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# GMAT Diagnostic Test Question 21

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GMAT Diagnostic Test Question 21 [#permalink]  06 Jun 2009, 21:59
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GMAT Diagnostic Test Question 21
Field: word problems (min/max)
Difficulty: 700

A set of 11 different integers has a median of 25 and a range of 50. What is the greatest possible integer that could be in this set?

A. 65
B. 70
C. 75
D. 80
E. 85
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Last edited by bb on 28 Sep 2013, 20:33, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 20 [#permalink]  08 Jul 2009, 05:56
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Consider 11 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{11}$$.

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 $$x_{6}=25$$;

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 $$50=x_{11}-x_{1}$$ --> $$x_{11}=50+x_{1}$$;

We want to maximize $$x_{11}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-5=25-5=20$$ and thus the maximum value of $$x_{11}$$ is $$x_{11}=50+20=70$$.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

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Re: GMAT Diagnostic Test Question 21 [#permalink]  20 Nov 2013, 11:24
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Why must the numbers in the set be different in order to calculate the median?

Couldn't I arrange a set like the following? S={25, 25, 25, 25, 25, 25, 75, 75, 75, 75, 75}?
(Note that after x6, the follwoing numbers could be anything between 26 and 74)

In this way, the median is still 25, but the máximum value of x would now be 75, making "C" the correct answer.

D.
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Re: GMAT Diagnostic Test Question 21 [#permalink]  21 Nov 2013, 00:55
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peti wrote:
Why must the numbers in the set be different in order to calculate the median?

Couldn't I arrange a set like the following? S={25, 25, 25, 25, 25, 25, 75, 75, 75, 75, 75}?
(Note that after x6, the follwoing numbers could be anything between 26 and 74)

In this way, the median is still 25, but the máximum value of x would now be 75, making "C" the correct answer.

D.

The number is the set must be different because we are told that they are different, check the stem: "A set of 11 different integers has ..."
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Re: GMAT Diagnostic Test Question 20 [#permalink]  05 Jan 2014, 16:45
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[quote="dzyubam"]Consider 11 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{11}$$.

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 $$x_{6}=25$$;

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 $$50=x_{11}-x_{1}$$ --> $$x_{11}=50+x_{1}$$;

We want to maximize $$x_{11}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-5=25-5=20$$ and thus the maximum value of $$x_{11}$$ is $$x_{11}=50+20=70$$.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

its clear till since....distict
i was not able to follow after that..??? can u please explain just that area
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Re: GMAT Diagnostic Test Question 20 [#permalink]  05 Jan 2014, 18:03
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Expert's post
lindt123 wrote:
dzyubam wrote:
Consider 11 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{11}$$.

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 $$x_{6}=25$$;

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 $$50=x_{11}-x_{1}$$ --> $$x_{11}=50+x_{1}$$;

We want to maximize $$x_{11}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-5=25-5=20$$ and thus the maximum value of $$x_{11}$$ is $$x_{11}=50+20=70$$.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

its clear till since....distict
i was not able to follow after that..??? can u please explain just that area

We know that the median, $$x_6$$, is 25. What is the maximum value of $$x_5$$. Since $$x_5<x_6$$, then the maximum value of $$x_5$$ is 24. Similarly the maximum value of $$x_4$$ is 23, the maximum value of $$x_3$$ is 22, the maximum value of $$x_2$$ is 21 and the maximum value of $$x_1$$ is 20.

Hope it's clear.
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Re: GMAT Diagnostic Test Question 20 [#permalink]  05 Jan 2014, 20:51
Bunuel wrote:
lindt123 wrote:
dzyubam wrote:
Consider 11 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{11}$$.

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 $$x_{6}=25$$;

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 $$50=x_{11}-x_{1}$$ --> $$x_{11}=50+x_{1}$$;

We want to maximize $$x_{11}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-5=25-5=20$$ and thus the maximum value of $$x_{11}$$ is $$x_{11}=50+20=70$$.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

its clear till since....distict

i was not able to follow after that..??? can u please explain just that area

We know that the median, $$x_6$$, is 25. What is the maximum value of $$x_5$$. Since $$x_5<x_6$$, then the maximum value of $$x_5$$ is 24. Similarly the maximum value of $$x_4$$ is 23, the maximum value of $$x_3$$ is 22, the maximum value of $$x_2$$ is 21 and the maximum value of $$x_1$$ is 20.

Hope it's clear.

THANX A LOT....IT DID HELP A LOT!!!
Re: GMAT Diagnostic Test Question 20   [#permalink] 05 Jan 2014, 20:51
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# GMAT Diagnostic Test Question 21

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