Another way to look at the second statement is this. this will save u a lot of time. won't even have to plug in for this.
Remember that |x| >y (or any such relation, no matter >,< or =) can be written as
(that is, just remember to keep the relation the same and just put negative on the left hand side and positive on the right hand side.)
so... statement 2 says r<|S|
meaning |s|>r ==> -r>s>r
so on the left hand side, S lies further left of -r, such that if r is 2 and thus -r is -2, s is even less and so s is -3 thus s is less than r, and so the main queston r>s is answered yes. but on the right hand side, s>r so the main question is answered no. hence stmt 2 is not sufficient.
Is r > s ?
(1) -r + s < 0
(2) r < | s |
Well, 1st one is clear but I have some difficulties with second statement. I guessed it's not sufficient but need clarification. Thank you!