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## Official Guide Explanation:Problem Solving #D04

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: D04
Page: 20
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Sets > 2 sets
Category 2: Arithmetic > Percents > other
Category 3: Word Problems > Sets >

Explanation: This is a classic overlapping sets problem. Don't waste your time by figuring out what absolute numbers the percentages correspond to. Since the question is asking for a probability, the fact that there are 2,500 people in the group is irrelevent.

We're looking for the fraction of people who invest in municipal bonds but not in oil stocks. We know that 35 percent of the group invests in municipal bonds. 7 percent of the group invests in both municipal bonds and oil stocks, meaning that 28 percent of the group (35 - 7) invests in municipal bonds, but not in oil stocks.

Thus, the probability is (28/100) = (14/50) = (7/25), choice (B).

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