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## Official Guide Explanation:Data Sufficiency #54

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.

Solution and Metadata

Question: 54
Page: 277
Difficulty: 5 (Moderate)
Category 1: Word Problems > Other >
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: If the number of miles in a trip is x, the price of the trip, in cents, can be expressed as follows:

f + m(x - 1)

In other words, m times one fewer than the total number of miles, since the first mile cost f cents. (The GMAT likes testing the "additional" concept.) The question is looking for f + m(10 - 1), so to answer the question, it looks like we'll need f and m.

Statement (1) is insufficient. If f + m(2 - 1) = 0.90, or f + m = 0.90, we don't know how much of the total is the first mile and how much is the second mile.

Statement (2) is also insufficient. Again, if f + m(4 - 1) = 1.20, or f + 3m = 1.20, we don't know how much of the total cost is the first mile, and how much is the rest.

Taken together, the statements are sufficient. We now have two equations with two variables:

f + 3m = 1.20

f + m = 0.90

To simplify, subtract the second from the first:

2m = 0.30

m = 0.15

From there, we can solve for f using either of the two equations, and finally find the cost of a 10 - mile trip. Since it's DS, we don't need to do that. Choice (C) is correct.

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