If $yz:zx:xy=1:2:3$, then $\dfrac{x}{yz}:\dfrac{y}{zx}$ is equal to
$\textbf{(A) }3:2\qquad \textbf{(B) }1:2\qquad \textbf{(C) }1:4\qquad \textbf{(D) }2:1\qquad  \textbf{(E) }4:1$
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