AMC 10 Step by Step
Log inSign up
Printable

2003 AMC 10A Problem 6

Include the solutionBack to the problem
2003 AMC 10A Problem 6AMC 10 Step by Step
Name:                             Date: October 28, 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♡y=y♡xx \heartsuit y = y \heartsuit x for all xx and yy
  2. B)2(x♡y)=(2x)♡(2y)2(x \heartsuit y) = (2x) \heartsuit (2y) for all xx and yy
  3. C)x♡0=xx \heartsuit 0 = x for all xx
  4. D)x♡x=0x \heartsuit x = 0 for all xx
  5. E)x♡y>0x \heartsuit y > 0 if x≠yx \neq y

Working