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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}

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.

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 ..."
_________________

[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

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.

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!!!

gmatclubot

Re: GMAT Diagnostic Test Question 20
[#permalink]
05 Jan 2014, 20:51