The first round involved two back to back 30 minute interviews. The interviews were mainly case-based with a few minutes at the very end for me to ask questions. The cases were similar to consulting cases, but with a private equity focus (would you recommend investing in this company? etc). There is a large mental math component (long division, etc).

Case interview, then a math / probability problem, then a behavioral interview. Lasted about half a day. Took me to the cafeteria for lunch--quite impressive. Felt pretty old school though.