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1972 AHSME Problems/Problem 7

Problem

If $yz:zx:xy=1:2:3$, then $\dfrac{x}{yz}:\dfrac{y}{zx}$ is equal to

$\textbf{(A) }3:2\qquad \textbf{(B) }1:2\qquad \textbf{(C) }1:4\qquad \textbf{(D) }2:1\qquad \textbf{(E) }4:1$

Solution

We want to find \[\dfrac{x}{yz}:\dfrac{y}{zx} = \dfrac{x}{yz} \cdot \dfrac{zx}{y} = \dfrac{x^2}{y^2}.\]

We are given $yz:zx=1:2,$ and dividing both sides by $z$ gives $y:x = 1:2.$ Therefore, \[\dfrac{x^2}{y^2} = \dfrac{1}{\dfrac{1}{2^2}} = 4.\]

The answer is $\textbf{(E)}.$

-edited by coolmath34

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