Average Problem

gmat009 wrote:If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

The average of a set of consecutive numbers with an odd number of terms will simply be the middle term of the set.

So, all we know at the moment is that x is an even number, since the middle term in our set will always be even.

I must be true.

II could be true (if our set were {2, 4, 6, 8, 10}) but also could be false (if our set were {-4, -2, 0, 2, 4}). Therefore, II is not a MUST be true.

III could be true (if our set were {-4, -2, 0, 2, 4}) but also could be false (if our set were {2, 4, 6, 8, 10}). Therefore, III is not a MUST be true.

Choose (A), I only.

Hi Stuart,

Is 0 considered an even integer? If not, then I is not necessarily true.

Asif

0 is an even integer.
But 0 is neither positive or negative. Nor is 0 prime or composite.

mals24 wrote:0 is an even integer.
But 0 is neither positive or negative. Nor is 0 prime or composite.

Bingo!