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## Official Guide Explanation:Problem Solving #166

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.

Question: 166
Page: 176
Difficulty: 5 (Moderate)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Percents > other

Explanation: If the team won 80% of its first 100 games, that means it won 80 games. If we say that the remaining number of games is x, and it won 50% of those, it won ((x)/2) more games. If the team won 70% of its games overall, we can set up a ratio: (70/100) = ((80 + ((x)/2))/(100 + x)). After simplifying the left side to (7/10), cross - multiply and solve for x:

7(100 + x) = 10(80 + ((x)/2))

700 + 7x = 800 + 5x

2x = 100

x = 50

Since x stood for the remaining games, and there were 100 games before that, the total number of games is 100 + 50 = 150, choice (D).

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