It seems the answer would be E.
It's given that the product of X & Y is negative. Hence one of the two numbers has to be negative.
X + Y=2
X can take the value -1, -2, -3, -4....
Corresponding to that Y can take the value 3, 4, 5, 6.....
Hence 1 is not enough.
It's given that both X & Y are integers. Hence X can be equal to -2, -1, 0.... Similarly Y can be any number more than X.
Thus no definite answer can be obtained using statament 2.
Statament 1 + 2
Since X+Y=2 and the product of the two numbers is negative, using statament 2, we can see that X can be either -2 or -1. Hence Y= 4 or 3
Thus X+Y= 6 or 4.
No definite answer. Hence Option E.