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?

Check out the whole set: 2016 AMC 12B Problems .