Official Guide Explanation:
Data Sufficiency #97

Background

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Solution and Metadata

Question: 97
Page: 281
Difficulty: 5 (Moderate)
Category 1: Algebra > Exponents >
Category 2: Algebra > Inequalities > Negatives

Explanation: Statement (1) is sufficient. If x² > 9, then either x > 3 or x< - 3. Since we know that x is negative, it must be latter: x< - 3. That answers the question directly.

Statement (2) is insufficient. We can take the cube root of both sides:

x< ³rt[ - 9]

You aren't expected to know the exact cube root of -9, so approximate. The cube root of -8 would be -2, so the cube root of -9 must be very close to -2. To keep it simple, let's say -2.1:

x< - 2.1

The value of x could be either greater or less than -3. Choice (A) is correct.

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