Discussion
If \(\dfrac{W}{X} = \dfrac{6}{11}, \dfrac{Y}{Z} = \dfrac{16}{23}\) and \(\dfrac{W}{Y} = \dfrac{9}{16}\), then what is the value of \(\dfrac{X}{Y}\) ?
Answer: B
\(\frac{X}{Y} = \) \(\frac{33}{32}\).
Chain the given ratios through W:
\[ \begin{aligned} \frac{X}{Y} &= \frac{X}{W} \times \frac{W}{Y} \\ &= \frac{11}{6} \times \frac{9}{16} = \frac{99}{96} = \frac{33}{32} \end{aligned} \]
The ratio \(\frac{Y}{Z}\) is not needed. \(\frac{32}{33}\) is \(\frac{Y}{X}\), the reciprocal, and \(\frac{16}{11}\) or \(\frac{11}{16}\) come from combining the wrong pair of ratios.
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