Does this condition "Only one of the recycling centers recycles plastic" should be taken to mean that necessarily one center MUST recycle plastic?

Or is this condition created by the passage itself, by saying "Exactly five kinds of material are recycled at these recycling centers"?

@jg.cassanello, happy to help! Both the claim that "exactly five kinds of material are recycled at these recycling centers" and the claim that "only one of the recycling centers recycles plastic" tell us that plastic must be recycled. Note how these claims would be different if they were instead phrased as "five kinds of material could be recycled at these recycling centers" and "only one of the recycling centers can recycle plastic." Does that make sense? Please let us know if you have any other questions!

Yes, it does. I failed to get this in the first reading. But, yeah, it makes sense.

Had exactly the same doubt here. Thanks!