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2012 AMC 10A Problem 24

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2012 AMC 10A Problem 24AMC 10 Step by Step
Name:                             Date: September 13, 2026
Algebraic Manipulation · difficulty 4 of 5 · about 8 min · position P21-25

Let aa , bb , and cc be positive integers with a≥a\ge b≥b\ge cc such that \begin{align}a^2-b^2-c^2+ab&=2011\text{ and}\\ a^2+3b^2+3c^2-3ab-2ac-2bc&=-1997.\end{align}

What is aa ?

  1. A)

    249249

  2. B)

    250250

  3. C)

    251251

  4. D)

    252252

  5. E)

    253253

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