###### Answer: C

###### Difficulty: Hard

The first thing we should notice is that I is true in all 4 choices. This means that we know I is true and we don’t have to test it. Yay! We need to test the other two options.

The first thing I would try is x = 1, y = 2. This means it fits the model of -2 < 1 < 2. This would mean that II and III are both true since II. 1 > 0 and III. 2 > 0 are both true.

Next I would try to mix it up and make x and y negative. I would find that there isn’t a way to make y negative. The model is -y < x < y. If we chose -2 for y, it would mean -(-2) < x < -2. Even if we don’t think about x at all, it would still lead to 2 < x < -2, which would mean 2 is less than -2, which is obviously not the case. Since y can’t be negative, I’m close to knowing that III is true, but I need to make sure y can’t be equal to zero first.

If I plug zero in for y in the model, I get 0 < x < 0. This doesn’t make any sense since zero is not less than itself. Therefore, I now know that III. y > 0 must be true. I can cross out A) and B), since these answers don’t include III.

Next I need to test options II, so I need to see if x can be negative or zero. I could use x = -1 and y = 2. This would fit the model of -2 < -1 < 2. Since this works, x does not need to be greater than 0, so II is not true. I can cross out D) and I am left with C) as my answer!