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## Official Guide Explanation:Data Sufficiency #89

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: 89
Page: 159
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other

Explanation: Statement (1) is insufficient. To translate the statement into something resembling plain English: "z is more than one greater than x + y." In that case, z could be greater than 1, but if it is, say, (3/4), x + y could be -(1/2), for a sum of (1/4), which is greater than 0.

Statement (2) is sufficient. x + y + 1 < 0 is equivalent to x + y< - 1. If x + y is less than -1 and x + y + z is greater than 0, z must be greater than 1. This is easiest to see by rewriting the initial inequality:

x + y + z > 0

z>-(x + y)

z>-(something less than -1)

z > (something greater than 1)

Choice (B) is correct.

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