IMO C.

Let me try to explain my approach for this one.

Addition of 2 numbers will be even when both of them are either even or odd.

Now lets check option 1.

3a + 4b is even. 3a can be either even or odd depending value of a. 4b will be even irrespective b being even or odd. Hence, 3a should be even if the sum has to be even. But, we cannot confirm whether b is odd or even with this statement.

Now lets check option 2.

3a + 5b is even. 3a can be either even or odd depending value of a. 5b can be either even or odd depending value of a. Hence, a and b can be either even or odd. This also not sufficient to conclude whether b is even or off.

Combing these 2 statements.

Both 3a + 4b and 3a + 5b are even.

Then as per first statement 3a should be even.

Then 4b and 5b should be even if the sum has to be even in both the cases.

Then b should be even. Hence, C is the answer.

Please let us know the OA and explanation if I am wrong or ambiguous.

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