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# For a certain set of n numbers, where n > 2, is the average (arithmeti

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
For a certain set of n numbers, where n > 2, is the average (arithmeti  [#permalink]

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24 Dec 2017, 00:23
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Difficulty:

55% (hard)

Question Stats:

50% (01:39) correct 50% (01:17) wrong based on 25 sessions

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For a certain set of n numbers, where n > 2, is the average (arithmetic mean) equal to the median?

(1) The difference between the smallest number in the set and the middle number is equal to the difference between the largest number and the middle number.
(2) n = 3

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Re: For a certain set of n numbers, where n > 2, is the average (arithmeti  [#permalink]

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24 Dec 2017, 04:08
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Bunuel wrote:
For a certain set of n numbers, where n > 2, is the average (arithmetic mean) equal to the median?

(1) The difference between the smallest number in the set and the middle number is equal to the difference between the largest number and the middle number.
(2) n = 3

Statement 1: if the set is {-1,0,1,1,3}, then 1-(-1)=3-1 but the median is 1 and the average is 0.8. So we have a NO

but if the set is {1,2,3}, then we have a Yes. Insufficient

Statement 2: if we have {1,2,3}. We have a yes but if we have {1,2,9}, then we have a NO. Insufficient

Combining 1 & 2 we know the set has only 3 numbers and Middle-Lowest=Largest-Middle, so the set is an AP series.

In an AP series, with odd number of elements, Median = Mean. Sufficient

Option C
Re: For a certain set of n numbers, where n > 2, is the average (arithmeti   [#permalink] 24 Dec 2017, 04:08
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