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2008 AMC 10A Problem 9

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2008 AMC 10A Problem 9AMC 10 Step by Step
Name:                             Date: October 28, 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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