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# M30-04

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:45
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Difficulty:

75% (hard)

Question Stats:

44% (00:56) correct 56% (01:02) wrong based on 178 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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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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22 Oct 2016, 16:11
Shouldn't the mention of Set A in (2) be Set S instead?
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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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14 Jan 2018, 09:01
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Bunuel
M28-47 and M30-04 are the same question
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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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01 Jan 2019, 07:23
Can't the Data Set A (using Both the statements) be {1} , {2,2} or {3,3,3} etc ?
median can be 1,2 or 3 too.

Could you please explain why the above numbers can't be Data Set A.
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Joined: 02 Oct 2016
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01 Jan 2019, 10:06
{2,2} or {3,3,3} does not satisfy statement 2.
In the above mentioned set Average is not equal to Range
For , {2,2} Average = 2, Range = 0
{3,3,3}, Average = 3, range =0
Only set A= { x, x,x,x...} where x=0 satisfies both the statement, hence ans C.
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Joined: 17 Apr 2017
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08 Jan 2019, 08:05
Hi Bunuel
Can you please explain why we consider {0,0,0,0} & {1,2,2,3} for Set A? Is repetition of elements allowed in Sets?
How a Set is different from a List?
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09 Jan 2019, 00:49
mukulmehta57 wrote:
Hi Bunuel
Can you please explain why we consider {0,0,0,0} & {1,2,2,3} for Set A? Is repetition of elements allowed in Sets?
How a Set is different from a List?

Set is different from data set and list in that in data set and list repetitions are allowed.
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Re: M30-04   [#permalink] 09 Jan 2019, 00:49
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# M30-04

Moderators: chetan2u, Bunuel