Most likely range

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LulaBrazilia: Master | Next Rank: 500 Posts; Posts: 116; Joined: Tue Mar 31, 2009 10:50 am; Followed by:1 members

Most likely range

by LulaBrazilia » Thu Jan 16, 2014 8:22 am

If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

A) 0 and 3/20

B) 3/20 and 1/5

C) 1/5 and 1/4

D) 1/4 and 3/10

E) 3/10 and 1/2

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Source: Beat The GMAT — Problem Solving | Thu Jan 16, 2014 8:22 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 16, 2014 8:28 am

LulaBrazilia wrote:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

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

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

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 16, 2014 8:31 am

LulaBrazilia wrote:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

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

Alternatively, we might rewrite each fraction with a common denominator of 20 to get:

A) 0 and 3/20 (interval length = 3/20)
B) 3/20 and 4/20 (interval length = 1/20)
C) 4/20 and 5/20 (interval length = 1/20)
D) 5/20 and 6/20 (interval length = 1/20)
E) 6/20 and 10/20 (interval length = 4/20)

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com