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## Official Guide Explanation:Problem Solving #155

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 155
Page: 82
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Percents > Percent Change
Category 3: Arithmetic > Ratio and Proportion >

Explanation: This is essentially a weighted average problem. All the numbers are given in terms of 1996 revenues, so call 1996 car revenues c and 1996 truck revenues t. An 11% decrease in c and a 7% increase in t combines for a 1 percent increase in c + t. We can express that algebraically, multiplying all the percentages by 100 to keep the numbers simple:

7t - 11c = 1(c + t)

7t - 11c = c + t

6t = 12c

((c)/(t)) = (6/12) = (1/2)

We're looking for the ratio of car revenues to truck revenues, so 1 to 2 is our answer, choice (B).

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