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2003 AMC 10A Problem 6

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2003 AMC 10A Problem 6AMC 10 Step by Step
Name:                             Date: September 13, 2026
Absolute Value & Inequalities · difficulty 1 of 5 · about 1 min · position P1-10

Define x♡yx \heartsuit y to be ∣x−y∣|x-y| for all real numbers xx and yy . Which of the following statements is not true?

  1. A)

    x \heartsuit y = y \heartsuit xforall for all xand and y

  2. B)

    2(x \heartsuit y) = (2x) \heartsuit (2y)forall for all xand and y

  3. C)

    x \heartsuit 0 = xforall for all x

  4. D)

    x \heartsuit x = 0forall for all x

  5. E)

    x♡y>0x \heartsuit y > 0

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