MU-NLPC/Calc-aqua_rat huggingface dataset:
If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III. If x is positive, y must be positive Choose the correct choice from the following choices:
A) I only B) II only C) III only D) I and II E) II and III

Solution: If x-y=8, which of the following must be true?   I. Both x and y are positive   II. If x is positive, y must be positive   III. If x is negative, y must be negative   1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D   2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate II only and E   A) I only   II only) II only   C) III only   D) I and II   E) II and III   Answer II only
Answer: B
Six years back, a father was 42 years older than his son. At present the father is 4 times as old as the son. How old will the son be three years from now?	Choose the correct choice from the following:
A) 20 years
B) 19 years
C) 18 years
D) 17 years
E) 16 years

Solution: Using linear equations to convert the word problem:   ** F = fathers current ageS = sons current age   #1 Six years back, a father was 42 years older than his son: F-6 = 42 + (S - 6)   #2 At present the father is 4 times as old as the son: F = 4*S   How old will the son be three years from now?: S + 3 = ?   With two variables and two linear equations we are able to solve the problem:   (S*4) - 6 = 42 +S -6   3S=42   S = 14   S + 3 = 14 + 3= 
14 + 3 = 17
17   Answer: 17 years
Answer: D
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1904? Choose the correct choice from the following options
A) 1700  B) 2777  C) 2889  D) 27670  E) 2771

Solution: 1904 = P [1 + (5*12/5)/100]   P= 1700.1700nswer:1700
Answer: A
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 340 m long? Choose the correct choice from the following choices.
A) 56 sec B) 42 sec C) 45 sec D) 48 sec E) 50 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 340= 
360 + 340 = 700
700 m   Required time= 700 * 2/25= 
700 * 2/25 = 56
56 sec   56 secNSWER:56 sec
Answer: A
Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he  Select the correct option:
A) broke even
B) lost 4 cents
C) gained 4 cents
D) lost 10 cents
E) gained 10 cents

Solution: 20 % profit on $ 1.20   = $ 20/100 × 1.20   = $ 0.20 × 1.20   = $ 0.24   Similarly, 20 % loss on $ 1.20   = $ 20/100 × 1.20   = $ 0.20 × 1.20   = $ 0.24   Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.   Since both profit and loss amount is same so, it’s broke even.   The answer is (broke even)
Answer: A
If 5 (A's capital) = 7 (B's capital) = 9 (C's capital). Then the ratio of their capitals is? Choose the correct choice
A) 63:55:35
B) 63:45:38
C) 62:45:35
D) 63:45:35
E) 63:44:35

Solution: 5A = 7B = 9C   A:B:C = 1/5:1/7:1/9   = 63:45:35   Answer: 63:45:35
Answer: D
At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? Choices:
A) 5
B) 10
C) 720
D) 32
E) 120

Solution: Has to be C.   Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle   hence (7-1)= 
(7-1) = 6
6!= 720
Answer: C
Find: S.l on Rs 68000 at 16 2/3%per annum for 9 months	Choose the correct choice from the following answers: A) 6500 B) 7500 C) 8500 D) 9500 E) 9000

Solution: Explanation:   P = 68000, R =50/3% & T=9 months (3/4 years)   S.I=(68000 *50/3 * 3/4)/100=Rs.8500   ANSWER IS 8500
Answer: C
If four coins are tossed, the probability of getting two heads and two tails is ?  Choose the correct choice from the following choices:  A) 3/8  B) 3/5  C) 3/2  D) 3/1  E) 3/9

Solution: Since four coins are tossed, sample space = 24   Getting two heads and two tails can happen in six ways.   n(E) = six ways   p(E) = 6/24 = 3/8   3/8nswer:3/8
Answer: A
Worker A takes 5 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?	Choose the most appropriate option.
A) 20/9 B) 40/9 C) 50/9 D) 60/9 E) 10/3

Solution: one day work of A = 1/5   one day work of B = 1/10   so one day work of A and B together = 1/5 + 1/10 = 3/10   so total days required = 10/3   ANSW10/3R:10/3
Answer: E
A consignment of 20 picture tubes contains 5 defectives. Two tubes are selected one after the other at random. The probability that both are defective assuming that the first tube is not replaced before drawing
the second, would be:	Pick one:
A) 1/16
B) 1/19
C) 1/4
D) 1/3
E) none of these

Solution: Probability of drawing a defective tube in first draw is 5/20   Probability of drawing a defective tube in second draw (without replacing first tube) is 4/19.   Therefore probability of getting both defective is = (5/20)*(4/19) = 1/19   ANSWER:1/19
Answer: B
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 50 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
Select the correct option:
A) 26%
B) 30%
C) 32%
D) 34%
E) 40%

Solution: 1. 20% of 400=80 pounds of decaffeinated coffee   2. 50% of 100=50 pounds of decaffeinated coffee   3. Wt have 130 pounds of decaffeinated out of 500 pounds, that means 130/500*100= 
130/500*100 = 26
26%. The correct answer is 26%.
Answer: A
A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. The rate per annum is?
Choose the correct option:  A) 5 5/9 %  B) 5 5/6 %  C) 5 8/9 %  D) 5 1/9 %  E) 5 5/5 %

Solution: Let sum = x. Then, amount = 7x/6   S.I. = 7x/6 - x = x/6; Time = 3 years.   Rate = (100 * x) / (x * 6 * 3) = 5 5/9 %.   5 5/9 %nswer: 5 5/9 %
Answer: A
By selling 12 pencils for a rupee a man loses 12%. How many for a rupee should he sell in order to gain 18%?
Choose one
A) 12
B) 9
C) 10
D) 89
E) 81

Solution: 88% --- 12   112% --- ?   88/112 * 12 = 9   12nswer: 12
Answer: A
On a certain island, 5% of the 10000 inhabitants are one-legged and half of the others go barefooted. What is the least number of Shoes needed in the island?  Choose the correct choice from the following answers: A) 9000 B) 10000 C) 9500 D) 9700 E) 9900

Solution: one-legged =5% of 10000=500   remaining=10000-500= 
10000-500 = 9_500
9500   barefooted=9500/2= 
9500/2 = 4_750
4750   remaining people= 9500-4750= 
9500-4750 = 4_750
4750   hence required number of shoes= 4750*2+500*1= 
4750*2+500*1 = 10_000
10000   ANSWER:10000
Answer: B
In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Choose one
A) 5/6	B) 5/9	C) 5/0	D) 5/3	E) 5/8

Solution: Explanation:   Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6   5/6nswer: Option 5/6
Answer: A
A sauce is composed of tomato, chilly, and soybean. To make 10 kg of sauce containing twice as much tomato as chilly, and three times as much chilly as soybean how many grams of chilly is required? (1kg=1000gm) Choose the correct answer:
A) 1200gm	B) 700gm	C) 600gm	D) 150gm	E) 1000gm

Solution: 1kg=1000gm   10kg=10,000   tomato=2 chilly   chilly=3 soybean   tomato+chilly+soybean=10,000   2 chilly+chilly+1/3 chilly=10,000   10 chilly=10,000   chilly=1000gm   Answer is 1000gm
Answer: E
If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.7
II. 9.2
III. 9.7  Pick one:
A) I only B) I and II only C) II only D) III only E) I and III only

Solution: Mean = 12   SD = 1.3   2 SD above mean = 12+2*1.3= 
12+2*1.3 = 14.6
14.6   2 SD below mean= 12-2*1.3= 
12-2*1.3 = 9.4
9.4   only 9.7 lies in the range of 2SD from mean   Answer: Option I and II only
Answer: B
Find the product of the localvalue and absolutevalue of 1 in 20168?	Options.
A) 100	B) 110	C) 151	D) 120	E) 140

Solution: Local value of 1 = 1 x 100 = 100   Place value of 1 = 1   There fore = 1 x 100 = 100   100
Answer: A
A motor cyclist participant of a race says "We drove with the speed of 15 miles an hour one way, but while returning because of less traffic we drove on the same route with 21 miles per hour." What was their average speed in the whole journey? Options:
A) 10 miles/hour B) 12 miles/hour C) 11 miles/hour D) 13 miles/hour E) 17.5 miles/hour

Solution: 2xy/x+y=17.5 miles/hour   ANSW17.5 miles/hourR:17.5 miles/hour
Answer: E
On multiplying a number B by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result. Select
A) 104345  B) 107375  C) 108385  D) 109395  E) 105355

Solution: The only thing you actually know about the correct number B is that it is divisible by 153 and has 5 as a factor.   You should immediately try to find the factors of 153 and look for them in the options.   153 = 9*17   Divisibility by 9 is easy to check. Only (109395) satisfies.
Answer: D
P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 336 is divided among them . What is R's share?	Choose the correct choice from the following.
A) 96
B) 120
C) 134
D) 144
E) None of these

Solution: Explanation :   The ratio of their initial investment = 1/2 : 1/3 : 1/4   = 6 : 4: 3   Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively   A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12   = (12+30) : 4*12 : 3*12   =(4+10) : 4*4 : 12   = 14 : 16 : 12   = 7 : 8 : 6   R's share = 336 * (6/21)= 
336 * (6/21) = 96
96. 96nswer : Option 96
Answer: A
The income derived from a Rs. 100, 13% stock at Rs. 105,is :	Options:
A) Rs. 5
B) Rs. 8
C) Rs. 13
D) Rs. 18
E) Rs. 19

Solution: Solution   Income on Rs. 100 stock = Rs. 13   Answer Rs. 13
Answer: C
If there are 6 men and 55 tasks , how many tasks will be left undone if they perform equal number of tasks?  Select:
A) 5	B) 2	C) 3	D) 1	E) 4

Solution: There are 6 men   There are 55 tasks   If they perform equal number of tasks, divide 55 by 6 and the remainder will be the number of tasks left undone   55 = (6 x 9) + 1   So 1 task is left undone   ANSWER 1
Answer: D
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 900 m long? Pick one.
A) 266 Sec
B) 210 Sec
C) 776 Sec
D) 166 Sec
E) 997 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 2100 m   T = D/S   T = 2100/10= 
2100/10 = 210
210 Sec   Answer: 210 Sec
Answer: B
The expression (a+b+c)10 is expanded and simplified. How many terms are in the resulting
expression?	Choose the most appropriate option:  A) 30  B) 44  C) 55  D) 66  E) 133

Solution: (a+b+c)10 = [(a+b)+c]10. Let x = a+b. We see that (x+c)10 = x10+10x9c+   + c10 has 11 distinct terms. Also, the ith term of this expansion has 11 - i distinct terms   (since x10-i = (a + b)10-i has 11 - i distinct terms). Hence there are 11 + 10 +...+ 1 = 66   terms in this expansion.   correct answer 66
Answer: D
How many integer values Q are there for x such that 1 < 3x + 5 < 17?	Choices.
A) Two	B) Three	C) Four	D) Five	E) Six

Solution: 1 < 3x + 5 < 17   => -4 < 3x < 12   => -4/3 < x < 4   x can take integer values Q=-1,0 , 1 , 2 , 3   Answer Five
Answer: D
In a 500 m race, the ratio of speeds of two runners P and Q is 3:5. P has a start of 200 m then the distance between P and Q at the finish of the race is:	Answers:
A) Both reach at the same time	B) P wins by 100 m	C) Q wins by 50 m	D) Q wins by 100 m	E) None of these

Solution: Explanation :   When P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5.   According to question P has already covered 200 m when Q is starting at starting point and Q needs to cove 300 m more mean while P covers this 300 m when Q can cover 500 m. So, both P and Q will reach the finishing point at the same time.   Thus, Both reach at the same time.   Both reach at the same timenswer : Both reach at the same time
Answer: A
Andy solves problems 75 to 125 inclusive in a Math exercise. How many problems does he solve?	Choose the correct choice:	A) 53	B) 52	C) 51	D) 50	E) 49

Solution: 125-75+1= 
125-75+1 = 51
51   '51' is the answer
Answer: C
0,1,2.9,5.61,9.05,?  Options
A) 11.15 B) 12.15 C) 13.15 D) 14.15 E) 15.15

Solution: The series is 0, 1, 2.9, 5.61, 9.05, ...   Fisrt oder differences are 1, 1.9, 2.71, 3.44, ...   Second order differences are 0.9, 0.81, 0.73, ...   Note that the second order differences are powers of 0.9 (0.9, 0.81, 0.729, ...), rounded off to two decimal digits. So next term in second order difference is 0.9^4 = 0.6561 = 0.66. Then, the next term in first order difference is 3.44+0.66 = 4.1. So, the term in the series is 9.05+4.1= 
9.05+4.1 = 13.15
13.15   ANSWER:13.15
Answer: C
There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is	Choices:  A) 21  B) 52  C) 45  D) 63  E) 23

Solution: List down possibilities: From only 1 box all the way to all 6   If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.   If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.   If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.   If all 6 boxes have green balls, there is just 1 possibility.   Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1= 
6 + 5 + 4 + 3 + 2 + 1 = 21
21.   21ns: 21
Answer: A
How long does a train 110 m long traveling at 90 kmph takes to cross a bridge of 170 m in length?	Select the correct option
A) sec B) sec C) sec D) sec E) sec

Solution: sec = 110 + 170= 
110 + 170 = 280
280 m   S= 90 * 5/18 = 50/2   T = 280 * 2/50= 
280 * 2/50 = 56/5 = around 11.2
11.2 sec   Answer: sec
Answer: D
A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 6 people to travel x miles if he decides to give them a 50% discount? Choose the correct choice from the following choices:
A) 3xr/100 B) 3x/200r C) 3r/200x D) 3xr/200 E) xr/600

Solution: 6xr/2 is in cents - 6xr/200 dollars = 3xr/100 dollars   3xr/100nswer : 3xr/100
Answer: A
Nine persons went to a hotel for taking their meals. Eight of them spent 16 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?
Answers
A) 115	B) 117	C) 119	D) 122	E) 153

Solution: Let the average expenditure of all the nine be x.   Then, 16 × 8 + (x + 8) = 9x or 8x = 136 or x = 17.   ∴ Total money spent = 9x = (9 × 17) = 153.   Answer 153
Answer: E
In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase?	Choices:	A) $32	B) $50	C) $320	D) $400	E) $500

Solution: Property tax as a percentage of its assessed value = 8%   Increase in assessed value of the property = 24000 - 20000 = 4,000 $   Increase in property tax = (8/100)* 4000= 
(8/100)* 4000 = 320
320 $   Answer $320
Answer: C
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Choices
A) 100 B) 110 C) 120 D) 130 E) 140

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.   Answer: Option 120
Answer: C
A fruit vendor purchased 20 dozens of apples at $15 per dozen. But one-fourth of the apples were rotten and had to be thrown away. He sold two-third of the remaining apples at a$22.50 per dozen. At what price per dozen should he sell the remaining apples to make neither a profit nor a loss?  Choose the correct option.
A) $17 B) $14 C) $15 D) $18 E) $20

Solution: C   $15   CP of 20 dozen of apples = 15 * 20= 
15 * 20 = 300
$300   Number of apples which are rotten= 1/4 * 20= 
1/4 * 20 = 5
5 dozen.   SP of two-third of remaining apples= (2/3 * 15) * 22.5= 
(2/3 * 15) * 22.5 = 225
$225   SP of remaining 5 dozens of apples to make no profit and no loss=(300 - 225)= 
(300 - 225) = 75
$75.   SP of 1 dozen apples= 75/5= 
75/5 = 15
$15.
Answer: C
A person crosses a 1080 m long street in 10 minutes. What is his speed in km per hour? Choose the correct option:
A) 4.1 B) 6.4 C) 4.8 D) 5.4 E) 5.5

Solution: Speed = 1080/(10x60) m/sec   = 1.8 m/sec.   Converting m/sec to km/hr =1.8 x(18/5) km/hr   = 6.4 km/hr.   ANSWER :6.4
Answer: B
1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10
what is....?  Choose the correct option.
A) 7	B) 8	C) 9	D) 6	E) 10

Solution: 10quation 28 + 8 + 92 = 10 can be derived from   twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10   Similarly for equation,   1 + 9 + 8   One (o) + nine (n) + eight (e) => one (1)   correct answer is 10)10
Answer: E
If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following? Pick:
A) 2
B) 4
C) 5
D) 8
E) 9

Solution: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.   Hence, n=2mn=2m, where mm is a positive integer. Then,   (n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)   =4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8   Hence, the answer is (8).
Answer: D
The ratio between the length and the breadth of a rectangular park is 1 : 2. If a man cycling along the boundary of the park at the speed of 6 km/hr completes one round in 6 min, then the area of the park (in sq. m) is?	Choose one:	A) 600m	B) 6000 m	C) 20000 m	D) 100 m	E) 2000 m

Solution: Perimeter = Distance covered in 6 min. = (6000 x 6)/60 m = 600 m.   Let length = 1x metres and breadth = 2x metres.   Then, 2(1x + 2x) = 600 or x = 100.   Length = 100 m and Breadth = 200 m.   Area = (100 x 200) m2 = 20000 m   20000 m
Answer: C
A standard-sized cigarette can be rolled out of 6 standard-sized cigarette butts. How many cigarettes can be made and smoked from 36 butts?  Choose the correct choice from the following.
A) 2
B) 3
C) 5
D) 7
E) 1

Solution: D   No, 6 is not the answer! It is not correct, because after the 6 cigarettes have been smoked there will again be 6 butts which can be made into another cigarette.   The answer is 7
Answer: D
The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 100 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire? Choose the correct choice from the following answers:
A) 90  B) 120  C) 160  D) 360  E) 400

Solution: If we exclude those cases and take the question at face value, then it seems straightforward.   Group #1 = (didn't like, didn't understand) = 100   Group #2 = (likeunderstood) = 3/4   (1/4)N = 100   N = 400   Answer =(400)
Answer: E
A certain galaxy is known to comprise approximately 2x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?  Select:
A) 800 B) 1,250 C) 8,000 D) 4,000 E) 80,000

Solution: 2*10^11   50 mln = 5*10^7   we divide 10^11 by 10^7 and we get (10^4)*2 = 20,000 and divide by 5. the result is 4,000 (c)   4,000
Answer: D
3 singers will pick a song among a list of 3 songs. What is the probability that exactly one singer will pick a different song?
Pick one
A) 3!/3^3
B) 1/3^3
C) 3/3!
D) 3/3^3
E) 1/3!

Solution: Each singer out of 3 has 3 options, hence total # of outcomes is 3^3;   Favorable outcomes will be 3!, which is # of ways to assign 3 different song to 3 singers.   P=favorable/total=3!/3^3   3!/3^3nswer: 3!/3^3.
Answer: A
If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word
"ROD" would be  Choices:
A) 156  B) 174  C) 176  D) 180  E) 182

Solution: R-1   O-7   D-6   so for mango the code is 176   ANSWER:176
Answer: C
x and y are positive integers of J. If 1/x + 1/y < 2, which of the following must be true? Choose the correct choice from the following answers
A) x + y > 4	B) xy>1	C) x/y + y/x < 1	D) (x - y)^2 > 0	E) None of the above

Solution: Answer is B:   1/X + 1/Y < 2   The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.   So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.   Another way of putting it is:   X*Y>1.xy>1
Answer: B
Working alone at its constant rate, pump U pumped out ¼ of the water in a tank in 2 hours. Then pumps V and W started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump V, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump W, working alone at its constant rate, to pump out all of the water that was pumped out of the tank? Select:
A) 6
B) 12
C) 15
D) 18
E) 24

Solution: Rate of pump U = 1/8   3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4   Rate of U + Rate of V + Rate of W = 1/4   Rate of V + Rate of W = 1/4 - 1/8 = 1/8   V takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.   Rate of V = 1/24   1/24 + Rate of W = 1/8   Rate of W = 1/8 - 1/24 = 1/12   Time required to pump out all the water by W = 12 hrs   Answer: 12
Answer: B
A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 7 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720? Choose the correct answer:
A) $54.00	B) $78.40	C) $90.00	D) $100.80	E) $154.80

Solution: Correct Answer: B   The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.07 ($1120) 1720 -  600= 
1720 -  600 = 1_120
$1120. Thus, the amount of tax he has to pay is 0.07 ($1120)= $78.40. The correct answer is $78.40.
Answer: B
The average age of an adult class is 40years. 12new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class? Choose the correct choice from the following choices
A) 8
B) 12
C) 15
D) 17
E) 18

Solution: Let original strength = y   Then , 40y + 12 x 32 = ( y + 12) x 36   ⇒ 40y + 384 = 36y + 432   ⇒ 4y = 48   ∴ y = 12   12
Answer: B