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2000 AMC 8 Question 17

AMC8 · 2000 AMC 8

Question 17

The operation $\otimes$ is defined for all nonzero numbers by $$
a\otimes b =\dfrac{a^{2}}{b}.
$$

Determine $$
[(1\otimes 2)\otimes 3]-[1\otimes (2\otimes 3)].
$$
  1. $-\dfrac{2}{3}$
  2. $-\dfrac{1}{4}$
  3. $0$
  4. $\dfrac{1}{4}$
  5. $\dfrac{2}{3}$