1993 AMC 8 Problem 9

Attempt Problem 9 of the 1993 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 1993 AMC 8 solutions, or check the answer key.

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

9.

Consider the operation ∗* defined by the following table:
∗123411234224133314244321\begin{array}{c|cccc} * & 1 & 2 & 3 & 4 \\ \hline 1 & 1 & 2 & 3 & 4 \\ 2 & 2 & 4 & 1 & 3 \\ 3 & 3 & 1 & 4 & 2 \\ 4 & 4 & 3 & 2 & 1 \end{array}
For example, 3∗2=1.3 * 2 = 1. Then (2∗4)∗(1∗3)=(2 * 4) * (1 * 3) =
11
22
33
44
55
Answer: D
Concepts:custom operation
Small hint:
Read 2∗42 * 4 from row 2,2, column 4,4, and 1∗31 * 3 from row 1,1, column 33
Big hint:
Both inner values equal 3,3, so compute 3∗33 * 3 from the table
Solution:
From the table, 2∗4=32 * 4 = 3 and 1∗3=3.1 * 3 = 3.
Then (2∗4)∗(1∗3)=3∗3=4.(2 * 4) * (1 * 3) = 3 * 3 = 4.
Thus, the correct answer is D .
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