{"status": "success", "data": {"description_md": "Let $p$ and $q$ be positive integers such that $$\\frac{5}{9} < \\frac{p}{q} < \\frac{4}{7}$$and $q$ is as small as possible. What is $q-p$?\n\n$\\textbf{(A) } 7 \\qquad \\textbf{(B) } 11 \\qquad \\textbf{(C) } 13 \\qquad \\textbf{(D) } 17 \\qquad \\textbf{(E) } 19$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">p</span>  and  <span class=\"katex--inline\">q</span>  be positive integers such that  <span class=\"katex--display\">\\frac{5}{9} &lt; \\frac{p}{q} &lt; \\frac{4}{7}</span> and  <span class=\"katex--inline\">q</span>  is as small as possible. What is  <span class=\"katex--inline\">q-p</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 7 \\qquad \\textbf{(B) } 11 \\qquad \\textbf{(C) } 13 \\qquad \\textbf{(D) } 17 \\qquad \\textbf{(E) } 19</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2018 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12B_p18", "prev": "/problem/18_amc12B_p16"}}