mathewhe/aqua_rat huggingface dataset:
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 9 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 11
(B) 10
(C) 8
(D) 12
(E) 15
Rationale: Suppose they meet x hours after 9 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 12 a.m.
Answer: D
Answer: (D) 12
Question: In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class?
(A) A)10
(B) B)12
(C) C)15
(D) D)20
(E) E)25
Rationale: the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C)
Answer: (C) C)15
Question: A man is 24 years older than his son. In six years, his age will be twice the age of his son. The present age of the son is
(A) 14 years
(B) 28 years
(C) 20 years
(D) 22 years
(E) None
Rationale: Solution
Let the son's present age be x years .Then, man's present age	= (x+24)years.
Then	â€¹=â€º(x+24)+6= 2(x+6)
â€¹=â€ºx+30=2x+12
x= 18.
Answer E
Answer: (E) None
Question: There are 20 girls inhostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
(A) 1 year
(B) 2 years
(C) 3 years
(D) 4 years
(E) None
Rationale: Total decrease = 20 * 2 = 40 month
= 3 years 4 month
E)None
Answer: (E) None
Question: If P = 2Q+1 where P is an Integer then which of the following is true?
(A) P is always Odd
(B) P is even if Q is a non integer and a multiple of 0.5
(C) P is a non multiple of 2
(D) P= 1
(E) P IS ALWAYS EVEN
Rationale: B
Answer: (B) P is even if Q is a non integer and a multiple of 0.5
Question: Four athletes, Wendy, Michelle, Brenda, and Jamal, scored in a soccer (football) game. If Michelle scored 1 more goal than Brenda did, Jamal scored 3 less than Wendy did, and Wendy scored 3 more than Michelle did, how many fewer goals did Brenda score than Jamal?
(A) -8
(B) -6
(C) -2
(D) -1
(E) -3
Rationale: In this word problem, the first key is to turn the story into equations:
Michelle scored 1 more than Brenda did: M = 1 + B
Jamal scored 3 less than Wendy did: J = W - 3
Wendy scored 3 more than Michelle did: W = 3 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and J (how many more goals did Brenda score than Jamal did?). This means that your goal is to get the equations in terms of B and J so that you can solve for the expression B - J.
Taking the first equation and solving for B, you have B = M - 1.
Taking the second equation and solving for J you have J = W - 3, and then with the third equation you can replace W with 3 + M so that both B and J are in terms of M: J = (3 + M) - 3.
So if B = M - 1 and J = M, then:
B - J = (M - 1) - (M)
B - J = M - 1 - M (remove the parentheses by distributing the multiplication)
B - J = -1, so the answer is D.
Answer: (D) -1
Question: Five years ago, John’s age was half of the age he will be in 4 years. How old is he now?
(A) 14years
(B) 15years
(C) 16years
(D) 17years
(E) 18years
Rationale: Let John=j,j-5=(j+4)/2,then j=14years
ANSWER:A
Answer: (A) 14years
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) 358m
(B) 850m
(C) 350m
(D) 150m
(E) 340m
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: A train 440 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 80
(B) 26
(C) 24
(D) 54
(E) 15
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 440 * 3/55 = 24 sec.
Answer: C
Answer: (C) 24
Question: The mean of 50 observations was 36. It was found later that an observation 60 was wrongly taken as 23. The corrected new mean is?
(A) 36.7
(B) 36.1
(C) 36.5
(D) 36.9
(E) 36.3
Rationale: Correct sum
= (36 * 50 + 60 - 23)
= 1837.
Correct mean = 1837/50
= 36.7
Answer:A
Answer: (A) 36.7
Question: A bag contains 5 red & 3 black balls and the second one 4 red and 5 black balls. One of is selected at random and a draw of two balls is made from it. What is the chances that one of them is red and the other is black?
(A) .5456
(B) 1.5456
(C) 2.5456
(D) 3.5456
(E) 4.5456
Rationale: secet 1 bag from two=1/2
from 1 st bag=5c1*3c1/8c2=15/28
from 2nd bag=4c1*5c1/9c2=20/36
toatl p(s)=1/2(15/28 + 20/36)=.5456
ANSWER:A
Answer: (A) .5456
Question: n a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 127.6
(B) 127.5
(C) 127.0
(D) 127.2
(E) 127.3
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.Answer: OB
Answer: (B) 127.5
Question: The average of fifteen numbers is 0. In those 15, at the most, how many may be greater than zero?
(A) 0
(B) 1
(C) 10
(D) 14
(E) 17
Rationale: Explanation :
Average of 15 numbers = 0
Sum of 15 numbers =(0 x 15) =0.
It is quite possible that 14 of these numbers may be positive and if there sum is a, then 15th number is (-a).
Answer : D
Answer: (D) 14
Question: If n is a natural number, then (6n^2+6n) is always divisible by?
(A) 6 only
(B) 6 and 12
(C) 12 only
(D) by 18 only
(E) None of these
Rationale: (6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Correct Option: B
Answer: (B) 6 and 12
Question: Jonathan can type a 40 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
(A) 5 minutes
(B) 10 minutes
(C) 15 minutes
(D) 18 minutes
(E) 20 minutes
Rationale: You may set up common equation like this:
job/A+job/B+job/C=job/x
Memorize this universal formula, you will need it definitely for GMAT.
and find x from this equation
In this specific case, the equation will look like this:
40/40+40/30+40/24=40/x
If you solve this equation, you get the same answer B (10)
Answer: (B) 10 minutes
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 9 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)  19/900
(E)  1/900
Rationale: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/9 = 19
P = 19/900
Ans:D
Answer: (D)  19/900
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 2
(B) 6
(C) 8
(D) 4
(E) 10
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =(9/54x 60) min= 10 min.
ANSWER E
Answer: (E) 10
Question: A batsman scores 26 runs and increases his average from 14 to 15. Find the runs to be made if he wants top increasing the average to 19 in the same match ?
(A) 12
(B) 18
(C) 25
(D) 74
(E) 88
Rationale: Number of runs scored more to increase the ratio by 1 is 26 - 14 = 12
To raise the average by one (from 14 to 15), he scored 12 more than the existing average.
Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5 = 60 more than the existing average. Thus he should score 14 + 60 = 74.
Answer D
Answer: (D) 74
Question: How many different three-digit multiples of 5 can be composed of digits 1, 3, 4, and 5 if none of the digits is repeated?
(A) 3
(B) 6
(C) 10
(D) 12
(E) 18
Rationale: = 3c2 x 2 = 6
can you explain your method. i solved it differently
XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 3 possible choices.
X can be any of the 2 possible choices.
2+3+1= 6
B
Answer: (B) 6
Question: If n is an integer greater than 6, which of the following must be divisible by 3?
(A) N(N+1)(N-4)
(B) N(N+2)(N-1)
(C) N(N+3)(N-5)
(D) N(N+4)(N-2)
(E) N(N+5)(N-6)
Rationale: The product of 3 numbers to be divisible by 3 at least one of them must be divisible by 3. So, to ensure that the product of 3 integers shown is divisible by 3 all 3 numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. We should have something like n(n+1)(n+2) (for example: if n divided by 3 yields remainder of 1, then n+1 yields remainder of 2 and n+2 yields remainder of 0, thus it's divisible by 3 OR if n divided by 3 yields remainder of 2, then n+2 yields remainder of 1 and n+1 yields remainder of 0, thus it's divisible by 3).
Only option A satisfies this, because n(n+1)(n−4)=n(n+1)(n−6+2) and n−6has the same remainder as nn upon division by 3 thus we can replace it by n.
Answer: A.
Answer: (A) N(N+1)(N-4)
Question: When x is divided by 3, the quotient is y and the remainder is 1. When x is divided by 5, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?
(A) 4z/7 + 5
(B) (7z + 5) / 6
(C) (6z + 7) / 4
(D) (5z + 5) / 3
(E) (4z + 6) / 7
Rationale: When x is divided by 3, the quotient is y and the remainder is 1: x = 3y + 1.
When x is divided by 5, the quotient is z and the remainder is 6: x = 5z + 6.
Equate those two:
3y + 1 = 5z + 6;
y = (5z + 5)/3.
Answer: D.
Answer: (D) (5z + 5) / 3
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 20 mangoes. Find the gain percent?
(A) 27%
(B) 25%
(C) 21%
(D) 15%
(E) 24%
Rationale: SP = CP + g
150 SP = 150 CP + 20 SP
130 SP = 150 CP
130 --- 20 CP
100 --- ? => 15%
Answer:D
Answer: (D) 15%
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 63?
(A) 68
(B) 69
(C) 128
(D) 68^2
(E) 68·69
Rationale: In order to get the lowest LCM, we have to take the first number as 64 and the next number as its multiple.
So, I can take 64 and 128 as two distinct numbers, such that Lowest LCM = 128.
Answer should be C.
Answer: (C) 128
Question: How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
(A) 100
(B) 50
(C) 26
(D) 1000
(E) None of these
Rationale: Solution:
1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be 'n'.
Therefore, using 'n' alphabets we can form n *n *n = n3 distinct 3 digit initials.
NOTE:
Distinct initials are different from initials where the digits are different. For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This n3 different initials = 1 million.
i.e. n3 = 106 (1 million =106).
n3 = 1023.
=> n = 102 = 100.
Hence, the language needs to have a minimum of 100 alphabets
Answer: Option A
Answer: (A) 100
Question: If Finn was 17 months old one year ago, how old was he, in months, x months ago?
(A) x − 30
(B) x − 12
(C) 18 − x
(D) 29 − x
(E) 30 − x
Rationale: Age Today = 17 months + 12 months (1year) = 29 months
X months ago- Today's Age - X = 29 - X
Ans- D
Answer: (D) 29 − x
Question: What should come in place of the question mark (?) in the following equation?
9568 – 6548 – 1024 = ?
(A) 2086
(B) 1996
(C) 2293
(D) 1896
(E) None of these
Rationale: ? = 9568 – 6548 – 1024 = 1996.
Answer B
Answer: (B) 1996
Question: A cyclist bikes x distance at 8 miles per hour and returns over the same path at 812miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
(A) 8.1
(B) 8.3
(C) 8.6
(D) 9.6
(E) 9.0
Rationale: Distance = d1 = x miles
Speed = s1 = 8 miles per hour
Time = t1 = Distance/ Speed = x/8
2. Going from B to A
Distance = d2 = x miles
Speed = s2 = 12 miles per hour
Time = t2 = Distance/ Speed = x/12
3. Average Speed = Total Distance/Total Time
Total Distance = x + x = 2x
Total Time = x/12 + x/8 = x (1/12 + 1/8) = =5x/24
Speed = 2x/(5x/24) = 48/5
= 9.6
Answer : D
Answer: (D) 9.6
Question: If x = -6 and y = -3, what is the value of 4(x-y)^2 - xy ?
(A) 20
(B) 18
(C) 17
(D) 22
(E) 23
Rationale: x = -6 and y = -3
x-y = -6 - (-3) = -6+3 = -3
x*y = -6 * -3 = 18
Now we apply it in the equation 4(x-y)^2 - xy =4 (-3)^2-18
==>4*9 -18 = 36-18 =18
Answer : B
Answer: (B) 18
Question: Eleven men and eleven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
(A) 5!*6!
(B) 7!*8!
(C) 10!*11!
(D) 10!*12!
(E) 11!*12!
Rationale: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 11 men in a circle can be arranged in (11-1)! ways and if we place 11 women in empty slots between them then no two women will be together. The # of arrangement of these 11 women will be 11! and not 10! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 10!*11!.
C
Answer: (C) 10!*11!
Question: The average runs scored by a batsman in 30 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
(A) 24.3
(B) 25.3
(C) 26.3
(D) 28.3
(E) 34.5
Rationale: Total score of the batsman in 30 matches = 600.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 730.
Average score of the batsman = 730/30 = 24.3.
ANSWER:A
Answer: (A) 24.3
Question: What is the prime factors’ number of 36?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 24 = 2^2*3^2
prime factors’ number will be 2+2 = 4.
Hence, answer is C.
Answer: (C) 4
Question: A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
(A) a) 5 inches
(B) b) 6 inches
(C) c) 7 inches
(D) d) 8 inches
(E) e) 10 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
25=5*5
35=5*7
GCF = 5
P.S you can make squares with side of 5
Answer : A
Answer: (A) a) 5 inches
Question: A courtyard is 20 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
(A) 16000
(B) 27778
(C) 20000
(D) 27999
(E) 17799
Rationale: Number of bricks =Courtyard area/1 brick area
=(2000×1600/20×10)=16000
Answer: A
Answer: (A) 16000
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.9880. Find the share of B?
(A) 2880
(B) 3000
(C) 3018
(D) 3019
(E) 3012
Rationale: 60*5:36*6:75*3
100: 72: 75
72/247 * 9880 = 2880
Answer: A
Answer: (A) 2880
Question: How many pieces can a square pizza be cut into by making 4 linear cuts?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 1 cut makes two pieces
a second cut can make 4 pieces by cutting through 2 of the pieces
a third cut can make 7 pieces by cutting through 3 of the pieces
a fourth cut can make 11 pieces by cutting through 4 of the pieces
B
Answer: (B) 11
Question: The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time W will it take to fill the tank now?
(A)  50% less time
(B)  50% more time
(C)  75% less time
(D)  75% more time
(E)  100% more time
Rationale: (VC)Volume of the cylinderical vessal is directly proportional to R^2.
So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)
Now if with velocity V tank can be filled in T1 time of volume VC
So now Velocity is 50% less i..e V/2
So time taken to fill the capacity VC/4 by V/2 velocity is T2.
VT1 = VC
V/2*T2 = VC/4
So T1/T2 = 1/2
So Tank will be filled in less time. that W=is 50 % less.A
Answer: (A)  50% less time
Question: What approximate value should come in the place of question mark (?) in the following equation?
1325√(17) + 508.24 of 20% – 85.39 of 3⁄4 = ?
(A) 5500
(B) 5200
(C) 5800
(D) 4900
(E) 5900
Rationale: ? = 1325√(17) + 508.24 of 20% – 85.39 of 3⁄4
= 1325√(17) + 500 of 20% – 85 × 0.75
= 5460 + 100 – 60 = 5500
Answer A
Answer: (A) 5500
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
(A) 18
(B) 76
(C) 48
(D) 27
(E) 12
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer:C
Answer: (C) 48
Question: A box contains five bulbs out of which 3 are defective. If three bulbs are chosen at random, find the probability that all the four bulbs are defective?
(A) 1/12
(B) 1/11
(C) 1/10
(D) 1/198
(E) 1/126
Rationale: Out of five, two are good and three are defective. Required probability
= 3C3/5C3
= 1/10
Answer: C
Answer: (C) 1/10
Question: hree seventh of a number is 12 more than 40% of that number. What will be the 60% of that number?
(A) 238
(B) 129
(C) 126
(D) 197
(E) 112
Rationale: Explanation:
3/7 x â€“ 40/100 x = 12
x = 35 * 12
35 * 12 * 60/100 = 252/2 = 126
Answer:C
Answer: (C) 126
Question: Find the largest number of four digits which is exactly divisible by 25,18,12,15
(A) 9900
(B) 9710
(C) 9720
(D) 9730
(E) 9740
Rationale: Explanation:
LCM of 25-18-12-15 is 900.
After dividing 9999 by 900 we get 99 remainder.
So answer will be 9999-99 = 9900
Option A
Answer: (A) 9900
Question: In expressing a length of 102.472 km as nearly as possible with the three significant digits, find the percentage error
(A) 0.38%
(B) 0.27%
(C) 0.027%
(D) 0.038%
(E) None of these
Rationale: Explanation:
Error = (102.5 - 102.472) = 0.028
Required percentage =
0.028/ 102.472Ã—100=0.027
Option C
Answer: (C) 0.027%
Question: What is the remainder when 1273 * 1275 * 1277 *1285 is divided by 12?
(A)  9
(B)  1
(C)  11
(D)  0
(E)  7
Rationale: 1271*1275*1277*1285 = (1272 + 1)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (1)(3)(-7)(1) = 21. Thus the question becomes: what is the remainder upon division of 21 by 12? The answer to this question is 9.
Answer: A
Answer: (A)  9
Question: In what time will a train 50 m long cross an electric pole, it its speed be 144 km/hr?
(A) 1.25 sec
(B) 2.75 sec
(C) 3.5 sec
(D) 2.39 sec
(E) 9.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 50/40
= 1.25 sec.
Answer: A
Answer: (A) 1.25 sec
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 4th position from either end of the row.
Can you find out how many girls are practicing together?
(A) 4
(B) 9
(C) 7
(D) 6
(E) 8
Rationale: As judith is 4th from either end of the row, it means that 3 girls are on one of her sides and 3 are present on the other.
3 + 3 + 1(judith herself) = 7.
Hence, 7 girls are practicing the dance together.
correct answer is C)7
Answer: (C) 7
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
(A) 228
(B) 224
(C) 288
(D) 266
(E) 121
Rationale: Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
Answer: B
Answer: (B) 224
Question: For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/3, what are the odds of it burning out during the period from 6months to 1 year following its purchase?
(A) 5/27
(B) 2/9
(C) 1/3
(D) 4/9
(E) 2/3
Rationale: Probability of not burning out during the first 6 months 1-1/3=2/3
Probability of not burning out during the next 6 months 2/3/2=1/3, hence probability of burning out 1-1/3=2/3.
Probability of burning out during the period from 6 months to 1 year = Probability of not burning out in first 6 months * Probability of burning out in next 6 months = 2/3 * 2/3 =4/9
Answer: D.
Answer: (D) 4/9
Question: A thief steels a car at 6a.m. and drives it at 40kmph. The theft is discovered at 7a.m. and the owner sets off in another car at 60 kmph. When will he overtake the thief?
(A) 9a.m.
(B) 9.30a.m.
(C) 10a.m.
(D) 11.45a.m.
(E) 10.15a.m.
Rationale: Suppose the thief overtakes x hours after 6a.m.
Distance covered by the thief in x hrs = distance covered by the owner in (x-1 hours)
40x = 60(x-1)
20x = 60
x = 3 hrs
Thief is overtaken at 9 a.m.
Answer is A
Answer: (A) 9a.m.
Question: Two trains 110 meters and 180 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.2
(B) 7.85
(C) 6.85
(D) 5.85
(E) 6.15
Rationale: T = (110+ 180)/ (80 + 65) * 18/5
T = 7.20
ANSWER:A
Answer: (A) 7.2