{"status": "success", "data": {"description_md": "A base-10 three digit number $n$ is selected at random. Which of the following is closest to the probability that the base-9 representation and the base-11 representation of $n$ are both three-digit numerals? \n\n$\\mathrm{(A) \\ } 0.3\\qquad \\mathrm{(B) \\ } 0.4\\qquad \\mathrm{(C) \\ } 0.5\\qquad \\mathrm{(D) \\ } 0.6\\qquad \\mathrm{(E) \\ } 0.7$", "description_html": "<p>A base-10 three digit number  <span class=\"katex--inline\">n</span>  is selected at random. Which of the following is closest to the probability that the base-9 representation and the base-11 representation of  <span class=\"katex--inline\">n</span>  are both three-digit numerals?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 0.3\\qquad \\mathrm{(B) \\ } 0.4\\qquad \\mathrm{(C) \\ } 0.5\\qquad \\mathrm{(D) \\ } 0.6\\qquad \\mathrm{(E) \\ } 0.7</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": "2003 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10A_p21", "prev": "/problem/03_amc10A_p19"}}