Track / Stage 4 / 22 of 340 #282 of 2000

Problem 282

AMC 12 late, AIME early

Algebra Difficulty 4.5 Find the answer

8. If $\frac{x}{a-b}=\frac{y}{b-c}=\frac{z}{c-a}, x y z \neq 0$ , and $a, b, c$ are pairwise distinct, then ( ).
(A) $a x+b y+c z=0$
(B) $x+y+z=0$
(C) $c x=a y=b z$
(D) $x=y=z$

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

8. B

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