MU-NLPC/Calc-aqua_rat huggingface dataset:
The area of a rectangular plot is 23 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth? Choose the correct choice from the following answers:
A) 13 metres
B) 5 metres
C) 7.5 metres
D) Data inadequate
E) None of these

Solution: L × B = 23 × B   ∴ L = 23 m   and L – B = 10   ∴ B = 23 – 10 = 13 m   13 metresnswer 13 metres
Answer: A
10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs. 170000, find the cost of a camel?	Select the correct option
A) 3278
B) 2669
C) 2770
D) Rs.6800
E) 2791

Solution: Cost of the camel = P   10 camels = 24 horses   16 horses = 4 oxen   6 oxen = 4 elephants   10 elephants = Rs.170000   P = Rs.[(24 * 4 * 4 * 170000)/(10 * 16 * 6 * 10)]   P = Rs.(65280000/9600) => P = Rs.6800   Answer: Rs.6800
Answer: D
A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?	Pick one.
A) 90  B) 100  C) 126  D) 154  E) 167

Solution: There are 8 students and the maximum capacity of the cars together is 9.   We may divide the 8 students as follows   Case I: 5 students in the first car and 3 in the second   Or Case II: 4 students in the first car and 4 in the second   Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.   Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.   Therefore, the total number of ways in which 8 students can travel is:   \inline {\color{Blue}8126_{3}+8126_{4}}=56 + 70= 
56 + 70 = 126
126   126
Answer: C
A composer’s guild is planning its spring concert, and twelve pieces have been submitted for consideration. The director of the guild knows that they will only have time to present eight of them. If the pieces can be played in any order, how many combinations of pieces are possible? Choose the correct choice.
A) 402	B) 210	C) 109	D) 504	E) 495

Solution: Combination question..   12C8 = 495..   IMO option 495 is correct..
Answer: E
The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.
Choose the correct choice from the following answers:
A) Rs 30	B) Rs 40	C) Rs 50	D) Rs 60	E) Rs 90

Solution: Let the price of gift pack be 'aa'   Then number of packs bought =a+1=a+1   Hence total cost is a(a+1)a(a+1)   It is given that 380<a(a+1)380<a(a+1)   If a=19a=19, the total cost =19×20=380=19×20=380   Dexter would not have fallen short, If:   a=20a=20, a(a+1)=420a(a+1)=420   So he would have fallen short by Rs 40.   This is the minimum amount by which he may have fallen short.   Rs 40)
Answer: B
The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)?
Select the correct option
A) 20043.94
B) 20043.92
C) 20043.98
D) 20043.21
E) 20043.12

Solution: Let the rate of interest be R% p.a.   (49500)(3)(R)/100 = 17820   495R = 5940   R = 12   CI on Rs.49500 at 12% p.a. for three years   = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500   = Rs.20043.94   when rounded off to two decimal places.   20043.94nswer: 20043.94
Answer: A
An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 400 sculptures are not on display, how many pieces of art does the gallery have?  Pick.
A) 360  B) 900  C) 540  D) 640  E) 720

Solution: Too many words and redundant info there.   (i) 1/3 of the pieces of art are displayed, hence2/3 of the pieces of art are NOT displayed.   (ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.   (iii) 1/3 of the pieces NOT on display are paintings, hence2/3 of the pieces NOT on display are sculptures.   400 sculptures are not on display, so according to (iii) 2/3*{not on display} = 400 --> {not on display} = 600.   According to (i) 2/3*{total} = 600 --> {total} = 900.   Answer: 900.
Answer: B
The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
Choose the correct choice from the following choices:
A) 6 kmph
B) 8 kmph
C) 9 kmph
D) 10 kmph
E) 3 kmph

Solution: S = 1   M = x   DS = x + 1   US = x - 1   35/(x + 1) + 35/(x - 1) = 12   x = 6   6 kmphnswer:6 kmph
Answer: A
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: Choose the most appropriate option
A) 50 m
B) 150 m
C) 200 m
D) data inadequate
E) None of these

Solution: Explanation:   Let the length of the train be x metres and its speed be y m/sec.   Then, (x/y)= 15 y =(x/15)   =x+100/25=x/15   => 15(x + 100) = 25x   => 15x + 1500 = 25x   => 1500 = 10x   => x = 150 m.   Answer: 150 m
Answer: B
There is a work which can be completed by A with 12 days and B by 18 days. A and B works together for 3 days and B left. After that how many days for A to complete the work?
Answers:
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: work done by A per day=1/12   work done by B per day=1/18   work done by A and B per day=1/12+1/18=5/36   work done by A and B for 3 days=5*3/36=5/12   work remasining=1-5/12=7/12   . After that A takes 7days to complete the work   ANSWER:7
Answer: D
What will be the value of a+b , if |ab|=1 and a=b/a? Choose the correct choice from the following answers.
A) (1-b)/a	B) (1+a)/b	C) 1	D) a/b	E) (1+b)/a

Solution: Option E is answer.   a+b=(b/a)+b(a=b/a).   =(b+ab)/a   =(1+b)/a(ab=1)
Answer: E
A computer store offers employees a 10% discount off the retail price. If the store purchased a computer from the manufacturer for $800 dollars and marked up the price 10% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (10% off retail price) as opposed to the final retail price.  Choose one.
A) 86 B) 88 C) 90 D) 92 E) 94

Solution: Cost price=800   Profit=10% =10% of 800=80   selling price=CP+ Profit   SP=880   a Discount of 10% to employees means 10% off on 880   so 10% of 880= 88   Ans 88
Answer: B
A single discount equivalent to the discount series of 25%, 10% and 5% is? Choose the correct choice from the following answers:
A) 31.6 B) 31.0 C) 35.875 D) 31.1 E) 31.5

Solution: 100*(75/100)*(90/100)*(95/100)   = 68.4   100 - 64.125= 
100 - 64.125 = 35.875
35.875   Answer: 35.875
Answer: C
If two painters can complete two rooms in two hours, how many painters would it take to do 18 rooms in 6 hours?  Select the correct option
A) 8 B) 6 C) 5 D) 4 E) 1

Solution: Explanation:   Two painters can complete two rooms in two hours.So 18 rooms can be painted in 6 hrs by 6 painters   Answer: 6) 6 painters
Answer: B
A merchant purchased a jacket for $210 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?  Choose the most appropriate option.
A) $0 B) $3 C) $4 D) $12 E) $14

Solution: Let selling price = x   So, x = 210 + 25x/100   Calculating above, x = 280   Selling price = 280   20% Discount on Selling price = 224   So, profit = 224-210= 
224-210 = 14
14 Answer= $14
Answer: E
Find the odd man out. 18, 16, 12, 24, 11, 34, 46 Choices
A) 16
B) 46
C) 24
D) 11
E) 18

Solution: Explanation :   11 is the only odd number in the given series   Answer : Option 11
Answer: D
? 370 860 1550 2440 3530	Choose the correct option:
A) 900
B) 840
C) 750
D) 860
E) 80

Solution: 10^2 - 20 = 80   20^2 - 30 = 370   30^2 - 40 = 860   40^2 - 50 = 1550   50^2 - 60 = 2440   60^2 - 70 = 3530.   ANSW80R:80
Answer: E
The area of a triangle is with base 4m and height 5m?	Choices.
A) 11	B) 10 m2	C) 88	D) 26	E) 32

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer: 10 m2
Answer: B
The difference between the simple interest received from two different sources on Rs.2000 for 3 years is Rs.13.50. The difference between their rates of interest is Choose the correct option
A) 0.12%
B) 0.22%
C) 0.32%
D) 0.42%
E) 0.52%

Solution: (2000xR1x3)/100-(100xR2x3)/100 =13.50   6000(R1-R2)=1350   R1-R2 = 1350/6000=0.22%   answer : 0.22%
Answer: B
An urn contains g green marbles and b blue marbles. If 3 green marbles and 6 blue marbles are added, and then one marble is selected at random from the urn, what is the probability that a blue marble will be drawn? Answers:
A) b+6/(b+g+9)	B) (b+5)/(g+3)	C) (b+5)/(b+g+8)	D) (b+5)/(b+g+3)	E) b/(b+g+5)

Solution: no of fav outcomes i.e. blue MArbles = b+6   Total no of outcomes i.e. total Marbles = (b+6)+(g+3)= b+g+9   probability = (b+6) /(b+g+9)   b+6/(b+g+9)nswer b+6/(b+g+9)
Answer: A
P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?  Choose the correct choice from the following answers:
A) 8/15
B) 7/15
C) 11/15
D) 2/11
E) 3/11

Solution: Explanation :   8/15mount of work P can do in 1 day = 1/15   8/15mount of work Q can do in 1 day = 1/20   8/15mount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60   8/15mount of work P and Q can together do in 4 days = 4 Ã— (7/60) = 7/15   Fraction of work left = 1 â€“ 7/15= 8/15   8/15nswer IS 8/15
Answer: A
12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it so to be completed in 3 days? Select the correct option:  A) 22  B) 15  C) 66  D) 77  E) 88

Solution: 1 man's 1 day work = 1/48; 1 woman's 1 day work = 1/60.   6 men's 2 day's work = 6/48 * 2 = 1/4.   Remaining work = (1 - 1/4) = 3/4   Now, 1/60 work is done in 1 day by 1 woman.   So, 3/4 work will be done in 3 days by (60 * 3/4 * 1/3)= 
(60 * 3/4 * 1/3) = 15
15 women.   Answer: 15
Answer: B
There are 12 yes or no questions. How many ways can these be answered? Choose one
A) 1024	B) 2048	C) 4096	D) 144	E) 2140

Solution: Each of the questions can be answered in 2 ways (yes or no)   Therefore, no. of ways of answering 12 questions = 212 = 4096 ways.   Option 4096
Answer: C
How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed	Choose the correct option:
A) 7845  B) 1278  C) 4561  D) 5040  E) 3654

Solution: 'LOGARITHMS' contains 10 different letters   Required number of words   = Number of arrangements of 100 letters taking   4 at a time   = 10P4   = 10 * 9 * 8 * 7= 
10 * 9 * 8 * 7 = 5_040
5040   Ans: 5040
Answer: D
A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be:	Choose the correct choice from the following answers
A) 40
B) 100
C) 120
D) 140
E) 160

Solution: Let C.P. = Rs. x.   Then, S.P. = Rs. (12% of x) = Rs. 6x/5   New S.P. = 2 * 6x/5 = Rs. 12x/5   Profit = 12x/5 - x = Rs. 7x/5   Profit = 7x/5 * 1/x * 100 = 140%.   ANSWER:140
Answer: D
In a class of 10 students, a group of 4 will be selected for a trip. How many different groups are possible, if 2 of those 10 students are a married couple and will only travel together?  Choose the correct choice from the following answers.
A) 98
B) 115
C) 122
D) 126
E) 165

Solution: We need to break the grouping down to 2 scenarios : with the married couple or without the married couple in the group of 4 people for the trip   1) With the married couple in the group, we have to find the number of possibilities for the other 2 spots in the group from the left 8 people = 8!/(2!*6!) = 28   2) Without the married couple in the group, we have to find the number of possibilities for picking 4 people from the 8 unmarried people from the group = 8!/(4! * 4! ) = 70   Total number of possibilities = 28 + 70= 
28 + 70 = 98
98 (98)
Answer: A
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?  Choose the correct choice from the following.
A) 12 min B) 15 min C) 20 min D) 25 min E) 30 min

Solution: art filled by A in 1 min. = 1/20   Part filled by B in 1 min. = 1/30   part filled by (A + B) in 1 min. = 1/20 + 1/30 = 1/12.   Both the pipes can fill the tank in 12 minutes.   12 minNSWER 12 min
Answer: A
Rachel has ribbons that are blue, green, red, orange, and yellow. To identify the plants in her garden, she ties either 1 ribbon, or 2 ribbons of different colors, to each plant. How many different plants can Rachel label in this way without labeling more than one plant the same way?	Choose the most appropriate option
A) 5 B) 10 C) 15 D) 20 E) 25

Solution: Number of plants identified by one color= 5.   Number of plants identified by a combination of 2 colors= 5152=105152=10   Total number = 5+10=15.5+10=15.	ANS:15
Answer: C
Which of the following equations represents a line that is perpendicular to the line described by the equation 4x + 3y = 9?	Choose the correct choice from the following options:	A) 3x + 4y = 18	B) 3x – 4y = 24	C) 5y – 3x = 26	D) 1.5y + 2x = 18	E) 8x – 6y = 24

Solution: Perpendicular lines have slopes which are negative reciprocals of each other.   The line 4x + 3y = 9 in slope-intercept form is y = -(4/3)x + 3   The slope of this line is -4/3.   The slope of a perpendicular line is 3/4.   3x - 4y = 24 in slope-intercept form is y = (3/4)x - 6   The answer is 3x – 4y = 24.
Answer: B
at a special sale 5 ticket can be purchased as a price of 3 ticket, if 5 ticket are purchased at the sale, the amount saved will be what % of the original price of the 5 ticket.  Answers:
A) 10%
B) 20%
C) 30%
D) 40%
E) 50%

Solution: let the price of 1 ticket be Rs.10   Original C.P. of 5 tickets = Rs.50   After sale 5 Tickets were bought for Rs. 30   %amount saved = ((50-30)/50)*100= 
((50-30)/50)*100 = 40
40%   ANSWER:40%
Answer: D
If x is equal to the sum of the integers from 40 to 50, inclusive, and y is the number of EVEN integers from 40 to 50, inclusive, what is the value of x+y ?	Select: A) 171 B) 281 C) 391 D) 501 E) 613

Solution: sum s= n/2{2a+(n-1)d} = 11/2{2*40+ (11-1)*1} =11*45= 
11*45 = 495
495=X   number of even number =( 50-40)/2 +1= 
( 50-40)/2 +1 = 6
6= Y   X+Y = 495+6= 
495+6 = 501
501   501
Answer: D
Sumit and Ravi started a business by investing Rs 85000 and 15000 respectively. In what ratio the profit earned after 2 years be divided between Sumit and Ravi respectively.
Choices
A) 17:1  B) 17:2  C) 17:3  D) 17:4  E) 17:5

Solution: Explanation:   Note: If you have clear concept of ratio and proportion chapter then it will really easy for you to solve partnership problems.   P:Q = 85000:15000 = 17:3   Important to note there that if both have invested for different period of times then we had to multiply with number of months to get the desired ratio.   Option 17:3
Answer: C
Having received his weekly allowance, a student spent 2/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.20 at the candy store. What is this student’s weekly allowance?  Choices
A) $2.00 B) $2.25 C) $2.50 D) $2.75 E) $3.00

Solution: Let x be the value of the weekly allowance.   (2/3)(3/5)x = 120 cents   (2/5)x = 120   x = $3.00   The answer is $3.00.
Answer: E
Find the average of all the numbers between 6 and 34 which are divisible by 5.
Pick one:
A) 15
B) 18
C) 20
D) 22
E) None

Solution: Sol.   Average = (10 + 15 + 20 + 25 + 30 / 5) = 100 / 5= 
100 / 5 = 20
20.   Answer 20
Answer: C
Find the total number of prime factors in the expression (4)11 x (7)5 x (11)2. Choices:
A) 27
B) 28
C) 29
D) 30
E) 31

Solution: (4)11x (7)5 x (11)2 = (2 x 2)11 x (7)5 x (11)2 = 211 x 211 x75x 112 = 222 x 75 x112   Total number of prime factors = (22 + 5 + 2)= 
(22 + 5 + 2) = 29
29.   ANSWER 29 29
Answer: C
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 44 hours. If one additional machine were used under the same operating conditions, in how manyfewerhours of simultaneous operation could the production order be fulfilled?
Pick: A) 6 B) 9 C) 12 D) 11 E) 48

Solution: If 3 Machines can do the work in 44 hr then 4 Machines can do the work in   3/4*44= 
  3/4*44 = 33
33 Hrs. hence time saved will be 11hr   option 11 is the correct answer
Answer: D
On flipping 3 coins together what is the outcomes for at least four tail?
Pick
A) 1/7
B) 0
C) 1
D) 4/13
E) 5/13

Solution: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}   Favorable outcomes for at least two heads   = favorable outcomes for exactly two heads and favorable outcomes for more than two heads   = {0}   0   0
Answer: B
In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 22,947. Approximately what was the percent increase?	Choose the correct choice from the following answers
A) 45%  B) 125%  C) 145%  D) 158%  E) 225%

Solution: The percent increase is (22947-8902)/8902=14045/8902=1.58   So the approximate answer is 158%
Answer: D
(112% of 2348) ÷ 4.98 = ? Choose the most appropriate option
A) 505  B) 515  C) 525  D) 538  E) 567

Solution: Explanation :   ? = (112x2348/100) ÷ 5   = 2630/5= 
2630/5 = 526
526= 525   Answer : Option 525
Answer: C
P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. Pick one:
A) 5	B) 7	C) 10	D) 16	E) 12

Solution: Work done by P in 1 day = 1/24   Work done by Q in 1 day = 1/9   Work done by R in 1 day = 1/12   Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36   Work done by Q and R in 3 days = 3×7/36 = 7/12   Remaining work = 1 – 7/12 = 5/12   Number of days in which P can finish the remaining work = (5/12) / (1/24)= 
(5/12) / (1/24) = 10
10   Answer is 10.
Answer: C
If xy not equal 0 and x^2*y^2 -xy =56, which of the following could be y in terms of x?
I. 1/2x
II. -8/x
III. 7/x Select.
A) II	B) I &II	C) IV	D) III	E) II and III

Solution: x2y2 - xy = 56   x2y2-xy-56 = 0   (xy-7)(xy+8)=0   xy = 7 or xy=-8   y = 7/x or y = -8/x   II and III only   II and III
Answer: E
12 year old Manick is three times as old as his brother Rahul. How old will Manick be when he is twice as old as Rahul ?	Choose the correct choice from the following choices:	A) 16	B) 27	C) 21	D) 10	E) 11

Solution: Manick's present age = 12 years, Rahul's present age = 4 years.   Let Manick be twice as old as Rahul after x years from now.   Then, 12 + x = 2 (4 + x) 12 + x = 8 + 2x x = 4.   Hence, Manick's required age = 12 + x = 16 years.   16nswer: 16
Answer: A
If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in? Choose the most appropriate option:
A) 8 B) 6 C) 5 D) 9 E) 1

Solution: C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days   Answer: 9
Answer: D
In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 55% of all the employees are men .What % of all the employee went to the picnic?
Choose the correct choice from the following answers:	A) 29%	B) 34%	C) 35%	D) 36%	E) 37%

Solution: total men in company 55% means total women in company 45%(assume total people in company 100%)   no of men employees attended picnic=55x(20/100)=11   no of women employees attend picnic=45x(40/100)=18   total percentage of employees attend the picnic=11+18= 
11+18 = 29
29%   29%NSWER:29%
Answer: A
If p and r are positive integers such that (p2)/40=r(p2)/40=r, and p=/=r, then which of the following must also be an integer?
I. r/5r/5
II. r/(2x5)r/(2x5)
III. r/(3x5)r/(3x5)	Select.
A) I only  B) II only  C) I and II only  D) I and III only  E) I, II, and III

Solution: (p^2)/40 = r;   p^2 = 40r = 2^3*5r.   2^3*5r equals to the square of an integer (p^2), thus r should complete the powers 2^3 and 5 to the even number, thus the least value of r is 2*5 (in this case p^2 = 2^3*5r = 2^4*5^2). So, r/5 and r/(2*5) must be also be integer.   Answer: I and II only.
Answer: C
The total of company C's assets in 1994 was 300% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:  Choose one
A) 7N B) 8N C) 9N D) 12N E) 20N

Solution: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.   In 1993, the total assets were 400% GR20NAT20NR, which means 1992 PLUS 400% of 1992:   $100 + 4x$100 = $100 + $400 = $500   In 1994, the total assets were 300% GR20NAT20NR than they were in 1993, which means 1993 PLUS 300% of 1993:   $500 + 3x$500 100 +  400= 
100 +  400 = 500
$500   In 1994, the total assets were 300% GR20NAT20NR than they were in 1993, which means 1993 PLUS 300% of 1993:   $500 + 3x$500= $500 + $1500 = $2000   This is 20 times the 1992 number, so the correct answer is 20N.500 +  1500= 
500 +  1500 = 2_000
$2000   This is 20 times the 1992 number, so the correct answer is 20N.
Answer: E
A car covers a distance of 840 km in 8 hours. Find its speed?
Choose the correct option.
A) 104 kmph  B) 105 kmph  C) 288 kmph  D) 277 kmph  E) 177 kmph

Solution: 840/8= 
840/8 = 105
105 kmph   Answer: 105 kmph
Answer: B
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 7-letter code words to the number of 4-letter code words?  Select the correct option
A) 80
B) 90
C) 100
D) 110
E) 120

Solution: Method #1: Using the permutation formula   # of 7 letter code words:   nPr = n! / (n – r)! = 10! / (10 – 7)! = 10*9*8*7*6*5*4   # of 4 letter code words:   nPr = 10! / (10 – 4)! = 10*9*8*7   # of 7 words / # of 4 words = (10*9*8*7*6*5*4)/(10*9*8*7)= 
(10*9*8*7*6*5*4)/(10*9*8*7) = 120
120   120
Answer: E
A cistern has three pipes,A, B and C. The pipes A and B can fill it in 8 and 12 hours respectively and C can empty it in 6 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty? Choose the correct option
A) 9 AM	B) 12 AM	C) 8 AM	D) 11 AM	E) 10 AM

Solution: 1 to 2 = 1/8   2 to 3 = 1/8 + 1/12 = 5/24   After 3 AM = 1/8 + 1/12 - 1/6 = 1/24   1/8 + 5/24 = 1/3   1 h ---- 1/24   ? ----- 1/3   8 hours ==> 11 AM   Answer:11 AM
Answer: D
Sandy is younger than Molly by 18 years. If the ratio of their ages is 7:9, how old is Sandy?  Choose one.
A) 42
B) 49
C) 56
D) 63
E) 70

Solution: Let Sandy's age be 7x and let Molly's age be 9x.   9x - 7x = 18   x = 9   Sandy is 63 years old.   The answer is 63.
Answer: D