Statement (1) alone is obviously not sufficient.

Consider just statement (2).
x X lyl is not a positive number implies x X lyl can be zero or negative.
If x X lyl is 0, then either x is zero or y is zero or both are zero.
If x is zero then we know, it is not negative.
If y is zero, x can be negative, zero or positive.
If x X lyl is negative, then since lyl cannot be negative, x has to be negative.
Since we cannot say anything definite about x, (2) alone is not sufficient.

Next combine both the statements and check.
Since x^2 > 0, x is not 0.
Still x X lyl can be zero or negative.
If x X lyl is zero, y has to be zero and x can be negative or positive.
If x X lyl is negative, obviously, x has to be negative.
So on combining what we have is if x X lyl is zero, then x can be positive or negative,
and if x X lyl is negative, then x is negative.
So we cannot say definitely whether x can be negative or not.
Or both the statements together are not sufficient to answer the question.

The correct answer is hence (E).