{"status": "success", "data": {"description_md": "A pair of standard $6$-sided dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle's circumference?\n\n$\\textbf{(A)}\\ \\frac{1}{36} \\qquad<br>\\textbf{(B)}\\ \\frac{1}{12} \\qquad<br>\\textbf{(C)}\\ \\frac{1}{6} \\qquad<br>\\textbf{(D)}\\ \\frac{1}{4} \\qquad<br>\\textbf{(E)}\\ \\frac{5}{18}$\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>A pair of standard  <span class=\"katex--inline\">6</span> -sided dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle&#8217;s circumference?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{36} \\qquad\\textbf{(B)}\\ \\frac{1}{12} \\qquad\\textbf{(C)}\\ \\frac{1}{6} \\qquad\\textbf{(D)}\\ \\frac{1}{4} \\qquad\\textbf{(E)}\\ \\frac{5}{18}</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": "2011 AMC 12A Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12A_p11", "prev": "/problem/11_amc12A_p09"}}