Logical reasoning PrepTest 112 · Section 4 · Question 14

Question prompt

Joseph: My encyclopedia says Remaining source text redacted.
Why the credited answer is right

Credited answer: C

The notes below walk through why it fits the stem and how to eliminate the rest.

Argument or Facts

Argument/Argument

Valid or Flawed

Flawed/Flawed

Question Type

Errors in Reasoning Questions

Stimulus Summary

J: Fermat’s theorem hasn’t been proven since his death, so it probably can’t be proven, and thus Fermat’s claims to have proven it are wrong or a lie.
L: Someone recently proved the theorem, so it’s provable, and so Fermat did prove it.

Answer Anticipation

We’re shifting to Laura’s argument now after focusing on Joseph’s in the previous question! So let’s focus there.
First, let’s start with properly summarizing the argument. Here, Laura’s conclusion is that a claim is “wrong.” We should rephrase that to be a positive statement of what Laura believes. Since she believes claims that Fermat was lying or mistaken is wrong, she must believe that Fermat wasn’t lying or mistaken - in other words, Fermat did prove his theorem.
What’s this very definitive statement based on? Someone recently proved the theorem. So the theorem is provable, thus the person who claimed to prove it must be telling the truth…
That’s not a good argument! Fermat could have failed to prove it while claiming that he did, hoping someone in the future would clear it up and people would credit him with the proof. Just because it was provable doesn’t mean that Fermat proved it. Let’s find an answer highlighting that.

Answer choices

  1. A
    It purports to establish Remaining source text redacted.
    Why choice A is not credited
    A theorem being proven is completely compatible with someone having proven it earlier, so Laura’s premise doesn’t contradict her conclusion.
  2. B
    It mistakenly assumes that Remaining source text redacted.
    Why choice B is not credited
    Laura doesn’t discuss Fermat’s character, so this answer is out of scope.
  3. C
    It mistakes something that Remaining source text redacted.
    Why choice C matches the stem
    Don’t rule this answer out so quickly! It can be easy to do so because it uses necessary/sufficient language, but it’s not talking about necessary/sufficient conditions. Rather, it’s talking about necessary/sufficient information, so we should check to see if Laura’s premise is necessary for the conclusion. And what is her premise? That the theorem in question is provable. Well, for Fermat to have proven it, it must be provable, so Laura’s premise is necessary for her conclusion to follow. Does she treat it as sufficient to prove the conclusion? Yep - she says since it was provable, Fermat proved it. So Laura does confuse something necessary for her conclusion as something sufficient to prove it, so this is the correct answer.
  4. D
    It uses the term Remaining source text redacted.
    Why choice D is not credited
    Not all words need to be defined (imagine how long that argument would be…), and provable has a standard definition that applies here.
  5. E
    It fails to distinguish Remaining source text redacted.
    Why choice E is not credited
    There’s no clarity around whether Fermat’s statement was true or false, so it’s unclear what claim this statement is applying to.

What this tests

Question analytics

Based on historical answer selection rates for this question.

Answer choice distribution

  1. A 11%
  2. B 5%
  3. C Credited 60%
  4. D 2%
  5. E 22%

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Discussion

  • B VS. C 3 replies

    Started by hfatima1

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