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Numerator and Denominator Increased by One

Source: 2015 AMC 10A #15

February 4, 2015
SFFTAMCAIMEnumber theoryrelatively prime

Problem Statement

Consider the set of all fractions xy,\tfrac{x}{y}, where xx and yy are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by 11, the value of the fraction is increased by 10%10\%?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>infinitely many <span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>3\qquad<span class='latex-bold'>(E) </span>\text{infinitely many}
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