Late in the tournament BB decisions

This happens to me often and it seems I make the wrong decision more often than not.

Say theres about 40 left in a 500 person MTT. Before posting, you are in the BB with 15k chips. SB has 30k. Blinds 3k/1.5k.

Folded around to SB. SB completes.

What range of hands do you need to push here? And what range to see a flop? Recently this has happened to me with KQs and Q7o, what would you do with those hands?

-Chris

With this stack, you probably should push any two into an unknown. If SB's a sheriff, I push any hand that's favorite over a random hand, which is a lot.