For the nonzero numbers a, b, and c, define (a, b, c) = (abc)/(a+b+c). What is (2, 4, 6)?

2002 AMC 10B Problem 2

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For the nonzero numbers

a,

b,

and

c,

define

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

What is

(2, 4, 6)?

1

2

4

6

24

Substitute

a=2,

b=4,

c=6

into the definition

The numerator is

2\cdot4\cdot6

and the denominator is

2+4+6

Substituting directly,

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

Thus, the correct answer is C.