Official Guide Explanation:
Data Sufficiency #51




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Solution and Metadata

Question: 51
Page: 156
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other
Category 2: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: Since n is positive, we can square both sides of all of these inequalities without considering whether we need to reverse the sign (as we'd need to do if n were negative). The inequality in the question can be simplified:

( rt[n])2 > (100)2 ?

n > 10,000 ?

Statement (1) can be simplified the same way:

( rt[n - 1])2 > (100 - 1)2

n - 1 > 10,000 - 200 + 1

n > 9,802

If n is greater than 9,802, we don't know whether it is greater than 10,000.

Statement (2) can be simplified this way as well:

( rt[n + 1])2 > (100 + 1)2

n + 1 > 10,000 + 200 + 1

n > 10,200

If n is greater than 10,200, it must be greater than 10,000. The statement is sufficient, and choice (B) is correct.

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