Since x + y >0, both x and y cannot be -ve. Also when one of them is +ve and the other -ve, the +ve number has to be numerically greater than the -ve.

now let us take (1) x >y.

If both x and y are +ve then, since x > y, x > |y|.

let one of them be -ve. Since x > y, x has to be +ve and y has to be -ve.
Also as stated above the +ve number has to be numerically greater than the -ve. So x should be numerically greater than y, so x > |y|.

So (1) alone is sufficient.

Consider (2) y<0.

Now the case of both +ve doesnot exist.
y has to be -ve and x has to be +ve. And the condition we have the +ve number has to be numerically greater than the -ve. So x should be numerically greater than y, so x > |y|.

So (2) alone is sufficient.

Hence (1) and (2) alone are sufficient.

Iam positive about the answer but correct me if anything is wrong.