Welcome to the forum.
There are anecdotal relationships - or, if you like, "rules of thumb" - between the number of beds in a typical hospital and the amount of medical equipment scattered around the place. Crude figures like that are sometimes used for initial planning purposes. But I would suggest that to think in such terms could lead to missing the point!
As I have mentioned on here a few times before:-"Patients are cared for by nurses, not beds"!
And Neil's comment is spot on. This is one of the "basics" of biomedical engineering. How can you begin to manage and maintain the equipment you are responsible for if you don't have an accurate idea of what those are. In short, you need a list of the kit you are to maintain. You have to survey your patch. It's the first step. Job No.1. Only then can you move on to organizing the work in an efficient manner, carrying out properly conducted PM ... and all such good stuff as that.
So ... take my tip:- forget about "number of beds". At best that just gives an overall idea of the size of the hospital. Concentrate instead upon the total inventory of equipment, and ask yourself how you are going to maintain each item. Think in terms of man-hours, and do you have enough techs. And yes (before you ask), there are also empirical rules of thumb about the number of techs required to maintain this or that amounts of kit (equipment). But you may as well ignore those, as (in my experience) you will never have too many
biomed technicians available to apply to the task.
Maybe your interviewer just wasn't that smart. What s/he should
have been asking was something along the the lines of:-
1) How many items do you have on inventory?
2) Do you maintain all those items in-house?
3) Which equipment (if any) do you have on service contract?
4) How many items are down (out of order) at this time?
5) How long have they been out of order?
6) How many items are awaiting parts?
7) Do you have manuals for all items?
8) Do you have all the tools and test equipment you need?
9) Are you up to date with your PM schedule?
10) Are your equipment histories in place and up to date?
11) How do you maintain good relations with the user staff?
... and stuff like that.
But ... "biomedical executive"? That's a new one for me.