mathewhe/aqua_rat huggingface dataset:
Question: A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?
(A) 16.16%
(B) 15.55%
(C) 14.44%
(D) 13.33%
(E) 12.22%
Rationale: (100%+7%)*(100%-19%) = 1.07*.81 = 0.8667
1-0.8667 = 13.33% lost = -13.33%
The Answer is D
The organization has lost 13.33% of its total volunteers from fall to spring.
Answer: (D) 13.33%
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 278
(C) 282
(D) 202
(E) 270
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: A
Answer: (A) 200
Question: The average age of 'a' boys is ‘b’ years and of ‘n’ girls ‘c’ years. The average age of all together is?
(A) (ab – nc)/ (a + n) years
(B) (ab + nc)/ (a - n) years
(C) (ab + nc)/ (a + n) years
(D) (ab – nc)/ (a - n) years
(E) None of these
Rationale: (ab + nc) / (a+ n)
ANSWER:C
Answer: (C) (ab + nc)/ (a + n) years
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 18/32
(C) 18/19
(D) 18/10
(E) 18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer: A
Answer: (A) 18/35
Question: A cycle is bought for Rs.900 and sold for Rs.1350, find the gain percent?
(A) 39%
(B) 20%
(C) 23%
(D) 50%
(E) 83%
Rationale: 900 ---- 450
100 ---- ? =>
50%
Answer:D
Answer: (D) 50%
Question: a person travels from his house to office from 11:00am to 11:30 am and covers a distance of 20km. find the average speed of the person.
(A) 20.1km/h
(B) 20.5km/h
(C) 21.1km/h
(D) 10km/h
(E) 20.9km/h
Rationale: time=11:30-11:00=30min=1/2hour
distance=20km
speed=20*1/2=10km/h
ANSWER:D
Answer: (D) 10km/h
Question: If books bought at prices ranging from Rs. 90 to Rs. 190 are sold at prices ranging from Rs. 120 to Rs 260, what is the greatest possible profit that might be made in selling 21 books ?
(A) Rs. 2500
(B) Rs. 3000
(C) Rs. 3570
(D) Rs. 3200
(E) Rs. 3600
Rationale: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 21 books = 90*21 = Rs. 1,890
Maximum selling price of 21 books = 260 *21 = Rs. 5,460
So, maximum profit = 5460 - 1890 = Rs. 3,570
ANSWER : OPTION C
Answer: (C) Rs. 3570
Question: A’s speed is 20/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 1/17
(B) 3/17
(C) 1/10
(D) 7/20
(E) 3/10
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 20 meters, B covers 13 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 7 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 7 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 13 meters) to reach the finish line.
So B should get a head start of 7/20th of the race.
Answer (D)
Answer: (D) 7/20
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 12km/hr, then find the area of square field.
(A) 81
(B) 225
(C) 325
(D) 425
(E) None of these
Rationale: Explanation :
D = 12*3/2 = 18 km. So side of square is 9km, so area – 81km^2
Answer – A
Answer: (A) 81
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 52
(B) 45
(C) 67
(D) 89
(E) 90
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
ANSWER A
Answer: (A) 52
Question: There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 45 possible combinations in which Michael is not selected, what is the value of n?
(A) 11
(B) 12
(C) 15
(D) 18
(E) 22
Rationale: The combinations of two people, in which Michael was not selected = 45
The number of ways two people can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael.
Then m*(m-1) = 90 = 10*9
Thus, n = m + 1(Michael) = 11
The answer is A.
Answer: (A) 11
Question: If U is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, U, 0, 1, 3, K, 7}?
I. -1.5
II. -2
III. 0
(A)  I only
(B)  II only
(C)  III only
(D)  I and III only
(E)  None
Rationale: If U is a negative integer and K is a positive integer, The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either.E
Answer: (E)  None
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 8.6%
(B) 6.6%
(C) 5.6%
(D) 1.6%
(E) 4.6%
Rationale: Explanation:
C.P. of 1 toy = 375/12 = Rs. 31.25
S.P of 1 toy = Rs. 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6%
Answer:C
Answer: (C) 5.6%
Question: A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 65 percent of its games that season, what was the total number of games that the team played?
(A) 180
(B) 120
(C) 90
(D) 85
(E) 70
Rationale: 65% is 15%-points above 50% and 15%-points below 80%.
Thus the ratio of "the first 60 games" to "remaining games" is 1:1.
So the team played a total of 60+60 = 120 games.
The answer is B.
Answer: (B) 120
Question: Brand A coffee costs twice as much as brand B coffee. If a certain blend is 1/4 brand A and 3/4 brand B. what fraction of the cost of the blend is Brand A?
(A) 1/3
(B) 2/5
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: Assume Cost of A= Ca = 200 , Cost of B = Cb=100
The blend contains 0.25 A and 0.75 B ---> Cost of the blend = Cbl = 0.25*200+0.75*100= 125
Thus fraction of A in the blend = 0.25*200/125 = 2/5. B is the correct answer.
Answer: (B) 2/5
Question: A rickshaw dealer buys 30 rickshaws for Rs. 4725. Of these, 8 are four-seaters and the rest are two seaters. At what price must he sell the four-seaters so that if he sells the two-two seaters at 3/4th of this price, he makes a profit 40% on his outlay?
(A) Rs. 180
(B) Rs. 279
(C) Rs. 360
(D) Rs. 450
(E) None of these
Rationale: Solution: On an investment of Rs. 4725, a profit of 40% means a profit of 1890.
Hence, the targeted sales realization is Rs. 6615.
The required equation;
8p+22*(3p)/4 = 6615;
Or, 8p+(33p/2) = 6615;
In the expression for LHS = RHS; we need 33p/4 to be odd number.
This can only happen when p is not a multiple of 4.
Hence, option a and c gets eliminated automatically.
Now, we check for option b which is correct.
Answer: Option B
Answer: (B) Rs. 279
Question: The probability of two events A and B are0.25 and 0.35 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________
(A) 0.55
(B) 0.4
(C) 0.5
(D) 0.05
(E) 0.6
Rationale: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.25+.35-.15
=.45
but the probability of neither A nor B=1-.45
=0.55
ANSWER:A
Answer: (A) 0.55
Question: A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route?
(A) 12km
(B) 15km
(C) 18km
(D) 24km
(E) Data Inadequate
Rationale: time=distance/speed
so,
let the distance to the level road from home be x km
and the distance to the hillock from the level road be y km
so, (x/4+y/3)+(y/6+x/4)=6
x+y=12 km.
ANSWER:A
Answer: (A) 12km
Question: In his ranch, Doug Bo can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that he will be able to place a lasso around a cow’s neck at least once in 5 attempts?
(A)  1/5
(B)  15/32
(C)  1/2
(D)  31/32
(E)  1
Rationale: This prompt is worded in an odd way, but essentially tells us that the probability of lasso-ing a cow is 1/2. The question asks for the probability of lasso-ing a cow AT LEAST ONCE in 5 attempts.
When it comes to probability questions, there are only 2 things that you can calculate: what you WANT to have happen OR what you DON'T WANT to have happen. Those two fractions will always add up to 1. Sometimes it's much easier to calculate what you DON'T WANT and then subtract that fraction from 1 (which will give you the probability of what you DO want).
Here, the work that would be required to calculate 1, 2, 3, 4, and 5 lasso-ings of a cow would take some time and effort. It's far easier to calculate what we DON'T WANT (0 lasso-ings) and subtract that fraction from 1.
The probability of NOT lasso-ing the cow on 5 attempts is:
(1/2)(1/2)(1/2)(1/2)(1/2) = 1/32
1 - 1/32 = 31/32
The probability of lasso-ing a cow AT LEAST ONCE in 5 attempts is 31/32
Final Answer:
D
Answer: (D)  31/32
Question: A and B can do a piece of work in 10 days, B and C in 5 days, C and A in 15 days. How long will C take to do it?
(A) 77 days
(B) 55 days
(C) 12 days
(D) 33 days
(E) 11 days
Rationale: 2c = 1/5 + 1/15 – 1/10 = 1/6
c = 1/12 => 12 days
Answer: C
Answer: (C) 12 days
Question: If X> 0 and X is divisible by the product of the first nine positive integers, all of the following must be factors of X except
(A) 35
(B) 40
(C) 63
(D) 315
(E) 704
Rationale: The question states taht X is divisible by 9!,which is 1*2*3*4*5*6*7*8*9
X=(9!) * some number
A. 35 = 5*7 so will divide X
B. 40 =5*8 so will divide X
C. 63 =9*7 so will divide X
D. 315 =5*7*9 so will divide X
E. 704 =8*8*11 This will not divide X
Ans E
Answer: (E) 704
Question: Company Z has 50 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
(A) 6
(B) 7
(C) 8
(D) 9
(E) 12
Rationale: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y = 50.
Now, plug options for x. Only A and E give an integer value for y. But only for E x > y as needed.
Answer: E.
Answer: (E) 12
Question: If a and b are consecutive integers (b>a), which of the following statements could be false?
1. The multiplication a+b is an even number.
2. (b/a) > 1.
3. (a + b) is always an odd number.
(A) 1 only.
(B) 2 only.
(C) 1 and 2 only.
(D) 1 and 3 only.
(E) 1, 2 and 3.
Rationale: Consecutive numbers means that one will be even and one will be odd.
(b/a) > 1.
If b= 1 and a=0
b/a= Undefined
Or if b =-1 and a=-2
b/a= 1/2 <1
Could be False
3. (a +b) is always an odd number.
Even+ Odd= Odd. True
C is the answer
Answer: (C) 1 and 2 only.
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 10 million bacteria in the dish at 2: 00 p.m., at what time will there be 22.5 million bacteria in the dish?
(A) 6: 00 p.m.
(B) 8: 00 p.m.
(C) 6: 00 a.m.
(D) 8: 00 a.m.
(E) 10: 00 a.m.
Rationale: Given:
he number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 10 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time will there be 22.5 million bacteria in the dish?
Assume that there are n intervals of 2 hours between 10 million and 62.5 million.
10 * (1.5)^n = 22.5
(15/10)^n = 22.5/10 = 225/100 = (15/10)^2
Hence n = 2 intervals.
Each interval is of 2 hours. Therefore, the number of hours = 4
Adding 4 hours to 2 PM, we get 6 PM as the answer.
Option A
Answer: (A) 6: 00 p.m.
Question: A train 284 m in length crosses a telegraph post in 18 seconds. The speed of the train is?
(A) 77 kmph
(B) 55 kmph
(C) 57 kmph
(D) 58 kmph
(E) 76 kmph
Rationale: S = 284/18 * 18/5
= 57 kmph
Answer: C
Answer: (C) 57 kmph
Question: In a theatre the ratio of car & two wheeler is 1:8. Total Number of tyres are 100. Find how many are cars and how many are two wheelers?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: let the no of cars be 1x and no of two wheelers be 8x
(1x*4)+(8x*2)=100
20x=100 ...x=5
1x=no of cars=5 8x=no of two wheelers=40
ANSWER:C
Answer: (C) 40
Question: A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 54 km downstream
(A) 5 hours
(B) 4 hours
(C) 3 hours
(D) 2 hours
(E) None of these
Rationale: Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 54 km
Time taken = distance/speed = 54/27 = 2 hours. Answer : Option D
Answer: (D) 2 hours
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:
(A) 5324
(B) 5334
(C) 6300
(D) 6356
(E) 6400
Rationale: Divisor = (5 * 50) = 250
= 10 * Quotient = Divisor
=> Quotient = 250/10 = 25
Dividend = (Divisor * Quotient) + Remainder
Dividend = (250 * 25) + 50 = 6300
C
Answer: (C) 6300
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?
(A) 2 1/4
(B) 2 1/6
(C) 2 1/0
(D) 2 1/2
(E) 2 1/1
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer: A
Answer: (A) 2 1/4
Question: What is the value of 17^2 + 18^2 + 19^2 + 20^2 + 21^2 + 22^2 + 23^2 ?
(A) 2898
(B) 2808
(C) 2818
(D) 2828
(E) 2838
Rationale: This is what I did, all the nos are close to 20, and squared, so 20^2 plus there are 7 numbers, so (20)^2 x 7 =2800,
now squaring the last digits of each no individually comes up to (9+4+1+0+1+4+9) = 28.
when you add the 2 up it gives you a (2800+28) =2828,
Answer is D IMO.
Answer: (D) 2828
Question: P and Q started a business by investing Rs.4400/- and Rs.5500/- respectively. Find the P’s share out of a total profit of Rs.2700:
(A) 800
(B) 1000
(C) 1200
(D) 1400
(E) 1600
Rationale: P = Rs.4400/-
Q = Rs.5500/-
P share 4 parts & Q share 5 parts
Total 9 parts -----> Rs.2700/-
----> 1 part -------> Rs.300/-
P share = 4 parts -----> Rs.1200/-
C
Answer: (C) 1200
Question: In honor of the year 2013, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
(A) 18
(B) 36
(C) 42
(D) 52
(E) 56
Rationale: All options other than 'D' are factors of 2013. Hence, 'D' is the answer
Answer: (D) 52
Question: Seven people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 7/8
(B) 1/8
(C) 1/3
(D) 1/6
(E) 1/9
Rationale: Original share of 1 person =1/7
New share of 1 person =1/6
Increase =1/6 -	1/7	=1/42
Required fraction =	(1/42)/(1/7)=1/6
Answer is D.
Answer: (D) 1/6
Question: A classroom has equal number of boys and girls. 6 girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
(A) 16
(B) 24
(C) 32
(D) 48
(E) 54
Rationale: after 6 girls left remaining 6 girls
now boys 12 are twice as many as remaining girls.
initially boys=12 and girls=12.
ANSWER:B
Answer: (B) 24
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.86
(B) 2.88
(C) 2.29
(D) 2.24
(E) 2.97
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x =2.88
Answer:B
Answer: (B) 2.88
Question: A tailor trims 11 feet from opposite edges of a square piece of cloth, and 7 feet from the other two edges. If 84 square feet of cloth remain, what was the length of a side of the original piece of cloth?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: Let the original side of the square be x.
(x-22)*(x-14) = 84 = 6*14
x = 28
The answer is C.
Answer: (C) 28
Question: If −2≤q≤0 and n > 19, which of the following CANNOT be the value of qn?
(A) -48
(B) -38
(C) -20
(D) 0
(E) 19
Rationale: value of qn not equal to -19=E -19....Rest all are achievable
Answer: (E) 19
Question: If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 22?
(A) 101
(B) 187
(C) 191
(D) 201
(E) 242
Rationale: ok, not sure if this is the best explanation, but here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 22 = t 3 + 3 + 4 + 5 + 6....+ 21
the 3 + 4 + 5 + ... + 21 sequence is equal the sequence 1 + 2 + ... + 21, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 21 sequence is equal to n*(n+1)/2 with n being 21, so equal to 21 * 22 / 2 = 231
so :
t 22 = t 3 + 231 - 3
t 22 = 14 + 231 - 3 = 231 + 11 = 242, hence answer E
Answer: (E) 242
Question: 36 welders work at a constant rate they complete an order in 3 days. If after the first day, 12 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
(A) 3
(B) 2
(C) 8
(D) 4
(E) 6
Rationale: 1. We need to find out the time taken by 24 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 36*3 = 108 days
4. But on day 1 thirty-six workers had already worked finishing 1/3 of the job. So 24 workers have to finish only 2/3 of the job.
5. Total time taken by 24 workers can be got from formula used at (2). i.e., 24* total time taken = 108. Total time taken by 6 workers to finish the complete job is 108/ 24 = 4.5 days.
6. Time taken by 24 workers to finish 2/3 of the job is 2/3 * 4.5 = 3 days.
The answer is choice A
Answer: (A) 3
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 500. then his monthly salary is
(A) Rs. 2500
(B) Rs. 3500
(C) Rs. 1500
(D) Rs. 500
(E) Rs. 2000
Rationale: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 500
â‡” 20 / 100x = 500
â‡” x = 500 Ã— 5 = 2500.
Answer A
Answer: (A) Rs. 2500
Question: What is the probability of rolling four six-sided dice, and getting a different number on each die?
(A) 1/12
(B) 1/3
(C) 4/9
(D) 5/9
(E) 5/13
Rationale: MAGOOSHOFFICIAL SOLUTION
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.
6 x 5 x 4 x 3 = 360 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6x6 = 1296).
360/1296 = 5/13
Answer: E.
Answer: (E) 5/13
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 165
(B) 771
(C) 245
(D) 177
(E) 121
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C
Answer: (C) 245
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 29
(B) 15
(C) 16
(D) 17
(E) 19
Rationale: 10 * 15 + 36 – 26 = 160/10
= 16
Answer:C
Answer: (C) 16
Question: At a school, three-fifths of the male students and one-half of the female students speak a foreign language. If the number of males is equal to the number of females, what fraction of the students speak a foreign language?
(A) 11/20
(B) 13/20
(C) 7/10
(D) 3/5
(E) 2/5
Rationale: Let x be the number of students in the school.
The number of males who speak a foreign language is (3/5)(1/2)x = (3/10)x
The number of females who speak a foreign language is (1/2)(1/2)x = (1/4)x
The total number of students who speak a foreign language is (3/10)x + (1/4)x = (11/20)x
The answer is A.
Answer: (A) 11/20
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent. Overall he make a.
(A) 228
(B) 288
(C) 500
(D) 200
(E) 881
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 2/100) = 15000 - 300
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -300 + 800 = Rs. 500
As this is positive, an overall profit of Rs. 500 was made.Answer:C
Answer: (C) 500
Question: Two friends are training for a marathon together. Billie is faster than Joey, so they agree to giving Joey a half-hour head start, Joey leaving their warm up at 1:30. Joey runs a 3 minute mile (an average of 20 mph), and Billie runs at an average of 50 mph. When will Billie catch up to Joey?
(A) 3:00
(B) 3:30
(C) 4:00
(D) 4:30
(E) 5:00
Rationale: Distance covered by the Joey in 1/2 hour = 20 miles
Now, 10 miles is compensated in 1 hour
Therefore 20 miles will be compensated in 2 hours
So, Billie meets Joey at 4 p.m.
Correct Answer: C
Answer: (C) 4:00
Question: In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?
(A) 18
(B) 36
(C) 45
(D) 55
(E) None of these
Rationale: Explanation:
Let R, G and B represent the number of balls in red, green and blue boxes respectively.
Then, .
R + G + B = 108 ...(i),
G + R = 2B ...(ii)
B = 2R ...(iii)
From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.
Putting G = 3R and B = 2R in (i), we get:
R + 3R + 2R = 108 6R = 108 R = 18.
Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.
Answer: E
Answer: (E) None of these
Question: A and B invests Rs.2000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 3:5
(B) 3:4
(C) 9:2
(D) 9:9
(E) 3:1
Rationale: (2*6 + 4*6): (4*12)
36:48 =>
3:4
Answer:B
Answer: (B) 3:4
Question: A mixture of 125 gallons of wine and water contains 20% of water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?
(A) 10 gallons
(B) 8.5gallons
(C) 8gallons
(D) 8.33gallons
(E) 9.33gallons
Rationale: In 125 gallons of the solution there are 0.2∗125=25 gallons of water. We want to add w gallons of water to 125 gallons of solution so that 25+w gallons of water to be 25% of new solution: 25+w=0.25(125+w) --> w=253≈8.33.
ANSWER:D
Answer: (D) 8.33gallons
Question: What is the least valueof y. So that 23x57 is divisible by 3?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
A
Answer: (A) 1