Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem1

11&12 Video Solutions 2011 problem1

Video Transcription

Video Summary

The difference between a positive integer and the sum of its digits is always divisible by 9. This is demonstrated using both two-digit and three-digit examples—such as 13 and 120—and then extended to an n-digit integer by analyzing its base-10 representation. By simplifying the expression where each term is a multiple of 9, the proof shows that the difference always results in a number divisible by 9. Thus, the correct answer to the multiple-choice question is 9.

Keywords

positive integer

sum of digits

divisible by 9

base-10 representation

mathematical proof