Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 15"
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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 19:43, 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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