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Found problems: 1

2016 AMC 12/AHSME, 22
For a certain positive integer $n$ less than $1000$, the decimal equivalent of $\frac{1}{n}$ is $0.\overline{abcdef}$, a repeating decimal of period $6$, and the decimal equivalent of $\frac{1}{n+6}$ is $0.\overline{wxyz}$, a repeating decimal of period $4$. In which interval does $n$ lie? $\textbf{(A)}\ [1,200] \qquad \textbf{(B)}\ [201,400] \qquad \textbf{(C)}\ [401,600] \qquad \textbf{(D)}\ [601,800] \qquad \textbf{(E)}\ [801,999] $
amc 12b modular arithmetic number theory