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Number theory Difficulty 3.0 AMC 10/12 Prove it Canada

A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8. For example, the number $47\,389\,248$ is divisible by 8 because $248$ is divisible by 8. However, $47\,389\,284$ is not divisible by 8 because $284$ is not divisible by 8. If $992\,466\,1A6$ is divisible by 8, where $A$ represents one digit, what are the possible values of $A$ ? Explain how you obtained your answer.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.