1. x > x^2 - let's work a bit around this inequality:
0 > x^2 - x
x(x - 1) < 0
Now use one of the basic rules of second degree equations:
A second degree equation is negative ONLY between the roots.
The roots or solutions of x(x - 1) are x = 0 and x = 1 (points where the equation is equal to zero). This means that x(x - 1) is negative only between 0 and 1, which means that x is smaller than 1. So 1 is enough.
2. -x < -x^2 is equivalent to the first stmt. Just multiply each side by -1 on get that:
x > x^2
Remember: when multiplying or dividing by a negative number (in this case, -1), not only are the signs reversed, but so is the relationship (i.e. > becomes < or vice verso).
Since you're back at stmt 1 and we've proved that that is sufficient, so is 2.
This is why indeed the answer is D.
I'm going to have to ask you to use the spoiler function to hide the OA. Trust me, it's much more fun to solve and equation without knowing the OA, since it adds to the "mystery".
