mathewhe/aqua_rat huggingface dataset:
Question: Albert buys 4 cows and 9 cows for $13,400. If he sells the cows at 10% profit and the cows at 20% profit, then he earns a total profit of $1880. The cost of a cow is:
(A) 1000
(B) 3000
(C) 2000
(D) 4000
(E) 5000
Rationale: C
2000
Let C.P. of each cow be $x and C.P. of each cow be $y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each cow = $2000.
Answer: (C) 2000
Question: A wheel that has 4 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 49
(B) 4
(C) 12
(D) 6
(E) 27
Rationale: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 4 :: 21 : x 14 * x = 4 x 21
x =	(4 x 21)/14
x = 6.
Answer is D.
Answer: (D) 6
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 94 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 10
Rationale: Total Distance = 94 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 90 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken to meet Brad after Brad Started = 90 / 10 = 9 hrs
Distance traveled by Maxwell = Maxwell's speed * time taken = 4 * 9 = 36+4 = 40 kms...
Therefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 40 /4 = 10 hrs ... Answer E
Answer: (E) 10
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1230
(B) 1340
(C) 1350
(D) 1540
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
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) 10
(B) 99
(C) 87
(D) 66
(E) 12
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer: A
Answer: (A) 10
Question: Two children want to walk together to visit their aunt, who lives exactly 8 blocks north and 7 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 15 blocks. How many different 15-block routes may they take to travel the shortest possible distance to their aunt’s house?
(A) 15!*8!*7!
(B) 15!*8*7
(C) 23!/(8!*7!)
(D) 15!/(8!*7!)
(E) 15/(8*7)
Rationale: If they need to walk 8 blocks north and 7 blocks east, we can express this route as NNNNNNNNEEEEEEE. The question thus asks us how many ways we can arrange those letters.
The number of arrangements of 15 things is 15!
We then divide by the repetitions of N's and E's, which are 8! and 7! respectively.
The number of walking routes is 15!/(8!*7!).
The answer is D.
Answer: (D) 15!/(8!*7!)
Question: If the square root of 1,600 is 40, then what is 40 squared?
(A) 1,600
(B) 16
(C) 4
(D) 440
(E) 64,000
Rationale: A number squared is a number multiplied by itself
Ex) 4 squared is 16 because 4*4=16
The square root of a number is a number, that if squared, would equal the number you're trying to find the square root of.
Ex) What is the square root of 16? The square root of 16=4, so 4 squared equals 16
So to solve this equation you would do:
The square root of 1,600=40, so 40 squared equals 1,600
(A)
Answer: (A) 1,600
Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of $ 12,000 after 3 years at the same rate?
(A) 2160
(B) 3120
(C) 3972
(D) 6240
(E) None of these
Rationale: Let P = $ 100. Then, S.I. $. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = $ 12000. T = 3 years and R = 10% p.a.
CI = 3972
ANSWER C
Answer: (C) 3972
Question: A can complete a project in 20 days and B can complete the same project in 40 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
(A) 18 days
(B) 20 days
(C) 26.67 days
(D) 16 days
(E) 12 days
Rationale: Let X = the number of days taken to complete the project.
The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/40).
(1/20)*(x-10) + (1/40)*(x) = 1
(x/20) + (x/40) - (10/20) = 1
3x/40 = 3/2
x = 20
Therefore, the answer is B: 20.
Answer: (B) 20 days
Question: How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
(A) 5040
(B) 2548
(C) 300
(D) 547
(E) 3000
Rationale: LOGARITHMS' contains 10 different letters.
Required number of words	= Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= (10 x 9 x 8 x 7)
= 5040.
ANSWER A
Answer: (A) 5040
Question: Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.65%, what fraction of the products was checked by worker y?
(A) 1/5
(B) 1/2
(C) 2/3
(D) 1/4
(E) 2/5
Rationale: x: 0.5% is 0.15%-points from 0.65%.
y: 0.8% is 0.15%-points from 0.65%.
Therefore the ratio of products checked by y:x is 1:1.
Thus, worker y checked 1/2 of the products.
The answer is B.
Answer: (B) 1/2
Question: 50 men took a dip in a water tank 30 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be:
(A) 20 cm
(B) 25 cm
(C) 33.3 cm
(D) 50 cm
(E) None of these
Rationale: Explanation:
Total volume of water displaced =(4 x 50) m3 = 200 m3
Rise in water level = 200/30Ã—20= 0.333m = 33.3cm
Answer: C
Answer: (C) 33.3 cm
Question: The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers?
(A) 29
(B) 70
(C) 92
(D) Cannot be determined
(E) None of these
Rationale: Explanation:
Let the ten's digit be x and units digit by y.
Then,
(10x + y) - (10y + x) = 63
9(x - y) = 63
x - y = 7
Thus, none of the numbers can be determined.
ANSWER IS D
Answer: (D) Cannot be determined
Question: Mrs. Napier has 26 stickers to give to 4 students for a reward. How many
stickers will each student get? Will there be any stickers left over?
(A) 6-5
(B) 5-4
(C) 3-6
(D) 2-3
(E) 2-8
Rationale: 26/4 = 2 R 5 Mrs. Napier will give each student 6 stickers and there
will be 5 left over.
correct answer A
Answer: (A) 6-5
Question: A motor pool has 300 vehicles of which 30 percent are trucks. 15 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
(A) 165%
(B) 90%
(C) 60%
(D) 55%
(E) 10%
Rationale: Trucks = 30% of 300 = 90
Other Vehicles (Excluding Trucks) = 300-90 = 210
Diesel Vehicle = 15% of 300 = 45 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 45-15 = 30
Trucks that are NOT diesel = 90 - 15 = 75
Other Vehicles that are NOT diesel Vehicles = 210-30 = 180
Required % = (180/300)*100 = 60%
Answer: option C
Answer: (C) 60%
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) 2000
(B) 2098
(C) 2028
(D) 2218
(E) 2021
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.Answer: A
Answer: (A) 2000
Question: As a bicycle salesperson, David earns a fixed salary of $40 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>3
(A) I only
(B) III only
(C) II,III only
(D) I,III only
(E) II only
Rationale: II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>3 --> if David sold 3 bicycles this week then this week he earned 40+3*6=$58, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $40. So y must be more than 3;
I. y<3x --> is not always true.
Answer: C
Answer: (C) II,III only
Question: In a group of 100 people, 55 have visited Iceland and 43 have visited Norway. If 61 people have visited both Iceland and Norway, how many people have visited neither country?
(A) 60
(B) 61
(C) 62
(D) 63
(E) 64
Rationale: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:
100= 55 + 43 - 61 + (# in Neither Group)
=63
The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.
D
Answer: (D) 63
Question: In a race of 4Kms A beats B by 100m or 25 seconds, then time taken by A is
(A) 15 min 8 sec
(B) 16 min 15 sec.
(C) 8 min 15 sec.
(D) 10 min 17 sec.
(E) 10 min 18 sec.
Rationale: s=d/t
where t=d/s
therefore 4000*25/100=1000sec
convert 1000sec into min
we get 16min 15sec
ANSWER:B
Answer: (B) 16 min 15 sec.
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
(A) 3 9/87 hrs
(B) 3 9/27 hrs
(C) 3 9/17 hrs
(D) 3 2/17 hrs
(E) 3 9/11 hrs
Rationale: Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
Answer: C
Answer: (C) 3 9/17 hrs
Question: The ratio, by volume, of soap to alcohol to water in a certain solution is 6:30:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 150 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
(A) 1200
(B) 1300
(C) 1500
(D) 1800
(E) 1900
Rationale: soap:alcohol
Initial ratio soap:alcohol: water --> 6:30:90
Initial soap:alcohol = 6/30 =6:30
after doubled soap:alcohol =2* 6/30 = 12/30=12:30
Initial soap:water = 6/90=6:90
after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360
After soap: alcohol:water --> 12:30:360
given alcohol 150 cubic centimeter.
ratio is 60:150:1800 (12:30:360)
For 150 cubic centimeter of Alcohol ---1800 cu cm water is required.
Answer-D
Answer: (D) 1800
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) 337
(B) 278
(C) 189
(D) 271
(E) 211
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
Answer:C
Answer: (C) 189
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: Sol. Required change = (20*100)/(100-20)=25%
C
Answer: (C) 25%
Question: In a camp, there is a meal for 120 men or 200 children. If 100 children have taken the meal, how many men will be catered to with remaining meal?
(A) 41
(B) 30
(C) 35
(D) 60
(E) 49
Rationale: D
60
There is a meal for 200 children.
100 children have taken the meal.
Remaining meal is to be catered to 100 children.
Now, 200 children 120 men.
100 children = (120/200)x 100 = 60 men.
Answer: (D) 60
Question: If Henry were to add 5 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?
(A) 25
(B) 40
(C) 64
(D) 80
(E) 96
Rationale: 7/8x-3/4x=5 galls
1/8*x=5gallons
x=40 gallons
ANSWER:B
Answer: (B) 40
Question: During a recent track meet, Peter ran x meters of the 100 meter dash in 4 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
(A) 4zx
(B) 4z/x
(C) 4x/z
(D) 4/xz
(E) xz/4
Rationale: Speed of Peter = x/4 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/4) = 4z/x
Option B
The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: (B) 4z/x
Question: A person want to give his money of $3600 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?
(A) $2000
(B) $1200
(C) $2500
(D) $1800
(E) $1600
Rationale: B's share = 3600*3/9 = $1200
Answer is B
Answer: (B) $1200
Question: On decreasing the price of a cooler by 25 %, its sale is increased by 50%. The effect on the revenue is?
(A) 4 % decrease
(B) 12.5 % increase
(C) 16% decrease
(D) 16% increase
(E) none of these
Rationale: Net% change in revenue
= ( x + y + xy/100) %
= [-25 + 50+ ( -25 x 50)/100]% or 12.5%
ANSWER:B
Answer: (B) 12.5 % increase
Question: The average (arithmetic mean) of eight numbers is 47.1. If the sum of half of these numbers is 158.4, what is the average of the other half?
(A) 12.8
(B) 24.2
(C) 54.6
(D) 72.1
(E) 96.8
Rationale: arithmetic mean = sum / total numbers
sum = 47.1 * 8 = 376.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 376.8-158.4 = 218.4
Arithmetic mean of the 4 nos = 218.4/4 = 54.6
Hence, C is the answer.
Answer: (C) 54.6
Question: In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?
(A) None of these
(B) 64
(C) 120
(D) 36
(E) 22
Rationale: Explanation :
The word 'DETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)
The 3 vowels(EAI) must occupy only the odd positions.
Let's mark the positions as (1) (2) (3) (4) (5) (6).
Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.
Hence, number of ways to arrange these vowels = 3P3
= 3! = 3 x 2 x 1 = 6
Now we have 3 consonants(DTL) which can be arranged in the remaining 3 positions in any order
Hence, number of ways to arrange these consonants = 3P3
= 3! = 3 x 2 x 1 = 6
Total number of ways
= number of ways to arrange the vowels x number of ways to arrange the consonants
= 6 x 6 = 36. Answer : Option D
Answer: (D) 36
Question: Machine R takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine R to make 40 widgets?
(A)  5
(B)  6
(C)  8
(D)  10
(E)  12
Rationale: i approached this one by plugging in numbers...started with C.
if 40 are made in 8 hours, then 20 are made in 4 hours. so time of R is 4, and time of B is 2.
rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and R reduces the time - the total # of widgets made will be even higher.
now between D and E -> try only one ..if it doesn't work, then the other one is the answer.
i picked E:
12h to make 40 widgets, and 6 hours to make 20. this is the time of R. time of B=4 hours.
20/6 + 20/4 = 10/3 + 20/4
find LCM of 3 and 4 = 12. multiply first by 4, and second by 3:
40+60/12 = 100/12
divide by 4:
25/3
so this is the rate given.
E is the correct answer
Answer: (E)  12
Question: 3 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
(A) 10
(B) 15
(C) 3
(D) 9
(E) 12
Rationale: the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 3(3-1)/2 = 3*2/2 = 6/2 = 3
=> the answer is C(3)
Answer: (C) 3
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
(A) 2:7
(B) 5:2
(C) 7:2
(D) Data inadequate
(E) None of these
Rationale: Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
ANSWER:E
Answer: (E) None of these
Question: Out of a classroom of 7 boys and 4 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions?
(A) 2/165
(B) 4/165
(C) 7/165
(D) 2/33
(E) 5/33
Rationale: The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 4C3=4.
P(only girls are chosen)=4/165
The answer is B.
Answer: (B) 4/165
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 2000
(B) 2978
(C) 2682
(D) 2688
(E) 2786
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 =>
Rs.2000
Answer:A
Answer: (A) 2000
Question: . Star question:
If f(1)=4 and f(x+y)=f(x)+f(y)+7xy+4,then f(2)+f(5)=?
(A) 125
(B) 977
(C) 289
(D) 1077
(E) 111
Rationale: Let x =1 and y = 1
f(1 + 1) = f(1) + f(1) + 7 x 1 x 1 + 4 ⇒⇒ f(2) = 19
Let x =2 and y = 2
f(2 + 2) = 19 + 19 + 7 x 2 x 2 + 4 ⇒⇒ f(4) = 70
Let x = 1 and y = 4
f( 1 + 4) = 4 + 70 + 28 + 4 = 106
f(2) + f(5) = 125
Answer:A
Answer: (A) 125
Question: The perimeter of a square is 52 m. Find the area of the square.
(A) 132 m².
(B) 169 m².
(C) 146 m².
(D) 189 m².
(E) 269 m².
Rationale: Perimeter of square = 52 m
But perimeter of square = 4 × side
Therefore, 4 × side = 52 m
Therefore, side= 52/4 m = 13m
Now, the area of the square = (side × side)
Therefore, area of the square = 13 × 13 m² = 169 m².
ANSWER :B
Answer: (B) 169 m².
Question: A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent should the number of hours worked be increased?
(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) 100%
Rationale: Assume
Hours Worked: 10 hours
Hourly Wage: 10 $
Weekly Wage: 100 $
After decrease of 20 % in Hourly Wage would become 8 $
Hours Worked would have to be 12.5 hours in order to maintain Weekly Wage of 100 $
% increase in number of hours worked = (12.5 - 10 ) / 10
= 0.25 * 100
= 25%
Answer is C
Answer: (C) 25%
Question: If xy > 0, which of the following must be negative?
(A) -x/-y
(B) x/y
(C) -x/y
(D) 2xy
(E) x+y
Rationale: - / + = -
Answer : C
Answer: (C) -x/y
Question: Of the goose eggs laid at a certain pond, 1/4 hatched and 4/5 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
(A) 1200
(B) 1300
(C) 1400
(D) 1500
(E) 1600
Rationale: Let x be the number of eggs that were laid.
(2/5)(4/5)(1/4)x = 120
(8/100)x = 120
x = 1500
The answer is D.
Answer: (D) 1500
Question: It takes 40 identical printing presses 12 hours to print 500,000 papers. How many hours would it take 30 of these printing presses to print 500,000 papers?
(A) 14
(B) 15
(C) 16
(D) 18
(E) 20
Rationale: 40 printing presses can do 1/12 of the job each hour.
30 printing presses can do 3/4*1/12 = 1/16 of the job each hour.
The answer is C.
Answer: (C) 16
Question: 10 % of 2 is equal to
(A) 0.2
(B) 0.4
(C) 0.6
(D) 0.7
(E) 0.9
Rationale: 10 % of 2 = (10 / 100) * 2 = 0.2
Answer: Option A
Answer: (A) 0.2
Question: 3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is
(A) 1 years
(B) 2 years
(C) 3 years
(D) 4 years
(E) None
Rationale: Sol.
Total age of 5 members, 3 years ago = (17 x 5)years = 85 years.
Total age of 5 members now = (85 + 3 x 5)years = 100 years.
Total age of 6 members now = (17 x 6)years = 102 years.
∴ Age of the baby = (102 - 100)years = 2 years
Answer B
Answer: (B) 2 years
Question: If a quarter kg of onions costs 50 paise, how many paise will 100 gm cost?
(A) 20 paise
(B) 65 paise
(C) 56 paise
(D) 87 paise
(E) 15 paise
Rationale: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 50 : x
250 * x = (100 * 50)
x = (100 * 50) / 250
x = 20
ANSWER: A
Answer: (A) 20 paise
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 5 employees to 2 different offices?
(A) 30
(B) 32
(C) 31
(D) 33
(E) 35
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2*2=2^5=32.
Answer: B.
Answer: (B) 32
Question: A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 227
(B) 266
(C) 230
(D) 500
(E) 271
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 48 = 50/3
3(x + 300) = 2400 è x = 500m.
Answer: D
Answer: (D) 500
Question: A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
(A) $40 and $42
(B) $39 and $41
(C) $38 and 40
(D) $37 and $39
(E) $36 and $37
Rationale: let tip=t
meal cost=35.50
range of tip = from 10% of 35.5 to 15% of 35.5 = 3.55 to 5.325
hence range of amount paid= 35.5+T= 39.05 to 40.825
ANSWER:B
Answer: (B) $39 and $41
Question: The average of 2,7,6 and x is 5. Find the value of x?
(A) 10
(B) 8
(C) 12
(D) 15
(E) 5
Rationale: average = (2+7+6+x)/4 = 5
x = 5
Answer is E
Answer: (E) 5
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 16 2/3%
(B) 30%
(C) 33 1/3%
(D) 33 1/6%
(E) 33 1/9%
Rationale: Explanation:
675 ---- 225
100 ---- ? => 33 1/3%
ANSWER IS C
Answer: (C) 33 1/3%
Question: The difference between the local value and the face value of 7 in the numeral 32675149 is?
(A) 75142
(B) 64851
(C) 5149
(D) 69993
(E) None of these
Rationale: (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
D)
Answer: (D) 69993
Question: Lola rolls a die 3 times. What is the probability that she gets a 4 on the last one of the 3 rolls?
(A) 215/216
(B) 216
(C) 1/216
(D) none
(E) 2
Rationale: the die has 6 sides and it was rolle 3 times, then 6*6*6=216
the number of ways to get 4 is 1
then 1/216
the probability would be
1-1/216=215/216
Answer A
Answer: (A) 215/216
Question: A can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: A's 1day work=1/20;
B's 1day work=1/30;
(A+B) 1day work=(1/20+1/30)=1/12;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 1/12 work in 1 day...
They did 2/3 w in 8 days.
Total days=(8+10) = 18
ANSWER:A
Answer: (A) 18
Question: Calculate the share of profit that belongs to Mark in a partnership business he invested Rs 31,000. His partner Abel invested RS.36,800 and the business made a profit of Rs 18,400.
(A) 8499.98
(B) 8489.98
(C) 8412.98
(D) 8732.98
(E) 2112.98
Rationale: Explanation:
Ratio of their shares = 31,000 : 36,800 = 155 : 184.
Mark's share = Rs. (18400 * 155/339) = Rs. 8412.98.
Answer: C) 8412.98
Answer: (C) 8412.98