2008 AMC 8 Problem 2

Attempt Problem 2 of the 2008 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 2008 AMC 8 solutions, or check the answer key.

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

2.

The ten-letter code BEST OF LUCK\text{BEST OF LUCK} represents the ten digits 0−9,0-9, in order. What 44-digit number is represented by the code word CLUE?\text{CLUE}?
 8671 \ 8671
 8672 \ 8672
 9781 \ 9781
 9782 \ 9782
 9872 \ 9872
Answer: A
Concepts:place value
Small hint:
Write the digit under each letter in BEST OF LUCK.
Big hint:
Because the first letter represents 0,0, each letter represents one less than its position in the code.
Solution:
The code BEST OF LUCK represents the digits 00 through 99 in order, so C=8C=8, L=6L=6, U=7U=7, and E=1E=1.
Therefore, CLUE=8671\text{CLUE}=8671.
Thus, A is the correct answer.
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