Official Guide Explanation:
Problem Solving #182




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Solution and Metadata

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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