Hi ash4gmat,

While this question might look a little 'weird', it's just asking us to deal with a function. In real basic terms, functions are just a different way to write a line formula. For example...

Y = 2X + 1
f(X) = 2X + 1

These two equations 'mean' the same thing. Here's how each would look if we plugged in X = 3:

Y = 2(3) + 1 = 7
f(3) = 2(3) + 1 = 7

That having been established, we're told that X is POSITIVE. We're asked if the f(X^2) = f(X)^2. This is a YES/NO question.

1) f(X) = Sqrt(X)

This tells us what math to do when we use the function. Now we have to determine whether f(X^2) = f(X)^2 or not...

As an example, let's TEST X=1

f(1^2) = f(1) = Sqrt(1) = 1
f(1)^2 = [Sqrt(1)]^2 = 1^2 = 1
1 = 1, so the answer to the question is YES.

As another simple example, let's TEST X=4

f(4^2) = f(16) = Sqrt(16) = 4
f(4)^2 = [Sqrt(4)]^2 = 2^2 = 4
4 = 4, so the answer to the question is YES.

At this point, you should recognize a pattern. We're squaring a number and then square-rooting it OR we're square-rooting it and then squaring it. Squaring and square-rooting are "opposites", and since we're dealing with positive numbers only, they 'cancel out' and the values of f(X^2) and f(X)^2 will always be the same: X. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

2) X=9

This tells us NOTHING about how the function 'works', so there's no way to answer the question.
Fact 2 is INSUFFICIENT.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich