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Median of 5 numbers

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Median of 5 numbers

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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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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by Gmat09_5ALL » Thu Sep 17, 2009 12:10 am
Thanks Brent
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by viju9162 » Thu Sep 17, 2009 2:35 am
nice reply..Thanks Brent..
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