# 2016 AMC 12B Problem 22

For a certain positive integer $$n$$ less than 1000, the decimal equivalent of $$\dfrac{1}{n}$$ is $$0.\overline{abcdef}$$, a repeating decimal of period 6, and the decimal equivalent of $$\dfrac{1}{n+6}$$ is $$0.\overline{wxyz}$$ a repeating decimal of period 4. In which interval does $$n$$ lie?

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