2019 AMC 8 Problems/Problem 13

Problem 13

A $\textit{palindrome}$ is a number that has the same value when read from left to right or from right to left. (For example 12321 is a palindrome.) Let $N$ be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of $N$ ?

$\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }4\qquad\textbf{(D) }5\qquad\textbf{(E) }6$

Solution 1

All the two digit palindromes are multiples of 11. The least 3 digit integer that is the sum of 2 two digit integers is a multiple of 11! The least 3 digit multiple of 11 is 110! The sum of the digits of 110 is 1+1+0= $\boxed{\textbf{(A)}\ 2}$ . ~heeeeeeheeeee

2019 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
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2019 AMC 8 Problems/Problem 13

Problem 13

Solution 1

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