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 45=(4+5)(4−5)=−9, it follows that
3 (4) 5)=3(−9)=(3+(−9))(3−(−9))=(−6)(12)=(A)−72
The problems on this page are the property of the MAA's American Mathematics Competitions