2002 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

For the nonzero numbers

a,

b,

and

c,

define

(a, b, c) = \dfrac{abc}{a+b+c}.

What is

(2, 4, 6)?

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Solution

Substituting directly,

(2, 4, 6) = \dfrac{2\cdot4\cdot6}{2+4+6} = \dfrac{48}{12} = 4.

Thus, the correct answer is C.

Concepts: custom operation · fraction

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.