Statement 1:
xy > 0
That can mean that either both are positive or both are negative. Hence, insufficient.

Statement 2:
x + y > 0
That can mean:
i) both are positive
ii) x is positive, y is less negative
iii) x is negative, y is more positive
Hence, this is insufficient.

Combining both statements:
We can definitely say that both are positive. Hence x > 0

Answer is C.