Question 202 Data Sufficiency 2019 GMAT Quantitative Review

Question 202 Data Sufficiency 2019 GMAT Quantitative Review

Video explanation: What is the value of $2^{x} + 2^{-x}$?…

Comments

SUDHANSHU SINGHsays

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

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 $5$.

SUDHANSHU SINGH says

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

GMAT Quantum says

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