Problem:
If a⊗b=a−ba+b​, then (6⊗4)⊗3=
Answer Choices:
A. 4
B. 13
C. 15
D. 30
E. 72
Solution:
6⊗4=6−46+4​=210​=5, and 5⊗3=5−35+3​=28​=4.
Note: (6⊗4)⊗3î€ =6⊗(4⊗3). Does (6⊗4)⊗3=3⊗(6⊗4)?
Answer: A​.
The problems on this page are the property of the MAA's American Mathematics Competitions