For the nonzero numbers a, b, and c, define (a,b,c)=(a)/(b)+(b)/(c)+(c)/(a). Find (2,12,9).

2002 AMC 10A Problem 2 — Solution

2002 AMC 10A Problem 2

Attempt Problem 2 of the 2002 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 10A solutions, or check the answer key.

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For the nonzero numbers $a,$ $b,$ and $c,$ define $(a,b,c)=\dfrac{a}{b}+\dfrac{b}{c}+\dfrac{c}{a}.$ Find $(2,12,9).$

$4$

$5$

$6$

$7$

$8$

Answer: C

Concepts:custom operation fraction

Difficulty rating: 960

Solution:

$\begin{aligned} (2,12,9) &= \dfrac{2}{12}+\dfrac{12}{9}+\dfrac{9}{2} \\ &= \dfrac{1}{6}+\dfrac{4}{3}+\dfrac{9}{2}. \end{aligned}$ Over a denominator of $6,$ this is $\dfrac{1+8+27}{6}=\dfrac{36}{6}=6.$

Thus, the correct answer is C.

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