{"status": "success", "data": {"description_md": "Let $n$ be the smallest positive integer such that $n$ is divisible by $20$, $n^2$ is a perfect cube, and $n^3$ is a perfect square. What is the number of digits of $n$?\n\n$\\textbf{(A)}\\ 3 \\qquad \\textbf{(B)}\\ 4 \\qquad \\textbf{(C)}\\ 5 \\qquad \\textbf{(D)}\\ 6 \\qquad \\textbf{(E)}\\ 7$\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\">n</span>  be the smallest positive integer such that  <span class=\"katex--inline\">n</span>  is divisible by  <span class=\"katex--inline\">20</span> ,  <span class=\"katex--inline\">n^2</span>  is a perfect cube, and  <span class=\"katex--inline\">n^3</span>  is a perfect square. What is the number of digits of  <span class=\"katex--inline\">n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 3 \\qquad \\textbf{(B)}\\ 4 \\qquad \\textbf{(C)}\\ 5 \\qquad \\textbf{(D)}\\ 6 \\qquad \\textbf{(E)}\\ 7</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": "2010 AMC 12B Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12B_p10", "prev": "/problem/10_amc12B_p08"}}