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If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m

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If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m  [#permalink]

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New post 16 Jan 2019, 01:21
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[Math Revolution GMAT math practice question]

If the median and the range of the data set \(1, 1, 2, 2, 3, 3, 4, 4, m\) are the same, which of the following could be the value of \(m\)?

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 2\)
\(E. 3\)

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Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m  [#permalink]

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New post 16 Jan 2019, 02:04
Ans: E
There are 9 numbers so median in the series is 5th number which is 3.
Now for Range to be 3: Max element- Min element = 3
so m-1 = 3; so m=4, which is not in the answers.

Now if m =3 then median remains the same and range = median so m=3 is the answer.
check if m=2 then range is 3 but median will be 2; not possible.

Ans: E
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If the median and the range of the data set \(1, 1, 2, 2, 3, 3, 4, 4, m\) are the same, which of the following could be the value of \(m\)?

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 2\)
\(E. 3\)

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If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m  [#permalink]

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New post 16 Jan 2019, 02:12
If the median and the range of the data set 1,1,2,2,3,3,4,4,m are the same, which of the following could be the value of m?

'm' may take any value median can take only two values,
1) median = 2 if m <= 2
2) median = 3 if m>=3


But m <= 2 doesn't satisfy the condition median = range
Range = Max - Min
consider m = -2
median = 2
Range = 4-(-2) = 6
median != Range

Or
m = 2
Range = 4-1 = 3
median = 2


2) Let median = 3, range should be 3 implies max - min = 3
4-1 = 3
So, in order to satisfy above condition m should be 3 OR 4


OR we can solve it logically
1) median = 2 if m <= 2
2) median = 3 if m>=3

From given 4-1 = 3 (Range) and clearly it can't be less than 3, so m = 3 OR 4 are the only possibilities
But in option we have only 3


Option E is correct
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Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m  [#permalink]

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New post 16 Jan 2019, 04:23
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If the median and the range of the data set \(1, 1, 2, 2, 3, 3, 4, 4, m\) are the same, which of the following could be the value of \(m\)?

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 2\)
\(E. 3\)


We can PLUG IN THE ANSWERS, which represent the value of \(m\).
When the correct answer is plugged in, the median will be equal to the range.
Note:
When the prompt includes the phrase which of the following, the correct answer is likely to be D or E.

E: m=3
Resulting set: 1, 1, 2, 2, m=3, 3, 3, 4, 4
Median = 3
Range = 4-1 = 3
Success!


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Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m  [#permalink]

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New post 16 Jan 2019, 05:17
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If the median and the range of the data set \(1, 1, 2, 2, 3, 3, 4, 4, m\) are the same, which of the following could be the value of \(m\)?

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 2\)
\(E. 3\)

\(?\,\, = m\,\,\,\,\,\,\left( {{\rm{range = median}}} \right)\)

\(m < 4\,\,\,\left( {{\rm{alternative}}\,\,{\rm{choices}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{range}} = \left\{ \matrix{
\,4 - 1 = 3\,\,\,{\rm{if}}\,\,\,m \in \left\{ {1,2,3} \right\}\,\,\,\,\left( * \right) \hfill \cr
\,4 - 0 = 4\,\,\,{\rm{if}}\,\,\,m = 0 \hfill \cr
\,4 - \left( { - 1} \right) = 5\,\,\,{\rm{if}}\,\,\,m = - 1 \hfill \cr} \right.\)

\(m = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{Med}}\left( {\left\{ {1,1,2,2,3,3,4,4} \right\} \cup \left\{ 3 \right\}} \right)\,\,\, = \,\,\,3\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{\rm{range}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left( {\rm{E}} \right)\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m  [#permalink]

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New post 16 Jan 2019, 05:38
Lets see, Median = Range

For this to be true, whichever term you enter will be responsible in making the median = Range(higest number - lowest number)

Since it is a series of 9 numbers
Median will be the 5th term

And in this series the only number which will make the question true is 3

5th term = 3
Range = 4-1 = 3

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Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m  [#permalink]

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New post 16 Jan 2019, 06:14
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If the median and the range of the data set \(1, 1, 2, 2, 3, 3, 4, 4, m\) are the same, which of the following could be the value of \(m\)?

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 2\)
\(E. 3\)



we can plugin given options
option e 3
gives us both mean and range as 3
IMO E
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Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m  [#permalink]

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New post 18 Jan 2019, 05:10
=>

If \(3 ≤ m ≤ 4\), then the median is \(3\) and the range of the data is \(3\). Thus, any number between \(3\) and \(4\), inclusive, is possible.
If \(2 ≤ m < 3\), then the median is \(m\) and the range of the data is \(3\). Thus, there is no possible value of \(m\) in the interval \(2 ≤ m < 3\).
If \(m < 2\), then the median is \(2\) and the range of the data is greater than \(2\). Thus, there is no possible value of \(m\) less than \(2\).
If \(m > 4\), then the median is \(3\) and the range of the data is greater than \(3\). Thus, there is no possible value of \(m\) greater than \(4\).


Therefore, the answer is E.
Answer: E
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Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m   [#permalink] 18 Jan 2019, 05:10
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