"We accept 20% of candidates and I'm 90% good at my job..."

The answer would simply be:

because

example

There are a lot of assumption that go into this, but this is probably the intended answer:

From the 20% intended accept rate, we get that

From the 90% success rate (assuming each kind on failed classification is as likely), we get that

Continuing from these,

The problem with this result is that

This means we should probably also count the interviewer as being one of the people who shouldn't have been accepted. :-)

The answer is quite simple:

The answer is:

For example in a group of 100 hundred employees we might have:

Alternatively we might find:

Or:

Most people here have zeroed in on the underdefined statement of "90% good". I would try to be a good Bayesian here and start with a few of my personal observations about the real world as priors.

From these two, we can conclude that

Which we can combine with another set of priors:

The above observations point in one direction: the metric he uses must be

This assumption about the metric leads to the simplest possible solution:

The reason why this is likely considered a brain teaser is

A few further thoughts on the underspecified metric

Morale of the story: Metrology is not for hobbyists.

Also, this guy is a self-important jerk, and I wouldn't want to work for him anyway.

I'm going to assume that when the partner says that they are 90% good at vetting they mean they accept an unqualified candidate 10% of the time, and reject a qualified one 10% of the time.

My answer:

Explanation: