Black box with O(n) calls
I believe you have misunderstood the question. You are given a black box that can answer queries of the form "does $X$ have a subset summing to $Q$", and you need to construct an algorithm that given $X$ and $Q$, finds a subset summing to $Q$ if one exists.

Here is a hint:


  Choose an arbitrary $x \in X$. Ask the black box whether there is a subset of $X - x$ summing to $Q - x$.