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Set S contains five distinct positive integers, each of which

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

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New post 08 Aug 2018, 21:46
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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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Re: Set S contains five distinct positive integers, each of which  [#permalink]

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New post 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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Re: Set S contains five distinct positive integers, each of which  [#permalink]

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New post 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

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