common number in both the sets. Hence k = 17   Answer : 3
Answer: C
Two drivers began their journey with the same amount of petrol in their cars at the same time. The only difference is that the first driver�s car could drive 4 hours in that amount of petrol and the second one could drive 5 hours.
However, they only drove for some time and found that the amount of petrol that was left in one of the cars was four times the petrol left in the other one.
For how long had they driven at this point of time?  Choices:
A) 3.75 hours	B) 5.45 hours	C) 7.10 hours	D) 4.75 hours	E) 3.33 hours

Solution: A   3.75 hours   While you can solve it as you like, a simple mathematical equation can be used to find out.   Let M be the amount of petrol initially.   Let N be the time for which they drove.   According to the question, the amount of petrol used by first car in N hours = MN / 4   The amount of petrol used by second car in N hours = MN / 5   Hence, the amount of petrol left in the first car = (M - MN / 4)   The amount of petrol left in the second car = (M - MN / 5)   AS per the details given in the question, we can form the below equation:   M - MN / 5 = 4(M - MN / 4)   N = 15 / 4 or 3.75 hours.   Hence, both the drivers have driven the car for 3.75 hours at that particular time.
Answer: A
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
Choose the correct choice from the following options:
A) 44ft B) 88ft C) 22ft D) 11ft E) 66ft

Solution: Given that length and area, so we can find the breadth.   Length x 88ftreadth = Area   20 x 88ftreadth = 680   88ftreadth = 34 feet   Area to be fenced = 288ft + L = 2 (34) + 20 = 88 feet   Answer: 88ft) 88ft
Answer: B
Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length L of time will elapse before they chime together again?  Select:  A) 2 hr. and 24 min.  B) 4 hr. and 48 min.  C) 1 hr. and 36 min.  D) 5 hr.  E) 2 hr.

Solution: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.   So the LCM of the three time intervals (18, 24,32) would be the answer.   LCM (18, 24, 32) L= 288 => 4 hours 48 mins.4 hr. and 48 min.
Answer: B
Last year Elaine spent 20% of her annual earnings on rent. This year she earned 15% more than last year and she spent 25% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year? Choose one
A) 152.5  B) 143.75  C) 155.5  D) 165.5  E) 117.5

Solution: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.   She would've spent $20 of this on rent.   This year she earned 15% more, or $115.   She would've spent 25% of this on rent, or $28.75   Do $34.5/$20   This will give you 143.75%   143.75 is the correct answer.
Answer: B
The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is? Choose the correct choice from the following answers.
A) 328	B) 279	C) 225	D) 288	E) 211

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==> 2(150 + X) = 750 ==> X = 225 m.Answer: 225
Answer: C
A box contains 20 balls, numbered from 1 to 20. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?	Pick one.
A) 1/4 B) 3/8 C) 1/2 D) 5/8 E) 3/4

Solution: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2   My answer is: 1/4   1/4
Answer: A
The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 40 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?
Choose the correct choice from the following answers
A) 8
B) 9
C) 10
D) 12
E) 16

Solution: M + Tu + W + Th = 4 * 48= 
4 * 48 = 192
192   Tu + W + Th + F= 4 * 40= 
4 * 40 = 160
160   M= 42   Tu + W + Th = 192 -42= 
192 -42 = 150
150   F= 160 – 150 = 10   ANSWER:10
Answer: C
On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $240,000?  Choose the correct choice from the following:
A) 27 B) 16 C) 18 D) 20 E) 24

Solution: if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....   I found a method: Rule of 72.   Given an x% return, it takes 10,000 to quadralope 12 years.   So according to the rule: 72/x is the no of years 10,000.00 took to double 20,000.00.   Again, 20,000.00 took to double 40,000.00 same (72/x) no of years.   72/x+ 72/x = 12   x = 12% (though rate here is not very much required).   Again, 40,000.00 takes the same (72/x) no of years to double 240,000.00.   72/x = 6 years.   So altogather:   10,000 - 20,000 = 6 years   20,000 - 40,000 = 6 years   40,000 - 80,000 = 6 years   80,000 - 160,000 = 6 years   160,000 - 240,000 = 3 years   total 27 years.   27nswer 27
Answer: A