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## Official Guide Explanation:Data Sufficiency #45

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: 45
Page: 276
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Functions > Sequences

Explanation: Whenever we're given a formula with a constant, a high priority is finding the value of the constant. Once we get that, it never changes.

Statement (1) is sufficient.

an = rn

so: a50 = 50r

Since we know that a50 = 500:

50r = 500

r = 10

So from now on, we know that an = 10n

We don't need to work through all of the possibilities, but we could find the value of an for every possible value of n. For instance, if n = 1 , an = 10(1) = 10.

Statement (2) is also sufficient, though it takes more work to establish that:

a100 = 100r

a105 = 105r

100r + 105r = 2,050

205r = 2,050

r = 10

From here, it's the same as in (1). Choice (D) is correct.

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