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## Official Guide Explanation:Data Sufficiency #36

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: 36
Page: 276
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Functions > other
Category 2: Algebra > Exponents >

Explanation: Function questions can look intimidating, but they don't have to be that way. In this case, we're told that a is a constant, so once we solve for it, we'll know what it is in all cases. Since we're looking for f(1), we want to know the value of an when n = 1. In other words, we need the value of a.

Statement (1) is insufficient. f(2) simply means that n = 2. Since f(n) = an, f(2) = a2. We know that's 100, so a2 = 100. a could be 10 or -10. Since we don't know the precise value of a, we can't answer the question.

Statement (2) is sufficient. We can use much of the same reasoning as in (1):

f(3) = a3= - 1,000

a= - 10

There's only one possible value for a, so we can find f(1). Choice (B) is correct.

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