Minimums
Stated minimums in most cases are there to discourage the masses and to have a reason to turn down someone who they don't wish to hire anyway. Every company hires people below their stated "minimums". Some hire significantly below their announced "bottom line". If you are a wall flower and politely waits for minimums and then quietly submits a resume then you had better rethink your approach. Every companies HR department is well adapted to say no. You have to rise above that and try again.
SkyHigh