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Consecutive Integers: What Must be True?

GMAT-SIK5SM

If $x$, $y$, and $z$ are a set of positive, consecutive integers where $x< y< z$, which of the following must be TRUE?

I. $x\times y$ is an even number
II. $y\times z$ is an even number
III. $x\times y\times z$ is an even number.

A

I only

B

II only

C

III only

D

I and II

E

I, II, and III