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## Official Guide Explanation:Problem Solving #193

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: 193
Page: 179
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Sets > 2 sets
Category 2: Word Problems > Sets >

Explanation: This is a perfect scenario for the equation T = G1 + G2-B + N. G1 = 75 (the percent of students who answered the first question correctly), G2 = 55 (the percent who answered the second question correctly), and N = 20 (the percent who answered neither correctly). T = 100, since we're working with percents--the total is 100, regardless of the number of students. To solve for those who answered both correctly (B):

100 = 75 + 55 - B + 20

100 = 150 - B

B = 50, choice (D).

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