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From 2) we get -z+1 < 0 I.e. z>1 ==> 2) sufficient

1) is not sufficient: for example, consider (x,y,z)=(-0.5,-0.2,1): x+y+z>0 and z>x+y+1 and for (x,y,z)=(-0.5,-0.2,3): also both inequalities are verified

I didn't understand how statement 2 is sufficient as stated by echizen

according to statement 2 , x+y+1 < 0 , so x+y < -1 , so say x+y = -2

from qs, x+y+z>0 , -2+z>0 , z>2 , but that does not necessarily mean z>1 ?? Hence statement 2 is also insufficient.

Whats the QA ? ( pls post it along with explanation if given )

The two inequalities say x+y<-1, and x+y+z>0, therefore, z will need to be greater than 1 (and in your example, greater than 2), otherwise x+y(which is <-1)+z will be less than 0.