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# A set of 25 integers has a median of 50 and a range of 50

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Manager
Joined: 12 Oct 2011
Posts: 133
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
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Kudos [?]: 79 [0], given: 23

A set of 25 integers has a median of 50 and a range of 50 [#permalink]  02 Mar 2012, 06:20
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A set of 25 integers has a median of 50 and a range of 50. What is the greatest possible integer that could be in this set?

A. 62
B. 68
C. 75
D. 88
E. 100
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Sep 2013, 01:04, edited 1 time in total.
Edited the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4199

Kudos [?]: 40544 [7] , given: 5540

Re: A set of 25 integers has a median of 50... [#permalink]  02 Mar 2012, 06:59
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BN1989 wrote:
A set of 25 integers has a median of 50 and a range of 50. What is the greatest possible integer that could be in this set?

A. 62
B. 68
C. 75
D. 88
E. 100

Consider 25 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{25}$$.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is $$x_{13}=50$$;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is $$50=x_{25}-x_{1}$$ --> $$x_{25}=50+x_{1}$$;

We want to maximize $$x_{25}$$, hence we need to maximize $$x_{1}$$. The maximum value of $$x_{1}$$ is the median, so 50, hence the maximum value of $$x_{25}$$ is $$x_{25}=50+50=100$$.

The set could be {50, 50, 50, ..., 50, 100}

Now, in order the answer to be 88, as given in the OA, the question should state that "A set of 25 different integers has a median of 50..."

In this case since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$ and thus the maximum value of $$x_{25}$$ is $$x_{25}=38+50=88$$.

The set could be {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 88}

Hope it's clear.
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Manager
Joined: 31 Mar 2013
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Kudos [?]: 12 [0], given: 109

Re: A set of 25 integers has a median of 50 and a range of 50 [#permalink]  03 Sep 2013, 00:58
Shouldn't the question actually be "25 different positive integers" then?
Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4199

Kudos [?]: 40544 [0], given: 5540

Re: A set of 25 integers has a median of 50 and a range of 50 [#permalink]  03 Sep 2013, 01:05
Expert's post
emailmkarthik wrote:
Shouldn't the question actually be "25 different positive integers" then?

That question is here: a-set-of-25-different-integers-has-a-median-of-50-and-a-129345.html
_________________
Re: A set of 25 integers has a median of 50 and a range of 50   [#permalink] 03 Sep 2013, 01:05
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