If A, B, and C are integers and AB + C is even, which of the following

The question asks what MUST be true. So, we can ELIMINATE any answer choice where we can find an example that makes the statement false.

A) A+C is even
If A = 1, B = 2 and C = 2, then the given statement (AB+C is even) is true.
HOWEVER, statement A is FALSE since A + C = 1 + 2 = 3, and 3 is NOT even.
Since statement A is not necessarily true, we can ELIMINATE answer choices 2 and 4

IMPORTANT: Answer choices 1 and 3 both suggest that statement C is true. So, let's check C

C) ABC is even
If A = 1, B = 1 and C = 1, then the given statement (AB+C is even) is true.
HOWEVER, statement C is FALSE since ABC = (1)(1)(1) = 1, and 1 is NOT even.
Since statement C is not necessarily true, we can ELIMINATE answer choices 1 and 3

This leaves only one answer choice: 5 (aka E)