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⊗b=a+ba−b,a \otimes b = \dfrac{a + b}{a - b}, then (6⊗4)⊗3=(6 \otimes 4) \otimes 3 =
44
1313
1515
3030
7272
Answer: A
Concepts:custom operationfraction
Small hint:
Evaluate 6⊗46\otimes4 first
Big hint:
Then use the result as the first input with 33
Solution:
We can evaluate it as follows (6⊗4)⊗3=6+46−4⊗3=5⊗3=5+35−3=4. \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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