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2021 AMC Fall 10B Problem 12

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2021 AMC Fall 10B Problem 12AMC 10 Step by Step
Name:                             Date: October 28, 2026
Algebraic Manipulation · difficulty 3 of 5 · about 4 min · position P11-15

Which of the following conditions is sufficient to guarantee that integers xx , yy , and zz satisfy the equation x(x−y)+y(y−z)+z(z−x)=1?x(x-y)+y(y-z)+z(z-x) = 1?

  1. A)x>yx>y and y=zy=z
  2. B)x=y−1x=y-1 and y=z−1y=z-1
  3. C)x=z+1x=z+1 and y=x+1y=x+1
  4. D)x=zx=z and y−1=xy-1=x
  5. E)x+y+z=1x+y+z=1

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