{"status": "success", "data": {"description_md": "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 of $6$, 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?\n\n$\\textbf{(A)}\\ [1,200]\\qquad\\textbf{(B)}\\ [201,400]\\qquad\\textbf{(C)}\\ [401,600]\\qquad\\textbf{(D)}\\ [601,800]\\qquad\\textbf{(E)}\\ [801,999]$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>For a certain positive integer  <span class=\"katex--inline\">n</span>  less than  <span class=\"katex--inline\">1000</span> , the decimal equivalent of  <span class=\"katex--inline\">\\frac{1}{n}</span>  is  <span class=\"katex--inline\">0.\\overline{abcdef}</span> , a repeating decimal of period of  <span class=\"katex--inline\">6</span> , and the decimal equivalent of  <span class=\"katex--inline\">\\frac{1}{n+6}</span>  is  <span class=\"katex--inline\">0.\\overline{wxyz}</span> , a repeating decimal of period  <span class=\"katex--inline\">4</span> . In which interval does  <span class=\"katex--inline\">n</span>  lie?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ [1,200]\\qquad\\textbf{(B)}\\ [201,400]\\qquad\\textbf{(C)}\\ [401,600]\\qquad\\textbf{(D)}\\ [601,800]\\qquad\\textbf{(E)}\\ [801,999]</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2016 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12B_p23", "prev": "/problem/16_amc12B_p21"}}