I don’t have direct experience with OC&C, however in general the criteria for being selected in interviews at MBB for junior positions are very similar to other top-consulting firms (Roland Berger, Oliver Wyman, ATK etc.).
As you mentioned, there are two main elements that may influence this general rule:
- Demand. MBB gets more applications, as some people apply for MBB only as for the prestige and better exit opportunities they have. This means you will have more competition, and since consulting companies normally hire specific numbers, lower likelihood to get an offer compared to other consulting firms, everything equal.
- Supply. There are two reasons why consulting companies look for new hires: (i) new projects sold and (ii) replacements for consultants leaving the company. In boom periods MBB are more likely to hire more as their projects are usually bigger; however, this also means they may be less likely to hire after a high recruiting season, unless there is an occasional high need for replacement (typical after the bonuses are provided).
Given this demand-supply equation, so far that your performance is ok (not exceptional, but also not bad), you may end or not with an offer on the basis of the demand-supply equilibrium of the firm in that particular moment, whether the company is a MBB or not. Usually, the demand side of the equation weights more, making more difficult to be hired by MBB compared to other companies with an equivalent performance, but this is not always the case. I have heard several times of people who got invited by MBB and got rejected by all the smaller consulting companies due to the fact they were not in need of people in that period.
As for my experience at McKinsey, you can ask for help during the case, but you will have to do great in all the remaining areas to move to the next round. The degree to which that may be an issue would depend on what exactly you needed support with (it is very different to need help on simple math or on some specific details of a very complex industry) and their comparison between you and other candidates for the position.