Official Guide Explanation:
Data Sufficiency #165

Background

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Solution and Metadata

Question: 165
Page: 288
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Exponents >
Category 2: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: To determine whether Statement (1) has any relevance to the question, square both sides so that b is not under a radical sign:

b + 2 = (3^x + 3^-x)²

b + 2 = (3^x)² + 2(3^x3^-x) + (3^-x)²

b + 2 = 3^2x + 2(((3^x)/(3^x))) + 3^2(-x)

b + 2 = (3²)^x + 2(1) + (3²)^-x

b + 2 = 9^x + 2 + 9^-x

b = 9^x + 9^-x

In other words, the answer is "yes:" the equation in (1) is equivalent to the one in the question.

Statement (2) is not sufficient: it has no information about b. Choice (A) is correct.

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