{"status": "success", "data": {"description_md": "Let $A$ be the set of positive integers that have no prime factors other than $2$, $3$, or $5$. The infinite sum $$\\frac{1}{1} + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} + \\frac{1}{8} + \\frac{1}{9} + \\frac{1}{10} + \\frac{1}{12} + \\frac{1}{15} + \\frac{1}{16} + \\frac{1}{18} + \\frac{1}{20} + \\cdots$$of the reciprocals of the elements of $A$ can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?\n\n$\\textbf{(A) } 16 \\qquad \\textbf{(B) } 17 \\qquad \\textbf{(C) } 19 \\qquad \\textbf{(D) } 23 \\qquad \\textbf{(E) } 36$\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": "

Let A be the set of positive integers that have no prime factors other than 2 , 3 , or 5 . The infinite sum \\frac{1}{1} + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} + \\frac{1}{8} + \\frac{1}{9} + \\frac{1}{10} + \\frac{1}{12} + \\frac{1}{15} + \\frac{1}{16} + \\frac{1}{18} + \\frac{1}{20} + \\cdots of the reciprocals of the elements of A can be expressed as \\frac{m}{n} , where m and n are relatively prime positive integers. What is m+n ?

\\textbf{(A) } 16 \\qquad \\textbf{(B) } 17 \\qquad \\textbf{(C) } 19 \\qquad \\textbf{(D) } 23 \\qquad \\textbf{(E) } 36

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2018 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12A_p20", "prev": "/problem/18_amc12A_p18"}}