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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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6985
GMAT 1: 760 Q51 V42
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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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16 Jan 2019, 00:21
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Difficulty:

25% (medium)

Question Stats:

69% (00:55) correct 31% (01:33) wrong based on 38 sessions

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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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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 21 Jan 2015 Posts: 449 Location: India Concentration: Strategy, Marketing GMAT 1: 620 Q48 V28 GMAT 2: 690 Q49 V35 WE: Sales (Consumer Products) Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m [#permalink] ### Show Tags 16 Jan 2019, 01:04 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 $$m$$? $$A. -1$$ $$B. 0$$ $$C. 1$$ $$D. 2$$ $$E. 3$$ _________________ -------------------------------------------------------------------- The Mind is Everything, What we Think we Become. Manager Joined: 01 May 2017 Posts: 69 Location: India If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m [#permalink] ### Show Tags 16 Jan 2019, 01:12 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 Senior Manager Joined: 04 Aug 2010 Posts: 357 Schools: Dartmouth College Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m [#permalink] ### Show Tags 16 Jan 2019, 03:23 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! _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 772 Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m [#permalink] ### Show Tags 16 Jan 2019, 04:17 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. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net VP Joined: 09 Mar 2018 Posts: 1002 Location: India If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m [#permalink] ### Show Tags 16 Jan 2019, 04:38 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 Posted from my mobile device _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. SVP Joined: 18 Aug 2017 Posts: 1928 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m [#permalink] ### Show Tags 16 Jan 2019, 05:14 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 _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6985 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If the median and the range of the data set 1, 1, 2, 2, 3, 3, 4, 4, m [#permalink] ### Show Tags 18 Jan 2019, 04:10 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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, 04:10
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