mathewhe/aqua_rat huggingface dataset:
Question: In Kiran's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Kiran and he thinks that Kiran's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Kiran?
(A) 67
(B) 68
(C) 69
(D) 70
(E) 71
Rationale: Let Kiran's weight = x. Then
According to Kiran, 65 < x < 72 ----(equation 1)
According to brother, 60 < x < 70 ----(equation 2)
According to mother, x ≤ 68 ----(equation 3)
Given that equation 1,equation 2 and equation 3 are correct. By combining these equations,we can write as
65<x≤68
i.e., x = 66 or 67 or 68
Average of different probable weights of Kiran = (66+67+68)/3=67
Answer is A.
Answer: (A) 67
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
(A) 14400
(B) 26400
(C) 12000
(D) 12500
(E) 14500
Rationale: Explanation:
Ratio of the investment
=21000:17500=210:175
=42:35=6:5
Share of X in the profit
=2400 x 6/11
=2400×6=14400
Answer: Option A
Answer: (A) 14400
Question: Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 10 pages a minute more than printer A ?
(A) 600
(B) 800
(C) 1000
(D) 1200
(E) 1500
Rationale: Answer: D.
Answer: (D) 1200
Question: Find the roots of quadratic equation: 2x2 + 5x + 2 = 0?
(A) -2, -1/2
(B) 4, -1
(C) 4, 1
(D) -2, 5/2
(E) None of these
Rationale: 2x2 + 4x + x + 2 = 0
2x(x + 2) + 1(x + 2) = 0
(x + 2)(2x + 1) = 0 => x = -2, -1/2
ANSWER:A
Answer: (A) -2, -1/2
Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
(A) 3/5
(B) 3/10
(C) 4/5
(D) 5/4
(E) 6/4
Rationale: Let the required fraction be x. Then,
1/x - x = 9/20
20x2 + 9x - 20 = 0
20x2 + 25x - 16x - 20 = 0
5x(4x + 5) -4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
x = 4/5
ANSWER:C
Answer: (C) 4/5
Question: If the mean of a data set is 75 and the standard deviation is 10, what is the range of scores that fall within one standard deviation of the mean?
(A) 65, 80}
(B) 65, 90}
(C) 65, 70}
(D) 65, 80}
(E) 65, 85}
Rationale: score ranges between 85 and 65, where 85 is within one Standard deviation above the mean and 65 is within one standard deviation below the mean
Answer is E
Answer: (E) 65, 85}
Question: What percent of 60 is 80?
(A) 133 1⁄3
(B) 75
(C) 60
(D) 33 1⁄3
(E) 25
Rationale: % of 60 is 80?
= 80/60 = 4/3 = 133.33%
Thus A is the correct answer.
Answer: (A) 133 1⁄3
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
(A) 13 1/8 days
(B) 13 1/3 days
(C) 83 1/3 days
(D) 13 8/3 days
(E) 19 1/3 days
Rationale: 5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer: B
Answer: (B) 13 1/3 days
Question: Some man have some apples with him.He gave half of the apples and half an apple.This gets repeated for 4 time.After that he has no more apple with him.How many number of apples were there initially?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: some apples=x
he gave half of an apples and half of an apple and reaming he have are x/2-1/2
It is repeated four times
2nd time x/4-1/2-1/2
3d time x/8-1/2-1/2-1/2
4th time x/16-1/2-1/2-1/2-1/2=0
x/16-2=0
x=32
ANSWER:C
Answer: (C) 32
Question: If the cost price of 50 articles is equal to the selling price of 30 articles, then the gain or loss percent is?
(A) 22
(B) 65
(C) 78
(D) 66.67
(E) 25
Rationale: Given that, cost price of 50 article is equal to selling price of 30 articles.
Let cost price of one article = Rs. 1
Selling price of 30 articles = Rs. 50
But Cost price of 30 articles = Rs. 30
Therefore, the trader made profit.\Percentage of profit = 20/30 * 100 = 66.67%
Answer:D
Answer: (D) 66.67
Question: Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 1 hours; pumps A and C, operating simultaneously, can fill the tank in 1 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
(A) 1/3
(B) 1/2
(C) 1/4
(D) 1
(E) 5/6
Rationale: A+B =1 ; A+C =1 ,B+C =2 ; ADD THEN 2*(A+B+C) = 4
A+B+C = 2 HRS
B
Answer: (B) 1/2
Question: Kira's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ?
(A) 7cdx/100
(B) d + 7cx/100
(C) 7d + xc/100
(D) 7d + 7xc/100
(E) 7cdx
Rationale: Answer is D.
Answer: (D) 7d + 7xc/100
Question: Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 120 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?
(A) 100%
(B) 20%
(C) 25%
(D) 33 1/3%
(E) 40%
Rationale: 0.4*75 + 0.6x = 120
30 + 0.6x=120
0.6x = 90
x= 150
150/75=2
Ans:A
Answer: (A) 100%
Question: The average of 15 result is 60. Average of the first 10 of them is 10 and that of the last 10 is 80. Find the 8th result?
(A) 35
(B) 200
(C) 150
(D) 250
(E) 300
Rationale: Sum of all the 13 results = 15 * 60 = 900
Sum of the first 7 of them = 10 * 10 = 100
Sum of the last 7 of them = 10 * 80 = 800
So, the 8th number = 900 + 100 - 800 = 200.
B
Answer: (B) 200
Question: Lilly has 10 fish and Rosy has 11 fish. In total, how many fish do they have in all?
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: 10+11=21
The answer is C.
Answer: (C) 21
Question: Ten years ago, P was half of Q's age. If the ratio of their present ages is
3:4, what will be the total of their present ages?
(A) 45
(B) 40
(C) 35
(D) 30
(E) 38
Rationale: Let present age P and Q be 3x 4x respectively
Ten years ago, P was half of Q's age
(3x-10) = 1/2 (4x-10)
2x = 10
x=5
Total of their present ages = 3x+4x = 7x = 7 * 5 = 35
ANSWER C
Answer: (C) 35
Question: The effective annual rate of interest corresponding to a nominal rate of 12% per annum payable half-yearly is?
(A) 16.06%
(B) 16.07%
(C) 12.36%
(D) 6.09%
(E) 6.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 6/100)2] = Rs. 112.36 Effective rate = (112.36 - 100) = 12.36%
ANSWER:C
Answer: (C) 12.36%
Question: The average age of husband, wife and their child 3 years ago was 26 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
(A) 22
(B) 40
(C) 38
(D) 21
(E) 37
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (26 x 3 + 3 x 3) years = 87 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (87 - 50) years = 37 years.
Answer: E
Answer: (E) 37
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is
(A) 38%
(B) 40%
(C) 44%
(D) 48%
(E) 50%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120 x m = 6 x m.
100 5
New breadth = 120 y m = 6 y m.
100 5
New Area = 6 x x 6 y m2 = 36 xy m2.
5 5 25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11 xy x 1 x 100 % = 44%.
25 xy
C)
Answer: (C) 44%
Question: The average (arithmetic mean) of the even integers from 0 to 40 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 20 inclusive?
(A) 10
(B) 20
(C) 5
(D) 30
(E) 15
Rationale: So, according to A mean of a set of even numbers from 0 to 40 =(0+40)/2=20 and mean of a set of even numbers from 0 to 20 =(0+20)/2=10
Difference=20-10=10
Answer: A.
Answer: (A) 10
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 15 hours
(B) 14 hours
(C) 12 hours
(D) 74 hours
(E) 79 hours
Rationale: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
B's 1 hour work = (7/12 + 1/2) = 1/12
B alone will take 12 hours to do the work.
Answer:C
Answer: (C) 12 hours
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 4 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
(A) 3 1/5min
(B) 2 10/13min
(C) 3 3/5min
(D) 3 4/5min
(E) 3 min
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(1/9+1/4)=(13/36)
So both punctures will make the type flat in
(36/13)mins=2 10/13mins
Option B
Answer: (B) 2 10/13min
Question: A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 1.4
(C) 3
(D) 1.5
(E) 1.9
Rationale: M = 9
S = x
DS = 9+ x
US = 9 + x
9 + x = (9 - x)2
9+ x = 18 -2x
3x = 9
x = 3
Answer:C
Answer: (C) 3
Question: If 5x^2 has two different prime factors, at most how many different prime factors does x have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x cannot have more than 2 prime factors, because in this case 5x^2 would also have more than 2 prime factors.
Can x have 2 prime factors? Yes, consider x=2*5=10 (in this case 5x^2 still has 2 prime factors).
Answer: B.
Answer: (B) 2
Question: How many different ways can you select a pilot and a co pilot if you have 30 people to choose from?
(A)  199
(B)  200
(C)  398
(D)  4950
(E)  870
Rationale: You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (30C2) x 2 = 870E
Answer: (E)  870
Question: A big container is 30% full with water. If 27 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
(A) 36 liters
(B) 40 liters
(C) 45 liters
(D) 54 liters
(E) 60 liters
Rationale: A big container is 30% full with water and after 27 liters of water is added, the container becomes 75% full. Hence these 27 liters account for 45% of the container, which means that the capacity of it is 27/0.45=60 liters.
OR: if the capacity of the container is x liters then: 0.3x+27=0.75x --> x=60 liters.
Answer: E.
Answer: (E) 60 liters
Question: A person bought a certain quantity of rice at the rate of Rs. 150/quintal. 10% of the rice was spoiled. At what rate(per quintal) should he sell the remaining rice to earn 20% profit.
(A) Rs. 180
(B) Rs. 200
(C) Rs. 210
(D) Rs. 220
(E) NONE
Rationale: Solution: Suppose he buy 1 quintal of Rice in Rs.150.
10% is spoiled so he now have to sell of 90 kg remaining)
.But he has to make a profit of 20%,so he will sell
90kg for Rs. 180
This means his selling price is Rs. 200 per quintal.
Answer: Option B
Answer: (B) Rs. 200
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 30%?
(A) 448
(B) 480
(C) 267
(D) 288
(E) 276
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.192
SP = CP - Loss = 640 - 192 = Rs.448
Answer: A
Answer: (A) 448
Question: If 7log(4*5^2) = x, find x
(A) 12
(B) 11
(C) 10
(D) 14
(E) 13
Rationale: 7(log2^2*5^2)=x
7log(5*2)^2=x
7*2log(5*2)=x
14log10=x
log10 base 10=1
so
14*1=x
x=14
ANSWER:D
Answer: (D) 14
Question: There is 2/5 chance it will rain today.
There is a probability of 1/2 I will find the love of my life today.
What is the probability I will find the love of my life in the rain today?
(A) 2/5
(B) 3/5
(C) 3/10
(D) 1/5
(E) 7/10
Rationale: In order to find the answer we need to multiply the probabilities - 2/5*1/2=1/5
Answer:D
Answer: (D) 1/5
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 27 minutes is:
(A) 9.25
(B) 5.25
(C) 7.25
(D) 6.25
(E) 11.25
Rationale: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(27/60)) km = 11.25 km.
ANSWER:E
Answer: (E) 11.25
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 61 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 55
Rationale: The total number of books is 75.
Let x be the number of books which were loaned out.
65% of books that were loaned out are returned.
35% of books that were loaned out are NOT returned.
Now, there are 61 books, thus the number of un-returned books is 75-61 = 14 books.
0.35x = 14
x = 40
The answer is D.
Answer: (D) 40
Question: Which of the following CANNOT be weighed using a balance scale and these unit weights: 1, 4, 7, and 10
(A) 14
(B) 15
(C) 17
(D) 21
(E) 20
Rationale: A. 13 (can be weighed by keeping weights of 10 and 4)
B. 15 (can be weighed by keeping weights of 10,4 and 1 kg)
C. 17 (can be weighed by keeping weights of 10 and 7 kg)
D. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)
E. 19(cannot be weighed)
E
Answer: (E) 20
Question: The distance from City A to City B is 180 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 60 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
(A) 42
(B) 44
(C) 46
(D) 36
(E) 50
Rationale: The time it takes Cara to drive to City B is 180 / 30 = 6 hours.
Dan needs to take less than 5 hours for the trip.
Dan needs to exceed a constant speed of 180 / 5 = 36 miles per hour.
The answer is D.
Answer: (D) 36
Question: At a school dance, 40% of the students had a date, 70% of the remaining students arrived at the dance with a group. What percentage of the students arrived alone?
(A) 40% of the students arrived alone.
(B) 10% of the students arrived alone.
(C) 42% of the students arrived alone.
(D) 18% of the students arrived alone.
(E) None of these.
Rationale: Explanation:Let total number of students be 100,Then, number of students with a date = 40.Number of students arriving with a group= 70% of 60 = 42.Total number of students arriving alone = 100 – (40 + 42) = 18.Thus, 18% of the students are arriving alone.Answer: Option D.
Answer: (D) 18% of the students arrived alone.
Question: With both inlets open, a water tank will be filled with water in 24 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
(A) 2,000
(B) 10,500
(C) 11,750
(D) 12,000
(E) 13,000
Rationale: The work Done by Inlet A and B together in 1 min = 1/24
The work Done by Inlet A (First Inlet) in 1 min = 1/120
The work Done by Inlet B (Second Inlet) in 1 min = (1/24)- (1/120) = 1/30
DIfference of Work done by B and A = B - A = 50 Cubic meter
i.e. (1/30)- (1/120) = 50 Cubic meter
i.e. Tank = 40*50 = 2000 Cubic Meter
Answer: option A
Answer: (A) 2,000
Question: By selling 8 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 10%?
(A) 6.54
(B) 9.45
(C) 7.34
(D) 6.67
(E) 5.09
Rationale: 90% --- 8
110% --- ?
90/110 * 8 = 6.54
Answer: A
Answer: (A) 6.54
Question: The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?
(A) 20.8
(B) 30.4
(C) 31.8
(D) 32.5
(E) 33.8
Rationale: $69-$48=21$
(21/69)*100=30.434%
ANSWER:B
Answer: (B) 30.4
Question: If x+1/x=5 then find out the value of x^5+1/x^5=?
(A) 2515
(B) 2525
(C) 2535
(D) 2545
(E) 2555
Rationale: given,(x+ 1/x) = 5
x^2 + 1/x^2 = (x+ 1/x)^2 - 2*x*1/x = 5^2 - 2 = 23 -------(1)
x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2)
multiplying (1)& (2), we get
=>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110
=> x^5 + 1/x + x + 1/x^5 = 2530
=> x^5 + 1/x^5 + (x+ 1/x)= 2530
=> x^5 + 1/x^5 + 5 = 2530
=> (x^5+ 1/x^5)= 2525
ANSWER:B
Answer: (B) 2525
Question: A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 4 games?
(A) x + 3y/(n + 3)
(B) x + y/(n + 3)
(C) (x + 3y)/(n + 3)
(D) (nx + 3y)/(n + 4)
(E) (3x + ny)/(n + 3)
Rationale: Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 4 games = (nx+3y)/(n+4)
Hence, correct answer will be (D)
Answer: (D) (nx + 3y)/(n + 4)
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 15 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Area of first rectangle is 15*24=360 hence area of second would be 8x=360x
x=45
answer is D
Answer: (D) 45
Question: What is the unit digit in 14^100?
(A) 0
(B) 5
(C) 2
(D) 3
(E) 6
Rationale: Unit digit in 14^100 = unit digit in [(14^4)^25 ]But unit digit in 14^4=6unit digit 14^100= 6Answer is E
Answer: (E) 6
Question: Sandy invested a certain sum of money at 12% p.a. simple interest for 'n' years. At the end of 'n' years, Sandy got back 7 times the original investment. What is the value of n?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: n* 0.12 * principal + principal = 7 * principal
n * 0.12 = 6
n = 50 years
The answer is E.
Answer: (E) 50
Question: Prabhu purchased 30 kg of rice at the rate of 17.50 per kg and another 30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of 18.60 per kg and made 20 per cent overall profit. At what price per kg did he purchase the lot of another 30 kg rice?
(A) 14.5
(B) 12.5
(C) 15.5
(D) 13.5
(E) None of these
Rationale: Let he purchase of x/kg.
∴ (525 + 30x) × 120⁄100 = 60 × 18.60
⇒ x = 13.5/kg.
Answer D
Answer: (D) 13.5
Question: A BOWLER CAN TAKE MAX. 3WICKETS IN A OVER.IF HE BOWLS 6OVERS IN AN INNINGS, HOW MANY MAXIMUM WICKETS CAN HE TAKE?
(A) 8
(B) 9
(C) 11
(D) 7
(E) 10
Rationale: 10 because after 10 wickets, the innings is complete.
ANSWER:E
Answer: (E) 10
Question: A and C can finish 100,000 piece of work in 15 days each. B can do 30% faster than A and B.Approximately how many days would it take to finish million piece of work with all three working simultaneously?
(A) 40
(B) 46
(C) 51
(D) 42
(E) 54
Rationale: since B is 30% faster , thus it will finish130,000 piece of work in 15 days
in 15 days total piece of work finish by all three will be :
100,000+100,000+130,000 = 330,000
in 30 days:
330,000+330,000 = 660,000
in 45 days:
660,000+330,000 = 990,000
now only 10,000 more piece of work are required to finish , which will take 1 day
thus in all 46 days.
Ans:B
Answer: (B) 46
Question: Find the missing in the series: 60, 54, 45, 41,___
(A) 22
(B) 287
(C) 267
(D) 2767
(E) 2771
Rationale: Answer:C
Answer: (C) 267
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 1/13
(B) 2/23
(C) 5/26
(D) 4/27
(E) 3/23
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: What is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1?
(A) 50
(B) 100
(C) 200
(D) 300
(E) 400
Rationale: Since 500=2^2*5^3 then a number can not have 2 and/or 5 as a factor.
The odd numbers do not have 2 as a factor and there are 250 odd numbers from 1 to 500.
We then need to eliminate the 50 numbers that end with 5, that is 5, 15, 25,...,495.
There are a total of 250 - 50 = 200 such numbers between 1 and 500.
The answer is C.
Answer: (C) 200
Question: Two women started running simultaneously around a circular track of length 1800 m from the same point at speeds of 10 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 72
(B) 74
(C) 76
(D) 78
(E) 80
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 1800 / (30 + 60)5/18 = 1800* 18 / 90 * 5 = 72 seconds.
Answer:A
Answer: (A) 72
Question: Three people have $28, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money?
(A) $72
(B) $85
(C) $99
(D) $101
(E) $202
Rationale: Solution -
Total money distributed is $198. In order to maximize median, one person has to accept $0 and remaining two people share $99 each. Hence median is $99.
ANS C
Answer: (C) $99
Question: Find the length of the altitude of an equilateral triangle of side 3√3 cm.
(A) 4.5cm
(B) 7.2cm
(C) 4.3cm
(D) 5.6cm
(E) 5.7cm
Rationale: Area of the triangle = (√3/4) x (3√3)2 = 27√3. Let the height be h.
Then, (1/2) x 3√3 x h = (27√3/4) X(2/√3) = 4.5 cm.
Ans: A
Answer: (A) 4.5cm
Question: A single discount equivalent to the discount series of 20%, 15% and 10% is?
(A) 31.8
(B) 31.1
(C) 38.8
(D) 31.2
(E) 31.9
Rationale: Explanation:
100*(80/100)*(85/100)*(90/100) = 61.2
100 - 61.2 = 38.8
Answer: C
Answer: (C) 38.8
Question: The ratio 15:25 expressed as percent equals to
(A) 70 %
(B) 60 %
(C) 30 %
(D) 75 %
(E) None of above
Rationale: Explanation:
Actually it means 15 is what percent of 25, which can be calculated as,
(15/25)*100 = 15 * 4 = 60
Answer: Option B
Answer: (B) 60 %
Question: A store owner wants to mix cashews and almonds. Cashews cost 2 dollars per pound and almonds cost 5 dollars per pound. He plans to sell 150 pounds of a mixture. How many pounds of each type of nuts should be mixed if the mixture will cost 3 dollars?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Let x be the number of pounds of cashews
So, 150 - x will represent the number of almonds
Since each pound of the mixture cost 3 dollars, 150 pounds will cost 3 × 150 = 450 dollars
Cost of cashews + cost of almonds = 450
2 × x + (150 - x) × 5 = 450
2x + 150 × 5 - x × 5 = 450
2x + 750 - 5x = 450
2x - 5x + 750 = 450
-3x + 750 = 450
-3x + 750 - 750 = 450 - 750
-3x = -300
-3x/-3 = -300/-3
x = 100
150 - x = 150 - 100 = 50.
Answer C
Answer: (C) 50
Question: How much is 80% of 60 is greater than 4/5 of 25?
(A) 15
(B) 28
(C) 16
(D) 12
(E) 73
Rationale: (80/100) * 60 â€“ (4/5) * 25
48 - 20 = 28
Answer: B
Answer: (B) 28
Question: If x⁄2 + 3⁄4 = 9⁄4, what is the value of x?
(A) –2
(B) –1
(C) 1
(D) 3
(E) 5
Rationale: x⁄2 + 3⁄4 = 9⁄4
Let's multiply both sides by 4.
2x + 3 = 9
2x = 6
x = 3
The answer is D.
Answer: (D) 3
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 180° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 50%
Rationale: ANSWER: E
180° divided by 360° equals 0.5, therefore the sector is equal to 50% of the total
Answer: (E) 50%