I think that one of the reasons why this question is kind of tricky is because it can be hard at first to see what’s wrong with the argument- but it’s a strengthen question, so we know that the argument is indeed flawed. I’ll set up the reasoning structure first and then explain what’s wrong.
Conclusion: The number of early Byzantine documents sealed with lead seals must have been much more than 40,000.
1st premise: 40,000 lead seals from early Byzantine remain.
2nd premise: Most lead seals had served their purpose when the document was opened.
3rd premise: Most lead seals would have been recast once they had served their purpose- i.e. once the document was opened.
So, whenever a document with a lead seal was opened, more often than not the lead seal would then be recast. And assuming that a lot of the documents were actually opened, this means that there were more documents with lead seals than there were lead seals. For example, say there were 100 documents with lead seals delivered each week, and all of them were opened, most of those lead seals would be reused for, say, next week’s batch of documents, and so over the course of two weeks you would wind up with 200 documents with lead seals, but only 100 or so total lead seals, since most (if not all) of them had been reused.
All of this assumes that a lot of the documents were ACTUALLY OPENED. Now, I don’t know anything about the early Byzantine empire, but what if documents with lead seals were basically their version of junk mail? If the documents weren’t being opened, then the argument falls apart- the lead seals outnumber the documents if the lead seals are being reused, and the lead seals are being reused if the documents are being opened.
So the flaw here is that the argument assumes that a lot of the documents were ACTUALLY OPENED. It would strengthen the argument if we knew that a lot of the documents WERE opened. This is what (A) tells us.
(B) is tempting if you assume that the remaining lead seals are affixed to documents- in which case, you would have 40,000 remaining lead seals, the 40,000 documents that they are affixed to, and then all the documents that have since been destroyed- which adds up to way more documents than remaining lead seals. But we aren’t told that the remaining lead seals are affixed to documents. If the remaining lead seals are just hanging out by themselves, without any documents, then (B) does nothing to strengthen the argument.
(D) A big red flag term here is ‘at most’. So, no more than 40,000 documents were important enough to keep the seal. Ok, but that tells us that maybe there was only document of such importance. This answer choice wants you to think that there were way more than 40,000 documents with lead seals, but it doesn’t actually give us information that could lead us to that conclusion.
It’s definitely a tough question, hope this helps 🙂