1986 AMC 8 Problem 11

Attempt Problem 11 of the 1986 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1986 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

If A∗BA * B means A+B2,\dfrac{A + B}{2}, then (3∗5)∗8(3 * 5) * 8 is
66
88
1212
1616
3030
Answer: A
Concepts:custom operation
Small hint:
The operation A∗BA * B gives the average of AA and BB
Big hint:
First compute 3∗5,3 * 5, then combine that result with 88
Solution:
First, 3∗5=3+52=4.3 * 5 = \dfrac{3 + 5}{2} = 4. Then 4∗8=4+82=6.4 * 8 = \dfrac{4 + 8}{2} = 6.
Thus, the correct answer is A .
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