Let me make a few points with regards to to your solution of this Fermi problem.
Hiring committees have more than one member. The more applications received, the more members the committee usually has. Moreover, it is highly unlikely that every committee member looks at every application in the first round. Exactly what is done must depend strongly on the department, but I can describe my own experience. In my department -- mathematics, UGA -- we do usually get 300-400 applications for a tenure-track job opening (sometimes for two or three positions at once, but that doesn't help any!). The applications are processed by subject area. In fact in my department the "hiring committee" consists of all tenure-track faculty, so initially I look at applications in my field -- number theory -- and closely related fields. This usually gives me about 50 applications to look at. I look at them as they come in, not all at once at the end, so in the first phase I probably spend something like half an hour a day over the course of several weeks looking at applications. This gives me more like 10 minutes per application, on average.
Another point is that CVs can be 10-20 pages in length, but this is usually for people towards the end of an academic career who insist on putting every talk they ever gave and class they ever taught on their CV. For applicants for an assistant professor position, I would expect CVs to be in the 2-6 page range. (I am a 2003 PhD. My CV is holding steady at 8 pages.) Anyway, it is important to organize your CV carefully and put the information in the places that people are expecting to find it.
Finally, I want to say that amount of time spent on each application is far from uniform. I said above that I spend about 10 minutes per application on each of 50 applications. But most applications I am spending either more than 10 minutes on -- it takes more like half an hour to read an entire application, no matter how quickly -- or much less. I do try to read every application in my field however briefly, but "however briefly" can be awfully brief. Hundreds of applications can, and must, be eliminated essentially immediately.
Added: I see that I didn't fully answer the question asked. In a quick first pass on applications, I look at more than just the CV. Our applications come to us in a very convenient online format via the MathJobs service, so that one click brings to a screen where we see the candidate's basic information (name, date of PhD, PhD institution, PhD advisor, current institution) and can click on various documents they (and/or others) have uploaded, which generally include:
- cover letter
- research statement
- teaching statement
- publication list (sometimes)
- multiple recommendation letters
I usually look first at when, where and from whom they got their PhD, and then I click on the CV to see their background and their publication list. If I really don't like what I see -- e.g. no PhD, PhD is not in mathematics or something very closely related, clearly insufficient publications -- then I stop right there. This is maybe 20% of the applications. The next thing I do is to quickly read the advisor's letter and the research statement. Based on that information I decide whether to read on. (Maybe I've eliminated 50% of the applications at this point.) I next read the other letters and start to look more carefully at the candidate's research.