Problem Solving

AAPL wrote:Source: GMAT Prep

If a number between 0 and 1 is selected at random, which of the following will the number more likely be between?

A. 0 and 3/20
B. 30/20 and 1/5
C. 1/5 and 1/4
D. 1/4 and 3/10
E. 3/10 and 1/2

Another approach is to convert everything to decimals

We need to determine the LENGTH OF EACH INTERVAL.
The interval that has the greatest length, will be the most likely interval.
To determine the length of each interval, it may be faster to first convert the fractions to decimals. We get:
A) 0 and 0.15 (interval length = 0.15)
B) 0.15 and 0.2 (interval length = 0.05)
C) 0.2 and 0.25 (interval length = 0.05)
D) 0.25 and 0.3 (interval length = 0.05)
E) 0.3 and 0.5 (interval length = 0.2)

Answer: E

Cheers,
Brent

AAPL wrote:Source: GMAT Prep

If a number between 0 and 1 is selected at random, which of the following will the number more likely be between?

A. 0 and 3/20
B. 30/20 and 1/5
C. 1/5 and 1/4
D. 1/4 and 3/10
E. 3/10 and 1/2

The OA is E.

If each number has an equal chance to be selected, then the number A will be more likely to be selected than the number B if A is in an interval that is larger than the interval B is in. So let's look at the length of each interval (by finding the difference of the endpoints of the interval) given in the answer choices.

A) 3/20 - 0 = 3/20

B) 1/5 - 3/20 = 4/20 - 3/20 = 1/20

C) 1/4 - 1/5 = 5/20 - 4/20 = 1/20

D) 3/10 - 1/4 = 6/20 - 5/20 = 1/20

E) 1/2 - 3/10 = 5/10 - 3/10 = 2/10 = 4/20

We see that interval in choice E has the longest length, therefore, a number is more likely to be selected in that interval.

Answer: E