1952 AHSME Problem 34

The price of an article was increased p\%. Later the new price was decreased p\%. If the last price was one dollar, the original price was:

\begin{array}{l} \textbf{(A)}\ \frac{1-p^2}{200}\qquad \textbf{(B)}\ \frac{\sqrt{1-p^2}}{100}\qquad \textbf{(C)}\ \text{one dollar}\qquad\\ \textbf{(D)}\ 1-\frac{p^2}{10000-p^2}\qquad \textbf{(E)}\ \frac{10000}{10000-p^2} \end{array}

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