There are 111.5M adults in the US between age 22 and 55.
Of those, 64.9% are considered "participating" in the labor force. That brings us to 72.4M. Of those, 61% are considered "blue collar", i.e. manual labor. It's fairly safe to assume McKinsey isn't attracting that subset.
We're now down at 28M. Without further subdivision, I'm fairly comfortable in feeling skeptical that one in every 280 white collar workers in the US applies for a job with McKinsey every year.
There are a lot more people, you know, elsewhere. Further, applicants typically take a scattershot approach, and apply to hundred to thousands of companies in their course of finding employment.
100,000/365 = 273/day. You don't think the most reknowned consultancy in the world can garner that?
Second you assume that only white collar workers will apply to McKinsey.