Official Guide Explanation:
Data Sufficiency #123




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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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