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Evaluating a functional data graph

Source: 1993 AMC 8 Problem 9

June 28, 2011
AMC

Problem Statement

Consider the operation ∗* defined by the following table:
\begin{tabular}{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{tabular}
For example, 3∗2=13*2=1. Then (2∗4)∗(1∗3)=(2*4)*(1*3)=
(A) 1(B) 2(C) 3(D) 4(E) 5\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 5
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