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If m is a positive odd integer, what is the average (arithme

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If m is a positive odd integer, what is the average (arithme

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If m is a positive odd integer, what is the average (arithmetic mean) of a certain set of m integers

(1) The integers in the set are consecutive multiples of 3.
(2) The median of the set of integers is 33

OA C

Source: GMAT Prep

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BTGmoderatorDC wrote:
If m is a positive odd integer, what is the average (arithmetic mean) of a certain set of m integers

(1) The integers in the set are consecutive multiples of 3.
(2) The median of the set of integers is 33
For any EVENLY SPACED SET:
average = median

Statement 1:
Here, the set consists of consecutive multiples of 3 and thus is evenly spaced.
Case 1: 3, 6, 9
Average = median = 6.
Case 2: 6, 9, 12
Average = median = 9.
Since different averages are possible, INSUFFICIENT.

Statement 2:
Case 1: 33, 33, 33
Average = median = 33.
Case 2: 33, 33, 1000
Here, the average is clearly greater than 33.
Since different averages are possible, INSUFFICIENT.

Statements combined:
Since the set consists of multiples of 3 and thus is evenly spaced, average = median = 33.
SUFFICIENT.

The correct answer is C.

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