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 $(A)$ $8761$ .

2008 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2008 AMC 8 Problems/Problem 2

Contents

Problem

Solution

Solution 2

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