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