I have some experience regarding this.
I participated in one of these and had to crack a HBS case. My team ended up winning the Best Analysis Award and the judges (guys from MBB type firms and HBS) announced that the analysis from my team was closest to what they use in real life :D.
The key factors IMO
1) Team: We were a group of 4 engineers, a highly analytical team. Since I was the one who formed the team, I made sure my team was an engineering only team. Hence the key is choosing your team. But in a team of 4 I knew only 1 other guy, the other 2 I had just met once or twice in 3 years. Why did I choose these people and not people who were equally smart but I knew well? See the next point
2) Leader: At the very beginning I made clear that I will be the leader of the team. This is because when 4 people sit down to solve a case heated arguments are bound to happen. So one person needs to step in make a decision. Otherwise if we had tried to accomodate all 4 then it would have been the case of too many chefs spoiling the broth. Since 2 of the people in my team were just acquantainces I didn't care about hurting them by saying 'no'. If I chose a team with my friends, I would have been less rational and would have thought about what my friends felt and all that. Having strangers (almost) helped to toughen myself and approach the case using cold hard analysis.
3) Detail: We really went into detail and looked at all possible angles. This was tough. But we spent a good chunk of our time doing this analysis. I had noticed that as soon as the case was released other teams opened up their laptops and started preparing their slides before
they had their analysis done. But my team decided to first get a pen and paper solution and then put it on powerpoint. Ofcourse this resulted in our slides being not very pretty (the judges noted this and gave us some negative points).
4) Practise: Before the case competiton I did manage to print out the Tuck casebook and practise cases from some websites. This was helpful as I wasn't completely lost when we first encountered the case. Plus this helps with interview prep as well.
So hope that helps.
PS: Please note that this was in my undergrad and team dynamics might be a bit different at the MBA level. But I think choosing a proper team, putting your foot down when needed, detail and practise probably hold true at every level.
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