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P30 [Number Theory] - Turkish NMO 1st Round - 2003

Source:

May 31, 2014

Problem Statement

If the sum of digits in decimal representaion of positive integer nn is 111111 and the sum of digits in decimal representation of 7002n7002n is 990990, what is the sum of digits in decimal representation of 2003n2003n?
<spanclass=′latex−bold′>(A)</span> 309<spanclass=′latex−bold′>(B)</span> 330<spanclass=′latex−bold′>(C)</span> 550<spanclass=′latex−bold′>(D)</span> 555<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 309 \qquad<span class='latex-bold'>(B)</span>\ 330 \qquad<span class='latex-bold'>(C)</span>\ 550 \qquad<span class='latex-bold'>(D)</span>\ 555 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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