#24 - Over 40,000 lead seals from the early Byzantine Empire

[Administrator]

Complete Question Explanation

Strengthen—%/#. The correct answer choice is (A)

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.

[stsai]

Q24. "Over 40,000 lead seals..."
I chose (B) and cannot see why (A) is the right answer. (B) seems right for if there are more documents destroyed by now, it means that the current amount of seals remained represents a smaller portion of documents once existed, right?


Thanks so much!

[Nikki Siclunov]

The argument is structured as follows:

Premise: 40,000+ lead seals remain today

Premise: Most seals had served their purpose when the document was opened

Premise: Most lead seals would have been recast once they had served their purpose.

Conclusion: # of early Byzantine documents > # of remaining lead seals

The argument assumes, of course, that at least some of the documents affixed with such seals were opened, so that the seals would have been recast once they had served their purpose. If (A) most of the lead seals produced were affixed to documents that were then opened, 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 such seal we'd have at least two documents, proving that the number of documents exceeds the number of remaining lead seals.

Just because most of the seals were affixed to documents that have since been destroyed (B) does not prove that the seals would have been recast. They would be recast once they had served their purpose, i.e. when the document was opened. Destroying a document doesn't mean the seal actually served its purpose, so there is no evidence each seal was used multiple times. Furthermore, the word "since" in this answer choice implies that the destruction of the documents took place mostly after the early Byzantine Empire.

The only thing B proves is that there were more lead seals produced during the early Byzantine Empire than the number of remaining documents today is likely to suggest. The conclusion, however, is that the number of documents sealed in this fashion must have been greater than the number of remaining lead seals.

[eober]

Hi,

What would be a good prephrase for this question?

Also, how does answer choice A strengthen the argument that "number of sealed documents that have been recast once must have been more than 40,000"?

Thanks!

[BethRibet]

Hi eober,

It would be hard to anticipate a close-fitting prephrase that would help in this particular case, but a more general one would be something like: What would help ensure that the number of lead seals ever used far exceeded those remaining?

The crucial detail here is the phrase "served their purpose". If A were *not* true, then we would have a bunch of documents that remained sealed until later times, which means they might have been exempted from the process of recycling/re-casting seals once the documents were opened, and could still exist. If that were often true, then the number in existence now might be closer to the number used at the time. Answer choice A closes off that loophole or flaw, essentially, making the conclusion more certain.

Hope this helps!
Beth

[gwlsathelp]

I am not satisfied with the explanation provided by the administrator nor Nikki.

A and B are really closely phrased answers. They literally share half of the first part. The second half of the answer either depicts the letters being opened during the early Byzantine or being destroyed between its being written and the "present". I think it would make more sense if I diagrammed it out:

premise: 40,000 lead seals remain
premise: most seals served purpose when doc opened
premise: most lead seals re-casted when purpose served
conclusion: number of documents sealed with lead must have been more than discovered seals

answer: most lead seals made during early Byzantine (total seals excluding ones on doc of special importance) were affixed to docs that were opened during that period

What would happen if it were that they were opened after that period? This answer fits between the first and second premise and adds clarity to the claim the conclusion makes. Additionally, there is conditional reasoning present and the correct answer would feed into the beginning of the chain.

If you are still boggled by this question, you can use the Negation Technique for this question type (although not recommended every time you see a strength question). With B, it would be "none of the lead seals produced during the early Byzantine Empire were affixed to documents that were then opened during that period" or "most of the lead seals produced during the early Byzantine Empire were not affixed to documents that were then opened during that period". That would weaken the overall argument.

I didn't like this question.

[cgs174]

Hi!

I see why answer choice A is better but I'm struggling to understand the explanation for choice D. This answer suggests that, at most 40,000 documents sealed were important enough to not have their seals recast. However, I still saw this as strengthening the conclusion not weakening it, even if it doesn't as strongly as choice A. The stimulus states that there are more than 40,000 seals and, according to D, at most 40,000 of them were not recast. This means that there are an unknown number of seals which had the potential to be recast. Should I assume that while that number is unknown it is small? How did you draw the conclusion that "at most 40,000" and "more than 40,000" were "approximately equal".

I would assume that choice D creates a smaller number of seals to be recycled than the "most" that choice A does, but I see them as accomplishing similar things.

Thanks for the help!

[Adam Tyson]

gwlsathelp, I think you may be misreading or misunderstanding what answer B is telling us. Answer B is about what happened to the documents to which the seals had been affixed, but tells us nothing about what happened to the seals themselves. Who cares if the documents were subsequently destroyed? The issue is whether there were more lead seals or not, so what happened to the documents isn't relevant. Maybe they were all shredded years after the fact by marauders? Maybe there was a flood in the basement where they were stored, and only the lead seals survived the water damage? The difference in answer A is that what happened to the documents tells us something about what happened to the seals : document opened, seal served its purpose, seal usually recast and available to be reused. Thus, the 40,000 seals we have today were likely to have been used on more than just 40,000 documents, as some of them were probably used more than once. The argument was already pretty good, but this tidbit of information helps it out just a bit by eliminating the possibility that the documents were just left sealed most of the time.

cgs174, I see what you're saying about answer D, and you have a good point. But even if we treat that "at most 40,000" statement as just an upper limit, that upper limit doesn't add any support to the claim that there must have been many more sealed documents, for the same reason that answer A is the best answer: we still don't know how many documents were actually opened! It's only when they are opened that we can be sure the purpose is served and the seal recast and possibly used again.

Think of answer D this way: if the number of important documents had been MORE than 40,000, that would support the argument. Capping that number at 40,000 (which would allow it to be much less) may not weaken the argument, but it does eliminate something that would have helped. That's for sure not what we want to do if we want to strengthen an argument, right?

[BMM2021]

Hi,

I interpreted answer D in the same way that cgs174 does; almost as a (admittedly flawed) necessary assumption. Despite choosing D, I understand why it doesn't strengthen the conclusion.

However, I didn't like A off the bat because it didn't seem numerically strong enough to help the conclusion in my view. The conclusion specifically states that the number of documents "must have been many times the number of remaining lead seals." I, probably erroneously, understood this to mean that the author is concluding that the number of Byzantine documents must have numbered in the multiples of 40,000 (i.e. greater than 80,000 at minimum). Moreover, the stimulus does not clearly state that more than 40,000 seals ever existed - perhaps all seals survived to this day. If A is true, and "most" lead seals were used for documents after the opening of which the seals were repurposed, there could be a scenario in which 20,001 (out of 40,000 total) lead seals were repurposed only once, resulting in the total sealing of 60,001 Byzantine documents. This is not a multiple of 40,000, and thus I thought A was a trick answer that appeared attractive but was mathematically flawed.

Clearly, the LSAC is in my head. However, I'm wondering if there's a response to this issue that goes beyond the fact that other answers weren't better.

Thanks!

[BMM2021]

A correction:

- The bare minimum scenario resulting from the truth of Answer A, in my opinion, could result in 60,002 total Byzantine documents with seals. 60,002 is less than any multiple of 40,000.

Hi,

I interpreted answer D in the same way that cgs174 does; almost as a (admittedly flawed) necessary assumption. Despite choosing D, I understand why it doesn't strengthen the conclusion.

However, I didn't like A off the bat because it didn't seem numerically strong enough to help the conclusion in my view. The conclusion specifically states that the number of documents "must have been many times the number of remaining lead seals." I, probably erroneously, understood this to mean that the author is concluding that the number of Byzantine documents must have numbered in the multiples of 40,000 (i.e. greater than 80,000 at minimum). Moreover, the stimulus does not clearly state that more than 40,000 seals ever existed - perhaps all seals survived to this day. If A is true, and "most" lead seals were used for documents after the opening of which the seals were repurposed, there could be a scenario in which 20,001 (out of 40,000 total) lead seals were repurposed only once, resulting in the total sealing of 60,001 Byzantine documents. This is not a multiple of 40,000, and thus I thought A was a trick answer that appeared attractive but was mathematically flawed.

Clearly, the LSAC is in my head. However, I'm wondering if there's a response to this issue that goes beyond the fact that other answers weren't better.

Thanks!