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## Official Guide Explanation:Problem Solving #156

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 156
Page: 82
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other
Category 2: Algebra > Absolute Value >
Category 3: Algebra > Simplifying Algebraic Expressions >

Explanation: First, simplify the inequality:

4 < ((7 - x)/3)

12 < 7 - x

5< - x

x< - 5

Roman numeral I is not true. We know that x is less than -5, so it can't be greater than 5.

Roman II must be true. If x is less than -5, x + 3 must be less than -2, so the absolute value must be greater than 2.

Roman III must also be true. If x is less than -5, then x + 5 must be less than 0, so -(x + 5) must be greater than 0.

Choice (D) is correct.

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