$x=100+20\sqrt{y}+y$ $x-2y=100+20\sqrt{y}-y$ Let $t=\sqrt{y}$ Then we need to prove, that $t^2-20t+100 \ge 0$, which is obvious by $(t-10)^2 \ge 0$.

Can a mod put all of the PR 2013 TST Problems together in the contests page? Thank you

have a look here http://www.artofproblemsolving.com/community/c6h1071990p4665221

Ooohhh I thought those were instructions only for mods. Thanks.

Is it supposed to already appear on the Puerto Rico TST page or do I have to wait for a mod to make it visible or something?

It is already here : http://www.artofproblemsolving.com/community/c72388_2013_puerto_rico_team_selection_test They will add it in the Puerto Rico TST page.