On the number line, if w > x, y is the midpoint between w and z, and x

With number line problems it always helps tremendously to draw it out.

Start with the second statement, y is the midpoint between w and z. Then add in x to satisfy the first condition. You shoud get two scenarios that look like this:

x------w---y---z (1)
z------y--x----w (2)

Looking at scenario (1) first, say the distance between \(x\) and \(w\) is \(d\). Then the distance between \(w\) and \(y\) is \(d/2\), and the distance between \(w\) and \(z\) is \(d\).

Now, what we are being asked to find is:
\(\frac{w-y}{z-x}=\frac{-\frac{1}{2}d}{2d} = -\frac{1}{4}\)

This is one of our answer choices, so we can stop there, and the answer is B.

BUT, if you had started with number line scenario (2), then you could say the distance between \(z\) and \(w\) is \(d\). Then the distance between \(y\) and \(w\) is \(d/2\) and the distance between \(z\) and \(x\) is \(2d/3\). Now what we're being asked to find is:
\(\frac{w-y}{z-x}=\frac{\frac{1}{2}d}{-\frac{2}{3}d}=-\frac{3}{4}\)

This is not one of our answer choices, so if we had started with scenario (2), we would have to then go and work out scenario (1).

The tricky part of this question could be recognizing that there are 2 different possible scenarios for the arrangement of w, x, y, and z on the number line. One of the biggest clues that there could be multiple arrangements is the use of the word could in the question



This is essentially saying that the expression could also equal something else, implying that there is another scenario and other possible answers not listed in the answer choices. Always be on the lookout for telltale words like could in questions.