$32 \cdot 50$ Let $b$ take even numbers between $1 \sim 11$, $c$ take any natural number, then the number of quadratic equations $x^{2}+b x+c=0$ that can be formed with two distinct real roots is
(A) 50.
(B) 55.
(C) 57.
(D) 58.
(China Beijing Junior High School Mathematics Competition, 1992)
[Solution] The even numbers between 1 and 11 are $2, 4, 6, 8, 10$, five in total.
Also, the discriminant of the quadratic equation $\Delta=b^{2}-4 c>0$. If we set $b=2 k$, then
$$
4 k^{2}-4 c>0 \text {, i.e., } k^{2}>c \quad(k=1,2,3,4,5) \text {. }
$$

Thus, we have the following table, which shows the number of $c$ values that satisfy $k^{2}>c$:
\begin{tabular}{|c|c|c|c|c|c|}
\hline$k \quad$ value & 1 & 2 & 3 & 4 & 5 \\
\hline Number of $c$ & 0 & 3 & 8 & 15 & 24 \\
\hline
\end{tabular}

Therefore, the answer is $(A)$.