{"status": "success", "data": {"description_md": "Let $a$, $b$, and $c$ be positive integers with $a\\ge$ $b\\ge$ $c$ such that\n\n$$\n\\begin{aligned}\na^2-b^2-c^2+ab &= 2011\\\\\na^2+3b^2+3c^2-3ab-2ac-2bc &= -1997.\n\\end{aligned}\n$$\n\nWhat is $a$?\n\n$\\textbf{(A)}\\ 249\\qquad\\textbf{(B)}\\ 250\\qquad\\textbf{(C)}\\ 251\\qquad\\textbf{(D)}\\ 252\\qquad\\textbf{(E)}\\ 253$", "description_html": "<p>Let <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> be positive integers with <span class=\"katex--inline\">a\\ge</span> <span class=\"katex--inline\">b\\ge</span> <span class=\"katex--inline\">c</span> such that</p>&#10;<p><span class=\"katex--display\">&#10;\\begin{aligned}&#10;a^2-b^2-c^2+ab &amp;= 2011\\\\&#10;a^2+3b^2+3c^2-3ab-2ac-2bc &amp;= -1997.&#10;\\end{aligned}&#10;</span></p>&#10;<p>What is <span class=\"katex--inline\">a</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 249\\qquad\\textbf{(B)}\\ 250\\qquad\\textbf{(C)}\\ 251\\qquad\\textbf{(D)}\\ 252\\qquad\\textbf{(E)}\\ 253</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2012 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc10A_p25", "prev": "/problem/12_amc10A_p23"}}