MathDB
5-Digit Number Divided by 100

Source:

February 19, 2008

Problem Statement

Let n n be a 5 5-digit number, and let q q and r r be the quotient and remainder, respectively, when n n is divided by 100 100. For how many values of n n is q \plus{} r divisible by 11 11? <spanclass=′latex−bold′>(A)</span> 8180<spanclass=′latex−bold′>(B)</span> 8181<spanclass=′latex−bold′>(C)</span> 8182<spanclass=′latex−bold′>(D)</span> 9000<spanclass=′latex−bold′>(E)</span> 9090 <span class='latex-bold'>(A)</span>\ 8180 \qquad <span class='latex-bold'>(B)</span>\ 8181 \qquad <span class='latex-bold'>(C)</span>\ 8182 \qquad <span class='latex-bold'>(D)</span>\ 9000 \qquad <span class='latex-bold'>(E)</span>\ 9090
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