Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.3 AIME Find the answer

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

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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