MathDB
Counting Four-Digit Numbers

Source:

January 9, 2009
modular arithmetic

Problem Statement

How many distinct four-digit numbers are divisible by 3 3 and have 23 23 as their last two digits? <spanclass=′latex−bold′>(A)</span> 27<spanclass=′latex−bold′>(B)</span> 30<spanclass=′latex−bold′>(C)</span> 33<spanclass=′latex−bold′>(D)</span> 81<spanclass=′latex−bold′>(E)</span> 90 <span class='latex-bold'>(A)</span>\ 27 \qquad <span class='latex-bold'>(B)</span>\ 30 \qquad <span class='latex-bold'>(C)</span>\ 33 \qquad <span class='latex-bold'>(D)</span>\ 81 \qquad <span class='latex-bold'>(E)</span>\ 90
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