{"status": "success", "data": {"description_md": "For some positive integer $k$, the repeating base-$k$ representation of the (base-ten) fraction $\\frac{7}{51}$ is $0.\\overline{23}_k = 0.232323..._k$. What is $k$?\n\n$\\textbf{(A) } 13 \\qquad\\textbf{(B) } 14 \\qquad\\textbf{(C) } 15 \\qquad\\textbf{(D) } 16 \\qquad\\textbf{(E) } 17$\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>For some positive integer  <span class=\"katex--inline\">k</span> , the repeating base- <span class=\"katex--inline\">k</span>  representation of the (base-ten) fraction  <span class=\"katex--inline\">\\frac{7}{51}</span>  is  <span class=\"katex--inline\">0.\\overline{23}_k = 0.232323..._k</span> . What is  <span class=\"katex--inline\">k</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 13 \\qquad\\textbf{(B) } 14 \\qquad\\textbf{(C) } 15 \\qquad\\textbf{(D) } 16 \\qquad\\textbf{(E) } 17</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": "2019 AMC 12A Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12A_p12", "prev": "/problem/19_amc12A_p10"}}