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Australian AMC 2009 - Intermediate Question 18

AMC AUSTRALIA · Australian AMC 2009 - Intermediate

Question 18

$PQRS$ is a rectangle. $X$ is halfway along $PQ$, $Y$ is a third of the way along $QR$ and $Z$ is a quarter of the way along $RS$. What fraction of the area of $PQRS$ is represented by the quadrilateral $XYZS$?

Question illustration
  1. $\frac12$
  2. $\frac7{12}$
  3. $\frac23$
  4. $\frac34$
  5. $\frac35$