Most people get on the highly select list.  They then accept the people who send in LOI's first.  It's pretty interesting.  Some people send in a letter of intent and get the acceptance a week later.  You can do searches for old GT threads from the past 2 years and find this.  They do this so that they have people who really like GT and so they have a high matriculation rate (number of accepts per offers)  I would recommend to start sending in letters.