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## Official Guide Explanation:Problem Solving #177

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: 177
Page: 177
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Pythag
Category 3: Geometry > Rectangular Solids and Cylinders > Rectangular Solids

Explanation: The longest straight - line distance inside a rectangular solid is a diagonal from (for example) the lower front right corner to the upper back left corner. To find that, first find the length of a diagonal running through the base. In this case, it's the hypotenuse of a right triangle with sides 10 inches (width) and 10 inches (length). Since the sides of an isoceles right triangle are related in the ratio x:x:x rt[2], that means the diagonal running through the base has length 10 rt[2]. Now, imagine a triangle where the base is that diagonal and the height is one of the vertical sides that intersects that diagonal. The longest straight - line distance is the hypotenuse of the triangle formed by those two sides. Those sides have length 10 rt[2] and 5 (the height of the solid), so you can use the pythagorean theorem to find the hypotenuse:

(10 rt[2])2 + (5)2 = c2

200 + 25 = c2

c2 = 225

c = 15, choice (A).

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