1999 AMC 12 Problem 6

Below is the professionally curated solution for Problem 6 of the 1999 AMC 12, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1999 AMC 12 solutions, or check the answer key.

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Concepts:exponent digits

Difficulty rating: 1170

What is the sum of the digits of the decimal form of the product $2^{1999} \cdot 5^{2001}?$

$2$

$4$

$5$

$7$

$10$

Solution:

Write $2^{1999} \cdot 5^{2001} = 2^{1999} \cdot 5^{1999} \cdot 5^2 = 25 \cdot 10^{1999},$ which is $25$ followed by $1999$ zeros. The sum of the digits is $2 + 5 = 7.$

Thus, the correct answer is D.

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