Solution

The question's last line says "..*can serve* as a necessary condition to guarantee that system is not *approaching*.... a deadlock". So we just have to make sure the next move is not a deadlock.

Take an example when all the processes are in process and already having xi instances and requested yi instances.. and question says 2 of the processes p and q are not requesting additional y instances, so these will be the first one to complete. And after p and q complete they release xp and xq resources, So now any other waiting request can proceed provided (xp + xq) >= min(yi)  [means any 1 process having yi > (xp + xq) can proceed safely]