Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 15"

 
Line 1: Line 1:
 
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>
 +
 +
[[Mock AIME 1 2006-2007]]

Revision as of 14:59, 24 July 2006

15. Let $S$ be the set of integers $0,1,2,...,10^{11}-1$. An element $x\in S$ (in) is chosen at random. Let $\star (x)$ denote the sum of the digits of $x$. The probability that $\star(x)$ is divisible by 11 is $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Compute the last 3 digits of $m+n$

Mock AIME 1 2006-2007