Median of 5 numbers

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Gmat09_5ALL: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Tue Apr 14, 2009 1:23 am

by Gmat09_5ALL » Wed Sep 16, 2009 3:28 pm

If the average (arithmetic mean) of 5 different numbers is 12, what is the median of the 5 numbers?
(1) The median of the 5 numbers is equal to 1/3 of the sum of the 4 numbers other than the median.
(2) The sum of the 4 numbers other than the median is equal to 45.

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Source: Beat The GMAT — Data Sufficiency | Wed Sep 16, 2009 3:28 pm

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

Re: Median of 5 numbers

by Brent@GMATPrepNow » Wed Sep 16, 2009 4:26 pm

Gmat09_5ALL wrote:If the average (arithmetic mean) of 5 different numbers is 12, what is the median of the 5 numbers?
(1) The median of the 5 numbers is equal to 1/3 of the sum of the 4 numbers other than the median.
(2) The sum of the 4 numbers other than the median is equal to 45.

Nice question.
To answer a lot of questions involving the arithmetic mean, we need to know that "If m is the mean of n numbers, then the sum of the numbers is nm"

So, if the mean of 5 number is 12, then the sum of all 5 numbers must be 60 (5x12)

(1) Let m equal the median
60-m is the sum of the 4 numbers other than the median
We now get the equation (60-m)/3 = m
We can solve this equation for m to get m=15
SUFFICIENT

(2) If the sum of all 5 numbers is 60, we know that the median = 60-45
SUFFICIENT

Answer: D

Brent Hanneson - Creator of GMATPrepNow.com

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Gmat09_5ALL: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Tue Apr 14, 2009 1:23 am

by Gmat09_5ALL » Thu Sep 17, 2009 12:10 am

Thanks Brent

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viju9162: Master | Next Rank: 500 Posts; Posts: 434; Joined: Mon Jun 11, 2007 9:48 pm; Location: Bangalore; Thanked: 6 times; GMAT Score:600

by viju9162 » Thu Sep 17, 2009 2:35 am

nice reply..Thanks Brent..

"Native of" is used for a individual while "Native to" is used for a large group

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