Official Guide Explanation:
Data Sufficiency #151

Background

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Solution and Metadata

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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