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## Official Guide Explanation:Problem Solving #209

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.

Question: 209
Page: 182
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Triangles > Multiple figures
Category 2: Geometry > Intersecting Lines and Angles >

Explanation: The angles in a quadrilateral sum to 360, so 90 + 90 + z + y = 360, or y = 180 - z. The angles in a triangle sum to 180, so the angle opposite x\unit{%TCIMACRO{\U{b0}}%BeginExpansion {{}^ ο}%EndExpansion } is equivalent to 180 - 90 - z = 90 - z. Since 90 - z and x make up a straight line, they sum to 180, so 180 = 90 - z + x, or x = 90 + z. Putting all of that together, x + y = (90 + z) + (180 - z) = 270, choice (D).

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