Is x (squared) greater than x?

1.) x(squared) > 1
2.) x > -1

When testing these numbers, why can't you use a negative #? If you test out a -2 in statement 1, then it would yield a "No" answer, and therefore, statement 1 on it's own would not be sufficient.

If x=-2, then x(squared) is 4`-2. The statement is true for -1`x`1

You can certainly test a negative number when a statement allows you to (in fact, you should, as long as the statement allows you to!). You're fine as far as that goes, but then you make an error in your calculation.

First diagnose what the question is really asking. For the question "is x^2 > x?" the distinction here is whether you have:
0 <= x <= 1, in which case x^2 is not > x
or x < 0 or x > 1, in which case x^2 is > x

(1) x^2 > 1 tells me that x is either greater than 1 or less than negative 1. So try x = -2. Is x^2 > x? Yes: 4 > -2. (You said this scenario would yield a "no" answer. Don't forget that, when you square the number, it becomes positive, and a positive is always bigger than a negative.)

(2) x > -1. I can try anything I want as long as it's greater than -1. Any negative number I try will still yield a "yes" answer because any negative squared becomes a positive.