Problem: If A∗BA * BA∗B means A+B2\dfrac{A+B}{2}2A+B, then (3∗5)∗8(3 * 5) * 8(3∗5)∗8 is
Answer Choices:
A. 666 B. 888 C. 121212 D. 161616 E. 303030
Solution:
(3∗5)∗8=(3+52)∗8=4∗8=4+82=6.(3 * 5) * 8=\left(\dfrac{3+5}{2}\right) * 8=4 * 8=\dfrac{4+8}{2}=6. (3∗5)∗8=(23+5)∗8=4∗8=24+8=6.
Answer: A\boxed{A}A.
The problems on this page are the property of the MAA's American Mathematics Competitions