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AMC10 Prep - Base-k Numbers, with Past AMC10 Problems

AMC10 Prep - Base-k Numbers, with Past AMC Problems Base-10 and Base-k numbers are frequently covered in the AMC exams. We explain the key concepts and problem solving tricks through the following problems from past AMC10 exams: 2017 AMC10B Problem 23 2015 AMC 10A Problem 18 2019 AMC10B Problem 12 2021 Fall AMC 10A Problem 12 2021 Spring AMC 10A Problem 11 2019 AMC10B Problem 14 2013 AMC10A Problem 19 2003 AMC 10A Problem 20 00:00:00 Introduction: base-k numbers 00:01:20 Review of Modulus Arithmetics 00:02:24 Some Useful Modulus Properties 00:04:14 Property of Mod 9 in Base-10. How to check if a number is divisible by 9? 00:05:00 A Trick in Checking Mod 9 - not always add the individual digits 00:06:40 Example Problem: 2017 AMC10B Problem 23 (mod 45)/Chinese Remainder Theorem 00:10:01 Binary Numbers (base-2), Values of Powers of 2 00:12:45 An Example: Find Mod 8 of the Product of 3 Binary Numbers 00:15:27 Base-16: Hex or Hexadecimal Numbers 00:16:45 An Example: 2015 AMC 10A Problem 18 00:19:48 An Example (base-7) 2019 AMC10B Problem 12 00:21:29 An Example (base-9, mod 5) 2021 Fall AMC 10A Problem 12 (digit sum from alternating positions) 00 00:25:26 An Example: (mod 3) 2021 Spring AMC 10A Problem 11 00:29:02 An Example: (repeating decimals) 2019 AMC 10A Problem 18 00:32:34 Review: Property of numbers (in base-10) divisible by 11 00:33:38 An Example (19 factorial): 2019 AMC10B Problem 14 00:36:50 An Example(digit ending with 3) 2013 AMC10A Problem 19 00:39:29 An Example:(Range of 3-digit numbers in base-k) 2003 AMC 10A Problem 20