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Fairy Fractions

Source: 2018 AMC 12B #17

February 16, 2018
AMCAMC 12AMC 12 B2018 AMC 12B2018 AMC

Problem Statement

Let pp and qq be positive integers such that 59<pq<47\frac{5}{9} < \frac{p}{q} < \frac{4}{7} and qq is as small as possible. What is q−pq-p?
<spanclass=′latex−bold′>(A)</span>7<spanclass=′latex−bold′>(B)</span>11<spanclass=′latex−bold′>(C)</span>13<spanclass=′latex−bold′>(D)</span>17<spanclass=′latex−bold′>(E)</span>19<span class='latex-bold'>(A) </span> 7 \qquad <span class='latex-bold'>(B) </span> 11 \qquad <span class='latex-bold'>(C) </span> 13 \qquad <span class='latex-bold'>(D) </span> 17 \qquad <span class='latex-bold'>(E) </span> 19
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