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## Official Guide Explanation:Problem Solving #190

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: 190
Page: 179
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Other

Explanation: When looking for the units digit of very big numbers like this one, realize that you don't have to worry about the rest of the number. For instance, to find the units digit of 13 * 13, just multiply the units digits: 3 * 3 = 9. So, the units digit of 134 is the units digit 3 * 3 * 3 * 3 = 81, or 1. The units digit of 172 is the units digit of 7 * 7 = 49, or 9. \newline The units digit of 293 is the units digit of 9 * 9 * 9 = 729, or 9. So, the units digit of the whole thing is the units digit of 1 * 9 * 9 = 81, or 1, choice (E).

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