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Most recruit from local business schools. Preferred degrees include business, finance and accounting. The best way to get an interview is to find someone at those firms and ask them to sponsor your application. They get a referral fee if hired.
In addition to Ellis's comments, the top management consulting firms (Bain, McKinsey...etc) generally only hire from Ivy League schools and Stanford. However, if you have an internal referral and you have scored well on standardized tests, you may get an interview.
Best of luck! It's a tough nut to crack!