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## Official Guide Explanation:Problem Solving #76

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.

Question: 76
Page: 71
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Quadrilaterals >
Category 2: Algebra > Simplifying Algebraic Expressions >

Explanation: Call each side of a square s. If the area is n:

s2 = n

s= rt[n]

We're looking for the length of the diagonal. That's the hypotenuse of a right triangle formed by two sides and the diagonal; the two sides are the legs of the triangle. Because this is a square, the triangle is a 45:45:90 triangle, meaning that the hypotenuse (the diagonal) is rt[2] times the length of either leg. Since the legs are rt[n], the diagonal is:

rt[n] rt[2]= rt[2n], choice (A).

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