Mock AIME 1 2006-2007 Problems/Problem 15: Difference between revisions
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==Problem== | |||
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> | |||
==Solution== | |||
{{solution}} | |||
[[Mock AIME 1 2006-2007]] | ---- | ||
*[[Mock AIME 1 2006-2007/Problem 14 | Previous Problem]] | |||
*[[Mock AIME 1 2006-2007]] | |||
Revision as of 18:43, 22 August 2006
Problem
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 
Solution
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