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P06 [Number Theory] - Turkish NMO 1st Round - 2014

Source:

May 21, 2014

Problem Statement

The numbers which contain only even digits in their decimal representations are written in ascending order such that 2,4,6,8,20,22,24,26,28,40,42,…2,4,6,8,20,22,24,26,28,40,42,\dots What is the 2014th2014^{\text{th}} number in that sequence?
<spanclass=′latex−bold′>(A)</span> 66480<spanclass=′latex−bold′>(B)</span> 64096<spanclass=′latex−bold′>(C)</span> 62048<spanclass=′latex−bold′>(D)</span> 60288<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 66480 \qquad<span class='latex-bold'>(B)</span>\ 64096 \qquad<span class='latex-bold'>(C)</span>\ 62048 \qquad<span class='latex-bold'>(D)</span>\ 60288 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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