Problem:
For each pair of real numbers aî€ =b, define the operation ⋆ as
(a⋆b)=a−ba+b​
What is the value of ((1⋆2)⋆3)?
Answer Choices:
A. −32​
B. −51​
C. 0
D. 21​
E. This value is not defined.
Solution:
First we have
(1⋆2)=1−21+2​=−3
Then
((1⋆2)⋆3)=(−3⋆3)=−3−3−3+3​=−60​=0
Answer: C​.
The problems on this page are the property of the MAA's American Mathematics Competitions