Data Sufficiency

Hi,

Can anyone help with this problem?

Thanks.

Answer C:

The following conditions would equate an even sum:
Even + even
Odd + odd

The following conditions would equate an even product:
Even * even
Even * odd

The first statement:
b is even no matter what (it's even*odd). Because the sum is even, a must also be even.

The second statement:
a and b must either both be even or both be odd.

Together:
Since a is even according to statement 1, b must be even according to statement 2.

Yes answer is C. thanks