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1981 AMC 12 Question 12

AMC12 · 1981 AMC 12

Question 12

If $p,$ $q,$ and $M$ are positive numbers and $q\lt100,$ then the number obtained by increasing $M$ by $p\%$ and decreasing the result by $q\%$ exceeds $M$ if and only if
  1. $p\gt q$
  2. $p\gt\frac q{100-q}$
  3. $p\gt\frac q{1-q}$
  4. $p\gt\frac{100q}{100+q}$
  5. $p\gt\frac{100q}{100-q}$