Official Guide Explanation:
Problem Solving #104




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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 512 in this problem, there must be an easier way. You can simplify 25n by writing it as (52)n = 52n. Now, if 52n > 512, 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).

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