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## Official Guide Explanation:Problem Solving #64

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: 64
Page: 70
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Fractions >
Category 2: Arithmetic > Sets > 2 sets
Category 3: Word Problems > Sets >

Explanation: If (2/5) of the attendees were male, (3/5) of the attendees were female. We know what fraction of each gender arrived on time. For each gender, multiply the fraction of the total that is that gender by the fraction of that gender who arrived on time:

MaleOnTime = (2/5)((7/8)) = (14/40) = (7/20)

FemaleOnTime = (3/5)((9/10)) = (27/50)

The total number who arrived on time, then, is:

(7/20) + (27/50)

= (35/100) + (54/100) = (89/100)

If 89 of 100 arrived on time, that means 11 of 100 didn't. Choice (A) is correct.

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