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1993 AJHSME Problems/Problem 9

Revision as of 10:48, 29 July 2011 by Math Kirby (talk | contribs) (Created page with "== Problem 9 == Consider the operation <math>*</math> defined by the following table: <cmath>\begin{tabular}{c|cccc} * & 1 & 2 & 3 & 4 \\ \hline 1 & 1 & 2 & 3 & 4 \\ 2 & 2 & 4 ...")
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Problem 9

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, $3*2=1$. Then $(2*4)*(1*3)=$

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 5$

Solution

Using the chart, $(2*4)=3$ and $(1*3)=3$. Therefore, $(2*4)*(1*3)=3*3=\boxed{\text{(D)}\ 4}$.

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