MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 12 pieces of radioactive metal Q that look identical. 11 of the pieces give the same radiation count when measured, the 12th piece is a counterfeit and gives a different radiation level, which may be more or less than the other 11. We are given a radiation scale, which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different, which set has the higher level of radiation. What is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?  Select the correct option.
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: First of all if you are down to just 3 pieces and you know that if the offending piece is less or more active, then it takes exactly 1 measurement to find out the offending piece. So you know you have to reduce the problem to three.   Now when you are down to either A or B after measurement 1, you need the next measurement to (a) reduce the problem set to 3 and (b) to know whether anser is more or less. Now you cannot compare a group of 4 to 4, as in the best case it will only reduce the problem to 4 elements which is not good enough.   If you have to choose a set of 3 to compare, you cannot pick any 3 on the same side from the same set (A or B) because if you do this, a quick check will show you that in every choice there is a case where you can only get down to 4 elements. Eg. If you weighed {1,2,3} v/s {5,9,10} and they were equal you're problem would only reduce to {4,6,7,8}   The easiest way to solve this then is to compare 3 to 3, and make sure each side has elements from both AB such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only. Which is why the sets {1,5,9} and {2,6,7} OR {A,B,C}{A,B,B}. The extra element from C is just taken to make the problem symmetric so to say, we have 8 elements and we make it 9, to compose 3 sets of 3 each.=3
Answer: B
John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4290. What is the difference between Rose ’s and Tom ’s share in the profit?  Choose one:
A) s.340 B) s.362 C) s.370 D) s.382 E) s.390

Solution: John : Rose : Tom   Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8   = 6 : 3: 2   The difference between Rose’s and Tom’s share = 1 share   :.i.e. = Rs. 4290 × 1/11 = Rs.390.   s.390)
Answer: E
A leak in the bottom of a tank can empty the full tank in 7 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?
Select the correct option: A) 7580 B) 7960 C) 8290 D) 6048 E) None

Solution: Solution   Work done by the inlet in 1 hour	= (1/7 - 1/12)   = 5/84   Work done by the inlet in 1 min.	= (5/84 × 1/60)   = 0.000992   Volume of 0.000992 part = 6 litres.   Therefore, Volume of whole	= ((1/0.000992)×6)   ‹=› 6048 litres.   Answer 6048
Answer: D
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Choose the correct answer:
A) 118
B) 280
C) 886
D) 667
E) 198

Solution: x*(85/100) = (480 - x)119/100   x = 280   Answer: 280
Answer: B
The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
Pick one.
A) 6
B) 9
C) 6
D) 4
E) 1

Solution: 3x + 5x + 7x = 45   x =3   3x = 9   Answer:9
Answer: B
10, 18, x, 14
The median of the list of positive integers above is 12. Which of the following could be the average (arithmetic mean) of the list? Choose the correct choice:
A) 12
B) 5.5
C) 6.25
D) 7
E) 7.5

Solution: GivenThe median of the list of positive integers above is 12   So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 12   so the sequence will be x 10 14 18   Lets say x = 6, which gives us mean = sum/4 = 12   12 is correct
Answer: A
If 20 liters of chemical X are added to 80 liters of a mixture that is 20% chemical X and 80% chemical Y, then what percentage of the resulting mixture is chemical X? Select the correct option.
A) 30% B) 33% C) 36% D) 39% E) 42%

Solution: The amount of chemical X in the solution is 20 +0.2(80) = 36 liters.   36 liters / 100 liters = 36%   The answer is 36%.
Answer: C
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/2 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?	Select:	A) 6	B) 9	C) 11	D) D.13	E) 15

Solution: rate of bob to paint n rooms is n/T(bob)   rate of Albert to paint n rooms is n/T(albert).   albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1   Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time   Therefore   n/x + n/x-1 = (3n/5)/(4/3) =   n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic   4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.   2*3 = 3n   6 = 3n.   6nswer is 6
Answer: A
If y > 0, (7y)/20 + (3y)/10 is what percent of y?
Choose the correct choice from the following options:	A) 40%	B) 50%	C) 65%	D) 70%	E) 80%

Solution: can be reduced to 7y/20+6y/20 =13y/20=65%   Answer 65%
Answer: C
If 65 percent of a class answered the first question on a certain test correctly, 50 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?  Choose the correct option:
A) 25%
B) 30%
C) 35%
D) 40%
E) 45%

Solution: 65% answered the first question correctly and 20% answered neither correctly.   Then 15% missed the first question but answered the second question correctly.   Then the percent who answered both correctly is 50% - 15% = 35%.   The answer is 35%.50  - 15= 
50  - 15 = 35
35%.   The answer is 35%.
Answer: C
A fill pipe can fill 1/2 of cistern in 30 minutes. In how many minutes, it can fill 1/2 of the cistern?
Options:
A) 15 min
B) 20 min
C) 25 min
D) 30 min
E) 35 min

Solution: Required time = 30*2*1/2= 
30*2*1/2 = 30
30 minutes   Answer is 30 min
Answer: D
Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction? Choose the correct choice from the following options
A) Rs.21.60 B) Rs.21.29 C) Rs.22.29 D) Rs.21.26 E) Rs.21.12

Solution: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000   He lend the same amount for C.I at 6% p.a. for two years.   => Siddharth's income = C.I - S.I   = p[1 + r/ 100]n - p - pnr/100   = p{ [1 + r/ 100]2 - 1 - nr/100   = 6,000{ [1 + 6/100]2 - 1 - 12/100}   = 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)   = 6,000 (0.0036) = 6 * 3.6 = Rs.21.60   Rs.21.60nswer: Rs.21.60
Answer: A
A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Choices
A) 4/9	B) 4/7	C) 4/6	D) 4/1	E) 4/2

Solution: Explanation:   Let number of balls = (6 + 8)= 
(6 + 8) = 14
14.   Number of white balls= 8.   P (drawing a white ball) = 8 /14 = 4/7.   Answer: 4/7) 4/7
Answer: B
A package contains 8 black and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?	Choose the correct choice from the following options:
A) 3/5	B) 3/7	C) 6/8	D) 7/9	E) 1/3

Solution: Let number of balls = (8+6)= 
(8+6) = 14
14.   Number of white balls= 6.   P (drawing a white ball) =	6/14=3/7   3/7
Answer: B
If a number is 20% more than the another, how much % is the smaller number less than the first ? Select
A) 12(1/3)%	B) 16(2/3)%	C) 16(1/3)%	D) 16(4/3)%	E) none of these

Solution: Take a number 100,   Then the other number is 120   % the smaller number is less than the first = [(20/(120)) x 100]% = 16(2/3)%.   ANSWER:16(2/3)%
Answer: B
If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.	Choose the correct choice
A) 12
B) 14
C) 16
D) 18
E) 20

Solution: Explanation :   Wages of 1 woman for 1 day = 21600/40×30   Wages of 1 man for 1 day = 21600×2/40×30   Wages of 1 man for 25 days = 21600×2×25/40×30   Number of men = 14400/(21600×2×25/40×30)=144/(216×50/40×30)=144/9= 
144/9 = 16
16   Answer : Option 16
Answer: C
For all integers a and b, a%b = (a + b)(a - b). If 6%x = 11, then which of the following could be a value of x?
Choose the correct choice from the following:	A) -4	B) -3	C) 2	D) 5	E) 6

Solution: 6%x = (6+x)(6-x)   36-x^2 = 11   x^2 = 25   x=-5,5   Ans: 5
Answer: D
What percentage of numbers from 1 to 70 have squares that end in the digit 1?	Choose the correct choice from the following answers:	A) 1	B) 14	C) 17	D) 20	E) None

Solution: Solution   Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.   Number of such numbers = 14.   Required percentage = [14 / 70 x 100]%   = 20%.   Answer 20
Answer: D
A certain list of 200 test scores has an average (arithmetic mean) of 84 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 202 test scores with a standard deviation less than d ?
Choose the correct choice from the following
A) 84 and 84	B) 80 and 85	C) 80 and 90	D) 85 and 85	E) 85 and 90

Solution: The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.   So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.   According to the aboveadding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.   Closest to the mean are 84 and 84 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD most.   84 and 84nswer: 84 and 84
Answer: A
The average weight of 16 men in a committe is 50.25 kg and that of the remaining 8 men are45.15 kg. Find the average weights of all the men in the committe? Pick one:
A) 42  B) 48.55  C) 49.2  D) 50.1  E) 51.2

Solution: Required average   = 50.25 x 16 + 45.15 x 8   16 + 8   = 804 + 361.20   24   =	1165.20   24   = 48.55   48.55
Answer: B
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:
Choose the correct choice from the following options:  A) 51:52  B) 52:53  C) 51:53  D) 52:55  E) 52:56

Solution: Let C.P. of the article be Rs. x.   Then, required ratio = 104% of x / 106% of x   = 104/106 = 52/53 = 52:53   ANSWER:52:53
Answer: B
Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rohan’s and Sudhir’s share in the profit? Choose the correct choice from the following:	A) Rs.362	B) Rs.383	C) Rs.398	D) Rs.399	E) Rs.400

Solution: Suresh : Rohan : Sudhir   Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8   = 6 : 3: 2   The difference between Rohan’s and Sudhir’s share = 1 share   :.i.e. = Rs. 3982 × 1/11 = Rs.362.   Rs.362)
Answer: A
Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?  Answers:
A) 8% p.a.
B) 6% p.a.
C) 4% p.a.
D) 5% p.a.
E) None of these

Solution: Let the rate of interest be R% p.a.   17400[1 + R/100]2 = 17400 + 1783.50   [1 + R/100]2 = (17400 + 1783.50)/17400   = 1 + 1025/10000 = 1 + 41/400   = 441/400 = [21/20]2   [1 + R/100] = 21/20   R/100 = 1/20   Therefore R = 5   ANSWER:5% p.a.
Answer: D
3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last? Choose the correct answer.
A) 16 B) 17 C) 19 D) 18 E) 24

Solution: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days   So fodder will be available for  (60 + 8 + 12)= 
 (60 + 8 + 12) = 80
80 cows c 24x60 .0 .   for-^—=18 days.   18
Answer: D
A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?  Choose the correct choice from the following.
A) 32:46  B) 32:98  C) 32:45  D) 32:27  E) 32:42

Solution: A : B   (8000*4)+(4000*8) : (9000*6)+(6000*6)   64000 : 90000   32 : 45   Answer:32:45
Answer: C
A shopkeeper sold an article at $100 with 20% profit. Then find its cost price?  Select
A) $120 B) $100 C) $91 D) $83 E) $69

Solution: cost price = selling price *100/(100+profit)   C.P. = 100*100/120 = $83(approximately)   Answer is $83
Answer: D
In a two digit number, the digit in the units place is five times the digit in ten's place and sum of the digits is equal to six. What is the number?
Select the correct option:  A) 15  B) 28  C) 32  D) 36  E) 38

Solution: Solution   Let the ten digits be x. Then,units digit=5x   Therefore x +5x = 6   ‹=›6x = 6   ‹=›x= 1   So, ten's digit = 1, unit's digit = 5.   Hence, the required number is 15.   15nswer 15
Answer: A
Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 9, how many people got on at the first stop?  Pick one:
A) 128 B) 64 C) 32 D) 16 E) 256

Solution: 7 - > 1   6 - > 2   5 - > 4   4 - > 8   3 - > 16   2 - > 32   1 - > 64   because people get off after the first stop   => the formula will be : 2^(n-1) where n is the stop number   in this case n = 9   => 2^(9-1) = 2^8 = 256   => answer is 256
Answer: E
The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?	Choose the correct choice:
A) 65
B) 44
C) 18
D) 15.49
E) 14

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 240/3= 
240/3 = 80
80 sq m   l b= 80 i.e., l * l/3 = 240   l2 = 240 => l =15.49   Answer:15.49
Answer: D
A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed ? Choose the correct choice from the following options:
A) 55
B) 56
C) 57
D) 58
E) None of these

Solution: Solution   Perimeter of the plot = 2(90 + 50) = 280 m.   ∴ Number of poles = [280/5= 
280/5 = 56
56m Answer 56
Answer: B
How many ways can 8 friends be arranged around a circular dinner table?  Answers:  A) A)16  B) B)48  C) C)96  D) D)5040  E) E)720

Solution: The number of arrangements of n distinct objects in a row is given by n!n!.   The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:   n!n=(n−1)!n!n=(n−1)!.   So, the answer is (8 - 1)= 
(8 - 1) = 7
7!= 5040.   Answer: 5040.
Answer: D
The owner of a local jewelry store hired two watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and 2 more besides. He escaped with two diamonds. How many did he steal originally? Select
A) 20
B) 36
C) 25
D) None of these
E) Cannot be determined

Solution: Explanation :   Since, thief escaped with 2 diamonds,   Before 2nd watchman, he had ( 2 + 2 ) x 2 = 8 diamonds.   Before 1st watchman, he had ( 8 + 2 ) x 2 = 20 diamonds.   20nswer : 20
Answer: A
Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48.	Choose the correct choice from the following answers.
A) 240/1587 B) 240/1545 C) 240/1547 D) 240/1542 E) 240/1512

Solution: P : 2/13 = 5/34 : 7/48   As the product of the means is equal to the product of the extremes.   P*7/48 = 2/13 * 5/34   P*7/48 = 10/442   P = 480/3094 => P = 240/1547   Answer: 240/1547
Answer: C
If 6 women can color 180 m long cloth in 3 days, then 5 women can color 200 m long cloth in? Select:
A) 6 days  B) 5 days  C) 4 days  D) 2 days  E) 3 days

Solution: The length of cloth painted by one woman in one day = 180/ 6× 3 = 10 m   No. of days required to paint 200 m cloth by 5 women = 200/ 5 × 10 = 4 days   Answer : 4 days
Answer: C
If a*b denotes the greatest common divisor of a and b, then ((12*15)*(18*24)) = ?  Choose one: A) 24 B) 12 C) 6 D) 4 E) 3

Solution: The greatest common divisor of 12 and 15 is 3. Hence 12*15 = 3 (note that * here denotes the function not multiplication).   The greatest common divisor of 18 and 24 is 6. Hence 18*24 = 6.   Hence ((12*16)*(18*24)) = 3*6.   The greatest common divisor of 3 and 6 is 3.   Answer; 3.
Answer: E
The cost of 4 bags and 12 purses is Rs.620, what is the cost of 10 bags and 30 purses?	Choose the most appropriate option:	A) Rs.3600	B) Rs.3500	C) Rs.3800	D) Rs.3900	E) Rs.1550

Solution: Explanation:   Cost of 4 bags + 12 purses = Rs.620   Multiply each term by 5/2, we get,   Cost of 10 bags + 30 purses = Rs.1550.   Answer: Option Rs.1550
Answer: E
X men can do a work in 120 days. If there were 20 men less, the work would have taken 60 days more. What is the value of X? Choose the correct choice from the following choices:
A) 60	B) 99	C) 77	D) 55	E) 22

Solution: We have M1 D1 = M2 D2   120X = (X - 20)180   => 2X = (X - 20) 3 => 2X = 3X - 60   => X = 60   60nswer:a
Answer: A
P and Q invested in a business. They earned some profit which they divided in the ratio of 2:3. If P invested Rs.50, 000, the amount invested by Q is: Choose the correct choice.
A) Rs. 65,000	B) Rs. 70,000	C) Rs. 75,000	D) Rs. 90,000	E) Rs. 60,000

Solution: Q invested = 50000/2*3= 
50000/2*3 = 75_000
75000   Answer : Rs. 75,000
Answer: C
If x and y are positive integers, and x^3*y^4 = 10125, which of the following is the value of xy? Choose the correct choice from the following choices:
A) 6  B) 10  C) 14  D) 15  E) 21

Solution: 10125 = 3*3375 = 3^2*1125 = 3^3*375 = 3^4*125 = 3^4*5^3   xy = 3*5= 
3*5 = 15
15   The answer is 15.
Answer: D
Three of the following four are alike in a certain way and hence form a group. Which is the one that does not belong to that group? Choose one:  A) Shirt  B) Shoe  C) Ring  D) Cobbler  E) FRR

Solution: Explanation:   Cobbler is human being while all others are used by human beings.   Answer: Cobbler
Answer: D
In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?  Choose the correct choice from the following answers:
A) 927.5 m  B) 127.5 m  C) 167.5 m  D) 128.5 m  E) 127.1 m

Solution: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.   When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8= 
6300/8 = 1_575/2 = around 787.5
787.5 m.   In a race of 1000 m, A beats C by   (1000 - 787.5)= 
  (1000 - 787.5) = 212.5
212.5 m to C.   In a race of 600 m, the number of meters by which A beats C= (600 * 212.5)/1000= 
(600 * 212.5)/1000 = 127.5
127.5 m.   Answer:127.5 m
Answer: B
'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the minimum and maximum possible values of 'a + b'?  Select the correct option: A) 0 B) -24 C) -32 D) -20 E) -12

Solution: possible values of a and b can be 5,4; 4,5 (which are same for a+b) and 1,20; 20,1 (same result for a+b)   so 9-21 = -12. ans -12.
Answer: E
What is the sum of the first 22 natural numbers (starting from 1)?	Choose the correct choice from the following answers:	A) 223	B) 233	C) 243	D) 253	E) 263

Solution: The sum of n natural numbers = n*(n+1) / 2 = 22*23/2= 
22*23/2 = 253
253   The answer is 253.
Answer: D
Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 40 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following? Choose the correct option
A) 36 B) 50 C) 60 D) 75 E) 80

Solution: AnalystsNot AnalystsTotal   MBAx/32x/3x   No MBAy/4   Total2x/350y   We are asked for the value of x.   From the table: 2x/3 = y - 40   y - 40 + (y/4) = 40   5y/4 = 80   y = 64   2x/3 = 64 - 40= 
64 - 40 = 24
24   x= 72/2= 
72/2 = 36
36   36nswer: 36
Answer: A
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 3/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
Choose one.
A) 20  B) 25  C) 15  D) 30  E) 35

Solution: answer of 1st   just add the given probabilities p(blue)+p(red)+p(green) i.e   1/8+1/5+3/10=5+8+12/40 =25/40   now we know p(blue)+p(red)+p(green)+p(yellow)=1   25/40+p(yellow)=1   p(yellow)=15/40   i.e why yellow balls are 15.   15
Answer: C
An article is bought for Rs.600 and sold for Rs.550, find the loss percent?  Choose the correct answer:	A) 8.33%	B) 16 7/3%	C) 16 2/8%	D) 16 2/3%	E) 76 2/3%

Solution: 600 ---- 50   100 ---- ? =>8.33%   8.33%nswer:8.33%
Answer: A
The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base? Choose the correct choice from the following answers:
A) 1.4 metres
B) 2.8 metres
C) 28 metres
D) 14 metres
E) none of these

Solution: Capacity (volume) of a cylindrical tank = πr2h   (Here r = radius and h = height of the tank)   Now, from the question, 246.4 × 0.001 = 22⁄7 × r2 × 4   [∵ 1 litre = 1000 cm3 = 0.001 m3]   or, 0.2464×7/22×4 = r2   or,r = 0.14 m   or,diameter = 2r = 0.28 m   Answer none of these
Answer: E
The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?  Choose the most appropriate option.
A) 2/5	B) 7/9	C) 3/11	D) 8/5	E) 9/1

Solution: Explanation:   The denominator be P, the numerator will be (P - 8).   The fraction will be (P - 8)/P.   Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.   (P - 5)/(P - 3) = 3/4   P = 20 - 9 => P = 11.   The fraction is: 3/11.   ANSWER IS 3/11
Answer: C