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Official Guide Explanation:Data Sufficiency #160

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: 160
Page: 287
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Circles > Multiple figures
Category 2: Geometry > Circles > Sector/Arc
Category 3: Geometry > Triangles > Multiple figures

Explanation: To find the circumference of the circle, you need the radius, or something that can give you the radius. Statement (1) is sufficient: the triangle has angles in a ratio of 45:45:90, which means that the sides have a ratio of x:x:x rt[2]. So, if the perimeter of the triangle is 20 + 10 rt[2], x + x + x rt[2] = 20 + 10 rt[2]. You can solve for x, which is also a radius of the circle, so you can solve for the cirumference of the circle.

Statement (2) is also sufficient: arc XYZ is (1/4) the circumference of the entire circle, since it is defined by an angle of 90, which is one - quarter of 360, the angle measure of the entire circle. If 5 π is a quarter of the circumference, the circumference must be 4(5 π ) = 20 π . Choice (D) is correct.

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