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Median

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shantascherla
 Post subject: Median
 Post Posted: Wed Mar 02, 2011 6:04 pm 
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Course Students


Posts: 21
Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m
10m/7
10m/7 – 9/7
5m/7 + 3/7
5m

Correct answer is c

I couldnt understand the following explanation

We must choose the highest possible value for every member of the set. The maximum value of any member of the set is 2m, so the 7th value is 2m

How can we assume that the 7th value would be 2m - when the question states that all values are equal to or < 2m. Can anybody explain
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jnelson0612
 Post subject: Re: Median
 Post Posted: Thu Mar 03, 2011 10:20 am 
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ManhattanGMAT Staff


Posts: 1857
shantascherla wrote:
Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m
10m/7
10m/7 – 9/7
5m/7 + 3/7
5m

Correct answer is c

I couldnt understand the following explanation

We must choose the highest possible value for every member of the set. The maximum value of any member of the set is 2m, so the 7th value is 2m

How can we assume that the 7th value would be 2m - when the question states that all values are equal to or < 2m. Can anybody explain


shanta, keep in mind that our goal is to obtain the highest possible average for the seven numbers in the set. To do this, I must make each number in the set as large as possible.

Since I know that the largest value in the set is equal to or less than 2m, I will simply choose to set my largest value at 2m to maximize this value.

I hope this helps, thanks.

_________________
Jamie Nelson
ManhattanGMAT Instructor
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