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## Official Guide Explanation:Problem Solving #230

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.

Solution and Metadata

Question: 230
Page: 185
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Exponents >
Category 2: Algebra > Simplifying Algebraic Expressions >
Category 3: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: Algebraically, the question is looking for the value of x in the following equation:

((2-14 + 2-15 + 2-16 + 2-17)/5) = x(2-17)

Start simplifying by multiplying both sides by 5:

2-14 + 2-15 + 2-16 + 2-17 = 5(2-17)x

Next, recognize that every term can be related to 2-17. For instance, 2-16 = 2(2-17), and 2-15 = 22(2-17):

8(2-17) + 4(2-17) + 2(2-17) + 2-17 = 5(2-17)x

Divide everything by 2-17:

8 + 4 + 2 + 1 = 5x

15 = 5x

x = 3, choice (C).

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