It's best to start with Data Sufficiency problems by asking yourself at the outset: What do I need? Well, regardless of whether x is even or odd, the first two terms of the equation will end up being either both odd or both even. Accordingly, everything will come down to whether the third term is odd or even. Accordingly, only the y value is relevant to whether the whole formula turns out odd or even.

(1) Does this tell me whether the third term will be odd or even? No.
(2) Does this tell me whether the third term will be odd or even? Yes.

(B)

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Now, x^2+11x+13y = x(x+11)+13y. As x(x+11) is always an even integer (one of x and x + 11 must be even), x^2+11x+13y is even precisely when 13y is even. This is equivalent to y being even, so the question can be restated as 'Is y an even number?'.

Condition 1)
If x = 11 and y = 1, then x^2+11x+13y = 255 is an odd integer.
If x = 11 and y = 2, then x^2+11x+13y = 268 is an even integer.
Since the question does not have a unique answer, condition 1) is not sufficient.

Condition 2)
If y = 13, then y is odd, and the answer to the question is 'no'.
Condition 2) is sufficient.


Therefore, B is the answer.

Answer: B