If x and y are integer, is y > 0

If x and y are integer, is y > 0?
(1) x +1 > 0
(2) xy > 0

St. (1) : x + 1 > 0
Tells us nothing about y.
Insufficient.

St. (2) : xy > 0
Both x and y can either be positive or negative. Neither x nor y can be 0.
Insufficient.

St. (1) and (2) together :
Since x is an integer and cannot hold the value 0, it has to be greater than 1 in order to satisfy St. (1).
Since we know that x will be positive, y will also have to be a positive integer in order to satisfy St. (2).
Hence Sufficient.

Answer : C