2008 AMC 8 Problems/Problem 2

Problem

The ten-letter code $\text{BEST OF LUCK}$ represents the ten digits $0-9$, in order. What 4-digit number is represented by the code word $\text{CLUE}$?

$\textbf{(A)}\ 8671 \qquad \textbf{(B)}\ 8672 \qquad \textbf{(C)}\ 9781 \qquad \textbf{(D)}\ 9782 \qquad \textbf{(E)}\ 9872$

Solution

We can derive that $C=8$, $L=6$, $U=7$, and $E=1$. Therefore, the answer is $\boxed{\textbf{(A)}\ 8671}$ ~edited by Owencheng

Solution 2

We can easily see that $C=8$, which makes only $(A)$ $8761$ and $(B)$ $8762$ possible. Since the only difference between answer choices $A$ and $B$ is the last digit and that the last digit in the code word "CLUE" is $E$, we can just find that $E=1$ and that the answer is $\boxed{\textbf{(A)}\ 8671}$. ~solution by SuperVince1

See Also

2008 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All AJHSME/AMC 8 Problems and Solutions

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