Over 40,000 lead seals from the early Byzantine Empire remai

Answer D is incorrect because it does not really support the conclusion that "Thus the number of early Byzantine documents sealed in such a fashion must have been many times the number of remaining lead seals. " We can understand the argument in the following way:
number of remaining (reused) seals = X
The seals that were not recycled were probably destroyed together with documents and there is no correlation between their number and the number of the remaining seals. We don't know how many times a seal could be recast but probably many. Thus the total number of sealed documents of no special importance = X times Y
Y - how many times a seal was reused
Answer tells us that 40000 seals could not be recycled. The number of seals that could not be recycled has no influence on the number of the recycled/ remaining ones and thus answer D is irrelevant.

How is A correct here? I didn't quite get it . Would someone kindly elaborate?

Cheers!
J

EXPLANATION FROM POWER SCORE

The argument in the stimulus is structured as follows:

Premise: ..... Over 40,000 lead seals from the early Byzantine Empire remain today.

Premise: Most seals had served their purpose once the document to which they were attached was opened.

Premise: Most seals were recast after they had served their purpose.

Conclusion: The number of early Byzantine documents sealed in such a fashion must have been many times the number of remaining lead seals.

The author argues that since most seals would have been recast once they had served their purpose, we would expect that the number of documents sealed in such a fashion would be far greater than the number of lead seals remaining today (presumably, because most seals would have been “recycled” and used on a number of different documents). The argument assumes, of course, that at least some of the documents sealed in such a fashion were opened during that period, so that the seals would have been recast once they had served their purpose.

Answer choice (A): This is the correct answer choice. If most of the lead seals produced during the early Byzantine Empire were affixed to documents that were then opened during that period, this would support the theory that most of the seals would have served their purpose at least once, and therefore recast. As a result, for each recycled seal we would have at least two documents, proving that the number of early Byzantine documents sealed in such a fashion exceeds the number of remaining lead seals.

Answer choice (B): At first glance, this answer choice may seem attractive. Indeed, if most of the lead seals produced during the early Byzantine Empire were affixed to documents that have since been destroyed, this would suggest that there were probably more lead seals than the number of remaining documents would indicate today.

The conclusion we need to strengthen, however, is that the number of documents sealed during the early Byzantine Empire must have been greater than the number of lead seals remaining today. Clearly, this answer choice is a Shell Game that cannot support the exact conclusion of the argument. There is no reason to expect that destroying a document would have the same effect as opening it. Consequently, it would be wrong to assume that any seal affixed to such a document would have been recast and used on new documents after the destruction of the original one.

Furthermore, the word “since” in this answer choice implies that the destruction of the documents took place after the end of the early Byzantine Empire, when the seal-recycling program may no longer be in effect.

Answer choice (C): The amount of lead available for seals in the early Byzantine Empire has no bearing on the issue at hand. This answer choice is incorrect.

Answer choice (D): This answer choice suggests that at most 40,000 documents sealed during the early Byzantine Empire were important enough that their seals would not have been recast. But if the majority of lead seals remaining today were never recast, this would only weaken the conclusion of the argument as it would suggest that the number of early Byzantine documents sealed in such a fashion was approximately equal to the number of remaining lead seals.

Answer choice (E): Even if there were fewer than 40,000 seals affixed to documents at any given time during the early Byzantine Empire, this would not mean that any of the 40,000 seals remaining today had been recycled and used multiple times. It is entirely possible that each seal was only used once, just not all at the same time.

EXPLANATION FROM Fox LSAT

Superhard question.

This argument makes a lot of sense to me, which is usually a very bad sign. If there are 40,000 of these things remaining, and if the seals were recast (possibly as seals for other documents) then it seems almost impossible to avoid that there were more documents than seals. It makes me uncomfortable that we’re being asked to “strengthen” this argument, because I thought the logic was pretty tight already. Sounds like trouble.

A) I suppose this strengthens the argument somewhat, because once the documents were opened the seals would have “served their purpose” and “been recast,” possibly for other documents. I suppose the argument could be weakened by an attack that said, “None of the documents sealed with lead were ever opened.” If that were true, then there would be exactly the same number of remaining seals as documents… I think? And this answer, A, would defend against that attack. So there’s an argument for A. Let’s see what else is here.

B) I don’t see what this has to do with anything, because we aren’t told whether the seals from the destroyed documents remain or not. A was better, so we can cross this one off.

C) Nah, the amount of lead that was available is totally irrelevant.

D) I don’t see how this is relevant. Suppose there were exactly 25,000 documents “important enough to prevent the removing and recycling of the seal.” This says nothing about the total number of documents that were ever sealed in this fashion. It could be more or less than the 40,000 remaining seals.

E) This isn’t relevant either. Suppose there was a maximum of 25,000 documents with seals affixed at any given time. The total number of documents that were ever sealed in this fashion could still be more, or less, than the remaining 40,000 seals.

I really don’t like this question, but at least we could make an argument for A. So that’s got to be our answer. There will be other questions we can answer with more certainty; let’s not dwell too long on this one.