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Number theory Difficulty 4.0 AMC 10/12 Find the answer United States

Problem:

Let $a$ be a positive integer such that $2a$ has units digit $4$ . What is the sum of the possible units digits of $3a$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

If $2a$ has last digit $4$ , then the last digit of $a$ is either $2$ or $7$ . In the former case, $3a$ has last digit $6$ , and in the latter case, $3a$ has last digit $1$ . This gives a final answer of $6+1=7$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.