If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b

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