mathewhe/aqua_rat huggingface dataset:
Question: If the area of a circle is 81pi square feet, find its circumference.
(A) 18 pi feet
(B) 28 pi feet
(C) 38 pi feet
(D) 48 pi feet
(E) 58 pi feet
Rationale: The area is given by pi *r* r. Hence
pi * r *r = 81 pi
r * r = 81 ; hence r = 81 feet
The circumference is given by
2 * pi * r = 2 * pi * 9 = 18 pi feet
correct answer A
Answer: (A) 18 pi feet
Question: One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 16 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 2,000
(B) 5,000
(C) 10,000
(D) 40,000
(E) 52,000
Rationale: out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 2 bulbs, have broken glass
i.e 2 broken glass out of 5000 bulbs
16 broken glass will be from 40000 bulbs
Answer is D
Answer: (D) 40,000
Question: Kanul spent $80000 in buying raw materials, $30000 in buying machinery and 20% of the total amount he had as cash with him. What was the total amount?
(A) $135656
(B) $137500
(C) $134446
(D) $123265
(E) $124564
Rationale: Let the total amount be x
then, (100-20)% of x = 80000+30000
80% of x = 110000
80x/100 = 110000
x = $1100000/8
x = $137500
Answer is B
Answer: (B) $137500
Question: A TaTa company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 14 hrs and a machine of type S does the same job in 7 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R =1/14
Rate of machine S =1/7
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/14 +x/7 =1/2
3x/14=1/2
x=14/6=2.3=3
So no of machine R is 3
Answer A
Answer: (A) 3
Question: In one hour, a boat goes 6 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 3 km/hr
(B) 4 km/hr
(C) 5 km/hr
(D) 6 km/hr
(E) 8 km/hr
Rationale: Upstream relative speed is u + v=6km/hr
Downstream speed is u-v = 2
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =6+2
2u=8
Finally, u=4.
ANSWER : B
Answer: (B) 4 km/hr
Question: Albert borrowed a total of $ 6000 from john and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years?
(A) 571
(B) 581
(C) 441
(D) 445
(E) 631
Rationale: Let x be the amount borrowed form john. So amount borrowed form Charlie = 6000-x.
1494 = 21/100x + 27/100(6000-x)
=>x = 2100.
Interest paid = 3*7/100*2100 = 441.
C
Answer: (C) 441
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 5 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 4 min. to empty
(B) 6 min. to full
(C) 9 min. to empty
(D) 9 min. to full
(E) 8 min. to full
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/5 - 1/10) = 1/10
1/10 : 2/5 :: 1 : x
x = (2/5 * 1 * 10) = 4 min.
So, the tank will be emptied in 4 min.
ANSWER:A
Answer: (A) 4 min. to empty
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
(A) 256/175
(B) 451/784
(C) 125/487
(D) 148/546
(E) 175/256
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans: E
Answer: (E) 175/256
Question: A can do a piece of work in 5 days and B can do it in 7 days how long will they both work together to complete the work?
(A) 6/11
(B) 8/11
(C) 7/12
(D) 9/12
(E) 10/11
Rationale: Explanation:
A’s one day work = 1/5
B’s one day work = 1/7
(A+B)’s one day work = 1/5 + 1/7 = 12/35 => time = 35/12 = 2 9/12 days
Answer: Option D
Answer: (D) 9/12
Question: Fourteen people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
(A) 1/15
(B) 1/14
(C) 1/13
(D) 13/14
(E) 14/13
Rationale: Let P = total cost of the rental van.
The original share per person is P/14.
The new share per person is P/13.
P/13 = P/14 * 14/13 = (1 + 1/13)*original share
The answer is C.
Answer: (C) 1/13
Question: If (q-5)(y+2) = 0 which of the following must be true?
(A)  q = y
(B)  q > y
(C)  q < y
(D)  qy = -10
(E)  None of the above
Rationale: From (q-5)(y+2) = 0 it follows that either q=5 or y=-2.
(A) q = y --> not necessarily true. Consider q=5 and y=0.
(B) q > y --> not necessarily true. Consider q=5 and y=10.
(C) q < y --> not necessarily true. Consider q=5 and y=0.
(D) qy = -10 --> not necessarily true. Consider q=5 and y=0.
Thus, none of the statements must be true.
Answer: E.
Answer: (E)  None of the above
Question: A $72.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?
(A) 18%
(B) 20%
(C) 25%
(D) 60%
(E) 80%
Rationale: Listed selling price of chair = 72.95 $
Discounted selling price of chair = 59.95 $
Discount = 72.95 - 59.95 = 13 $
% decrease in price of chair = (13/72.95) * 100% = 18 % approx
Answer A
Answer: (A) 18%
Question: 6% of a towns eligible voters did not vote in a recent election. If 30 of the towns eligible voters did not vote, how many did vote?
(A) 470
(B) 500
(C) 440
(D) 400
(E) 530
Rationale: 30 is 6% of the total number of voters.
If the total number of voters in the town is X, then 6/100 = 30/X
Therefore 100/6 * 30 = X
3000/6 = X
There are 500 total voters in the town.
500 - 30 = 470
A)
Answer: (A) 470
Question: Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 3 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
(A) 1/3
(B) 2/5
(C) 3/10
(D) 7/15
(E) 9/25
Rationale: Tom paints 1/6 of the room in the first hour.
Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.
The three people then paint the remaining 2/6 in a time of (2/6) / (5/6) = 2/5 hours
Peter worked for 7/5 hours so he painted 7/5 * 1/3 = 7/15 of the room.
The answer is D.
Answer: (D) 7/15
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
(A) 14029
(B) 14027
(C) 11867
(D) 14000
(E) 14020
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Answer: (D) 14000
Question: The difference of two numbers is 1515. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) A)270
(B) B)280
(C) C)290
(D) D)300
(E) E)310
Rationale: Let the smaller number be x. Then larger number = (x + 1515).
x + 1515 = 6x + 15
5x = 1500
x = 300
Smaller number = 300.
D)
Answer: (D) D)300
Question: Two brother X and Y appeared for an exam. The probability of selection of X is 1/3 and that of B is 2/7. Find the probability that both of them are selected.
(A) 2/69
(B) 2/21
(C) 2/23
(D) 2/29
(E) 2/10
Rationale: Explanation:
Let A be the event that X is selected and B is the event that Y is selected.
P(A) = 1/3, P(B) = 2/7.
Let C be the event that both are selected.
P(C) = P(A) Ã— P(B) as A and B are independent events:
= (1/3) Ã— (2/7) = 2/21
Answer: B) 2/21
Answer: (B) 2/21
Question: The product of three consecutive numbers is 720. Then the sum of the smallest two numbers is ?
(A) 11
(B) 15
(C) 17
(D) 38
(E) 56
Rationale: Product of three numbers = 720
720 = 8*9*10
So, the three numbers are 8, 9 and 10.
And Sum of smallest of these two = 8 + 9 = 17.
ANSWER : OPTION C
Answer: (C) 17
Question: find the number of 5 digits numbers can be formed using the digits 1,2,3,4,5 if no digit is reapeted and two adjoint digits are not together
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 13524
14253
24153
24135
25314
31425
31524
+ 6 more numbers replicas of above numbers (total 12)
ANSWER:B
Answer: (B) 12
Question: Twelve men and six women together can complete a piece of work in four days. The work done by a women in one day is half the work done by a man in one day. If 12 men and six women started working and after two days, six men left and six women joined, then in hoe many more days will the work be completed?
(A) 2 (1/8) days
(B) 2 (1/6) days
(C) 3 (1/2) days
(D) 2 (1/2) days
(E) 2 (5/2) days
Rationale: Work done by a women in one day = 1/2 (work done by a man/day)
One women's capacity = 1/2(one man's capacity)
One man = 2 women.
12 men = 24 women.
12 men + 6 women = 30 women
30 women can complete the work in four days. In the first 2 days they can complete 1/2 of the work. Remaining part of the work = 1/2. If 6 men leave and 6 new women join, then new work force = 30 women - 12 women + 6 women = 24 women.
Time taken by them to complete the remaining work = 1/2 (Time taken by 24 women to complete the work) = 1/2 * (30 * 4)/24 = 2 (1/2) days.
Answer: D
Answer: (D) 2 (1/2) days
Question: At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 232 students study Scramjet rocket engines and 114 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
(A) 438
(B) 436
(C) 430
(D) 442
(E) 444
Rationale: 312 + 232 - 114 (since 112 is counted twice )= 430
C is the answer
Answer: (C) 430
Question: If 2 : 9 :: x : 18, then find the value of x
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Explanation:
Treat 2:9 as 2/9 and x:18 as x/18, treat :: as =
So we get 2/9 = x/18
=> 9x = 36
=> x = 4
Option C
Answer: (C) 4
Question: How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?
(A) 56
(B) 72
(C) 48
(D) 60
(E) 59
Rationale: The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged amongst themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48 ways.
Total number of words formed by using all the letters of the given words
= 5! = (5x4x3x2x1) = 120.
Number of words, each having vowels never together = (120-48) = 72.
Ans: B
Answer: (B) 72
Question: A can finish a work in 18 days and B can do the same work in 15 days. B
worked for 10 days and left the job. In how many days A alone can finish the
remaining work?
(A) 6days
(B) 5days
(C) 4days
(D) 3days
(E) 2days
Rationale: B's 10 day's work=10/15=2/3
Remaining work=(1-(2/3))=1/3
Now, 1/18 work is done by A in 1 day.
Therefore 1/3 work is done by A in 18*(1/3)=6 days.
ANSWER A 6days
Answer: (A) 6days
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability q that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: In order to determine the probability that the World Series will last less than 7 games, we can first determine the probability q that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.
Answer: (D)  68.75%
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
(A) 15 m,80 m
(B) 15 m,18 m
(C) 15 m,60 m
(D) 15 m,10 m
(E) 15 m,40 m
Rationale: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer:D
Answer: (D) 15 m,10 m
Question: A man whose bowling average is 22.2, takes 4 wickets for 36 runs and thereby decreases his average by 1.2. The number of wickets, taken by him before his last match is :
(A) 14
(B) 22
(C) 38
(D) 40
(E) 50
Rationale: Explanation :
Let the number of wickets taken before the last match is x.
Then, (22.2x + 36)/(x + 4) = 21
=> 22.2x+36 = 21x+84
=> 1.2x = 48
=> x = 48 / 1.2
= 40
Answer : D
Answer: (D) 40
Question: John read the quarter of the time that Tom read. Tom read only two-fifth of the time that Sasha read. Sasha read twice as long as Mike. If Mike read 5 hours, how long did John read?
(A) 4 h
(B) 3 h
(C) 2 h
(D) 6 h
(E) 1 h
Rationale: Mike read 5 hours. Sasha read twice as long as Mike. Hence Sasha read:
2 * 5 = 10 hours
Tom read two-fifths of the time that Sasha read. Hence Tom read:
(2 / 5) * 10 = 4 hours
John read the quarter of the time that Tom read. Hence John read:
(1 / 4) * 4 = 1 hour
correct answer E
Answer: (E) 1 h
Question: Find the average of first 25 natural numbers?
(A) 12
(B) 16
(C) 13
(D) 18
(E) 19
Rationale: Sum of first 100 natural numbers = 25*26/2 = 325Required average = 325/25 = 13Answer is C
Answer: (C) 13
Question: Seventy five percent of a number is 21 less than four fifth of that number. What is the number ?
(A) 240
(B) 340
(C) 420
(D) 130
(E) 125
Rationale: Let the number be x.
Then, 4*x/5 â€“(75% of x) = 21
4x/5 â€“ 75x/100 = 21
x = 420.
Answer C.
Answer: (C) 420
Question: A retailer sells 5 shirts. He sells first 2 shirts for $30 and $20. If the retailer wishes to sell the 5 shirts for an overall average price of over $30, what must be the minimum average price of the remaining 3 shirts?
(A) $28.50
(B) $30.50
(C) $33.33
(D) $40.50
(E) $50.00
Rationale: First 2 shirts are sold for $30 and $20=$50.
To get average price of $30,total sale should be 5*$30=$150
So remaining 3 shirts to be sold for $150-$50=$100
Answer should be 100/3=$33.33 that is C
Answer: (C) $33.33
Question: Two good train each 750 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
(A) 12 sec
(B) 24 sec
(C) 48 sec
(D) 72 sec
(E) None
Rationale: Sol.
Relative Speed = (45 + 30) km / hr
= (75 x 5 / 18) m/sec
= (125/6) m/sec.
Distance covered = (750 + 750) m = 1500m.
Required time = (1500 x 6 / 125) sec = 72 sec.
Answer D
Answer: (D) 72 sec
Question: One litre of water is evaporated from 6 litre of a solution containing 5% salt. The percentage of salt ?
(A) 4 4/19%
(B) 5 5/7%
(C) 5%
(D) 6%
(E) None
Rationale: Answer
Salt in 6 liter = 5% of 6 = 0.30 liter
Salt in new solution = (0.30/5) x 100% = 6%
Correct Option: D
Answer: (D) 6%
Question: A leak in the bottom of a tank can empty the full tank in 4 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?
(A) 7580
(B) 7960
(C) 8290
(D) 2160
(E) None
Rationale: Solution
Work done by the inlet in 1 hour	= (1/4 - 1/12)
= 1/6.
Work done by the inlet in 1 min.	= (1/6 × 1/60)
= 0.002778
Volume of 0.002778 part = 6 litres.
Therefore, Volume of whole	= (.002778×6)
‹=› 2160 litres.
Answer D
Answer: (D) 2160
Question: One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
(A) 5L/7 miles
(B) 4L/7 miles
(C) 3L/7 miles
(D) 2L/7 miles
(E) 6L/7 miles
Rationale: This is an infinite round problem means the bird will complete infinite rounds in this manner now for finding the total distance traveled by the bird let us consider the total distance between the two given stations as L. Here since the distance between these two stations is not given so answer will be in terms of L.
speed of the two trains moving in opposite directions are 15 mph and 20 mph.
so time taken for the collision between the trains will be L/(15+20) = L/35
In this much time the bird will move 25*L/35 miles = 5L/7 miles
ANSWER:A
Answer: (A) 5L/7 miles
Question: If x and y are positive numbers and z = xy^2, a 60 percent increase in x and a 30 percent decrease in y would result in which of the following changes in z?
(A) decrease of 12.5%
(B) decrease of 21.6%
(C) increase of 4.8%
(D) increase of 12.5%
(E) increase of 24.3%
Rationale: After the changes, z = 1.6x*(0.7y)^2 = (1.6*0.49)xy^2 = 0.784*z
The answer is B.
Answer: (B) decrease of 21.6%
Question: The probability that a computer company will get a computer hardware contract is 2/3 and the probability that it will not get a software contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts ?
(A) 14/45
(B) 4/9
(C) 4/5
(D) 4/6
(E) None of these
Rationale: Explanation :
Let, A ≡ event of getting hardware contract
B ≡ event of getting software contract
AB ≡ event of getting both hardware and software contract.
P(A) = 2/3, P(~B) =5/9
=> P(B) = 1- (5/9) = 4/9.
A and B are not mutually exclusive events but independent events. So,
P(at least one of A and B ) = P(A) + P(B) - P(AB).
=> 4/5 = (2/3) + (4/9) -P(AB).
=> P(AB) = 14/45.
Hence, the required probability is 14/45.
Answer : A
Answer: (A) 14/45
Question: The ratio between the present ages of A and B is 7:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
(A) 3:4
(B) 3:0
(C) 9:1
(D) 9:2
(E) 3:9
Rationale: Let the present ages of A and B be 7x and 3x years respectively.
Then, (7x - 4)/(3x + 4) = 1/1
4x = 8 => x = 2
Required ratio = (5x + 4):(3x - 4) = 18:2 = 9:1.Answer: C
Answer: (C) 9:1
Question: If 47.5% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
(A) 110
(B) 330
(C) 550
(D) 462
(E) 880
Rationale: Students enrolled in biology are 47.5% and therefore not enrolled are 52.5%. so of 880 is 880*.525 = 462
Answer is D 462
Answer: (D) 462
Question: From the integer n, if n*n*n is odd, then what is true from below options?
(A) n*n is odd
(B) n is even
(C) n is odd
(D) n*n is even
(E) n is odd and n*n is even
Rationale: n is odd and n*n is even
Option E
Answer: (E) n is odd and n*n is even
Question: Anil started a business with Rs.5000 and Rajesh joined afterwards with Rs.10,000. If profit at the end of the year is divided equally, then when did Rajesh join him?
(A) 6 months afterwards
(B) 8 months afterwards
(C) 9 months afterwards
(D) 5 months afterwards
(E) None
Rationale: 5000*12=10000*(12-x)
x=6
ANSWER:A
Answer: (A) 6 months afterwards
Question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many T hours will it take if Jim types the report and Mary edits it immediately after he is done?
(A) 41.4
(B) 34.1
(C) 13.4
(D) 12.4
(E) 10.8
Rationale: Break down the problem into two pieces: typing and editing.
Mary needs 30 hours to type the report--> Mary's typing rate = 1/30 (rate reciprocal of time)(point 1 in theory below);
Mary and Jim can type up a report in 12.5and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone)(point 23 in theory below)--> x=150/7;
Jim needs 12 hours to edit the report--> Jim's editing rate = 1/12;
Mary and Jim can edit a report in 7.5and --> 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) --> y=20;
How many T hours will it take if Jim types the report and Mary edits it immediately after he is done--> x+y=150/7+20=~41.4
Answer: A.
Answer: (A) 41.4
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
(A) 5
(B) 8
(C) 10
(D) 14
(E) 16
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: At Ram's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
(A) 700
(B) 1000
(C) 1300
(D) 1600
(E) 2000
Rationale: At Ram's firm's annual revenue grows twice as fast as its costs.First solve for how much revenue is increasing each year:
R2008= R2007*(1+x)
R2009= R2007*(1+x)^2=1.44*R2007
(1+x)^2 = 1.44
1+x=1.2
x=0.2 aka revenue increases 20% each year and cost increases 10% annually
Next solve for R2007and C2007:
R2007= C2007- 1000
1.2*R2007- 1.1*C2007= 0
1.2*[C2007- 1000] - 1.1*C2007= 0
0.1*C2007= 1,200
C2007= 12,000
R2007= 11,000
Finally find 2009 profits:
Profit2009= 1.44*11,000 - 1.21*12,000
Profit2009= 15,840 - 14,520
Profit2009= 1320
Answer: C
Answer: (C) 1300
Question: A boat moves upstream at the rate of 1 km in 30 minutes and down stream 1 km in 12 minutes. Then the speed of the current is :
(A) 1.5 kmph
(B) 2 kmph
(C) 3 kmph
(D) 2.5 kmph
(E) 3.5 kmph
Rationale: Rate upstream = (1/30 *60) = 2 kmph
Rate down stream = 1/12 * 60 = 5 kmph
Rate of the current = ½ (5-2) = 1.5 kmph
ANSWER:A
Answer: (A) 1.5 kmph
Question: It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 3.5 cms, How much did it rain on Wednesday?
(A) 10.9
(B) 10.5
(C) 12.25
(D) 10.1
(E) 10.6
Rationale: Explanation:
Let the rainfall on wednesday = 6x.
âˆ´ Rainfall on the remaining days = 6x
Given,
(6x + 6x )/7 = 3.5
â‡’12x = 24.5
â‡’6x = 12.25
Answer: C
Answer: (C) 12.25