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2003 AMC 10B Problem 10

Problem 10 of 25EasierAlgebraCounting & Probability

Nebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed by four digits. Each new license plate consists of three letters followed by three digits. By how many times is the number of possible license plates increased?

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Solution

The old scheme allows 26⋅10426 \cdot 10^4 plates and the new scheme allows 263⋅10326^3 \cdot 10^3 plates. The increase factor is 263⋅10326⋅104=26210.\dfrac{26^3 \cdot 10^3}{26 \cdot 10^4}=\dfrac{26^2}{10}. Thus, the correct answer is C.

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Concepts: multiplication principle · ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.