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## Official Guide Explanation:Data Sufficiency #151

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: 151
Page: 286
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Exponents >
Category 2: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: Since we know that n is a positive integer, k must be something like 51, 510, 5,100, and so on. That sharply limits the number of possibilities.

Statement (1) is sufficient. Consider the possible values of k in the given range. If we continue the list I started a moment ago, we have:

5,100

51,000

510,000

The first is less than 6,000 and the last is greater than 500,000. Thus, the only acceptable option is 51,000.

Statement (2) is also sufficient. Given the value of k2, we can find a positive and negative value of k. There's no need to do the math. Since 5.1 raised to any power will be positive, we can dismiss the negative value. Whatever the square root of 2.601 * 109, that's our answer. Choice (D) is correct.

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