Question 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 $Q(x)?$