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2008 AMC 10A Problem 9

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2008 AMC 10A Problem 9AMC 10 Step by Step
Name:                             Date: September 13, 2026
Divisibility & Factors · difficulty 2 of 5 · about 2 min · position P1-10

Suppose that 2x3−x6\frac{2x}{3}-\frac{x}{6} is an integer. Which of the following statements must be true about xx ?

  1. A)

    It is negative.\text{It is negative.}

  2. B)

    It is even, but not necessarily a multiple of 3.\text{It is even, but not necessarily a multiple of 3.}

  3. C)

    It is a multiple of 3, but not necessarily even.\text{It is a multiple of 3, but not necessarily even.}

  4. D)

    It is a multiple of 6, but not necessarily a multiple of 12.\text{It is a multiple of 6, but not necessarily a multiple of 12.}

  5. E)

    It is a multiple of 12.\text{It is a multiple of 12.}

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