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This questions source is the 2010 MMPC Part 1 Competition #33. The answers were released, but no solutions.

I am interested in the solution because I have no idea how to find a good way to do this problem. I will greatly appreciate help as tomorrow is the 2012 MMPC Part 1 Competition and I still cannot solve a problem from 2 years ago!

We let $x$ and $y$ be real numbers that satisfy |$x-1$| + |$y+1$| < 1 . The range of the expression for $\frac{x-1}{y-2}$ is which of the following?

A) $( - \frac{1}{3} , \frac{1}{3} ) $

B) $( - \frac{1}{2} , \frac{1}{2} ) $

C) $( - \frac{1}{2} , \frac{1}{3} ) $

D) $( - \frac{1}{3} , \frac{1}{2} ) $

I know the choices may not be needed but even if it helps slightly, then its worth it. Thank you and if you could, please give a thorough solution. Right now all I am doing is plugging in points in the intervals. On average each question is supposed to be $2$ and a half minutes long so that clearly isn't effective!

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