If xy 0, what is the value of x/|y| ?

Official Solution:


If \(xy ≠ 0\), what is the value of \(\frac{x}{|y|}\) ?

(1) \(|x| = |y|\)

The above means that \(x\) and \(y\) have the same magnitude but we don't know the sign of \(x\) to determine the value of \(\frac{x}{|y|}\). If \(x < 0\), then \(\frac{x}{|y|}=-1\) (for example, consider \(x=-1\) and \(y=1\)) but if \(x > 0\), then \(\frac{x}{|y|}=1\) (for example, consider \(x=1\) and \(y=1\)). Not sufficient.

(2) \(y = |x|\)

The above means that \(y > 0\) (it equals to the absolute value of non-negative number \(x\)) but again we don't know the sign of \(x\). If \(x < 0\), then \(\frac{x}{|y|}=-1\) (for example, consider \(x=-1\) and \(y=1\)) but if \(x > 0\), then \(\frac{x}{|y|}=1\) (for example, consider \(x=1\) and \(y=1\)). Not sufficient.

(1)+(2) We know that \(x\) and \(y\) have the same magnitude and that \(y > 0\). Still nothing about the sign of \(x\). Not sufficient.


Answer: E