MathDB
Sum of All Five-Digit Palindromes

Source: 2014 AMC 12A #15

February 5, 2014
arithmetic sequencearithmetic seriesAMC

Problem Statement

A five-digit palindrome is a positive integer with respective digits abcbaabcba, where aa is non-zero. Let SS be the sum of all five-digit palindromes. What is the sum of the digits of SS?
<spanclass=latexbold>(A)</span>9<spanclass=latexbold>(B)</span>18<spanclass=latexbold>(C)</span>27<spanclass=latexbold>(D)</span>36<spanclass=latexbold>(E)</span>45<span class='latex-bold'>(A) </span>9\qquad <span class='latex-bold'>(B) </span>18\qquad <span class='latex-bold'>(C) </span>27\qquad <span class='latex-bold'>(D) </span>36\qquad <span class='latex-bold'>(E) </span>45\qquad