{"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-<span class=\"katex--inline\">10</span> 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-<span class=\"katex--inline\">9</span> representation and the base-<span class=\"katex--inline\">11</span> representation of <span class=\"katex--inline\">n</span> are both three-digit numerals?</p>&#10;<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>&#10;", "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"}}