Data Sufficiency

If x-y>10, is x-y>x+y?
1) x = 8
2) y = -20

OA : D

I marked A.
Statement 1: if x = 8 and x-y>10, that means y is negative. therefore, 10> 8 + (a negative number). SUFFICIENT
Statement 2: if y = -20, x + 20 >10, x > - 10.
Assuming x to be a negative integer, say -9, 10 > - 9 - 20 , 10>-29.
Assuming x to be a positive integer, say 50, 10 > 50 -20, 10>30. Which is not correct. INSUFFICIENT.

Please tell me what is wrong wtih my reasoning above.