GMAT Data Sufficiency (DS) | If a and b are positive integers, is a + b even?

(1) 5a – 1 is odd
This is possible only when a is even.
However we have no information about b, which could be either odd or even.
If b is odd, a+b is not even whereas b being even means a+b iseven
Insufficient.
(2) ab is even
This statement is true when :
1.a,b are both even
2.a is odd, b is even
3.a is even, b is odd.
Using condition1, a+b is even. However using condition2 and 3, a+b is odd.
Insufficient.

Combining both the statements,
a being even and b being odd, makes a+b odd.
On the
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