Inapproximability Problem

I've been trying to solve this problem for over a week now and I can't seem to get anywhere:

"Given an optimization problem A, let the corresponding optimal solution value for A be opt(A). Prove that if deciding whether opt(A) = 0 is NP-Complete then there does not exist any approximate solution for problem A regardless of its approximation factor unless P=NP."

I figure that I need to reduce a known inapproximable problem(like max-clique or max-independent set) to the problem of deciding whether opt(A) = 0 for any optimization problem A. But the problem is so general that I can't seem to figure it out.

Any ideas?