SAT Prep

Answer to Math #7

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!