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## Official Guide Explanation:

Data Sufficiency #91

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

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**Solution and Metadata**

**Question****: 91**

Page: 159

Difficulty: **6** (Moderately Difficult)

Category 1: Geometry > Triangles > Special Tris

Category 2: Geometry > Triangles > Multiple figures

**Explanation:** The diagram is made up of two triangles: TUV and RSV. Each triangle has a right angle at V, and each has a familiar ratio: TUV has a 90 degree angle and a 45 degree angle, so it is a 45:45:90; RSV has a 90 degree angle and a 60 degree angle, so it is a 30:60:90. To find the difference between RV and TV, then, you'll need the length of any side of triangle RSV and the length of any side of triangle TUV. Fortunately, all of the lengths are related: because TU and RS represent the same ladder, they are equal.

Statement (1) is sufficient. Given the length of side TU, you can use the 45:45:90 triangle side ratio of x:x:x rt[2] to find the lengths of sides UV and TV. Because TU = RS, you also have the length of side RS , which allows you to solve for the length of side RV. Statement (2) is also sufficient: from RV, you can find the length of RS, which is equal to the side of TU. With TU, you can solve for the length of side TV, and then find the difference TV - RV. Choice (D) is correct.

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