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Official Guide Explanation:Problem Solving #182

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: 182
Page: 178
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples
Category 2: Arithmetic > Real Numbers >

Explanation: The two - digit integer XY can be written algebraically as 10X + Y. For example, if XY = 54, then 10X = 50 and Y = 4. So, if M and N are two - digit integers with the same digits in reverse order, they can be written as 10X + Y and 10Y + X. The sum of them is (10X + Y) + (10Y + X) = 11X + 11Y = 11(X + Y). In other words, the sum of M and N must be a multiple of 11, since X + Y, the sum of two digits, must be an integer. The only answer choice that is not a multiple of 11 is (A), 181.

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