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Problem 40

Geometry Difficulty 1.1 Multiple choice CEMC Gauss (Grade 8) · Canada · 2012

Points $P$ , $Q$ , $R$ lie in a straight line.

The value of $x$ is

Pick one

Official solution

A positive fraction increases in value as its numerator increases and also increases in value as its denominator decreases.

Since the numerators of all five fractions are equal, then the largest of these is the fraction with the smallest denominator.
The largest fraction in the set $\left\{ \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{10} \right\}$ is $\frac{1}{2}$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.