Official Guide Explanation:
Problem Solving #190




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Solution and Metadata

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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