Logical Reasoning

PT154 · S2 · Q22 Art critic: All of Dolores

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Art critic: All of Dolores Albarran’s oil paintings are highly original, though few of them are critically acclaimed or popular with collectors.

Statements

All oil are highly original O → HO

Most oil are not critically Most O are ~CA and ~P acclaimed or popular

All highly are late in HO → LC original career

Most abstract are not Most A are ~HO highly original

Evaluate

Since we see a lot of quantifiers / conditionals, we can probably expect that our job here is to make a Trait Overlap inference and/or to chain together conditionals.

First things first. We always flip negatives to positives:

No A's are B = All A's are ~B Few A's are B = Most A's are ~B Not all A's are B = Some A's are ~B

That's why I wrote the two few statements in most language and why I wrote the no statement in all language.

Now that are statements are in their more usable form, our #1 priority becomes the conditionals. We got two of them. Do they chain together? Do they have an overlapping idea?

O → HO HO → LC

Yes, they both talk about highly original, so we would just get a chain saying Oil → Highly Orig → Late Career ~Late Career → ~Highly Orig → ~Oil

Now we can look at the other quantified statements and see if any of them are using a trigger from these rules:

Most O are ~CA and ~P

Nope. This statement ends with ~CA and ~P, neither of which are triggers that allow us to extend that claim.

Most A are ~HO

Yes! This ends with ~HO, which is a trigger that leads to ~Oil.

Most A are ~HO + ~HO → ~O --------------------- Most A are ~O

Goal

We would expect that the correct answer will either give us the idea that , or it will be something derivable from the conditional chain we assembled:

Oil → Highly Orig → Late Career ~Late Career → ~Highly Orig → ~Oil

22.

If all of the art critic's statements are true, which one of the following must also be true?

  1. Most of Albarran’s works that

    Unknown Group

    We didn't think the fact about critically acclaimed / popular was usable, so this isn't appealing at first blush. This is talking about "Most non-popular works". We don't have any statements about most-unpopular, so it's never going to be a correct answer. By contrast, the inference we made, "Most abstract are not-oil" was possible because we did have a statement about "most abstract". You'll never see a correct answer say "Most X are ____ " if we were never provided a statement about Most / Few X.

    7% picked this

  2. Few of the works produced

    Unknown Group

    We would immediately translate this into positive: Most [late career] are [not abstract] This is talking about "Most late career works". We don't have any statements about most-late career, so it's not going to be a correct answer. By contrast, the inference we made, "Most abstract are not-oil" was possible because we did have a statement about "most abstract". You'll never see a correct answer say "Most X are ____ " if we were never provided a statement about Most / Few X. All we know about Albarran's late career work is that there were some highly original works produced. But we have no idea what proportion of her late career works were highly original.

    18% picked this

  3. Most, if not all, of

    Unknown Group

    This is talking about "Most late career works". We don't have any statements about most-late career, so it's not going to be a correct answer. By contrast, the inference we made, "Most abstract are not-oil" was possible because we did have a statement about "most abstract". You'll never see a correct answer say "Most X are ____ " if we were never provided a statement about Most / Few X. All we know about Albarran's late career work is that there were some highly original works produced. But we have no idea what proportion of her late career works were highly original.

    19% picked this

  4. Correct

    Most, if not all, of

    Why this is right

    This is one of the inferences we derived. Most abstract were not highly original. All her oil were highly original. So, most of her abstract were not oil. If you prefer the formal look: Most A's are ~HO ~HO → ~O So, Most A's are ~O. The whole "if not all" is meaningless. When we say something like, "Most, if not all, of the beers that Dave buys are Belgian", we are correct as long as more than 50% of his beers are Belgian. That's the only quantity we committed to in that statement.

    Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.

    50% picked this

  5. Few or none of Albarran’s

    Unknown Group

    We would immediately translate this into positive: Most [critically acclaimed] are [not highly orig] This is talking about "Most critically-acclaimed". We don't have any statements about most-critically acclaimed, so it's not going to be a correct answer. By contrast, the inference we made, "Most abstract are not-oil" was possible because we did have a statement about "most abstract". You'll never see a correct answer say "Most X are ____ " if we were never provided a statement about Most / Few X. We actually have zero information about Albarran's critically acclaimed works. We were only told that most oil paintings are not critically acclaimed.

    7% picked this

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