Beware of the GMAT question that seems too obvious!

Here, you might think that we can solve the original equation for b. If a and b are positive integers and a^(b+4) = a^(2b-4), then b + 4 = 2b - 4, right? Take a moment to question that. Are there any other possibilities?

Usually, if we set the bases equal, we can set the exponents equal. If 3^x = 3^(y - 1), then x = y - 1, because every power of 3 is unique. There are 3 exceptions to this rule, though: 0, 1, and -1.
1 raised to any power = 1, so we can't set the powers equal
0 raised to any power = 0, so we can't set the powers equal
-1 will alternate between positive 1 and -1, based on whether the exponent is even or odd, but the principle is the same.

So in your problem, one of two things must be true:
either a > 1 and therefore b + 4 = 2b - 4
or... a = 1

If you consider both of these possibilities, you can see that only statement 1 eliminates the 2nd scenario, and leave us with definite values for a and b.

Answer: A