Problem Solving

The average of a series of consecutive integers is an even integer. Which of the following could be true?

I. There is an even number of integers in the series.
II. The smallest number in the series is odd.
III. The product of the smallest and largest number in the series is odd.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

The OA is E