According to AAdvantage elite status here are the pre requisites for getting into each of the various elite statuses for American Airlines:
Do you need to have 25,000 EQMs -and- 30 EQSs -and- $3,000 EQDs or is any one of those sufficient to get you membership?
Also, let's say I bought a ticket for myself and my significant other for $1,500 each. Would my AAdvantage account get EQD credit for both purchases or just for the purchase of my ticket? Would it make a difference if my significant other had an AAdvantage number? I just ask about that because I note that purchases made for other people show up in the "My trips / Check-in" tab on the main page until I had the AAdvantage account for those other people.