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# Set S contains five distinct positive integers, each of which

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Manager
Joined: 20 Feb 2017
Posts: 164
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
Set S contains five distinct positive integers, each of which  [#permalink]

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08 Aug 2018, 21:46
3
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:58) correct 44% (03:04) wrong based on 30 sessions

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Set S contains five distinct positive integers, each of which is greater than 2. Is the mean of S greater than the median of S?

1) The sum of the elements of S is equal to 20 times the smallest element of S.
2) The median of S is 8 greater than the smallest element of S.

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Intern
Joined: 21 May 2017
Posts: 42
Re: Set S contains five distinct positive integers, each of which  [#permalink]

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08 Aug 2018, 22:27
1
1
C

Smallest possible number = 3

Statement1
Let one of the numbers be 3.
Sum = 20*3 = 60
{3, 4, 12, 14, 27} has mean = median.
{3, 4, 5, 6, 42} has mean > median
{3, 12, 13, 15, 17} has mean < median
Insufficient.

Statement2
Let one of the numbers be 3.
Median = 3 + 8 = 11
{3, 6, 11, 12, 23} has mean = median.
{3, 6, 11, 30, 40} has mean > median
{3, 6, 11, 12, 13} has mean < median
Insufficient

Statement1 and Statement2
Smallest possible number = 3
Smallest possible sum = 20*3=60
Smallest possible mean = 60/5=12
Smallest possible median = 3+8 = 11
Smallest possible mean > Smallest possible median
As we keep increasing the smallest number in the set from 3 to 4,5,6...... the median will increase from 11 to 12,13,14...... but the sum will increase from 60 to 80, 100, 120...... and the mean will increase from 12 to 16, 20, 24......
So, Mean will always be greater than the Median
Sufficient

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Intern
Joined: 05 Sep 2016
Posts: 29
Location: India
Concentration: General Management, Operations
WE: Engineering (Energy and Utilities)
Re: Set S contains five distinct positive integers, each of which  [#permalink]

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08 Aug 2018, 22:42
ankitsaroha wrote:
C

Smallest possible number = 3

Statement1
Let one of the numbers be 3.
Sum = 20*3 = 60
{3, 4, 12, 14, 27} has mean = median.
{3, 4, 5, 6, 42} has mean > median
{3, 12, 13, 15, 17} has mean < median
Insufficient.

Statement2
Let one of the numbers be 3.
Median = 3 + 8 = 11
{3, 6, 11, 12, 23} has mean = median.
{3, 6, 11, 30, 40} has mean > median
{3, 6, 11, 12, 13} has mean < median
Insufficient

Statement1 and Statement2
Smallest possible number = 3
Smallest possible sum = 20*3=60
Smallest possible mean = 60/5=12
Smallest possible median = 3+8 = 11
Smallest possible mean > Smallest possible median
As we keep increasing the smallest number in the set from 3 to 4,5,6...... the median will increase from 11 to 12,13,14...... but the sum will increase from 60 to 80, 100, 120...... and the mean will increase from 12 to 16, 20, 24......
So, Mean will always be greater than the Median
Sufficient

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

That was a neat explanation!!
Re: Set S contains five distinct positive integers, each of which   [#permalink] 08 Aug 2018, 22:42
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