Q24 - Over 40,000 lead seals from

[mshinners]

Question Type:
Strengthen

Stimulus Breakdown:
40,000 lead Byzantine seals exist (probably in museums and Indiana's Jones' cufflink drawer)
Almost all were recycled once the document was opened
Thus, there must have been many more than 40k documents

Answer Anticipation:
"Once the document was opened…" It's an interesting phrase. It is semi-conditional (I say semi because I wouldn't diagram it even though it is conditional). Because it's a trigger, in order to know that these seals were recycled, we need to know that the trigger happened. Since the argument relies on the vast majority of these seals being recycled, it also relies on the vast majority of these documents being opened. Since we're not told they were, that's what we should expect in the answer.

Correct Answer:
(A)

Answer Choice Analysis:
(A) Bingo. If this answer is true, then most seals served their purpose and were recycled, so the remaining ones are just a small fraction of the total, which is a good proxy for the number of documents.

(B) Out of scope. The argument cares about the destruction (recycling) of the seals, and the opening of the document. There's a subtle term shift here between a document being opened and being destroyed (wouldn't you destroy it after you read it, a la junk mail?), but it exists. The destruction might have happened later as they decayed.

(C) Out of scope. The argument cares about the seals themselves, not the total number of potential seals made. Since this answer talks about the available lead, and not the lead actually used, it's out of scope.

(D) Out of scope. The documents in excess of the 40k must have been ones that weren't important, or their seals would still be around. This answer choice speaks to the existence of under 40k important docs (which can't account for all the seals), but it doesn't speak to how many unimportant docs there were, so we can't say this strengthens it.

(E) Out of scope. Since there were fewer than 40k seals in use at any given time, our current pile of seals represents an extended period of time. However, this still doesn't speak to the number of times documents were opened and seals recycled.

Takeaway/Pattern: Sometimes, noticing a trigger outside of a normal conditional logic situation can be very helpful in identifying gaps in arguments. Language akin to, "Once X happens…" sets up a trigger.

#officialexplanation

[aileenann]

I'd spell out the core of this argument as follows:

Because most letter seals would have been melted down once they had served their purpose/their letter had been read and wasn't of special importance
----->
The number of documents sealed with lead must have been much higher than the number of lead seals that remain today.

We are looking to strengthen the argument, either by making whatever assumption is in the argument true or adding another supporting premise.

(A) makes one of the assumptions of the argument clear by indicating that most letters sealed this way would have been opened at that time, meaning that we don't just have a lot of seals left over because lots of documents weren't opened in that era.

(B) doesn't really tell us anything though it uses lots of the same words we might expect to see in an answer choice. For example, it's possible that the documents weren't opened right away but were later destroyed, or it's possible they were destroyed during that time period. To see that (B) doesn't really matter, try negating it. It has just about the same effect - that is, no effect. To think (B) told us anything about what we care about - strengthening the conclusion - we'd have to make assumptions of our own about what it might tell us that a document still does or does not exist. It's tempting to think it has something to do with how special that document was if it managed to survive, but we haven't got anything like that in there.

(C) is out of scope as well - how much lead tells us nothing about what portion of documents were melted down.

(D) is irrelevant or perhaps cuts against our argument. If this is going to put a max on the number of special documents - documents where the seals would have been kept rather than melted down - this doesn't tell us anything about how many not-so-special documents there were.

(E) has the same problem as (E) - we don't care how many seals were affixed at any given time. That, for example, doesn't tell us how many seals there were at any given time (and query whether such latter information would be helpful anyway).

So (A) is the clear answer, with (B) as the trickster answer.

I hope this is clearer, and apologize for the blip in my first posting. It's great to have such an alert and helpful readership!

Best of luck to those taking the test this weekend.

[dorbathedogslayer]

Wait, I'm still not convinced that D doesn't answer the question.

I shall use the word "permanent" to indicate a seal used to seal documents that were important enough not to remove the seal from the document.

We know that there are Over 40000 seals existing, and no more than 40,000 permanent seals. Let us say for example that there were 40,010 seals existing. Now that means there were only 10 seals that were potentially recycled. If these 10 seals were used for all the documents outside the 40,000 permanently sealed documents, they must have be recycled and recast several times (assuming more than 10 such documents existed).

So this seems to strengthen the argument.

[trevor.lovell]

This question made my brain hurt. To answer dorba's question, this stimulus combined with D does give you the impression that more than 40,000 seals would have been produced, but A does so more convincingly. This is a question where you want what MOST strengthens the argument.

A - Most sealed documents got opened.
This makes those seals eligible for recasting. Given that the stimulus tells us the "permanent" seals were the rare instances, this would definitely mean many more documents were sealed with lead than there are remaining lead seals.

Think about the inverse of A. If most sealed documents were never opened then even if "permanent" seals were rare, most seals would never have been reused b/c they have to meet two conditions to be re-used - they have to seal letters that are opened and not be "permanent".

D - At most 40,000 "permanent" seals existed.
This would imply that there were probably many more than 40,000 documents sealed with lead seals, but only b/c of what is already in the stimulus. We know "permanent" seals were "rare" but we don't know how this term relates to the term "many times" in the conclusion.

As was stated above, if we knew that at most 10 documents had permanent seals we would have more reason to believe there were many more than 40,000 seals, but even then what if the vast majority of sealed documents were never opened? It seems silly, but the presence of choice A forces us to consider it. In that case we could be talking about a total number of documents sealed this way in the range of 50,000 which does not justify the conclusion.

Therefore, A is the better answer.

[wguwguwgu]

HELP PLEASE I'm still confused on this one.

So is everyone assuming that "produced" in (A) only includes ORIGINAL production of seals, not includes the recasting?

---if a seal was affixed to one document, and then recast twice and used on two other documents, the number of production would be 3 or 1?.

in this case recastings would count, (A) does not have to strengthen so much at all. If the seals can be recast many times, the vast majority of seals in any time section can be original seals. So there may have been a bit more documents than the seals today, but not so much more.

If the recastings do NOT count, then--- if the number of seals today is 40,000, the original number has to be at least 60,000.---- It's still FAR FROM "many times" in the stimulus though!

I also don't agree that (B) is irrelevant. I think B for sure makes the original number of documents higher than the existing seals, we just don't know how much higher. Because we don't know the proportion between reused seals and seals kept on the same documents, and we don't know the distribution of DESTROYED seals between these two groups.

thanks so much!!

[bramon.elizabeth]

M problem with this one was maybe similar to chike_eze's.

If I think of "authenticated" as distinct from sealing a document, everything makes sense. Authenticating (say, notarizing) something would mean using the seal over and over again, or maybe keeping the seal in a museum because of the importance of the document it authenticated (say, a constitution, which is never sealed closed).

(A) eliminates the possibility that there were MORE seals designed for authenticating/notarizing things than for open-able documents.

Not a pretty explanation, but it hope it helps someone. :0)

[swcxm]

This argument goes like this:

(1) Today over 40k lead seals are still around
(2) Special docs = ~opened, so seals are not recast
(3) Non-special docs = if opened, most seals are recast
(4) Seals are not cheap, so, if opened, most of those seals are recast
-------
(C) # of seals opened/recast (used for non-special docs) > # of seals not opened/recast (used for special docs)

Actually, I don't believe the conclusion here is about the comparison between the amount of seals recast and that of seals not recast. Rather, it says that there used to be many times more documents ever existed than the remaining lead seals, which is the result of recycling used seals from opened documents.

Here is kinda funny an analogy but I think it can help here.

There are 100 pieces of forks in M restaurant.
For a VIP customer, after dining the fork used by him/her will be reserved for his/her use only.
For a common customer, the fork will be sterilized and reused by next customer.
-------------------
Conclusion: The number of different customers ever dined here must have been many times the number of the forks.

Problem: what if most of the customers, say 95%, ever dined in M restaurant are VIPs? In this case, the number of forks is quite a good indicator of the number of different customers that have eaten here.

(A) addresses this gap perfectly.

However, I still have some trouble eliminating (B). If most of the documents were destroyed, doesn't that confirm there were indeed more documents ever been created and existed? Is it because "many times" is too specific to be strengthened by (B), or because we have no idea what happened to the lead seals, preserved, recast or damaged together with the document, when the documents they were affixed to were destroyed?

[ericha3535]

Hey guys... let me try to explain this question in layman's terms.

Let's try to understand the argument.
This argument is rather simple. Don't worry about 40,000 seals remaining today or not. It's all about assumption that this argument makes.

Basically, there are some lead seals from early Byzantine (thereafter known as B). Most of seals were "recast" after serving its purpose.
---
Therefore, the number of documents that were sealed with lead seals is many times of the number of remaining seals.

It's really important to understand this concept of "recast." At first, I thought this argument was airtight.

Let's say you have 10 lead seals and 20 invitations to your party. After handing out the invitations to your 10 friends (assuming that 10 invitations were sealed), you asked them to return the 10 "seals" as a courtesy because you can actually recast or reuse them to seal additional 10 invitations that you are going to give out. And yes, you are being cheap.
--
conclusion: therefore, the number of invitations that was sealed was many times of the number of seals.

This is like THE analogy of the argument.

Isn't conclusion follow? Yeah, you could have sealed 20 invitations but you only had 10 seals. Yep... this is where it gets tricky.

What is the assumption?
Baam! the assumption is that the first 10 friends that received your invitation ACTUALLY OPENED UP THE invitations! What if you were the most unpopular geek in the whole world and nobody opened up the invitations? Then they would not have returned you the seals.

This is like A.
What if all the documents that were during early B were sealed yet were not opened up until very very very later? Then, since those seals are still serving their purposes, they would not have been recast. No recast means no reusing stuff!

By the way, the scope of conclusion is about "early B." Yes, its possible that those seals that were opened up very very very later could have been recast after being used, but it's out of scope: we only care about what has happened during EARLY B.

E: this hurts our argument. if there were fewer than 40,000, no recast could have been useful.

D: I believe anything else, this also hurts our argument. if there were 40,000 important documents (which means they were not allowed open or something?) this adds to the idea that recast could not have been useful.

C: It's irrelevant. Number of seals does not matter.

B: If the letter got destroyed yet seals survived... does it say anything about the actual number of seals vs the letters so that we could compare them? Not sure... it's irrelevant.

Hope this helps

[matthewyoung2008]

document opened --> served its purpose --> lead seal recast

therefore, if most lead seals were attached to docs that were opened, then most seals were recast

when a seal is recast, it can seal more docs

thus, # docs >> # of seals

[eve.lederman]

So the answer is (A) because basically we need t know that documents were opened in order for the conclusion to follow. if they were opened, they served their purpose, and were thus recast for another document. since there are 40k+ seals today, there must have been 40k++ documents that were opened.

is that the essence of (A)'s reasoning?

[ohthatpatrick]

That's exactly right.

The way we often have to find Objections/Assumptions is simply by arguing the Anti-Conclusion.

Here, we'd be trying to figure out how "the number of documents sealed with lead was NOT many times the number of remaining seals".

Let's clean that up: "the number of documents was basically about the same as the number of seals".

How do we make that counterargument? We know that for most seals, once a seal had served its purpose it would be recycled.

What does it mean to "serve its purpose"? The seal had served its purpose once the document was opened.

Okay, then to argue the counterargument, we have to argue "maybe most of the documents were never opened".

That's pretty much the only lever we have to pull. And so (A) strengthens by ruling out this objection.

Nice work.

[maria487]

Would (D) be correct had it omitted the "at most"? I rationalized that because it says at most 40,000, then that could mean anywhere from 0-40,000---that doesn't really give you much to work with. However, if it said 40,000 documents had permanent seals, then that is a different story because you know that these permanent seals were rare; so if there are 40,000 rare seals, you can know then that there are many more than 40,000 seals (permanent and reusable) in total. Yes or no to my reasoning?

[ohthatpatrick]

Ha! Yes, that’s awesome. I don’t think I would have ever had that thought.

40000 important ones
+
important ones were a rare usage
================
There must have been many more usages than just the 40000 remaining we know about


I would only suggest that you think about having a Spidey-sense when it comes to picking an answer like that, for which the whole gimmick is noticing the word “rare”, rather than engaging with what seems like the actual argument core.

You know that when LSAT authors use “despite/although/while”, or in this case, “apart from ____, ______” … the 2nd half of these sentences is always the REAL point the author is stressing.

So it would be highly atypical for an answer choice to strengthen by using a counterpoint, rather than the author’s actual premises.

But … nevertheless, YES, your tweaked version of the answer DOES provide support for the conclusion.

[XiaoranZ794]

At first I chose B because I took for granted that seals will also be destroyed when the documents were destroyed. Then if B is true,the real number of seals is much larger than the number of remaining seals, and since each seal represents at least one document, the number of document must be much larger than the remaining seals. But after reading the posts above, I found that what happened to seals after the documents were destroyed is uncertain. There could be several possibilities, such as destoyed with the document, recasted, or preserved but not recasted. If the seals remain to today without being destroyed or recasted, then the number of the documents is roughly equal to the number of the remaining seals and B would weaken the argument. I wonder if this explanation works? Have I misinterpreted the posts above?

Thanks in advance.

[Misti Duvall]

At first I chose B because I took for granted that seals will also be destroyed when the documents were destroyed. Then if B is true,the real number of seals is much larger than the number of remaining seals, and since each seal represents at least one document, the number of document must be much larger than the remaining seals. But after reading the posts above, I found that what happened to seals after the documents were destroyed is uncertain. There could be several possibilities, such as destoyed with the document, recasted, or preserved but not recasted. If the seals remain to today without being destroyed or recasted, then the number of the documents is roughly equal to the number of the remaining seals and B would weaken the argument. I wonder if this explanation works? Have I misinterpreted the posts above?

Thanks in advance.

I think you're on the right track. I'm not sure we know that the number of documents would be roughly equal to the number of remaining seals, though. The bigger issue with (B) is that the document is no longer relevant after it's opened.

For ex, let's say I break a seal, open a document, and toss the document in the corner. I then reuse the seal, so that same seal ends up being used on 100 documents. There are still lots more documents than seals, regardless of whether or not the document I just opened keeps sitting in the corner or is shredded by my cats the next day.

Hope this helps!