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1993 AMC 12 #16 - Sequence of Integers

Source:

January 2, 2012
AMC

Problem Statement

Consider the non-decreasing sequence of positive integers 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,... 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5,... in which the nthn^{\text{th}} positive integer appears nn times. The remainder when the 1993rd1993^{\text{rd}} term is divided by 55 is
<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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