If (2) just said x>0, then what can we answer about the question? What is b? How is the answer still D?

TehJay wrote:

If x is an integer, is \(9^x + 9^-^x = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\)

(2) \(x > 0 = b\)

The OA is A. I couldn't piece together (1) (I understand it now with the book's explanation), but I had answered B for this one. Why is the answer not D? (2) should be sufficient, because it gives you b = 0, and \(9^x + 9^-^x\) can't possibly be 0. So the answer would be NO and (2) should be sufficient.

Is \(9^x + 9^{-x} = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\) --> square both sides --> \(9^x+2*3^x*\frac{1}{3^x}+9^{-x}=b+2\) --> \(9^x + 9^{-x} = b\). So answer to the question is YES. Sufficient.

(2) \(x > 0 = b\) --> question becomes: is \(9^x+9^{-x}=0\)? Answer to this question would be NO, as LHS is the sum of two positive values and thus can not equal to zero. So, sufficient.

There must be something wrong with this question. Technically answer would be D, as

EACH statement ALONE is sufficient to answer the question.

But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as:

on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

So we can not have answer

YES from statement (1) and answer

NO from statement (2), as in this case statements would contradict each other.

I guess there is a typo in statement (2) and it should just state \(x>0\) instead of \(x>0=b\) (I've never seen such a notation in official sources).

Hope it helps