I think you misunderstand McKinsey's selectiveness. To illustrate, I don't think it would be a stretch to say that they take the best of Harvard(that is the baker's scholars). A first-class from a lower tiered university (that is, in this case, the local NUS/NTU/SMU) is simply not comparable to the pedigrees of the top ivies and UK Oxbridge/LSE. The fact is, perhaps at most a handful (countable using a single hand), of local graduates have made it onto to become McKinsey analysts/associates, and
none have made it to partner/director level.
The people at McKinsey are truly exceptional and excel at both academic and other skills. After all, their company remapped the power structure of the White House, and is involved in the very top strategic decisions of the largest companies (think Fortune 50), anything less than the
global elite of the entire applicant pool will not do.
That said, an MBA will not hurt, and will definitely give you a better chance of breaking into MBB in general. However, no one can advise on a definitive chance of being made an offer, it depends a lot on your past experience as well as school pedigree from my observation, and I would personally not drop 100k on school for a chance in breaking into MBB alone. The break into MBB is tough, climbing the ranks to a position where you can truly stand out (director/partner level) requires
exceptional skill and talent, the kind of talent that reaches the very top echelons of their chosen field, whether it is working on overall government directives or heading global conglomerates in C-suite positions.
A arbitrarily chosen look at McKinsey director: Hsieh Tsun-Yan (Singaporean)
1) Awarded President's Scholarship and Colombo Plan scholarship after A levels
2) Invited to join Administrative Service (you would know what this is since you are a ministry scholar)
3) Topped his cohort in Mech Eng at his undergraduate institution, UAlberta, Canada
4) OCS, but took up Canadian citizenship
5) First Chinese and Singaporean to be admitted to McKinsey
6) Harvard MBA
A range of other achievements, directorships at local think tanks, board member of global companies (Sony) complete his profile. He now guides the NUS MBA curriculum as he is on the advisory board, and his module is compulsory for all NUS MBA students from 2013 onwards.
Source:
If Only Singaporeans Stopped to Think: What it takes to succeed globally