Question : is (x+y)^2 > x^2 + Y^2
This reduces to : is 2xy>0,or is xy>0

Statement 1:
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x+y < 0

Picking numbers we can see that both x and y can be -ve in which case xy>0
say,
x=-10,y=5 , x+y < 0 but xy <0
Hence,insufficient.

Statement 2:
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|x|=y
==> x=-y or x=y
If x=y,whether both are +ve or -ve,xy will be +ve
if x=-y,then xy will be -ve
Insufficient

Combining 1 and 2 we get

We need x+y < 0 hence if x=-y then x+y = 0 which violates statement1.
Hence X=y and hence xy>0
Pick C.