Problem:
Consider the operation "minus the reciprocal" of, defined by a⋄b=a−b1. What is ((1⋄2)⋄3)−(1⋄(2⋄3))?
Answer Choices:
A. −307
B. −61
C. 0
D. 61
E. 307
Solution:
((1⋄2)⋄3)−(1⋄(2⋄3))=((1−21)−31)−(1−(2−31)−1)=61−(1−53)=61−52=(A)−307
The problems on this page are the property of the MAA's American Mathematics Competitions