2012 AMC 10A Problems/Problem 24

Problem 24

Let $a$ , $b$ , and $c$ be positive integers with $a\geb\gec$ (Error compiling LaTeX. Unknown error_msg) such that $a^2-b^2-c^2+ab=2011$ and $a^2+3b^2+3c^2-3ab-2ac-2bc=-1997$ .

What is $a$ ?

$\textbf{(A)}\ 249\qquad\textbf{(B)}\ 250\qquad\textbf{(C)}\ 251\qquad\textbf{(D)}\ 252\qquad\textbf{(E)}\ 253$

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2012 AMC 10A Problems/Problem 24

Problem 24