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# M05-37

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Math Expert
Joined: 02 Sep 2009
Posts: 46319

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16 Sep 2014, 00:26
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Difficulty:

65% (hard)

Question Stats:

54% (01:02) correct 46% (01:04) wrong based on 160 sessions

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Is the average of a set of 5 distinct positive integers {$$a$$, $$b$$, 4, 6, 2} greater than the median?

(1) The highest number in the set is 6

(2) The lowest number in the set is 2

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:26
Official Solution:

Statement (1) by itself is insufficient. It helps us limit the highest value and since we know that the values of $$a$$ and $$b$$ cannot be negative or 0, we can try a scenario such as $$a = 1$$ and $$b = 3$$ and find out that median is 3 and average is 3.2. However, if we try $$a = 3$$ and $$b = 5$$, the average will be equal to the median, 4.

Statement (2) by itself is insufficient. If $$a$$ and $$b$$ are very large numbers, the average will be greater than the median, which will be no higher than 6. But if $$a = 3$$ and $$b = 5$$, then the average is equal to the median.

Statements (1) and (2) combined are sufficient. We know that $$a = 3$$ and $$b = 5$$.

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Joined: 03 May 2016
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16 Nov 2016, 07:48
The question asks if the average is greater than the median. Statement one proves that the average is either equal to or less than the median, so couldn't we get a definitive NO answer for this question?
Math Expert
Joined: 02 Sep 2009
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17 Nov 2016, 23:24
banner03 wrote:
The question asks if the average is greater than the median. Statement one proves that the average is either equal to or less than the median, so couldn't we get a definitive NO answer for this question?

{a, b, 2, 4, 6}
{1, 3, 2, 4, 6} --> average = 3.2 and median = 3 --> the average IS greater than the median.
{3, 5, 2, 4, 6} --> average = 4 and median = 4 --> the average is NOT greater than the median.
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Joined: 03 May 2016
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18 Nov 2016, 07:49
Aww. I see where I went wrong. Thank you!
Intern
Joined: 25 Jun 2017
Posts: 2

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05 Aug 2017, 13:26
Bunuel wrote:
banner03 wrote:
The question asks if the average is greater than the median. Statement one proves that the average is either equal to or less than the median, so couldn't we get a definitive NO answer for this question?

{a, b, 2, 4, 6}
{1, 3, 2, 4, 6} --> average = 3.2 and median = 3 --> the average IS greater than the median.
{3, 5, 2, 4, 6} --> average = 4 and median = 4 --> the average is NOT greater than the median.

Hello Bunnel,

I got the answer as D

Case 1 {2 3 4 4 6} Median =4 Avg = 3.8 Avg is not greater than median
Case 2 {2 4 4 6 6} Median 4, Avg =4.4 Avg is greater than median
so i got the statement that both are insufficient.

Am i doing something wrong here?
Math Expert
Joined: 02 Sep 2009
Posts: 46319

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06 Aug 2017, 00:46
1
piyushasthita wrote:
Bunuel wrote:
banner03 wrote:
The question asks if the average is greater than the median. Statement one proves that the average is either equal to or less than the median, so couldn't we get a definitive NO answer for this question?

{a, b, 2, 4, 6}
{1, 3, 2, 4, 6} --> average = 3.2 and median = 3 --> the average IS greater than the median.
{3, 5, 2, 4, 6} --> average = 4 and median = 4 --> the average is NOT greater than the median.

Hello Bunnel,

I got the answer as D

Case 1 {2 3 4 4 6} Median =4 Avg = 3.8 Avg is not greater than median
Case 2 {2 4 4 6 6} Median 4, Avg =4.4 Avg is greater than median
so i got the statement that both are insufficient.

Am i doing something wrong here?

You should read more carefully: Is the average of a set of 5 distinct positive integers...
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Joined: 26 Feb 2018
Posts: 53
Location: India
WE: Web Development (Computer Software)

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22 Jun 2018, 14:32
I think this is a high-quality question and I agree with explanation.
Re M05-37   [#permalink] 22 Jun 2018, 14:32
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# M05-37

Moderators: chetan2u, Bunuel

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