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## Official Guide Explanation:Problem Solving #120

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: 120
Page: 77
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Other >
Category 2: Arithmetic > Percents > other

Explanation: This is a convoluted question. Faced with a lot of complexity, try to break it down to smaller parts. Say that the number of trucks rented out is t. Thus, before any trucks were returned, there were 20 - t trucks on the lot. Then, when half of the trucks were returned, the number of trucks on the lot was 20 - t + 0.5t = 20 - 0.5t. If that number is at least 12, we can set up an equation and solve for t:

20 - 0.5t ≥ 12

8 ≥ 0.5t

16 ≥ t

If t is less than or equal to 16, then the greatest number of trucks that could have been rented out is 16, choice (B).

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