Official Guide Explanation:
Data Sufficiency #152

 

 

Background

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Solution and Metadata

Question: 152
Page: 287
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-Two Unk >

Explanation: The first step in a question like this is to set up an equation to represent the information given in the question. If Carmen had 12 more tapes, she'd have c + 12. If that's twice as many as Rafael has, then:

c + 12 = 2r

Statement (1) is insufficient. Given an inequality, start by testing a value close to the edge of the acceptable range. Since Rafael must have more than 5, try r = 6. In that case:

c + 12 = 2(6)

c = 0

Carmen has fewer. Now try something much larger, like r = 60:

c + 12 = 2(60)

c = 108

In this case, Carmen has more. Contradictory answers mean that the statement is insufficient.

Statement (2) is sufficient. We already know that if c = 0, then r = 6, meaning that Rafael has more. To try a number close to the edge of the range given in (2), use c = 11:

11 + 12 = 2r

r = 11.5

That's not acceptable--common sense tells us we need an integer number of tapes. Instead, try c = 10:

10 + 12 = 2r

r = 11

We've gotten as close to the edge of the acceptable range as possible, and Rafael still has more than Carmen. Carmen can't have any more than 10 or fewer than 0, so we've tested both extremes. Since we keep getting the same answer, the statement is sufficient. Choice (B) is correct.

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