Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 15"
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15. Let <math>S</math> be the set of integers <math>0,1,2,...,10^{11}-1</math>. An element <math>x\in S</math> (in) is chosen at random. Let <math>\star (x)</math> denote the sum of the digits of <math>x</math>. The probability that <math>\star(x)</math> is divisible by 11 is <math>\frac{m}{n}</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Compute the last 3 digits of <math>m+n</math> | 15. Let <math>S</math> be the set of integers <math>0,1,2,...,10^{11}-1</math>. An element <math>x\in S</math> (in) is chosen at random. Let <math>\star (x)</math> denote the sum of the digits of <math>x</math>. The probability that <math>\star(x)</math> is divisible by 11 is <math>\frac{m}{n}</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Compute the last 3 digits of <math>m+n</math> | ||
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Revision as of 15:59, 24 July 2006
15. Let 
be the set of integers 
. An element 
(in) is chosen at random. Let 
denote the sum of the digits of 
. The probability that 
is divisible by 11 is 
where 
and 
are relatively prime positive integers. Compute the last 3 digits of 
