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## Official Guide Explanation:

Data Sufficiency #123

**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.

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**Solution and Metadata**

**Question****: 123**

Page: 162

Difficulty: **6** (Moderately Difficult)

Category 1: Geometry > Triangles > Multiple figures

Category 2: Geometry > Intersecting Lines and Angles >

**Explanation:** Since two of the angles in BCD are the same, side BD is equal to side BC. Also, ∠ ADB is 180 - 2x. Since the sum of ∠ ADB and ∠ BDC is 180 and the sum of the angles in triangle ADB is 180, ∠ BDC has the same total angle measure as ∠ ABD and ∠ DAB: 2x = x+ ∠ DAB. Thus, ∠ DAB = x, and since ∠ ABD and ∠ DAB are equal, sides AD and BD must be equal, as well.

Statement (1) is sufficient: if AD = 6, then BD = 6, and if BD = 6, then BC = 6. Statement (2) is insufficient: regardless of the angles, it's impossible to determine the length of a side without the length of at least one more side. Choice (A) is correct.

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