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Difference between revisions of "2017 AMC 8 Problems/Problem 7"

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Revision as of 15:11, 22 November 2017

Let $Z$ be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of $Z$?

$\textbf{(A) }11\qquad\textbf{(B) }19\qquad\textbf{(C) }101\qquad\textbf{(D) }111\qquad\textbf{(E) }1111$

$\boxed{A)}$. Let us use the divisibility rule for 11. $ABCABC, A+C+B=A+C+B.$ $ABCABC$ is clearly a multiple of 11.

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