LSAT 72, Logical Reasoning I, Q24, LSATHacks

QUESTION TEXT: Library preservationist: Due to the continual physical…

QUESTION TYPE: Must be True

FACTS: 

1. Widely acknowledge (most) ➞ restore
2. Authenticity suspect SOME restore
3. Restore ➞ Safety ensured
4. Frequently consulted ➞ restore
   Contrapositive: restore ➞ frequently consulted

Combined statements:

Widely acknowledged (most) ➞ Restore ➞ Safety ensured AND frequently consulted

Authenticity suspect SOME restore ➞ Safety ensured AND frequently consulted

Contrapositive:

(Note: You can’t take contrapositives of “some” and “most” statements. You can only take contrapositives of conditional statements)

Safety ensure OR frequently consulted ➞ restore

ANALYSIS: This question relies heavily on conditional reasoning. This is an excellent question to redo in order to master conditional reasoning. It has:

• Taking the contrapositive of a conditional and combining it with another statement
• Combining conditional statements to get multiple necessary conditions for a single sufficient condition
• Combining a “most” statement with a conditional
• Combining a “some” statement with a conditional

I’m going to take this opportunity to give a full explanation of how to combine “some” and “most” statements with conditional statements. This is a large topic that appears maybe once every LSAT. I’m explaining it in full here because I’ve never seen a question that illustrates this so completely. I’m going to use an abstract example to explain, with the letters Z, A, B and C. This is because “some” statements and conditionals are rather mathematical, and you should learn to look at them structurally, no matter what the subject is.

Note that this example with Z, A, B and C exactly parallels this combined statement from the question:

“Authenticity suspect SOME restore ➞ Safety ensured AND frequently consulted”

So if you aren’t sure how I created that, follow along with the abstract example, and replace Z with “authenticity suspect” etc. Here are our facts:

Z some A
A ➞ B
A ➞ C

So I’ve given two necessary conditions for A, and I’ve also said some Z’s are A. First, we want to simplify the conditional statements with A. You can combine them, like this. There’s no sense keeping two separate statements:

A ➞ B and C

This matches the combined conditional statement I made for the stimulus. By the way, a “conditional” statement is just a statement with sufficient and necessary conditions.

Next, “some” statements (and “most” statements) can combine with sufficient conditions. In other words, if a statement said “B some Q”, I couldn’t do anything with it, because B is a necessary condition. But since A is a sufficient condition, I can combine “Z some A” with it. 

Z some A ➞ B and C

(Note: If I had said “A some Z”, I could do the same thing, since “some” statements are reversible.)

This matches the “some” + conditional statement I made earlier, for the stimulus (A = restore, etc.)

Let’s talk about what it means. This means that if something is A, it’s always B and C. And if something is not C or not B, it’s not A.

That’s the conditional statement and its contrapositive, and most people know that. It’s
the “some” part that’s different.

We don’t know how many Z’s there are, or A’s, or B’s. There could be only one Z and 10,000,000 B’s, or 10,000,000 Z’s and all of them are B’s.

Let’s say there is one Z (maybe not the only one). This Z is named Zogbert. What do we know about Zogbert?

• She’s an A.
• Because she’s an A, she’s also a B.
• Because she’s an A, she’s also a C.

So Zogbert is a Z, A, B and C. If someone says “some Z’s are C” then that’s a true statement. It applies to Zogbert, at the very least.

We can go backwards and say “some B’s are Z”. Again, this applies to Zogbert, since she is a Z and a B. But we have no idea if many B’s are Z or if many Z’s are B. We only know about Zogbert and the other “some” Z’s that are A’s. 

Going back to the stimulus, I could say this:
“Some manuscripts with their authenticity suspect are frequently consulted.”

(This combines the first part of the “some” statement with one of the necessary conditions of “restore”)

You can always combine a “some” or a “most” statement with the left-hand side of a conditional statement, which I’ve done above. 

Hopefully “some” is clearer now. It’s a little abstract, but this abstract structure occurs on dozens of LSAT questions, including this one, so make sure you understand it. 

Let’s apply this to the original statements. Suppose there’s a document called the Odessa Palimpsest (I made that up). It’s going to be restored. All documents that will be restored are frequently consulted and have their safety ensured. So we can say of the Odessa Palimpsest:

• It will be restored.
• Its safety will be ensured.
• It is frequently consulted.

You can also go backwards and say “some” documents with safety ensured will be restored (i.e. the Odessa Palimpsest)

We can’t say the Odessa Palimpsest is widely acknowledged to be important or has its authenticity suspect. That’s because you can’t go backwards and say a specific document has the “some” or “most” statements apply to it.

The “most” and “some” statements only let me make general claims about a group. I can’t know if an individual item falls into those groups unless I’m told. It’s a question of quantity.

This is why you can’t go backwards with “most” statements. We saw this statement in the stimulus:

Widely acknowledged (most) ➞ Restore ➞ Safety ensured AND frequently consulted

There might only be 11 documents in the collection that have widely acknowledged significance. “Most” of them would be 6.

We can say that those 6 documents will be restored, and that their safety can be ensured, and that they are frequently consulted. So far, this is exactly what you can do with “some” statements.

But you can’t go backwards and say that “most documents with safety ensured” have widely acknowledged significance. That’s because there could be 10,000 documents with safely ensured. So when going backwards with a “most” statement, you can only say things like “some documents with their safety ensured have widely acknowledged significance”. This last statement refers to those 6 documents that are “most” of the documents with widely acknowledged significance. 

Phew. If this is the first time you’ve seen this kind of discussion of “some” and “most” combined with conditionals, I’m sure that was confusing. Refer back to this explanation often. And play around with “some” and “most”. Make up some examples that are true in real life, and see how they work.

For example, suppose you have three sisters. You can say “most of my family are women, and all women have legs”. You can go backwards to say “some people with legs are in my family”. But you can’t go backwards to say “most people with legs are in my family”. That’s just silly. All of these things the LSAT talks about are real. You can use real life examples to see what’s correct.

___________

1. CORRECT. This follows from reading the “some” statement + the conditional statement left-to-right. You can combine the “some” statement with both necessary conditions. So, some documents with authenticity suspect:
    
   * Will be restored
   * Are frequently consulted
   * Have their safety ensured
    
   We know the latter two points are true because they’re true of any documents that are restored. And some documents with authenticity suspect will be restored.
2. This isn’t true. We only know we’re restoring “most” documents of widely acknowledged cultural significance. It’s possible some won’t be restored, maybe because their safety can’t be ensured.
3. This is an incorrect reversal of the statement about safety. Everything restored can be restored safely. But it’s possible that some things that can be restored safely nonetheless won’t be restored.
4. The stimulus never mentioned “most susceptible to deterioration”. This can’t possibly be the right answer.
5. We don’t know. We know that “most” documents widely acknowledged to be significant will be restored. That might mean they’re all restored, or it might mean some won’t be. We don’t know why some won’t be restored. It COULD be because they’re not consulted, but it could also be for some other reason – perhaps they can’t be restored safely, or they fail to meet another necessary condition for restoration. (There could be other necessary conditions we don’t know about). 

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