Is y^2>y*|y|?

y^2>y*|y| can be possible if y is -ve

(1) y is an integer. It doesn't tell us if y is +ve, -ve or 0
Insufficient
(2) y is not a positive integer.
It doesn't tell us if y is -ve or 0
Insufficient

Both statements together are insufficient. Hence E should be the answer

We can modify the original condition and the question. If y>0, the sign of inequality does not change even if we divide each side by y. Then, we got y>|y|?. However, this is not possible in any cases.
If y<0, and if we divide each side by y, the sign of inequality change. Then we get y<|y|?. The answer is yes.
The questions states y^2>y|y|? and this is same as y<0?.
However, using the condition 1) and the condition 2), we do not have y<0. The condition, hence, is not sufficient and the correct answer is E. In other words, when y=0, the answer is no and when y=-1, the answer becomes yes. The conditions are not sufficient and the correct answer is E.