Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

A 3-digit palindrome is a number of the form a, b, a where the digits a and b can either be the same or different.  What is the sum of the digits of the largest 3-digit palindrome that is also a multiple of 6? Let's first consider the conditions so that a, b, a will become a multiple of 6.  For this to occur, we know that a must be even so that the last digit is even, and its digits also must add up to a multiple of 3.  The largest value possible to make the value of a even is 8, so we'll put an 8 at the beginning and an 8 at the end.  In order to add up to a multiple of 3, then b must also be 8, and therefore the digit sum is 24, and our answer is e.

Video Summary

A 3-digit palindrome is a number of the form a, b, a where the digits a and b can either be the same or different. What is the sum of the digits of the largest 3-digit palindrome that is also a multiple of 6? Let's first consider the conditions so that a, b, a will become a multiple of 6. For this to occur, we know that a must be even so that the last digit is even, and its digits also must add up to a multiple of 3. The largest value possible to make the value of a even is 8, so we'll put an 8 at the beginning and an 8 at the end. In order to add up to a multiple of 3, then b must also be 8, and therefore the digit sum is 24, and our answer is e.

Keywords

3-digit palindrome

multiple of 6

digit sum

largest palindrome

number theory