{"status": "success", "data": {"description_md": "How many pairs of positive integers $(a,b)$ are there such that $\\gcd{(a,b)}=1$ and $$\\frac{a}{b}+\\frac{14b}{9a}$$ is an integer?\n\n$\\mathrm {(A)} 4\\qquad \\mathrm {(B)} 6\\qquad \\mathrm {(C)} 9\\qquad \\mathrm {(D)} 12\\qquad \\mathrm {(E)} \\text{infinitely many}$\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>How many pairs of positive integers  <span class=\"katex--inline\">(a,b)</span>  are there such that  <span class=\"katex--inline\">\\gcd{(a,b)}=1</span>  and  <span class=\"katex--display\">\\frac{a}{b}+\\frac{14b}{9a}</span>  is an integer?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A)} 4\\qquad \\mathrm {(B)} 6\\qquad \\mathrm {(C)} 9\\qquad \\mathrm {(D)} 12\\qquad \\mathrm {(E)} \\text{infinitely many}</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": 5, "problem_name": "2007 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12B_p25", "prev": "/problem/07_amc12B_p23"}}