2019 AMC 8 Problem 13
Attempt Problem 13 of the 2019 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
A palindrome is a number that has the same value when read from left to right or from right to left. (For example, is a palindrome.) Let 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
Answer: A
Small hint:
Every two-digit palindrome is a multiple of
Big hint:
Check the first three-digit multiple of that is not a palindrome
Video solution:
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Written solution:
Note that -digit palindromes have the tens and units digits the same. This means that they are all multiples of
If a -digit number is the sum of -digit palindromes, then it itself must also be a multiple of
The smallest -digit multiple of that is not a palindrome is This can be achieved by adding
Therefore, The sum of its digits is
Thus, the correct answer is A.
Problem 13 in other years
- 1985 AMC 8
- 1986 AMC 8
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