Official Guide Explanation:
Data Sufficiency #154




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Solution and Metadata

Question: 154
Page: 287
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Exponents >
Category 2: Arithmetic > Powers and Roots of Numbers > Powers
Category 3: Arithmetic > Ratio and Proportion >

Explanation: To write the question in equation form:

b - a ≥ 2(3n-2n) ?

Statement (1) is sufficient, but it requires some crafty algebra to show why:

3n + 1-2n + 1 = 3n(31) - 2n(21) = 2(1.5(3n) - 2n)

So, is 2(1.5(3n) - 2n) ≥ 2(3n-2n) ?

Divide both sides by 2:

1.5(3n) - 2n ≥ 3n-2n?

Add 2n:

1.5(3n) ≥ 3n ?

Then divide by 3n:

1.5 ≥ 1 ?

Since 1.5 is greater than 1, we can conclusively answer the question.

Statement (2) is not enough information: it tells us nothing about b or a. Choice (A) is correct.

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