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## Official Guide Explanation:Problem Solving #226

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: 226
Page: 184
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Arithmetic > Decimals >
Category 3: Algebra > Linear Equations-One Unk >

Explanation: Since the right side of the equation contains a five and the fraction on the left has something related to (15/3), rewrite the top and bottom of the fraction to convert those numbers to 15 and 3. 0.0015 = 15 * 10-4, and 0.03 = 3 * 10-2. We can rewrite the left side of the equation as follows:

((15 * 10-4 * 10m)/(3 * 10-2 * 10k)) = ((15 * 10(m - 4))/(3 * 10k - 2))) = 5 * 10((m - 4) - (k - 2)) = 5 * 10(m - k - 2)

Then, divide both sides by 5, and the result is:

10(m - k - 2) = 107

m - k - 2 = 7

m - k = 9, choice (A).

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