Problem:
The operation ⊗ is defined for all nonzero numbers by a⊗b=ba2. Determine [(1⊗2)⊗3]−[1⊗(2⊗3)].
Answer Choices:
A. −32
B. −41
C. 0
D. 41
E. 32
Solution:
We have
(1⊗2)⊗3=212⊗3=21⊗3=3(21)2=341=121
and
1⊗(2⊗3)=1⊗(322)=1⊗34=3412=43
Therefore,
(1⊗2)⊗3−1⊗(2⊗3)=121−43=121−129=−128=−32.
Answer: A.
The problems on this page are the property of the MAA's American Mathematics Competitions