Arizona State University’s W.P. Carey School of Business received a lot of global attention after saying it would make its two-year M.B.A. program free starting this fall. It also got a lot more applicants than it bargained for. Since the announcement in October that it would drop the price tag on its full-time business program—which runs from $54,000 for in-state residents to $90,000 for international students—to $0, prospective students have inundated the Tempe, Ariz., school, breaking previous application records and forcing school leaders to man jammed phone lines and respond to email queries.