{"status": "success", "data": {"description_md": "Suppose $a$ and $b$ are single-digit positive integers chosen independently and at random. What is the probability that the point $(a,b)$ lies above the parabola $y=ax^2-bx$?\n\n$\\textbf{(A)}\\ \\frac{11}{81} \\qquad<br>\\textbf{(B)}\\ \\frac{13}{81} \\qquad<br>\\textbf{(C)}\\ \\frac{5}{27} \\qquad<br>\\textbf{(D)}\\ \\frac{17}{81} \\qquad<br>\\textbf{(E)}\\ \\frac{19}{81}$\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>Suppose  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are single-digit positive integers chosen independently and at random. What is the probability that the point  <span class=\"katex--inline\">(a,b)</span>  lies above the parabola  <span class=\"katex--inline\">y=ax^2-bx</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{11}{81} \\qquad\\textbf{(B)}\\ \\frac{13}{81} \\qquad\\textbf{(C)}\\ \\frac{5}{27} \\qquad\\textbf{(D)}\\ \\frac{17}{81} \\qquad\\textbf{(E)}\\ \\frac{19}{81}</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": 3, "problem_name": "2011 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12A_p15", "prev": "/problem/11_amc12A_p13"}}