If p, q, r are a series of three consecutive positive integers, is the

Tough and Tricky questions: Number Properties.

If p, q, r are a series of three consecutive positive integers, is the sum of all the integers odd?

(1) Two of the three numbers p, q, r are odd numbers.
(2) (p + q + r)/3 is an even integer.

Kudos for a correct solution.

Source: Chili Hot GMAT