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Strange thing: If I search [run a sweepstakes] it should be exact match but I see the 1300/800 you're seeing. If I search  run a sweepstakes and then use "match type: exact" I see the ones I posted, <10, <10. At any rate, Adwords tool aside, you can rank for this term although it depends on "how" you want to rank.  A page by itself will be hard.  The lower DA pages are all blogs (new content) and you're definitely competing with chron, ehow, etc. It's hard to give you specifics without knowing what you're trying to do, exactly.