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Evaluating arithmetic series

Source: AMC 10 2011 a Problem 4

June 25, 2011
AMC

Problem Statement

Let XX and YY be the following sums of arithmetic sequences: \begin{eqnarray*} X &=& 10 + 12 + 14 + \cdots + 100, \\ Y &=& 12 + 14 + 16 + \cdots + 102. \end{eqnarray*} What is the value of Y−XY - X?
<spanclass=′latex−bold′>(A)</span> 92<spanclass=′latex−bold′>(B)</span> 98<spanclass=′latex−bold′>(C)</span> 100<spanclass=′latex−bold′>(D)</span> 102<spanclass=′latex−bold′>(E)</span> 112 <span class='latex-bold'>(A)</span>\ 92\qquad<span class='latex-bold'>(B)</span>\ 98\qquad<span class='latex-bold'>(C)</span>\ 100\qquad<span class='latex-bold'>(D)</span>\ 102\qquad<span class='latex-bold'>(E)</span>\ 112
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