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Divisibility by 11 Generalizes

Source: 2021 AMC 12A Fall #10 / AMC 10A Fall #12

November 11, 2021
AMCAMC 12AMC10

Problem Statement

The base-nine representation of the number NN is 27,006,000,052nine27{,}006{,}000{,}052_{\rm nine}. What is the remainder when NN is divided by 5?5?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>4<span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>3\qquad<span class='latex-bold'>(E) </span>4
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