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## Official Guide Explanation:Problem Solving #146

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.

Question: 146
Page: 81
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Sets >
Category 2: Arithmetic > Sets > 2 sets

Explanation: Say the number of passengers is t. Thus, if 20% of the passengers held round - trip tickets and took their cars aboard, c&r = 0.2t . (c stands for those who took their cars aboard, and r for those with round - trip tickets.) If 60% of the passengers with round - trip tickets did not take their cars aboard, that means 40% DID take their cars aboard. Thus, c&r = 0.4r. Since we have two equations where one side is c&r, we can set the other sides equal to each other:

0.2t = 0.4r

r = ((0.2)/(0.4))t = 0.5t

Half of the total passengers held round - trip tickets. Choice (C) is correct.

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