Statement 1 is insufficient while statement 2 is sufficient.

1) is insufficient cause -

We have x + y + z > 0 given and by 1) z> x + y + 1.

Take x = -.75, y = 0.25 and z = 0.75. We satisfy both the equations.

Yet z<1.

Take x = 1, y = 1 and z =4. We again satisy both equations but z>1

So insufficient.

Mathematical proof.

Add both inequatities - Addition does not change signs.

we get x + y + 2z > x + y + 1

Which is 2z > 1 or z > 1/2

Thus if the question were - is z > 1/2 then answer would be D.

Hope this ends the debate....

_________________

To be or not to be....