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## Official Guide Explanation:Data Sufficiency #D48

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: D48
Page: 25
Difficulty: 5 (Moderate)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Pythag

Explanation: We're looking for the perimeter of a rectangle. To find that, we'll need both the length and width.

Statement (1) is insufficient. The diagonal is the same as the hypotenuse of a right triangle formed with the length and width as legs. Using the pythagorean theorem:

l2 + w2 = 102

Two variables and one equation isn't enough.

Statement (2) is also insufficient. This tells us that lw = 48. Again, it's two variables and one equation. The side lengths could be 12 and 4, 6 and 8, or any number of other possibilities.

Taken together, the statements are sufficient. Given two equations with two variables, we can solve. To do so algebraically would be unnecessary and too arduous for the time constraints of a DS question. However, if you recall common triangle ratios, if the hypotenuse is 10, the sides could be 6 and 8. Since that gives you an area of 48, 6 and 8 are the length and width, resulting in a perimeter of 28. Choice (C) is correct.

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