Official Guide Explanation:
Data Sufficiency #72




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Solution and Metadata

Question: 72
Page: 158
Difficulty: 5 (Moderate)
Category 1: Geometry > Lines >

Explanation: Statement (1) is insufficient: without any actual angle measures, it's impossible to calculate the measure of ABC, regardless of how many relationships we're given. Statement (2) is insufficient: the relationship between ABX and ABC is not known.

Taken together, the statements are sufficient. If BX bisects ABY, ABX = XBY. If BY bisects XBC, then XBY = YBC. If ABX = 40, then XBY = 40 and YBC = 40. Since those three angles make up ABC, ABC = 40 + 40 + 40 = 120. Choice (C) is correct.

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