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Range PS GMAT Prep

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Manager
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Joined: 19 Oct 2008
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Range PS GMAT Prep  [#permalink]

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New post 23 Mar 2009, 11:14
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A
B
C
D
E

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A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in the set?

A. 32
B. 37
C. 40
D. 43
E. 50

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Joined: 06 Mar 2006
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Re: Range PS GMAT Prep  [#permalink]

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New post 23 Mar 2009, 13:02
Accountant wrote:
A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in the set?

A. 32
B. 37
C. 40
D. 43
E. 50


This question is actually easier to back solve.
Since it is asking for the greatest possible integer, why don't we start with answer choice E.
For a range to equal 25, the smallest integer in the set will have to be 50-25=25. Since those 15 integers have to be different integers, and the median or the middle integers in the set is 25. This answer choice does not work.

Now look at answer D, the smallest integer would be 43-25=18. The seven integers less than the median would be 18,19,20,21,22,23,24. Bingo! This works and this is our answer.
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Re: Range PS GMAT Prep  [#permalink]

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New post 23 Mar 2009, 13:34
Many thanks, this method is very simple and quick.
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Re: Range PS GMAT Prep  [#permalink]

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New post 24 Mar 2009, 14:37
I thought of another way of doing this. Since we are looking for the greatest possible number and we know the range, greatest possible number is equal to mimum possible number plus the range. Since these are different integers, mimum possible number after median will be one lower, so 7th number is 24 and 8th number is 23------1st number will be 18 which is equal to the lowest possible number. Add the range 25 to lowest possible number 18 and you get 43. This method is also short.

--== Message from GMAT Club Team ==--

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Range PS GMAT Prep &nbs [#permalink] 24 Mar 2009, 14:37
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