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## Official Guide Explanation:Problem Solving #123

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: 123
Page: 169
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Discount >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Arithmetic > Percents > other

Explanation: If \$207 includes a 15% gratuity, then, if x is the pre - tip price of the meal, 207 = 1.15x. Expressed differently: x = (207/(1.15)). To find the average price per person, divide that by 15, leaving you with ((x)/15) = (207/(15(1.15))). From here, it's best to estimate. 207 is a little less than 210, which is 15(14), so we can simplify to a little less than (14/(1.15)). 1.15, obviously, goes into 11.50 ten times, so it goes into 12.65 eleven times and 13.80 twelve times. Thus, (14/(1.15)) is just a little more than \$12, and since we rounded up before, it's safe to assume that \$12, choice (B), is the correct answer.

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