{"status": "success", "data": {"description_md": "How many pairs of positive integers $(a,b)$ are there such that $a$ and $b$ have no common factors greater than $1$ and\n$$\\frac{a}{b} + \\frac{14b}{9a}$$\nis an integer?\n\n$\\textbf{(A) } 4 \\qquad\\textbf{(B) } 6 \\qquad\\textbf{(C) } 9 \\qquad\\textbf{(D) } 12 \\qquad\\textbf{(E) } \\text{infinitely many}$", "description_html": "<p>How many pairs of positive integers  <span class=\"katex--inline\">(a,b)</span>  are there such that  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  have no common factors greater than  <span class=\"katex--inline\">1</span>  and<br/>\n <span class=\"katex--display\">\\frac{a}{b} + \\frac{14b}{9a}</span> <br/>\nis an integer?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 4 \\qquad\\textbf{(B) } 6 \\qquad\\textbf{(C) } 9 \\qquad\\textbf{(D) } 12 \\qquad\\textbf{(E) } \\text{infinitely many}</span> </p>\n<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": 4, "problem_name": "2007 AMC 10B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/07_amc10B_p24"}}