x(r/q- s/p) = (pr-qs)/pq Then x*(pr - qs) /pg = (pr-qs)/pq. So either x = 1, or pr = qs
1. q/r<p/s So pr =/= qs. Then x is 0. Sufficient. 2. x^2 = x. x is either 0 or 1. But if x=0, the known equation x(r/q- s/p) = (pr-qs)/pq may or may not work. So this condition is not sufficient.