Official Guide Explanation:
Data Sufficiency #87




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Solution and Metadata

Question: 87
Page: 280
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Rate Problems > Speed

Explanation: Rate equals distance over time:

r = ((d)/(t))

so t = ((d)/(r)). Thus, the question boils down to this:

((d1)/(r1)) > ((d2)/(r2))?

Statement (1) is insufficient. It allows us to substitute one of the variables, since d1 = d2 + 30:

((d2 + 30)/(r1)) > ((d2)/(r2))?

While we know that the first distance is greater, we don't know anything about the rates.

Statement (2) is also insufficient. Again, it allows us to substitute one variable, but this time we don't know anything about distance:

((d1)/(r2 + 30)) > ((d2)/(r2))?

Taken together, the statements are still insufficient. We can substitute both statements into the original inequality:

((d2 + 30)/(r2 + 30)) > ((d2)/(r2))?

An easier way to see the relationship is to cross - multiply. We can do that because distances and rates must be positive:

(d2 + 30)r2 > (r2 + 30)d2 ?

d2r2 + 30r2 > d2r2 + 30d2 ?

30r2 > 30d2 ?

r2 > d2 ?

What matters is the relationship between the second rate and distance. We don't know that, so we can't answer the question. Choice (E) is correct.

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