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2018 AMC 12A Question 7

AMC12 · 2018 AMC 12A

Question 7

For how many (not necessarily positive) integer values of $n$ is the value of $$
4000 \cdot \left(\tfrac{2}{5}\right)^n
$$ an integer?
  1. $3$
  2. $4$
  3. $6$
  4. $8$
  5. $9$