Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem12

Levels 11&12 Video Solutions 2013 problem12

Video Transcription

Video Summary

The problem asks for the number of positive integers \( n \) such that both \( n/3 \) and \( 3n \) are three-digit integers. By letting \( k = n/3 \), this makes \( n = 3k \). Both \( k \) and \( 3k \) need to be integers. For \( n/3 \) to be a three-digit integer, \( k \) must be between 100 and 111, inclusive. This gives 12 possible values for \( k \), making for 12 positive integers \( n \) that satisfy the conditions.

Keywords

positive integers

three-digit

divisibility

range

conditions