Difference between revisions of "2016 AMC 12B Problems/Problem 22"
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For a certain positive integer n less than <math>1000</math>, the decimal equivalent of <math>\frac{1}{n}</math> is <math>0.\overline{abcdef}</math>, a repeating decimal of period of 6, and the decimal equivalent of <math>\frac{1}{n+6}</math> is <math>0.\overline{wxyz}</math>, a repeating decimal of period 4. In which interval does <math>n</math> lie? | For a certain positive integer n less than <math>1000</math>, the decimal equivalent of <math>\frac{1}{n}</math> is <math>0.\overline{abcdef}</math>, a repeating decimal of period of 6, and the decimal equivalent of <math>\frac{1}{n+6}</math> is <math>0.\overline{wxyz}</math>, a repeating decimal of period 4. In which interval does <math>n</math> lie? | ||
| − | <math>\textbf{(A)}\ [1,200]\qquad\textbf{(B)}\ [201,400]\qquad\textbf{(C)}\ [401,600] | + | <math>\textbf{(A)}\ [1,200]\qquad\textbf{(B)}\ [201,400]\qquad\textbf{(C)}\ [401,600]\qquad\textbf{(D)}\ [601,800]\qquad\textbf{(E)}\ [801,999]</math> |
Revision as of 12:54, 21 February 2016
Problem
For a certain positive integer n less than 
, the decimal equivalent of 
is 
, a repeating decimal of period of 6, and the decimal equivalent of 
is 
, a repeating decimal of period 4. In which interval does 
lie?
![$\textbf{(A)}\ [1,200]\qquad\textbf{(B)}\ [201,400]\qquad\textbf{(C)}\ [401,600]\qquad\textbf{(D)}\ [601,800]\qquad\textbf{(E)}\ [801,999]$](http://latex.artofproblemsolving.com/b/a/0/ba0b05d779134dbe18999e12efb223c3b9bdd656.png)
