If a \otimes b = (a + b)/(a - b), then (6 \otimes 4) \otimes 3 =

2001 AMC 8 Problem 12 — Solution

2001 AMC 8 Problem 12

Attempt Problem 12 of the 2001 AMC 8 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 2001 AMC 8 solutions, or check the answer key.

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12.

If $a \otimes b = \dfrac{a + b}{a - b},$ then $(6 \otimes 4) \otimes 3 =$

$4$

$13$

$15$

$30$

$72$

Answer: A

Concepts:custom operation fraction

Difficulty rating: 1170

Solution:

We can evaluate it as follows $\begin{align*} (6 \otimes 4) \otimes 3 &= \dfrac{6 + 4}{6 - 4} \otimes 3 \\ &= 5 \otimes 3 \\&= \dfrac{5 + 3}{5 - 3} \\&= 4. \end{align*}$

Thus, A is the correct answer.

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