AMC 12 2010b Problem 23

Monic quadratic polynomials $P(x)$ and $Q(x)$ have the property that $P(Q(x))$ has zeros at $x=-23, -21, -17,$ and $-15$, and $Q(P(x))$ has zeros at $x=-59,-57,-51$ and $-49$. What is the sum of the minimum values of $P(x)$ and $Q(x)$?

\textbf{(A)}\ -100 \textbf{(B)}\ -82 \textbf{(C)}\ -73 \textbf{(D)}\ -64 \textbf{(E)}\ 0