Official Guide Explanation:
Data Sufficiency #45

Background

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Solution and Metadata

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.

a_n = rn

so: a₅₀ = 50r

Since we know that a₅₀ = 500:

50r = 500

r = 10

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

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