Be in the top 12 so therefore it may only require top 9 but usually 5-7 would be necessary.
Once guarantees are done they have to go back to the highest ranked teams still available (regardless of how many are from each conference). So unless they do something to keep us out of one of those top deserved rankings if we get high enough they have to take us.
I did a series of posts (and I think I linked to most of them out of this one) that discusses how far down we could be ranked in a given year and they be required to still take us.
http://www.cougarboard.com/board/message.html?id=12367693
The gist is....
2014-15 - Rose/Sugar as Semi-Finals (3-5 at-large) must be ranked top 7, possibly as low as 9
2015–16 - Orange/Cotton (3 at-large) must be ranked top 7
2016–17 - Fiesta/Peach (1 at-large) must be ranked top 5
So if BYU ever finds itself in a 1996 type ranking (#5 before bowls) there is not a possibility that they can leave us out in any year. But a 1983 (#9 before the bowls) we have a chance in a Rose/Sugar year based on the other guaranteed teams but would be left out for certain in the other years.