In general, can we assume number lines like this are drawn to scale? The answer key says choice D is correct, which means I and III must be true. Statement III would be true if we can assume this number line is drawn to scale and that |y| > |x|. However, it would not necessarily be true if we don’t make this assumption.
What you say about statement III is not necessarily the case. From the graph you can only assume that y>0 and x<0. With that information then you need to work your way through. Notice that statement III x-y<0 is the same as saying that x<y, which is indeed true because we know that x<0<y.
The correct ans is D. Option 2 will become false if e.g y = 4 and x = -2