Difference between revisions of "2013 AMC 12B Problems/Problem 23"

Latest revision as of 11:14, 7 April 2013

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-==Problem==
+#REDIRECT [[2013 AMC 10B Problems/Problem 25]]
-Bernardo chooses a three-digit positive integer <math>N</math> and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer <math>S</math>. For example, if <math>N=749</math>, Bernardo writes the numbers 10,444 and 3,245, and LeRoy obtains the sum <math>S=13,689</math>. For how many choices of <math>N</math> are the two rightmost digits of <math>S</math>, in order, the same as those of <math>2N</math>?
-<math> \textbf{(A)}\ 5\qquad\textbf{(B)}\ 10\qquad\textbf{(C)}\ 15\qquad\textbf{(D}}\ 20\qquad\textbf{(E)}\ 25 </math>