Let's test some possible values of x and y

case i: Since \(|x| \geq 1\) and \(|y| < \frac{1}{2}\), one possible pair of values is \(x=1\) and \(y=\frac{1}{3}\)
We get
Quantity A: \(\frac{1}{\frac{1}{3}}=3\)

Quantity B: \(\frac{\frac{1}{3}}{1}=\frac{1}{3}\)
In this case, Quantity A is greater


case ii: Another possible pair of values is \(x=-1\) and \(y=\frac{1}{3}\)
We get
Quantity A: \(\frac{-1}{\frac{1}{3}}=-3\)

Quantity B: \(\frac{\frac{1}{3}}{-1}=\frac{-1}{3}\)
In this case, Quantity B is greater

Answer: D

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