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2020 AMC 10A Problem 6

Problem 6 of 25EasierNumber TheoryCounting & Probability

How many 44-digit positive integers (that is, integers between 10001000 and 9999,9999, inclusive) having only even digits are divisible by 5?5?

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Solution

The last digit must be 00, because the number is divisible by 55 and all digits are even. The thousands digit can be 2,4,6,2,4,6, or 88, and each of the hundreds and tens digits has 55 choices. Thus there are 455=1004\cdot5\cdot5=100 such integers. Thus, B is the correct answer.

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Concepts: multiplication principle · digits · divisibility

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