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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: September 13, 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>yand and y=z

  2. B)

    x=y-1and and y=z-1

  3. C)

    x=z+1and and y=x+1

  4. D)

    x=zand and y-1=x

  5. E)

    x+y+z=1x+y+z=1

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