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## Official Guide Explanation:Problem Solving #211

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: 211
Page: 182
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Other
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: If a two - digit integer has tens digit x and units digit y (for instance, in the number 51, x = 5 and y = 1), the number can be written algebraically as 10x + y. If the digits are reversed, the resulting number is 10y + x. If the difference between the two numbers is 27, that equation looks like:

(10x + y) - (10y + x) = 27

10x + y - 10y - x = 27

9x - 9y = 27

x - y = 3

Since we're looking for the difference between the two digits, x - y is what we're looking for; the correct choice is (A).

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