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GMAT Diagnostic Test Question 21

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GMAT Diagnostic Test Question 21 [#permalink] New post 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] New post 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}

Answer: B.
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Re: GMAT Diagnostic Test Question 21 [#permalink] New post 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.

Thanks for your comments!
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Re: GMAT Diagnostic Test Question 21 [#permalink] New post 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.

Thanks for your comments!
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] New post 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] New post 05 Jan 2014, 18:03
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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] New post 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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