Official Guide Explanation:
Data Sufficiency #36

Background

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Solution and Metadata

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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