1981 AHSME Problems/Problem 12

Problem

If $p$ , $q$ , and $M$ are positive numbers and $q<100$ , then the number obtained by increasing $M$ by $p\%$ and decreasing the result by $q\%$ exceeds $M$ if and only if

$\textbf{(A)}\ p>q \qquad\textbf{(B)}\ p>\dfrac{q}{100-q}\qquad\textbf{(C)}\ p>\dfrac{q}{1-q}\qquad \textbf{(D)}\ p>\dfrac{100q}{100+q}\qquad \\ \textbf{(E)}\ p>\dfrac{100q}{100-q}$

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1981 AHSME Problems/Problem 12

Problem

Solution (Answer Choices)