mathewhe/aqua_rat huggingface dataset:
Question: P can do the work in 12 days and Q can do the same work in 15 days. If they work together for 4 days, what is the fraction of work that is left?
(A) 1/5
(B) 2/5
(C) 7/15
(D) 11/15
(E) 23/30
Rationale: 4/12 + 4/15 = 1/3 + 4/15 = 9/15 = 3/5 (completed work)
The work that is left is 1 - 3/5 = 2/5
The answer is B.
Answer: (B) 2/5
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
(A) 10,000 square meters
(B) 20,000 square meters
(C) 30,000 square meters
(D) 40,000 square meters
(E) 50,000 square meters
Rationale: Let us first find the distance d jogged
distance = rate ? time = (12 km / hr) ? 30 minutes
= (12 km/hr) ? 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 ? 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer B
Answer: (B) 20,000 square meters
Question: A merchant marks his goods up by 40% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
(A) 8%
(B) 14%
(C) 26%
(D) 15%
(E) 17%
Rationale: Let the price be 100.
The price becomes 140 after a 40% markup.
Now a discount of 10% on 126.
Profit=126-100
26%
answer C
Answer: (C) 26%
Question: A committee of 6 is chosen from 6 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
(A) 275
(B) 700
(C) 1404
(D) 2620
(E) 3510
Rationale: The only cases possible are :
1. 2 men and 4 women : 6C2 * 5C4 = 75
2. 3 men and 3 women: 6C3*5C3 = 200
Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)
Total possible combinations = 75+200 = 275. Thus A is the correct answer.
Answer: (A) 275
Question: The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 40 percent of b, what is the value of m/x?
(A) 2/5
(B) 3/4
(C) 4/5
(D) 5/4
(E) 3/5
Rationale: a/b = 4/5
m/x = (3/5)*5 / (5/4)*4 = 3/5
The answer is E.
Answer: (E) 3/5
Question: A and B can do a piece of work in 6 days. With the help of C they finish the work in 3 days. C alone can do that piece of work in?
(A) 40 days
(B) 16 days
(C) 6 days
(D) 5 days
(E) 40 days
Rationale: C
6 days
C = 1/3 – 1/6 = 1/6 =>6 days
Answer: (C) 6 days
Question: Sheela deposits Rs. 3400 in bank savings account. If this is 15% of her monthly income. What is her monthly income in?
(A) 22666
(B) 20000
(C) 25000
(D) 22235
(E) None of these
Rationale: Explanation :
15% of income = Rs. 3400
100% of income = 3400 X 100/15 = Rs. 22666
Answer : A
Answer: (A) 22666
Question: In a box, there are 2 yellow, 4 grey and 4 white pencils. One pencil is picked up randomly. What is the probability that it is neither yellow nor grey?
(A) 2/5
(B) 1/5
(C) 3/5
(D) 4/5
(E) 5/6
Rationale: Explanation :
Neither yellow nor grey means the pencil drawn is white.
Total number of outcomes = (2+4+4) = 10.
Number of Favourable outcomes = 4 = Number of white pencils.
Hence, Probability of the event = 4/10 = 2/5.
Answer : A
Answer: (A) 2/5
Question: Which is the following is divisible by 11
(A) A)4305
(B) B)4825
(C) C)6594
(D) D)4905
(E) E)4906
Rationale: Explanation:
Sum of first 'n' natural numbers = n(n + 1)/2
Sum of first 9 natural numbers = 11(11 + 1)//2 = 11 x 6 = 66
Sum of first 99 natural numbers = 111(111 + 1)//2 = 111 x 60 = 6660
6660 - 66 = 6594
Answer: Option C
Answer: (C) C)6594
Question: A bag contains 2 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
(A) 19/20
(B) 17/20
(C) 21/25
(D) 8/10
(E) 9/40
Rationale: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.
Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.
P(A) = (2/5) x (6/10) = 6/25.
P(B) = (3/5) x (4/10) = 6/25.
Hence, the required probability is P(A) + P(B) which is nothing but 21/25.
ANSWER:C
Answer: (C) 21/25
Question: If an object travels at five feet per second, how many feet does it travel in one hour?
(A) 1700
(B) 1900
(C) 1400
(D) 1600
(E) 1800
Rationale: If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour.
Answer = 1800
Answer is E.
Answer: (E) 1800
Question: 1/(4-√15)=?
(A) 4+√15
(B) 9-4√5
(C) 9+2√5
(D) 9-2√5
(E) 4+9√5
Rationale: This question requires us to rationalize (fix) the denominator.
For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044
Given: 1/(4-√15)
Multiply top and bottom by the CONJUGATE of 4-√15, which is 4+√15
So, 1/(4-√15) = (1)(4+√15)/(4-√15)(4+√15)
= (4+√15)/(1)
= 4+√15
=
A
Answer: (A) 4+√15
Question: Which of the following options is an appropriate approximate value in the following equation’? 625.3 of 165.83+42% of 1560= ? - 625.7
(A) 104875.3
(B) 12825.3
(C) 1034825.3
(D) 104425.3
(E) 104825.3
Rationale: 625.3 of 165.83+42% of 1560= ? - 625.7
103693.5+506.1= ? - 625.7
103693.5+506.1 + 625.7= ?
≈ 104825.3
Answer E
Answer: (E) 104825.3
Question: 9 neighbors are to split the cost of topsoil. The cost of the 5 truck loads of dirt was $690.47. What is the least amount of money (in whole number of dollars) that they must add to bill if they wants to split this money evenly among his nine neighbors?
(A) 690.48
(B) 690.49
(C) 690.5
(D) 690.51
(E) 690.52
Rationale: If the bill was $690.47 dollars, how much money should be removed with 1 cent as the smallest unit?
This is equivalent to finding the first number that is divisible by 9 that occurs after 690.47.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 6+9+0+4+7 = 26. If you add 1 , the number is divisible by 9 (26 +1). 27 is divisible by 9.
Hence, we need to add 1 cent from this number for it to be divisible by 9.
Correct Option : A
Answer: (A) 690.48
Question: A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked at 7 miles per hour for 2 hours. How many miles in total did she walk?
(A) 24
(B) 52
(C) 58
(D) 60
(E) 62
Rationale: First day - 18 miles with 3 miles per hours then total - 6 hours for that day
Second day - 4 miles per hour and 5 hours - 20 miles
Third day - 7 miles per hour and 2 hours - 14 miles
Total 18+20+14 = 52
Answer: option B.
Answer: (B) 52
Question: At the end of the first quarter, the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 60 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?
(A) 20%
(B) 25%
(C) 30%
(D) 33.33%
(E) 40%
Rationale: Another method is to use the formula for 2 successive percentage changes:
Total = a + b + ab/100
60 = 20 + b + 20b/100
b = 33.33
Answer (D)
Answer: (D) 33.33%
Question: A man can row upstream at 60 kmph and downstream at 90 kmph, and then find the speed of the man in still water?
(A) 75 kmph
(B) 65 kmph
(C) 30 kmph
(D) 73 kmph
(E) 65 kmph
Rationale: US = 60
DS = 90
M = (60 + 90)/2 = 75
Answer:A
Answer: (A) 75 kmph
Question: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III. If x is positive, y must be positive
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D
2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E
A) I only
B) II only
C) III only
D) I and II
E) II and III
Answer B
Answer: (B) II only
Question: Six years back, a father was 42 years older than his son. At present the father is 4 times as old as the son. How old will the son be three years from now?
(A) 20 years
(B) 19 years
(C) 18 years
(D) 17 years
(E) 16 years
Rationale: Using linear equations to convert the word problem:
** F = fathers current ageS = sons current age
#1 Six years back, a father was 42 years older than his son: F-6 = 42 + (S - 6)
#2 At present the father is 4 times as old as the son: F = 4*S
How old will the son be three years from now?: S + 3 = ?
With two variables and two linear equations we are able to solve the problem:
(S*4) - 6 = 42 +S -6
3S=42
S = 14
S + 3 = 14 + 3 = 17
Answer: D
Answer: (D) 17 years
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1904?
(A) 1700
(B) 2777
(C) 2889
(D) 27670
(E) 2771
Rationale: 1904 = P [1 + (5*12/5)/100]
P= 1700.Answer:A
Answer: (A) 1700
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 340 m long?
(A) 56 sec
(B) 42 sec
(C) 45 sec
(D) 48 sec
(E) 50 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 340 = 700 m
Required time = 700 * 2/25 = 56 sec
ANSWER:A
Answer: (A) 56 sec
Question: Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he
(A)  broke even
(B)  lost 4 cents
(C)  gained 4 cents
(D)  lost 10 cents
(E)  gained 10 cents
Rationale: 20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
The answer is (A)
Answer: (A)  broke even
Question: If 5 (A's capital) = 7 (B's capital) = 9 (C's capital). Then the ratio of their capitals is?
(A) 63:55:35
(B) 63:45:38
(C) 62:45:35
(D) 63:45:35
(E) 63:44:35
Rationale: 5A = 7B = 9C
A:B:C = 1/5:1/7:1/9
= 63:45:35
Answer: D
Answer: (D) 63:45:35
Question: At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 720
(D) 32
(E) 120
Rationale: Has to be C.
Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle
hence (7-1)! = 6!= 720
Answer: (C) 720
Question: Find: S.l on Rs 68000 at 16 2/3%per annum for 9 months
(A) 6500
(B) 7500
(C) 8500
(D) 9500
(E) 9000
Rationale: Explanation:
P = 68000, R =50/3% & T=9 months (3/4 years)
S.I=(68000 *50/3 * 3/4)/100=Rs.8500
ANSWER IS C
Answer: (C) 8500
Question: If four coins are tossed, the probability of getting two heads and two tails is ?
(A) 3/8
(B) 3/5
(C) 3/2
(D) 3/1
(E) 3/9
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer:A
Answer: (A) 3/8
Question: Worker A takes 5 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
(A) 20/9
(B) 40/9
(C) 50/9
(D) 60/9
(E) 10/3
Rationale: one day work of A = 1/5
one day work of B = 1/10
so one day work of A and B together = 1/5 + 1/10 = 3/10
so total days required = 10/3
ANSWER:E
Answer: (E) 10/3
Question: A consignment of 20 picture tubes contains 5 defectives. Two tubes are selected one after the other at random. The probability that both are defective assuming that the first tube is not replaced before drawing
the second, would be:
(A) 1/16
(B) 1/19
(C) 1/4
(D) 1/3
(E) none of these
Rationale: Probability of drawing a defective tube in first draw is 5/20
Probability of drawing a defective tube in second draw (without replacing first tube) is 4/19.
Therefore probability of getting both defective is = (5/20)*(4/19) = 1/19
ANSWER:B
Answer: (B) 1/19
Question: A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 50 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
(A) 26%
(B) 30%
(C) 32%
(D) 34%
(E) 40%
Rationale: 1. 20% of 400=80 pounds of decaffeinated coffee
2. 50% of 100=50 pounds of decaffeinated coffee
3. Wt have 130 pounds of decaffeinated out of 500 pounds, that means 130/500*100%=26%. The correct answer is A.
Answer: (A) 26%
Question: A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. The rate per annum is?
(A) 5 5/9 %
(B) 5 5/6 %
(C) 5 8/9 %
(D) 5 1/9 %
(E) 5 5/5 %
Rationale: Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 3 years.
Rate = (100 * x) / (x * 6 * 3) = 5 5/9 %.
Answer: A
Answer: (A) 5 5/9 %
Question: By selling 12 pencils for a rupee a man loses 12%. How many for a rupee should he sell in order to gain 18%?
(A) 12
(B) 9
(C) 10
(D) 89
(E) 81
Rationale: 88% --- 12
112% --- ?
88/112 * 12 = 9
Answer: A
Answer: (A) 12
Question: On a certain island, 5% of the 10000 inhabitants are one-legged and half of the others go barefooted. What is the least number of Shoes needed in the island?
(A) 9000
(B) 10000
(C) 9500
(D) 9700
(E) 9900
Rationale: one-legged =5% of 10000=500
remaining=10000-500=9500
barefooted=9500/2=4750
remaining people= 9500-4750=4750
hence required number of shoes= 4750*2+500*1=10000
ANSWER:B
Answer: (B) 10000
Question: In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
(A) 5/6
(B) 5/9
(C) 5/0
(D) 5/3
(E) 5/8
Rationale: Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer: Option A
Answer: (A) 5/6
Question: A sauce is composed of tomato, chilly, and soybean. To make 10 kg of sauce containing twice as much tomato as chilly, and three times as much chilly as soybean how many grams of chilly is required? (1kg=1000gm)
(A) 1200gm
(B) 700gm
(C) 600gm
(D) 150gm
(E) 1000gm
Rationale: 1kg=1000gm
10kg=10,000
tomato=2 chilly
chilly=3 soybean
tomato+chilly+soybean=10,000
2 chilly+chilly+1/3 chilly=10,000
10 chilly=10,000
chilly=1000gm
Answer is E
Answer: (E) 1000gm
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.7
II. 9.2
III. 9.7
(A) I only
(B) I and II only
(C) II only
(D) III only
(E) I and III only
Rationale: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
only 9.7 lies in the range of 2SD from mean
Answer: Option B
Answer: (B) I and II only
Question: Find the product of the localvalue and absolutevalue of 1 in 20168?
(A) 100
(B) 110
(C) 151
(D) 120
(E) 140
Rationale: Local value of 1 = 1 x 100 = 100
Place value of 1 = 1
There fore = 1 x 100 = 100
A
Answer: (A) 100
Question: A motor cyclist participant of a race says "We drove with the speed of 15 miles an hour one way, but while returning because of less traffic we drove on the same route with 21 miles per hour." What was their average speed in the whole journey?
(A) 10 miles/hour
(B) 12 miles/hour
(C) 11 miles/hour
(D) 13 miles/hour
(E) 17.5 miles/hour
Rationale: 2xy/x+y=17.5 miles/hour
ANSWER:E
Answer: (E) 17.5 miles/hour
Question: On multiplying a number B by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result.
(A) 104345
(B) 107375
(C) 108385
(D) 109395
(E) 105355
Rationale: The only thing you actually know about the correct number B is that it is divisible by 153 and has 5 as a factor.
You should immediately try to find the factors of 153 and look for them in the options.
153 = 9*17
Divisibility by 9 is easy to check. Only (D) satisfies.
Answer: (D) 109395
Question: P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 336 is divided among them . What is R's share?
(A) 96
(B) 120
(C) 134
(D) 144
(E) None of these
Rationale: Explanation :
The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12
= (12+30) : 4*12 : 3*12
=(4+10) : 4*4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
R's share = 336 * (6/21) = 96. Answer : Option A
Answer: (A) 96
Question: The income derived from a Rs. 100, 13% stock at Rs. 105,is :
(A) Rs. 5
(B) Rs. 8
(C) Rs. 13
(D) Rs. 18
(E) Rs. 19
Rationale: Solution
Income on Rs. 100 stock = Rs. 13
Answer C
Answer: (C) Rs. 13
Question: If y = 2 + 2K and y≠0y≠0, then 5/y + 3/y + 1/y + 1/y = ?
(A) 1/(8+8k)
(B) 5/(1+k)
(C) 1/(8+k)
(D) 4/(8+k)
(E) 4/(1+k)
Rationale: 5/Y + 3/Y + 1/Y + 1/Y
= 10/Y
= 10/(2 + 2K)
= 5/(1 + K)
ANSWER:B
Answer: (B) 5/(1+k)
Question: If there are 6 men and 55 tasks , how many tasks will be left undone if they perform equal number of tasks?
(A) 5
(B) 2
(C) 3
(D) 1
(E) 4
Rationale: There are 6 men
There are 55 tasks
If they perform equal number of tasks, divide 55 by 6 and the remainder will be the number of tasks left undone
55 = (6 x 9) + 1
So 1 task is left undone
ANSWER D
Answer: (D) 1
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 900 m long?
(A) 266 Sec
(B) 210 Sec
(C) 776 Sec
(D) 166 Sec
(E) 997 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2100 m
T = D/S
T = 2100/10
T = 210 Sec
Answer: B
Answer: (B) 210 Sec
Question: The expression (a+b+c)10 is expanded and simplified. How many terms are in the resulting
expression?
(A) 30
(B) 44
(C) 55
(D) 66
(E) 133
Rationale: (a+b+c)10 = [(a+b)+c]10. Let x = a+b. We see that (x+c)10 = x10+10x9c+
+ c10 has 11 distinct terms. Also, the ith term of this expansion has 11 - i distinct terms
(since x10-i = (a + b)10-i has 11 - i distinct terms). Hence there are 11 + 10 +...+ 1 = 66
terms in this expansion.
correct answer D
Answer: (D) 66
Question: How many integer values Q are there for x such that 1 < 3x + 5 < 17?
(A) Two
(B) Three
(C) Four
(D) Five
(E) Six
Rationale: 1 < 3x + 5 < 17
=> -4 < 3x < 12
=> -4/3 < x < 4
x can take integer values Q=-1,0 , 1 , 2 , 3
Answer D
Answer: (D) Five
Question: In a 500 m race, the ratio of speeds of two runners P and Q is 3:5. P has a start of 200 m then the distance between P and Q at the finish of the race is:
(A) Both reach at the same time
(B) P wins by 100 m
(C) Q wins by 50 m
(D) Q wins by 100 m
(E) None of these
Rationale: Explanation :
When P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5.
According to question P has already covered 200 m when Q is starting at starting point and Q needs to cove 300 m more mean while P covers this 300 m when Q can cover 500 m. So, both P and Q will reach the finishing point at the same time.
Thus, Both reach at the same time.
Answer : A
Answer: (A) Both reach at the same time
Question: Andy solves problems 75 to 125 inclusive in a Math exercise. How many problems does he solve?
(A) 53
(B) 52
(C) 51
(D) 50
(E) 49
Rationale: 125-75+1= 51
'C' is the answer
Answer: (C) 51
Question: 0,1,2.9,5.61,9.05,?
(A) 11.15
(B) 12.15
(C) 13.15
(D) 14.15
(E) 15.15
Rationale: The series is 0, 1, 2.9, 5.61, 9.05, ...
Fisrt oder differences are 1, 1.9, 2.71, 3.44, ...
Second order differences are 0.9, 0.81, 0.73, ...
Note that the second order differences are powers of 0.9 (0.9, 0.81, 0.729, ...), rounded off to two decimal digits. So next term in second order difference is 0.9^4 = 0.6561 = 0.66. Then, the next term in first order difference is 3.44+0.66 = 4.1. So, the term in the series is 9.05+4.1 = 13.15
ANSWER:C
Answer: (C) 13.15
Question: There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
(A) 21
(B) 52
(C) 45
(D) 63
(E) 23
Rationale: List down possibilities: From only 1 box all the way to all 6
If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.
If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.
If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.
If all 6 boxes have green balls, there is just 1 possibility.
Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21.
Ans: A
Answer: (A) 21
Question: How long does a train 110 m long traveling at 90 kmph takes to cross a bridge of 170 m in length?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: D = 110 + 170 = 280 m
S = 90 * 5/18 = 50/2
T = 280 * 2/50= 11.2 sec
Answer: D
Answer: (D) sec
Question: A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 6 people to travel x miles if he decides to give them a 50% discount?
(A) 3xr/100
(B) 3x/200r
(C) 3r/200x
(D) 3xr/200
(E) xr/600
Rationale: 6xr/2 is in cents - 6xr/200 dollars = 3xr/100 dollars
Answer : A
Answer: (A) 3xr/100
Question: Nine persons went to a hotel for taking their meals. Eight of them spent 16 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?
(A) 115
(B) 117
(C) 119
(D) 122
(E) 153
Rationale: Let the average expenditure of all the nine be x.
Then, 16 × 8 + (x + 8) = 9x or 8x = 136 or x = 17.
∴ Total money spent = 9x = (9 × 17) = 153.
Answer E
Answer: (E) 153
Question: In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase?
(A) $32
(B) $50
(C) $320
(D) $400
(E) $500
Rationale: Property tax as a percentage of its assessed value = 8%
Increase in assessed value of the property = 24000 - 20000 = 4,000 $
Increase in property tax = (8/100)* 4000 = 320 $
Answer C
Answer: (C) $320
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) 100
(B) 110
(C) 120
(D) 130
(E) 140
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: Option C
Answer: (C) 120
Question: A fruit vendor purchased 20 dozens of apples at $15 per dozen. But one-fourth of the apples were rotten and had to be thrown away. He sold two-third of the remaining apples at a$22.50 per dozen. At what price per dozen should he sell the remaining apples to make neither a profit nor a loss?
(A) $17
(B) $14
(C) $15
(D) $18
(E) $20
Rationale: C
$15
CP of 20 dozen of apples = 15 * 20 = $300
Number of apples which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining apples = (2/3 * 15) * 22.5 = $225
SP of remaining 5 dozens of apples to make no profit and no loss =(300 - 225) = $75.
SP of 1 dozen apples = 75/5 = $15.
Answer: (C) $15
Question: A person crosses a 1080 m long street in 10 minutes. What is his speed in km per hour?
(A) 4.1
(B) 6.4
(C) 4.8
(D) 5.4
(E) 5.5
Rationale: Speed = 1080/(10x60) m/sec
= 1.8 m/sec.
Converting m/sec to km/hr =1.8 x(18/5) km/hr
= 6.4 km/hr.
ANSWER :B
Answer: (B) 6.4