mathewhe/aqua_rat huggingface dataset:
Question: If p is an even integer and q is an odd integer, which of the following must be an even integer?
(A) 2p-q
(B) 3p+2q-1
(C) p+q
(D) 3p-q
(E) 3p-2q
Rationale: p is even; for this assume p=2
q is odd; for this assume q = 1
(2*2)-1 = 3 Odd
(3*2)+(2*1)-1 = 7 Odd
2+1 = 3 Odd
(3*2)-1 = 5 Odd
(3*2)-(2*1) = 4 Even
Answer:E
Answer: (E) 3p-2q
Question: Difference between the length &breadth of a rectangle is 5 m. If its perimeter is 45 m, then its area is??
(A) 500 m^2
(B) 2340 m^2
(C) 2520 m^2
(D) 2556 m^2
(E) 2534 m^2
Rationale: We have: (l - b) = 5 and 2(l + b) = 90 or (l + b) = 45
2l = 50 => l = 25 & b = 20
area = 25 * 20 = 500 m^2
Answer : A
Answer: (A) 500 m^2
Question: Carl is facing very difficult financial times and can only pay the interest on a $20,000 loan he has taken. The bank charges him a quarterly compound rate of 5%. What is the approximate interest he pays annually?
(A) $1200
(B) $2000
(C) $2150
(D) $4000
(E) $12000
Rationale: Usually, you are given the annual rate of interest and it is mentioned that it is annual rate.
The bank charges him a quarterly compounded ANNUAL rate of 20%.
Here you find per quarter rate as (20/4)% = 5%
I have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5% annual rate of interest, it is apparent that the intent was a 5% quarterly rate. So the bank charges 5% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 5% of 20,000 = $4000 as our answer.
But since, the interest is compounded, it will be a bit more than $2000. Option (D) looks correct.
Answer: (D) $4000
Question: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 280-mile journey? Assume that the train makes no intermediate stops.
(A) 8
(B) 7
(C) 9
(D) 7.5
(E) 6
Rationale: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 280-mile journey? Assume that the train makes no intermediate stops.
I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)
Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
7 70 280
It takes a total of nine hours to cover the 280 mile distance.
ANSWER: B
Answer: (B) 7
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 5 rounds per hour and 5 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?
(A) A)5
(B) B)6
(C) C)8
(D) D)15
(E) E)9
Rationale: Relative speed = 5 + 5 = 10 rounds per hour.
So, they cross each other 10 times in an hour and 5 times in half an hour.
Hence, they cross each other 15 times before 9.30 a.m.
ANSWER:D
Answer: (D) D)15
Question: Elena purchased Brand X pens for $4.00 apiece and brand Y for $2.20 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many brand X pens did she purchase?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=6 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).
Answer: C.
Answer: (C) 6
Question: Fill in the sequence:
1 2 3 2 1 2 3 4 2 ?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: E
1
Number of characters used in writing the numbers in roman numerals
Answer: (E) 1
Question: The ratio of the volumes of two cubes is 729 : 1000. What is the ratio of their total surface areas?
(A) 1:12
(B) 81:13
(C) 46:51
(D) 86:16
(E) 56:13
Rationale: Ratio of the sides
= ³√729 : ³√1000 = 9 : 10
Ratio of surface areas
= 92 : 102 = 46:51
Answer:C
Answer: (C) 46:51
Question: Compute all real solutions to 16x + 4x+1 - 96 = 0
(A) 3/2
(B) 3/3
(C) 2/4
(D) 4/4
(E) 4/5
Rationale: If we substitute y = 4x, we have y2 +4y-96 = 0, so y = -4 or y = 8. The first does
not map to a real solution, while the second maps to x =3/2
correct answer A
Answer: (A) 3/2
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
(A) 18
(B) 87
(C) 57
(D) 17
(E) 16
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Answer: A
Answer: (A) 18
Question: Evaluate permutation
5P5
(A) 120
(B) 110
(C) 98
(D) 24
(E) None of these
Rationale: Explanation:
nPn=n!
5P5=5∗4∗3∗2∗1=120
Option A
Answer: (A) 120
Question: A half of Arunâ€™s marks in mathematics exceed a third of his marks in English by 50.If he got 250 marks in two subjects together how many marks did he got in English?
(A) 120,60
(B) 160,90
(C) 180,90
(D) 190,40
(E) None of them
Rationale: Let Arunâ€™s marks in mathematics and english be x and y
Then (1/2)x-(1/3)y=50
3x-2y=300â€¦â€¦>(1)
x+y=250â€¦â€¦.>(2)
solving (1) and (2)
x=160
and y=90
Answer is B.
Answer: (B) 160,90
Question: How many prime numbers between 1 and 100 are factors of 7,150?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Rationale: Make prime factorization of 7,150 --> 7,150=2*5^2*11*13. So 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150 (you shouldn't count one prime factor twice).
Answer: D.
Answer: (D) Four
Question: In simple interest what sum amounts of Rs.1120/-in 4 years and Rs.1200/-in 5 years ?
(A) Rs. 500
(B) Rs. 600
(C) Rs. 800
(D) Rs. 900
(E) Rs. 700
Rationale: For 1 year interest= 1200-1120=80
for 4 year 320
then sum= 1120-320=800
ANSWER:C
Answer: (C) Rs. 800
Question: Which of the following describes all values of x for which 36-x^2 ≥ 0 ?
(A) x ≥ 1
(B) x ≤ -1
(C) 0 ≤ x ≤ 1
(D) x ≤ -1 or x ≥ 1
(E) -6 ≤ x ≤ 6
Rationale: 36-x^2 >= 0 ---> x^2-36<=0
--> (x+6)(x-6)<=0
Above equation true for
i) x+6<=0 and x-6>=0 ---> x<= -6 and x>=6 ---> this is not possible ---Strike out this solution
ii) x+6>=0 and x-6<=0 ---> x>=-6 and x<=6 --> -6<=x<=6
Answer E
Answer: (E) -6 ≤ x ≤ 6
Question: Fresh grapes contains 90% water, and dry grapes contains 85% matter. To get 25 kgs of dry grapes who many kgs of fresh grapes have to be processed?
(A) 212
(B) 212.5
(C) 213.5
(D) 213
(E) None
Rationale: Ans. To solve problems which involves 2 variables, concentrate on the variable that won't change. In this problem we concentrate on the variable matter rather than water as it changes.
Let us take K kgs of fresh grapes. Now total mater in these grapes = K x 10%
In 25 kgs dry grapes total mater = 25 x 85%
We know that these two equation are equal so
K X 10% = 25 x 85%
Solving K = 212.5
Answer B
Answer: (B) 212.5
Question: When divided by 5, x has a remainder of 4 and y has a remainder of 1. Which of the following could be the remainder when x + y is divided by 10?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 0
Rationale: x = 5k+4 and y = 5j+1
x+y = 5(j+k) + 5
When divided by 10, the remainder is either 5 or 0.
The answer is E.
Answer: (E) 0
Question: A man can row downstream at 26 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 2, 9
(B) 4, 9
(C) 8, 9
(D) 18, 8
(E) 7, 9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 26 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 36 => x = 18, y = 8.
Answer:D
Answer: (D) 18, 8
Question: In how many ways can the letters D, I, S, I, N, O, I, C be arranged so that the three I's are not next to each other?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 6000
Rationale: 1 D
3 I
1 S
1 N
1 O
1 C
Number of ways these letters can be arranged = 8!/3! (3! to account 3 same Is) = 6720
Consider 3 Is as 1 entity and thus the number of arrangements for (III)DSNOC = 6! = 720
Total allowed cases = 6720-720 =6000
E is the correct answer.
Answer: (E) 6000
Question: The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is :
(A) 15 cm
(B) 25 cm
(C) 35 cm
(D) 42 cm
(E) 62 cm
Rationale: Solution
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C
Answer: (C) 35 cm
Question: Dividing by 3⁄9 and then multiplying by 5⁄6 is the same as dividing by what number?
(A) 31⁄5
(B) 16⁄5
(C) 20⁄9
(D) 5/2
(E) 5⁄16
Rationale: say X/3/9*5/6 = x*9/3*5/6 = x*5/2
D
Answer: (D) 5/2
Question: A sales representative receives a salary of $200 per week and earns a commission of 20% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?
(A) $3,000
(B) $2,000
(C) $4,000
(D) $4,150
(E) $5,000
Rationale: We're told that a sales representative receives a salary of $200 per week and earns a commission of 20% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $600.
Since the salesperson receives a $200 salary, the remaining $400 has to be accounted for by the 20% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.
Let's TEST Answer C: $4,000
Since 20% of $1,000 = $100
20% of $4,000 = 4($200) = $800
This is TOO HIGH (it's supposed to be $400), so we need a LOWER total sales figure.
Let's TEST Answer B: $2,000
Since 20% of $1,000 = $200
20% of $2,000 = 2($200) = $400
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
B
Answer: (B) $2,000
Question: Nr Books bought Nr of People
3 2
5 5
6 1
7 3
8 2
What is the median of books bought per person?
(A) a) 5
(B) b) 7
(C) c) 9
(D) d) 10
(E) e) 18
Rationale: 3,3,5,5,5,5,5,6,7,7,7,8,8
so you will observer that the median of the list is 5.
Ans A
Answer: (A) a) 5
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 10 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/50
(E) 1/900
Rationale: If it takes 10 minutes to inspect one vehicle, the # of vehicles that can be inspected in 3 hours (180 minutes) = 180/10 = 18. Hence, for calculating the probability that the police will find the transmitter within three hours, the favorable cases = 18. Now, we need to figure out the total # of cases.
The total # of cases = Total # of such cars possible. The details given about the car is that it starts with 79, which leaves 2 more digits, both of which can be filled by all 10 numbers (0-9). In addition, we have 3 letters, each of which can be filled by any from the set {A,B,C}. Hence the total # of such cars possible = 10*10*3*3 = 900
So, the probability that the police will find the transmitter within three hours = 18/900 = 1/50. Option D
Answer: (D) 1/50
Question: From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 8 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Soln:-
8x=45 --> 27/25*x=45 --> x=45*25/27=125/3=~42.
Answer: E.
Answer: (E) 42
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 1200 votes. What is the total number of votes polled?
(A) 4500
(B) 5200
(C) 6900
(D) 7520
(E) 6000
Rationale: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1200
20x/100 = 1200
x = 1200*100/20 = 6000
Answer is E
Answer: (E) 6000
Question: A man can row upstream at 20 kmph and downstream at 60 kmph, and then find the speed of the man in still water?
(A) 32 kmph
(B) 34 kmph
(C) 30 kmph
(D) 45 kmph
(E) 40 kmph
Rationale: US = 20
DS = 60
M = (20 + 60)/2 = 40
Answer:E
Answer: (E) 40 kmph
Question: If m^(-1) = -1/2 then m^(-2) is equal to
(A) -9
(B) -3
(C) -1/9
(D) 1/4
(E) 9
Rationale: You made a mistake here.
You're right till
m^-2 = 1/m^2 and m^-1 = 1/m^1 = 1/m
given m^-1 = -(1/2) so, 1/m = -(1/2) solving this, m = -2
Now, m^-2 = 1/m^2 = 1/(-2)^2 = 1/4 ANS D
Answer: (D) 1/4
Question: If the price of sugar rises from Rs. 2 per kg to Rs. 5 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 60%
Rationale: Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 2 = x × 5 = x = 40 kg.
∴ Reduction in consumption = 60%.
Answer E
Answer: (E) 60%
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 60 kmph
(B) 10 kmph
(C) 30 kmph
(D) 5 kmph
(E) 15 kmph
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
ANSWER:C
Answer: (C) 30 kmph
Question: A big container is 35% full with water. If 16 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container in liters?
(A) 32
(B) 40
(C) 48
(D) 54
(E) 60
Rationale: 16 liters is 40% of the capacity C.
16 = 0.4C
C = 16/0.4 = 40 liters.
The answer is B.
Answer: (B) 40
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) Rs 420
(B) Rs 550
(C) Rs 490
(D) Rs 450
(E) Rs 457
Rationale: 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
Answer:D
Answer: (D) Rs 450
Question: What Is The Next Number
12 13 15 17 111 113 117 119 123 ?
(A) 212
(B) 321
(C) 129
(D) 234
(E) 654
Rationale: C
129.
These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1
Answer: (C) 129
Question: In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiples the integer on the card by the next larger integer. If each possible product is between 27 and 200, then the least and greatest integers on the card could be
(A) 3 and 15
(B) 3 and 20
(C) 5 and 13
(D) 4 and 14
(E) 5 and 14
Rationale: There child draws one number then multiplies that number by the number above it. The number must be more than 27 and less than 200.
x * (x+1)
Answer gives us choices of 3,4 and 5 (JUST ABOVE 15)
3*(3+1) =12 <- WRONG
4*(4+1) =20 <- WRONG
5*(5+1) =30 <- CORRECT AS IT IS ABOVE 27
Answer gives us choices 13,14,15 and 20 (BELOW 200)
Immediately by knowing squares you should be able to rule out 15 (225) and 20 (400). And common sense dictates that as 14^2 is 196 that 14*(14+1) is above 200.
13*(13+1)=182 <- CORRECT
Answer is C) 5 and 13
Answer: (C) 5 and 13
Question: The perimeter of a semi circle is 144 cm then the radius is?
(A) 22
(B) 28
(C) 99
(D) 77
(E) 16
Rationale: 36/7 r = 144 => r = 28
Answer: B
Answer: (B) 28
Question: The product X of two prime numbers is between 17 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 11 but less than 25, then X =
(A) 18
(B) 29
(C) 37
(D) 44
(E) 65
Rationale: Option BC can be ruled out as they themselves are prime numbers
18 = 2*9 = 3*6 >> Ignore
44 = 2 * 22 = 4 * 11 >> Ignore
65 = 5*13 >> Answer
Answer = E
Answer: (E) 65
Question: The average of first seven multiples of 4 is:
(A) 9
(B) 16
(C) 15
(D) 8
(E) 10
Rationale: Explanation :
(4(1+2+3+4+5+6+7)/7
= 4x28/7
= 16
Answer : B
Answer: (B) 16
Question: A certain car increased its average speed by 3 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 20 miles per hour, how many miles did the car travel in the third 5-minute interval?
(A) 1.0
(B) 1.5
(C) 2.0
(D) 2.5
(E) 3.0
Rationale: In the third time interval the average speed of the car was 20+3+5=28 miles per hour;
In 5 minutes (1/12 hour) at that speed car would travel 28*1/12=2 miles.
Answer: C.
Answer: (C) 2.0
Question: x^2 + hx + 72 = 0 has two distinct integer roots; how many values are possible for h?
(A) 3
(B) 6
(C) 8
(D) 12
(E) 24
Rationale: For a quadratic equation ax^2+hx+c=0, we know that -h/a is sum of roots and c/a is product of roots.
The quadratic equation here is x^2 + hx + 72 = 0, where product of roots is 72.
If we find all the factors of 72, we have the answer.
By prime factorization, we get 72= 2^3*3^2.
We know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=D
Answer: (D) 12
Question: Jacob is now 12 years younger than Michael. If 11 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
(A)  3
(B)  7
(C)  15
(D)  5
(E)  25
Rationale: Jacob=x years, Mike=x+12 years
11 years from now,
2(x+11)=x+23
2x+22=x+23
x=1
x+4=5 years
Answer D
Answer: (D)  5
Question: A walks at 30 kmph and 30 hours after his start, B cycles after him at 45 kmph. How far from the start does B catch up with A?
(A) 1200km
(B) 1500km
(C) 2000km
(D) 2700km
(E) 3600km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 30 hours.
x/30 - x/45= 30
x = 2700 km
Answer is D
Answer: (D) 2700km
Question: Seven men can complete a work in 12 days. They started the work and after 5 days, two men left. In how many days will the work be completed by the remaining men?
(A) 5 days
(B) 6 days
(C) 9 days
(D) 10 days
(E) None of these
Rationale: 7 x 12 men complete the work in 1 day
Therefore, 1 man’s 1 day’s work = 1/84
7 men’s 5 days work = 5/12
Remaining work = 1- 5/12 = 7/12
5 men’s 1 day’s work = 5/84
5/84 work is don by them in 1 day
7/12 work is done by them in ((84/5) x (7/12)) = 49/5 days = 9 4/5 days
ANSWER:E
Answer: (E) None of these
Question: Line m lies in the xy-plane. The y-intercept of line m is -1, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -8). What is the slope of line m ?
(A) -3
(B) -1
(C) -1/3
(D) 0
(E) Undefined
Rationale: Ans: E
Solution: line m goes through midpoint of (2, 4) and (6, -8). midpoint is (4,-2)
as we can see that the y axis of intercept point is (0,-1) means line m is parallel to x axis
slope M= 0
Ans: E
Answer: (E) Undefined
Question: The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 128,000 locusts?
(A) 9
(B) 6
(C) 8
(D) 15
(E) 10
Rationale: - 4 hours: 1,000
-2 hours: 2,000
Now: 4,000
+ 2 hours: 8,000
+ 4 hours: 16,000
+ 6 hours: 32,000
+ 8 hours: 64,000
+ 10 hours: 128,000
Answer : E
Answer: (E) 10
Question: The length, breadth and height of a room are in the ratio 4: 6 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
(A) (a) remain the same
(B) (b) decrease by 13.64%
(C) (c) decrease by 15%
(D) (d) decrease by 81.82%
(E) (e) decrease by 30%
Rationale: Length (L) = 4
Breadth (B) = 6
Height (H) = 4
Total Area of Walls = 2(BH + LH) = 2*(6*4 + 4*4) = 2*(24+16) = 80
Then, Finally
Length (L) = 2*4 = 8
Breadth (B) = 6/2 = 3
Height (H) = 4/2 = 2
Total Area of Walls = 2(BH + LH) = 2*(3*2 + 8*2) = 2*(6+16) = 44
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (44-80)*100 /44=- 81.82% (Decrease)
Answer: Option D
Answer: (D) (d) decrease by 81.82%
Question: A school having four classes only have student strength of 10, 20, 30 and 40 respectively. The pass percentages of these classes are 20%, 30%, 60% and 100% respectively. What is the pass percentage for the entire school?
(A) 56%
(B) 76%
(C) 34%
(D) 66%
(E) 46%
Rationale: 20% of 10+30% of 20+60% of 30+100% of 40
=2+6+18+40 =
now 66 of 100
= 66%
ANSWER:D
Answer: (D) 66%
Question: For how many integers n is 2^n = n^2 ?
(A) None
(B) One
(C) Two
(D) Three
(E) More than Three
Rationale: => 2^n = n^2
Taking nth root on both sides
=> 2 = (n^2)^1/n
=> 2 = n ^ 2/n
Lets consider positive even multiples of 2 for n (since LHS = 2)
For n = 2
=> 2 = 2 ^ 2/2 - First value that satisfier
For n = 4
=> 2 = 4 ^ 2/4 - Second value that satisfier
For n = 8
=> 2 = 8 ^ 2/8 - Does Not satisfy
For n = 16
=> 2 = 16 ^ 2/16 - Does Not satisfy
Two values. Ans = C
Answer: (C) Two
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 287m
(B) 278m
(C) 350m
(D) 228m
(E) 282m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39
= 50/3
3(x + 300)
= 1950 è x
= 350m.
Answer:C
Answer: (C) 350m
Question: In 1990 a total of 100 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 25 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
(A) 2/8
(B) 1/3
(C) 2/7
(D) 1/4
(E) 1/25
Rationale: We're given a couple of facts to work with:
1) There were a total of 100 earthquakes
2) Of those earthquakes, 25 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 75 earthquakes that DID NOT occur in Asia....
The answer to the question is 25/75 ie. 1/3
Answer : B
Answer: (B) 1/3
Question: The price of a certain painting increased by 25% during the first year and decreased by 15% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?
(A) 109%
(B) 106.25%
(C) 120%
(D) 115%
(E) 110%
Rationale: Easiest thing to do: Assume that price is 100
Price at the end of yr 1: 100+ 25 = 125
Price at the end of year 2 = 125 - 125*0.15 = 125*0.85 = 106.25
Hence required answer = (106.25/100)*100% = 106.25%
Answer is B.
Answer: (B) 106.25%
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
(A) 1 hour
(B) 6 hours
(C) 8 hours
(D) 2 hours
(E) 9 hours
Rationale: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è
1 hour
Answer:A
Answer: (A) 1 hour
Question: 7 books consisting of 3 financial management, 2 marketing management and 2 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
(A) 1/1155
(B) 1/5040
(C) 1/2255
(D) 1/1355
(E) 1/1455
Rationale: Since the denominator will be 7! . And there is no way to divide 7 from numerator and denominator. Use a multiple of 7 in the denominator only answer
B
Answer: (B) 1/5040
Question: walking at ¾ of his usual speed ,a man is late by 2 ½ hr.
the usual time is.
(A) 7
(B) 8 ½
(C) 7 ½
(D) 7 ¾
(E) 9 ½
Rationale: Usual speed = S
Usual time = T
Distance = D
New Speed is ¾ S
New time is 4/3 T
4/3 T – T = 5/2
T=15/2 = 7 ½
Answer is C.
Answer: (C) 7 ½
Question: Before being simplified, the instructions for computing income tax in country R were to add 3 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I?
(A) 50 + I/200
(B) 50 + 7I/200
(C) 50+ I/40
(D) 100+ I/50
(E) 100+ 3I/100
Rationale: Income of a person is I
3 percent of ones annual income = 3I/100
100 units of Country R's currency = 100
1 percent of one's annual income = I/100
Average of 100 units and 1 percent annual income = 50 + I/200
Sum of average and 3 percent = 3I/100 + 50 + I/200
= 50 + 7I/200
= 50 + 7I/200
So answer is B.
Answer: (B) 50 + 7I/200