Official Guide Explanation:
Problem Solving #211




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Solution and Metadata

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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