mathewhe/aqua_rat huggingface dataset:
Question: Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
(A) 12 to 1
(B) 6 to 1
(C) 5 to 1
(D) 20 to 7
(E) 1 to 5
Rationale: The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job;
The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 3*7=21
The ratio thus is 60 to 21, or 20 to 7.
Answer: D.
Answer: (D) 20 to 7
Question: Convert the 9/36 m/s into kilometers per hour?
(A) 0.9 kmph
(B) 9.9 kmph
(C) 1.3 kmph
(D) 1.2 kmph
(E) 5.7 kmph
Rationale: 9/36 m/s = 9/36 * 18/5 = 9/10
= 0.9 kmph.
Answer: A
Answer: (A) 0.9 kmph
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 110 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10
(B) 25
(C) 77
(D) 55
(E) 22
Rationale: Speed of the boat in still water = (60+110)/2 = 85 kmph. Speed of the stream
= (110-60)/2
= 25 kmph.
Answer: B
Answer: (B) 25
Question: The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
(A) 187.89 cm
(B) 180.29 cm
(C) 123.98 cm
(D) 149.98 cm
(E) 146.89 cm
Rationale: Calculated average height of 35 boys = 182 cm.
Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182 cm - (166 cm - 106 cm)/35
= 182 cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm
= 182 cm - 1.71 cm = 180.29 cm.
Answer: B
Answer: (B) 180.29 cm
Question: John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him?
(A) 10
(B) 67
(C) 32
(D) 44
(E) 55
Rationale: 75-20=55. Answer is E
Answer: (E) 55
Question: Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
7 ~ 2 ~ 7 ~ 4 = ____
(A) 3538
(B) 2418
(C) 2873
(D) 3258
(E) 4268
Rationale: B
The rule that is being followed here is
P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]
Using the same rule in the incomplete equation,
7 ~ 2 ~ 7 ~ 4 = [first digit of (7 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (7 * 4)]
= 2418
Thus 2418 is the missing number.
Answer: (B) 2418
Question: The speed at which a man can row a boat in still water is 9.5 kmph. If he rows downstream, where the speed of current is 8.5 kmph, what time will he take to cover 45.5 metres?
(A) 18 seconds
(B) 8.4seconds
(C) 5 seconds
(D) 9.1 seconds
(E) 9.5econds
Rationale: Speed of the boat downstream = 9.5 +8.5
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 45.5 m = 45.5/5
= 9.1 seconds.
Answer:D
Answer: (D) 9.1 seconds
Question: If x is 20 percent more than y and y is 30 percent less than z, then x is what percent of z?
(A) 500%
(B) 250%
(C) 500/3%
(D) 84%
(E) 60%
Rationale: Z = 100 ; Y = 70 so X = 84
X as % of Z = 84/100 * 100 => 84%
Answer will be (D)
Answer: (D) 84%
Question: Tommer spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommer won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
(A) 330
(B) 500
(C) 520
(D) 540
(E) 620
Rationale: I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, tommer earned$520. Answer choice C.
Answer: (C) 520
Question: Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-7) = 0, then f(x) crosses the y-axis at what y-coordinate?
(A) -7
(B) -1
(C) 0
(D) 1
(E) 7
Rationale: When x = 1 and when x = -7, the expression f(x) = x² + bx + c equals 0.
Then f(x) = (x-1)(x+7)
f(0) = -7
The answer is A.
Answer: (A) -7
Question: In 2000 there were 10000 women stockbrokers in the United States. By 2005 the number had increased to 20000. Approximately what was the percent increase?
(A) 1%
(B) 2%
(C) 1.5%
(D) 3%
(E) 4%
Rationale: The percent increase is (20000-10000)/10000=10000/10000=1%
So the approximate answer is A
Answer: (A) 1%
Question: At present the son's age is same as was his father's age at the time of his birth. If father's age is 48. Find the son's age after 4 years from now.
(A) 30 years
(B) 24 years
(C) 28 years
(D) 29 years
(E) 38 years
Rationale: Let x be the son's age
And y be the father's age
Then, y=48.
And, x=y-x
==> 2x=y
==> x=y/2
So, x=48/2
x=24.
Son's age after four years,
x+4 = 24+4
= 28 years.
ANSWER:C
Answer: (C) 28 years
Question: A train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?
(A) 5
(B) 12
(C) 7
(D) 9
(E) 5
Rationale: Speed of train relative to man = 60 + 4 = 64 km/hr.
= 64 * 5/18 = 160/9 m/sec.
Time taken to pass the men = 220 * 9/160 = 12 sec.Answer: B
Answer: (B) 12
Question: If 2x=4y=z, what is x-y, in terms of z?
(A) z/4
(B) z/2
(C) z
(D) 2z
(E) 4z
Rationale: 2x=4y=z
i.e. x = z/2
and y = z/4
x-y = z/2 - z/4 = z/4
Answer: Option A
Answer: (A) z/4
Question: The population of cities A and B is equal. The population of city A increases in two successive years by 20% and 15% respectively and that of city B increases successively by 20% and 10% respectively. If the difference in the population of two cities after 2 years is 768, then what was the total population of the two cities initially?
(A) 12,800
(B) 26,500
(C) 24,600
(D) 25,600
(E) 27,600
Rationale: Population of city A = Population of city B = A
M . F of A = 120/100*115/100 = 138/100
M . F of B = 120/100*110/100 =132/100
Population of A after 2 years = A*138/100
Population of B after 2 years = A*132/100
Difference = A/100( 138 –132 ) = 768
A = 768*100/6 = 12800
Total initial population = 12800+12800 = 25,600
ANSWER:D
Answer: (D) 25,600
Question: A man deposits $1000 in a bank at 2% per annum and $ 1500 in UTI at 7% per annum. Find the rate of interest for the whole sum.
(A) 5%
(B) 8%
(C) 3%
(D) 7%
(E) 1%
Rationale: Following the above formula,we have the rate of interest for the whole sum
=(1000*2)+(1500*7)/1000+1500=12500/2500=5%.
Answer is A
Answer: (A) 5%
Question: Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 4
II. 12
III. 24
(A) I, II, and III
(B) I and II only
(C) II and III only
(D) I and III only
(E) II only
Rationale: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Answer: (A) I, II, and III
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
(A) 33 1/9%
(B) 73 1/3%
(C) 33 1/3%
(D) 33 1/9%
(E) 39 1/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 18 min
(B) 19 min
(C) 11 min
(D) 28 min
(E) 16 min
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D
Answer: (D) 28 min
Question: If 15 lions can kill 15 deers in 15 minutes how long will it take 100 lions to kill 100 deers?
(A) 1 minutes
(B) 15 minute
(C) 100 minutes
(D) 10000 minutes
(E) 1000 minutes
Rationale: we can try the logic of time and work,our work is to kill the deers so 15(lions)*15(min)/15(deers)=100(lions)*x(min)/100(deers)hence answer is x=15
ANSWER:B
Answer: (B) 15 minute
Question: The length of a rectangular floor is more thanits breadth by 200%. If Rs.324 is requiredto paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
(A) 12
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: 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 = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
B
Answer: (B) 18
Question: A military commander has to choose 3 soldiers out of a company of 6 for guarding the headquarters. How many different group combinations of 3 does he have to choose from?
(A) 20
(B) 15
(C) 16
(D) 27
(E) 35
Rationale: A military commander has to choose 3 soldiers out of a company of 7.
different group combinations of 3
He can do this in 6C3 ways
6*5*4/3*2*1= 20 ways
ANSWER:A
Answer: (A) 20
Question: I. x2 + 11x + 30 = 0,
II. y2 + 15y + 56 = 0 to solve both the equations to find the values of x and y?
(A) If x < y
(B) If x > y
(C) If x ≤ y
(D) If x ≥ y
(E) If x = y or the relationship between x and y cannot be established.
Rationale: I. x2 + 6x + 5x + 30 = 0
=>(x + 6)(x + 5) = 0 => x = -6, -5
II. y2 + 8y + 7y + 56 = 0
=>(y + 8)(y + 7) = 0 => y = -8, -7
=> x > y
ANSWER:B
Answer: (B) If x > y
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 3 consecutive spaces in a random direction, what is the probability the piece ends no more than 3 spaces from the square numbered 49?
(A) 10%
(B) 11%
(C) 12%
(D) 13%
(E) 7%
Rationale: No more than 3 spaces from 49 means in the rangefrom 49-3=46 to 49+3=52, inclusive. Total numbers in this range 52-46+1=7, the probability favorable/total=7/100
Answer: E
Answer: (E) 7%
Question: A room contains 120 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Say group of x people left the room.
# of women in the room was 0.15*120=18;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(120-x);
So, 18-0.3x= 0.1(120-x) --> x=30.
Answer: C.
Answer: (C) 30
Question: A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The distance between the nest and the ditch is 250 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 250 = 7500.
D = ST
7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km)
D)
Answer: (D) 5
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age 8 years back was:
(A) 13 years.
(B) 14 years.
(C) 17 years.
(D) 16 years.
(E) 19 years.
Rationale: Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21
Son's age 8 years back (21- 8) = 13 years.
ANSWER :A
Answer: (A) 13 years.
Question: A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
(A) 4 days
(B) 6 days
(C) 8 days
(D) 18 days
(E) 28 days
Rationale: Explanation:
Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.
B's 1 day's work =1/12
A's 1 day's work =	1/6 ; (2 times of B's work)
(A + B)'s 1 day's work = (1/6 +1/12)=3/12=1/4
So, A and B together can finish the work in 4 days.
ANSWER IS A
Answer: (A) 4 days
Question: A motorist travel to a place 150 km away at an avearge speed of 50 km/hr and returns ar 30
km/hr.His average speed for the whole jouney in km/hr is
(A) 36.5 km/hr
(B) 37.5 km/hr
(C) 35.5 km/hr
(D) 34.5 km/hr
(E) None of these
Rationale: Explanation:
Average speed will be
2xyx+ykm/hr
= \frac{2(50)(30)}{50+30} km/hr
= 37.5 km/hr
Answer: Option B
Answer: (B) 37.5 km/hr
Question: If a book has twelve thousand words, two long chapters, and four short chapters, how many words are in a short chapter if there are as many words in the four short chapters put together as in one long chapter?
(A) Eleven thousand words
(B) Five thousand words
(C) Two thousand words
(D) One thousand words
(E) Six hundred words
Rationale: D. A long chapter has 1/3 of the total words. A short chapter has 1/4 of 1/3 of the total words. 1/4 of 1/3 is 1/12. 1/12 of twelve thousand is one thousand, so the answer is D.
Answer: (D) One thousand words
Question: A set of five positive integers has an arithmetic mean of 150. A particular number among the five exceeds another by 100. The rest of the three numbers lie between these two numbers and are equal. How many different values can the largest number among the five take?
(A) 18
(B) 19
(C) 21
(D) 42
(E) 59
Rationale: Lets say numbers are in this order: x < y = y = y < x+100. Question is, how many different values can x take.
x+3y+x+100 = 750
2x+3y = 650
We have condition x < y < x + 100 so lets use it
2x + 3y < 2x + 3*(x+100) = 5x + 300
2x + 3y > 2x + 3x = 5x
2x + 3y = 650
So we got double inequality:
5x < 650 < 5x + 300 which turns into
350 < 5x < 650
70 < x < 130
x can take 130-70-1 = 59 values
ANSWER:E
Answer: (E) 59
Question: In a supermarket the single-yolk and double-yolk eggs got mixed. If the total number of yolks was 15 more than the total number of eggs. Find the number of double-yolk eggs.
(A) 8
(B) 13
(C) 15
(D) 11
(E) 5
Rationale: Let the number of single-yolk eggs be X and the number of double-yolk eggs be Y. Then
=> X+(2*Y)= 15+(X+Y)
=>2Y=15+Y
=>Y=15
Option C
Answer: (C) 15
Question: What is the smallest possible common multiple of three integers, all larger than 25?
(A) 27.
(B) 26
(C) 846.
(D) 19,656.
(E) 21,924.
Rationale: The Least common positive multiple would be for the immediate least number(s) after 25 i.e 26.
Since nowhere is it stated that the three integers must be different, the integers could be 26,26 and 26... leading to least possible positive common multiple to be 26. Answer B.
Answer: (B) 26
Question: The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 120 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?
(A) 30
(B) 50
(C) 70
(D) 80
(E) 90
Rationale: Let x be the number of new boarders.
The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10.
120 / (120+x) = 4/5
x = 30
The answer is A.
Answer: (A) 30
Question: A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $220. The cost for 1 bat and 6 balls is $190, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $270 for the purchase?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: IMO it should be C that is 4
reason:
formed an equation... bat = b ball = c
2b+4c=220
1b+6c=190
solving both we get b that is bat = 70 and c that is ball = 20
new equation 270 to be divided in equal
3b+3c=270
3*70 + 3*20 = 270
210+ 60 = 270
Answer: (C) 3
Question: Find large number from below question The difference of two numbers is 2415. On dividing the larger number by the smaller, we get 21 as quotient and the 15 as remainder
(A) 1209
(B) 1324
(C) 1245
(D) 1300
(E) 2535
Rationale: Let the smaller number be x. Then larger number = (x + 2415).
x + 2415 = 21x + 15
20x = 2400
x = 120
Large number = 120+2415 = 2535
Answer : E
Answer: (E) 2535
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets $2.40 per hour for regular work and $3.20 per hours for overtime. If he earns $432 in 4 weeks, then how many hours does he work for ?
(A) 135
(B) 278
(C) 175
(D) 195
(E) 200
Rationale: C
175
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer: (C) 175
Question: At a certain store, the price of a pair of shoes is ten dollars more than three times the price of a pair of jeans and the price of a sweater is fifty percent more than the price of a pair of shoes. If the price of a pair of jeans is j dollars at this store, then what is the price, in dollars, of a pair of shoes, a sweater and a pair of jeans, in terms of j ?
(A) 1.5j + 10
(B) 3j + 20
(C) 4.5j + 30
(D) 5.5j + 30
(E) 8.5j + 25
Rationale: Ans E
Given
Price of Jeans = J
Price of shoes = 10+3J
Price of Sweater = 1.5(10+3J)
Total Price of all three items = J+10+3J+1.5(10+3J) = 25+8.5J
Answer: (E) 8.5j + 25
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs. 40,000, the amount invested by Y is ?
(A) 60229
(B) 62887
(C) 60000
(D) 61298
(E) 61291
Rationale: Suppose Y invested Rs. y. Then 40000/y
= 2/3 or y
= 60000 .
Answer: C
Answer: (C) 60000
Question: 70 60 55 50 40 55 30 ? ?
(A) 25 15
(B) 55 85
(C) 35 55
(D) 20 55
(E) 25 55
Rationale: 70-10=60
again 55
60-10=50
50-10=40
again 55
40-10=30
30-10=20
again 55
then answer is 20 ,55
ANSWER:D
Answer: (D) 20 55
Question: In a four numbers set, the second number is twice the first number, the first is one-third of the third and the third is 5 times the fourth. The average of the numbers is 24.75. The largest of these numbers is:
(A) 9
(B) 25
(C) 30
(D) 35
(E) None of these
Rationale: Explanation :
Let the fourth number be x.
Then, third number = 5x, first number = 5x/3
And second number = 10x/3
x + 5x + 10x/3 + 5x/3 = (33 x 4) or 11x = 132 or x = 12.
So, the numbers are 20, 40, 60 and 12.
Largest number = 60.
Answer : D
Answer: (D) 35
Question: There are 84 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 14 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?
(A) 20
(B) 31
(C) 42
(D) 49
(E) 64
Rationale: x + (x - 14) = 84 --> x = 49.
Answer: D.
Answer: (D) 49
Question: In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
(A) 5 km/h
(B) 8 km/h
(C) 10 km/h
(D) 15 km/h
(E) 25 km/h
Rationale: Let A's speed be X km/hr.
Then, 30/x - 30/2x = 3
6x = 30
x = 5 km/hr.
Answer : A.
Answer: (A) 5 km/h
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
(A) 10
(B) 15
(C) 16
(D) 24
(E) 28
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: (D) 24
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
(A) 180
(B) 290
(C) 729
(D) 720
(E) 125
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer:A
Answer: (A) 180
Question: At Sandi’s Pet Shop, 25 cups of bird seed are used every 5 days to feed 15 parakeets. How many cups of bird seed would be required to feed 14 parakeets for 7 days?
(A) 40.5
(B) 32.34
(C) 6.23
(D) 9
(E) 15
Rationale: Let's go step-by-step.
25 cups are used over a 5 day period, which means 5 cups a day. This feeds 15 parakeets, which means each parakeet needs 1/3 of a cup every day.
For 14 parakeets, we need 14*1/3cups = 4.62 cups a day. Over 7 days, we need 32.34 cups. Choice B.
Answer: (B) 32.34
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 850 in 4 years. The
rate on interest per annum is.
(A) 4.20%
(B) 50%
(C) 60%
(D) 6.25%
(E) 8.10%
Rationale: Explanation:
S.I. on Rs 800 for 1 year = 50
Rate = (100*50)/(800*1) = 6.25%
Answer: D
Answer: (D) 6.25%
Question: The ratio of the age of a gentleman and his wife is 4 : 3. After 4 years this ratio will be 9 : 7. If at the time of their marriage the ratio was 5 : 3, how many years ago they were married?
(A) 10 years
(B) 8 years
(C) 12 years
(D) 15 years
(E) 17 years
Rationale: Let the present age of gentleman (G) and wife (W) be 4x and 3x resp....
thus after 4 yrs the ratio will be (4x+4)/(3x+4)=9:7..
on solving we get the value as x=8..i.e present ages are G=32,W=24...
Now at the time of marriage the ratio will be :
(32-y)/(24-y)=5:3
on solving we get y=12...
Thus 12 yrs ago they got married.
ANSWER:C
Answer: (C) 12 years
Question: Set A is {1, 3, 5, 7, 9}
Set B is {12, 14, 16, 18, 20}
For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: The mean and median of Set A is 5.
The mean and median of Set B is 16.
Thus statements I and II are both true.
The standard deviation is related to the distance from the mean.
Since the elements of both sets are spaced identically around the mean (+/- 2, +/- 4), the standard deviations of both sets are equal.
The answer is B.
Answer: (B) I and II only
Question: If r = 2^4 * 5^2 * 7 and s = 2^3 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?
(A) 2 * 5
(B) 2^2 * 5
(C) 2^3 * 5^2
(D) 2*3*5*7
(E) 2^3 * 3^2 * 5^2 * 7
Rationale: GCD = product of prime factors raised to the least power = 2^3 * 5
The answer is B.
Answer: (B) 2^2 * 5
Question: A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.33 per litre so as to make a profit of 25% on cost when he sells the resulting milk and water mixture for Rs.36 In what ratio should he mix the water and milk?
(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:4
(E) 21:124
Rationale: water = w (liter)
Milk = m (liter)
==> Cost = Price x Quantity = 0.33m
==> Revenue = Price x Quantity = 0.36(m + w)
==> Profit =0.36(m+w) - 0.33m = 0.25*(0.33m)[25% of cost]
==> 0.36m + 0.36w - 0.33m = 0.0825m
==> 0.0525m = 0.36w
==> m/w = 0.36/0.0525 = 124/21
--OR--
w/m = 21/124
E is correct.
Answer: (E) 21:124
Question: Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
(A) 9
(B) 5
(C) 6
(D) 2
(E) 1
Rationale: Explanation:
x + y = 15
2x â€“ 3y = 5
x = 10 y = 5
Answer: B
Answer: (B) 5
Question: 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?
(A) 238
(B) 177
(C) 120
(D) 298
(E) 1771
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Answer: (C) 120
Question: Sudhir started a business with Rs.10,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be
(A) 1:2
(B) 2:3
(C) 4:3
(D) 3:4
(E) 3:5
Rationale: 10000*12:60000*(12-8)
=120000 :240000
=1:2
ANSWER:A
Answer: (A) 1:2
Question: The average of 20, 70 and 180 is twice the average of 10, 30, and which of the following ?
(A) 1)10
(B) 2)30
(C) 3)60
(D) 4)90
(E) 5)95
Rationale: 20 70 180 = 180+90 = 270/3 = 90.
90/2 = 45
10 30 x = 40+x/3 should be smaller than 45
cross multiply 45*3-40 = 95
E
Answer: (E) 5)95