Problem:
For real numbers x and y, define x♠y=(x+y)(x−y). What is 3♠(4♠5)?
Answer Choices:
A. −72
B. −27
C. −24
D. 24
E. 72
Solution:
Because 4♠5=(4+5)(4−5)=−9, it follows that
3♠(4♠5)=3♠(−9)=(3+(−9))(3−(−9))=(−6)(12)=−72.
The problems on this page are the property of the MAA's American Mathematics Competitions