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## Official Guide Explanation:Problem Solving #103

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: 103
Page: 166
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Rate Problems > other
Category 3: Algebra > Linear Equations-One Unk >

Explanation: Say that there are x teachers currently at the school. Because the student - teacher ratio is currently 30:1, there are 30x students. If the student enrollment increased by 50, the number of students would be 30x + 50. If the number of teachers increased by 5, the number of teachers would be x + 5. Since, after those changes, the student - teacher ratio is 25:1, we can set up a ratio with the new numbers for students and teachers: (25/1) = ((30x + 50)/(x + 5)). The remaining steps are as follows:

25(x + 5) = 30x + 50

25x + 125 = 30x + 50

75 = 5x

x = 15

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