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## Official Guide Explanation:

Data Sufficiency #69

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th 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.

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**Solution and Metadata**

**Question****: 69**

Page: 278

Difficulty: **5** (Moderate)

Category 1: Algebra > Inequalities > Negatives

Category 2: Algebra > Absolute Value >

**Explanation:** While the number may not be drawn to scale, we can trust that the variables are in the right order, so q < r~~Statement (1) is sufficient. It tells us that q and s have the same absolute value--they are the same distance from zero, only in opposite directions. For instance, if q= - 3, s = 3. Since r is in between q and s, it is closer to zero than either of them. And because t must be greater than s (and thus, further from zero), r is the closest to zero of all four.
~~

Statement (2) is insufficient. The inequality tells us that t is further from zero than q--for instance, if q= - 2, t must be greater than 2 in order for -t to be less than -2. Consider a couple of different acceptable sets of values:

q= - 2, r = 3, s = 4, t = 5

q= - 2, r = 1, s = 4, t = 5

Both follow the rules in the question and (2), but give contradictory answers. Choice (A) is correct.

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