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## Official Guide Explanation:Data Sufficiency #144

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: 144
Page: 286
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Multiple figures
Category 3: Geometry > Triangles > Pythag

Explanation: To find the length of a side of A, it's most likely (given the way that GMAT questions with multiple figures generally work) that you'll have to find the lengths of the other sides of triangle D. It helps to know that the area of D is 4: the product of the base and the height, then, is 8.

Statement (1) is sufficient: if the area of B is 9, the length of a side of B is 3, which means the height of triangle D is 3. From there, you can find the length of the base, then the length of the hypotenuse (using the pythagorean theorem), which is a side of A.

Statement (2) is sufficient for the same reasons: from the area of C, you can deduce the length of a side of C, which is the base of triangle D. From there, using the product of the base and height of D, you can find the height of D, then the hypotenuse of D. Choice (D) is correct.

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