Question 11

Let $$x, y$$ and $$z$$ be positive real numbers and let $$x \geq y \geq z$$ so that $$x+y+z=20.1$$. Which of the following statements is true?

Solution

Testing values shows $$xy$$ can exceed 99 (e.g. $$x=y=10.05$$), can be made arbitrarily close to 0, and can equal 75 exactly (e.g. $$x=15, y=5, z=0.1$$), ruling out the first three options. For $$yz=49$$ with $$y \geq z$$, the constraint $$x \geq y$$ combined with $$x+y+z=20.1$$ can be shown to always fail, so $$yz \neq 49$$ always holds.

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Let $$x, y$$ and $$z$$ be positive real numbers and let $$x \geq y \geq z$$ so that $$x+y+z=20.1$$. Which of the following statements is true?

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