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# M30-04

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Math Expert
Joined: 02 Sep 2009
Posts: 46267

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16 Sep 2014, 01:45
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Difficulty:

55% (hard)

Question Stats:

57% (01:04) correct 43% (00:53) wrong based on 37 sessions

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What is the median of data set A?

(1) No number in data set A is less than the average (arithmetic mean) of the set.

(2) The average (arithmetic mean) of data set A is equal to the range of the set.

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Joined: 02 Sep 2009
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16 Sep 2014, 01:45
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Official Solution:

What is the median of data set A?

(1) No number in data set A is less than the average (arithmetic mean) of the set.

Since no number is less than the average, then no number is more than the average, which implies that the list contains identical elements: A={x, x, x, ...}. From this it follows that (the average)=(the median). But we don't know the value of $$x$$, thus this statement is NOT sufficient.

(2) The average (arithmetic mean) of data set A is equal to the range of the set.

Not sufficient: if A={0, 0, 0, 0}, then (the median)=0, but if A={1, 2, 2, 3}, then (the median)=2.

(1)+(2) From (1) we have that the list contains identical elements. The range of all such sets is 0. Therefore, from (2) we have that (the average)=(the range)=0 and since from (1) we also know that (the average)=(the median), then (the median)=0. Sufficient.

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Joined: 28 Nov 2011
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Location: United States
GMAT 1: 640 Q42 V35
GMAT 2: 710 Q47 V40
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22 Oct 2016, 16:11
Shouldn't the mention of Set A in (2) be Set S instead?
Math Expert
Joined: 02 Sep 2009
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23 Oct 2016, 00:37
lesliehh wrote:
Shouldn't the mention of Set A in (2) be Set S instead?

___________
Edited. Thank you.
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Joined: 11 Oct 2017
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14 Jan 2018, 09:01
1
Bunuel
M28-47 and M30-04 are the same question
Math Expert
Joined: 02 Sep 2009
Posts: 46267

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14 Jan 2018, 23:00
Zksgmat wrote:
Bunuel
M28-47 and M30-04 are the same question

Thank you for reporting. Removed M28-47 from the questions' pool.
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Re: M30-04   [#permalink] 14 Jan 2018, 23:00
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# M30-04

Moderators: chetan2u, Bunuel

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