{"status": "success", "data": {"description_md": "Let $S$ be the set of positive integers $n$ for which $\\tfrac{1}{n}$ has the repeating decimal representation $0.\\overline{ab} = 0.ababab\\cdots,$ with $a$ and $b$ different digits.  What is the sum of the elements of $S$?\n\n$\\textbf{(A)}\\ 11\\qquad\\textbf{(B)}\\ 44\\qquad\\textbf{(C)}\\ 110\\qquad\\textbf{(D)}\\ 143\\qquad\\textbf{(E)}\\ 155\\qquad$\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\">S</span>  be the set of positive integers  <span class=\"katex--inline\">n</span>  for which  <span class=\"katex--inline\">\\tfrac{1}{n}</span>  has the repeating decimal representation  <span class=\"katex--inline\">0.\\overline{ab} = 0.ababab\\cdots,</span>  with  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  different digits.  What is the sum of the elements of  <span class=\"katex--inline\">S</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 11\\qquad\\textbf{(B)}\\ 44\\qquad\\textbf{(C)}\\ 110\\qquad\\textbf{(D)}\\ 143\\qquad\\textbf{(E)}\\ 155\\qquad</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": 2, "problem_name": "2013 AMC 12A Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12A_p11", "prev": "/problem/13_amc12A_p09"}}