1958 AHSME Problem 13

The sum of two numbers is 10; their product is 20. The sum of their reciprocals is:

\textbf{(A)}\ \frac{1}{10}\qquad \textbf{(B)}\ \frac{1}{2}\qquad \textbf{(C)}\ 1\qquad \textbf{(D)}\ 2\qquad \textbf{(E)}\ 4

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