Problem:
Consider these two operations:
a⋄b=a2−b2
a⋆b=(a−b)2
Compute the value:
(5⋄3)⋆6
Answer Choices:
A. −20
B. 4
C. 16
D. 100
E. 220
Solution:
The value of the expression in parentheses is
(5⧫3)=52−32=25−9=16.
Substituting that value into the larger expression gives
(5⧫3)⋆6=16⋆6=(16−6)2=100
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions