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## Official Guide Explanation:

Data Sufficiency #43

**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.

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.

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**Solution and Metadata**

**Question****: 43**

Page: 156

Difficulty: **5** (Moderate)

Category 1: Geometry > Quadrilaterals >

Category 2: Geometry > Triangles > Pythag

**Explanation:** Statement (1) is insufficient. The diagonal is the hypotenuse of a right triangle with legs equal to the length and width of the rectangle. We can use the pythagorean theorem to represent what the statement tells us:

l^{2} + w^{2} = 5^{2}

Statement (2) is also insufficient. We're looking for lw, but we're told that 2l + 2w = 14, or l + w = 7.

Taken together, the statements are sufficient. We have two equations and two variables. Note that the first equation doesn't meet the usual standard of "linear" equations--having an exponent in one of the equations is a recipe for multiple results. However, there's a sort of twist on that twist. The multiple results in a case like this result in one positive and one negative answer (for instance, if x^{2} = 16, x = 4 or x= - 4). But since this question deals with a rectangle, all of the values must be positive. Choice (C) is correct.

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