Max@Math Revolution 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!


The correct answer is E.

Max@Math Revolution 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

$$?\,\, = m\,\,\,\,\,\,\left( {{\rm{range = median}}} \right)$$
$$m < 4\,\,\,\left( {{\rm{alternative}}\,\,{\rm{choices}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{range}} = \left\{ \matrix{
\,4 - 1 = 3\,\,\,{\rm{if}}\,\,\,m \in \left\{ {1,2,3} \right\}\,\,\,\,\left( * \right) \hfill \cr
\,4 - 0 = 4\,\,\,{\rm{if}}\,\,\,m = 0 \hfill \cr
\,4 - \left( { - 1} \right) = 5\,\,\,{\rm{if}}\,\,\,m = - 1 \hfill \cr} \right.$$
$$m = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{range}}\mathop = \limits^{\left( * \right)} 3 = {\rm{median}}\left( {\left\{ {1,1,2,2,3,3,4,4} \right\} \cup \left\{ 3 \right\}} \right)\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left( {\rm{E}} \right)$$


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

Regards,
Fabio.

=>

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