Interesting question.

If we want to estimate the number of elevators in Germany it is necessary to start by asking what type of elevator are we talking about (electrical, mechanical, a particular manufacturer, etc) for arguing sake lets consider all of them but to facilitate the estimation lets just consider elevators found in apartment buildings and then adding 10-20% more to allow for all the other elevators that are found elsewhere.

There are a lot of ways to estimate how many elevators are found in apartment buildings but let's consider the following:

80M pop. in Germany - if we consider 3 people per family we will have roughly 27M households - let's consider that 50% live in apartments (2+ units) and 50% live in single-family homes *(you may argue where the heck did you get that 50 %? **Well** you may argue that a regular apartment building has on average 20ish units so it is the equivalent of 20 single-family homes so If the ratio between apart. building and single homes are 1:20 they even out - obviously this is a very rough estimation but I actually went online and the number is certainly possible)* - that means that roughly 14M live in apartment buildings. If we consider the average apartment building to have 20 units (5 floors with 4 apartments per floor - again you can work around this number) means we will have 700,000 apartment buildings in Germany. If we consider that 50% of those have elevators (smaller buildings and older buildings usually don't have elevators) means that 350,000 elevators can be found in apartment buildings. Going back to my initial point that not only apartment building have elevators, you can add 10% do the value that we got ending up with 385,000.

It is always important to run a quick sanity check - you already provide us range so that's a start but if you haven't I would relate number of elevators with number of households for example - with this calculation we have 1 elevator for every 70 households (including every household) which is something that is certainly possible.

This is just a quick estimation but in my opinion something good enough for a case interview where you have to come up with a quick estimation.

Hope it was helpful

(edited)