Here's what the OE did, which I wasn't entirely convinced.
For statement 1: z > x+y+1
It says statement 1 is not sufficient. What it did was to use x + y + z > 0, so x+y > -z, so that using (1), z > x+y+1>-z+1, impllies z > 0.5. What happens here is it took x+y to be equal to -z and substituted it inside the inequality. But x+y is not equals -z, it is greater than -z. So x+y can be anything, say, -z+1, or -z+20 etc. So if x+y=-z+20, then z > -z+20+1, 2z > 21, z > 21/2 !
For statement 2: x+y<-1, so z>1 for x+y+z>0.
What do you think of the OE for statement (1) ?