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1. SUDHANSHU SINGH says

   May 24, 2019 at 6:54 AM

   In the stem of the question there is no restriction on x , so definitely x can be positive and negative both, however since the question is not asking for the value of x rather the value of expression is asked and luckily for both the values of x i.e 5 and -5 the expression will not change and neither the final result I.E
   FOR X =5 THE EXPRESSION WILL BE 2^5 +2^(-5) AND SIMILARLY FOR X=-5 THE EXPRESSION WILL BE 2^-5 + 2^5 ARE ESSENTIALLY THE SAME EXPRESSION, hence statement 2 is sufficient to answer the question.

   I believe your reasoning for rejection of -5 as exponent is not true,it seems like a forced attempt to match the answer to the QUESTION

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2. GMAT Quantum says

   June 6, 2019 at 5:04 PM

   Hi Sudhanshu,

   I am referring to the fact that $2^{x} + 2^{-x}$ cannot be equal to $-5$, I am not talking about the value of $x$, which could be negative. Statement 2 tells us that the $[2^{x} + 2^{-x}]^2 = 25$, the question is what can we conclude about the value of the expression $2^{x} + 2^{-x}$? Here $2^{x} + 2^{-x}$ is always positive, irrespective of the value of $x$, and therefore must equal $5$.

   Dabral

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