2013 AMC 10B Problems/Problem 25: Difference between revisions
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==Problem== | ==Problem== | ||
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 <math>10,444</math> and <math>3,245</math>, 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> | |||
==Solution== | |||
Revision as of 16:32, 21 February 2013
Problem
Bernardo chooses a three-digit positive integer 
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 
. For example, if 
, Bernardo writes the numbers 
and 
, and LeRoy obtains the sum 
. For how many choices of 
are the two rightmost digits of , in order, the same as those of 
?
