2010 AMC 12B 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 \qquad \textbf{(B)}\ -82 \qquad \textbf{(C)}\ -73 \qquad \textbf{(D)}\ -64 \qquad \textbf{(E)}\ 0

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.