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## Official Guide Explanation:

Problem Solving #104

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 104**

Page: 166

Difficulty: **6** (Moderately Difficult)

Category 1: Arithmetic > Powers and Roots of Numbers > Powers

Category 2: Algebra > Exponents >

Category 3: Algebra > Inequalities > other

**Explanation:** If the numbers you're being asked to compare are staggeringly large, like 5^{12} in this problem, there must be an easier way. You can simplify 25^{n} by writing it as (5^{2})^{n} = 5^{2n}. Now, if 5^{2n} > 5^{12}, it must also be true that 2n > 12, or n > 6. Since we're looking for the smallest integer n that fits this requirement, we know the correct answer is 7, choice (B).

Click here for the full list of GMAT OG12 explanations.

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