{"status": "success", "data": {"description_md": "Let $n$ be a positive integer and $d$ be a digit such that the value of the numeral $\\underline{32d}$ in base $n$ equals $263$, and the value of the numeral $\\underline{324}$ in base $n$ equals the value of the numeral $\\underline{11d1}$ in base six. What is $n + d ?$\n\n$\\textbf{(A)} ~10 \\qquad\\textbf{(B)} ~11 \\qquad\\textbf{(C)} ~13 \\qquad\\textbf{(D)} ~15 \\qquad\\textbf{(E)} ~16$", "description_html": "<p>Let  <span class=\"katex--inline\">n</span>  be a positive integer and  <span class=\"katex--inline\">d</span>  be a digit such that the value of the numeral  <span class=\"katex--inline\">\\underline{32d}</span>  in base  <span class=\"katex--inline\">n</span>  equals  <span class=\"katex--inline\">263</span> , and the value of the numeral  <span class=\"katex--inline\">\\underline{324}</span>  in base  <span class=\"katex--inline\">n</span>  equals the value of the numeral  <span class=\"katex--inline\">\\underline{11d1}</span>  in base six. What is  <span class=\"katex--inline\">n + d ?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A)} ~10 \\qquad\\textbf{(B)} ~11 \\qquad\\textbf{(C)} ~13 \\qquad\\textbf{(D)} ~15 \\qquad\\textbf{(E)} ~16</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": 3, "problem_name": "2021 AMC 10B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10B_p14", "prev": "/problem/21_amc10B_p12"}}