Joseph: My encyclopedia says that the mathematician Pierre

Question

Joseph:  My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed nonetheless to have proved. Probably this alleged theorem simply cannot be proved, since---as the article points out---no one else has been able to prove it. Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.

Laura:  Your encyclopedia is out of date. Recently someone has in fact proved Fermat’s theorem. And since the theorem is provable, your claim---that Fermat was lying or mistaken---clearly is wrong.

Which one of the following most accurately describes a reasoning error in Laura’s argument?

(A) It purports to establish its conclusion by making a claim that, if true, would actually contradict that conclusion.

(B) It mistakenly assumes that the quality of a person’s character can legitimately be taken to guarantee the accuracy of the claims that person has made.

(C) It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows.

(D) It uses the term “provable” without defining it.

(E) It fails to distinguish between a true claim that has mistakenly between believed to be false and a false claim that has mistakenly been believed to be true.

GMATNinja · Accepted Answer

Let's start with Laura's conclusion, which is that Joseph's claim---that Fermat was lying or mistaken when he claimed that he proved the theorem---is clearly wrong. If Fermat was not lying or mistaken, then the theorem must be provable (this is the  necessary  part). However, just because the theorem is provable does not necessarily mean that Fermat himself proved it. Thus, even if the theorem was known to be provable, Fermat may still have been lying or mistaken. Something that  ensures  that Fermat was not lying or mistaken would show that Fermat himself proved the theorem, not just that the theorem is provable.

AbhayPrasanna · Answer

J - Fermat may have lied or did not actually prove the theorem since 1. he did not leave behind any proof. 2. no one else has been able to prove it

L - J's claim is wrong since his point 2 is invalid - someone has proved it.

What is a FLAW in L's argument?

A. L's claim supports her conclusion.

B. Not true, the quality of character is actually J's inference, and even he doesn't use it to guarantee his own claim at all.

C. Exactly. If you notice L has only refuted point no. 2 and forgotten about point 1 - that Fermat didn't leave any proof. This still brings doubt to whether he was able to prove it at all. Though her claim about point 2 is valid and necessary for her conclusion it does not necessarily LEAD to the conclusion since there is another counter-claim which she has ignored.

D. Provable is being used in its standard english meaning and need not be defined.

E. This is just meant to confuse you. There is no true claim or false claim that was previously misconstrued - it's simple - L is only saying that point 2 is not true.

Pick C.

Mahmud6 · Answer

Would you please help me to figure out the followings?

C. It mistakes something that is necessary (what is necessary?) for its conclusion (what is conclusion?) to follow for something (what is this something?) that ensures that the conclusion follows.

sriamlan · Answer

Thanks , your explanations clarifies the OA. But it will be difficult to understand for those members who doesn't have an idea about the relation between necessary condition and sufficient condition.

Could you please make a post explaining about those.

GMATNinja · Answer

It's funny, we're working on a Topic of the Week on the distinction between necessary and sufficient. There are a few topics in line ahead of it, but we'll get to it.

And in the meantime, there are a couple of pretty good explanations of the issue here: https://gmatclub.com/forum/a-sufficient ... 50740.html I hope this helps!

shekyonline · Answer

Joseph: My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed nonetheless to have proved. Probably this alleged theorem simply cannot be proved, since---as the article points out---no one else has been able to prove it. Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.

Laura: Your encyclopedia is out of date. Recently someone has in fact proved Fermat’s theorem. And since the theorem is provable, your claim---that Fermat was lying or mistaken---clearly is wrong.

Which one of the following most accurately describes a reasoning error in Laura’s argument?

(A) It purports to establish its conclusion by making a claim that, if true, would actually contradict that conclusion.

(B) It mistakenly assumes that the quality of a person’s character can legitimately be taken to guarantee the accuracy of the claims that person has made.

(C) It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows. 
 
Laura's argument says what is necessary for its conclusion to follow. But, her argument  DOES NOT  ensure that the conclusion follows, because even if the the theorem is provable, there is no mention whether Fermat has proved it or not. So, still the fact that - "Fermat was lying or...." can be true.

Hence C is right.

(D) It uses the term “provable” without defining it.

(E) It fails to distinguish between a true claim that has mistakenly between believed to be false and a false claim that has mistakenly been believed to be true.

mallya12 · Answer

Conufsed between B and C.

"It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows."

Not able to understand what is necessary for conlcusion and what is ensures the conclusion??

GMATNinja  I read your post but could you please explain in more detail. I am always confused between necessary and sufficient.

And why is option B wrong?? I didn't understand the meaning of option B. Is it talking about the quality of laura or the person who proved it..

GMATNinja · Answer

Based on Laura's statements, we now KNOW that Fermat’s theorem is  provable . But does that mean that Fermat himself proved the theorem? In order for it to be true that Fermat himself proved the theorem, the theorem MUST be provable (it would be impossible to prove a theorem that is not provable!).

If the theorem is not provable, then we definitely cannot conclude that Fermat himself proved the theorem (and, thus, that he was not lying or mistaken).

The claims discussed in this passage are those made by Fermat. Specifically, Fermat claimed that he proved the theorem. So (B) must be referring to the accuracy of Fermat's claim.

So does Laura "mistakenly assume that the quality of   character can legitimately be taken to guarantee the accuracy of the claims that   has made"? In other words, does Laura conclude that Fermat was not lying because of his personal qualities (i.e. how trustworthy/honest he is)? No, this does not accurately describe Laura's logic, so (B) should be eliminated.

I hope that helps!

Ahmed9955 · Answer

GMATNinja

Can help me in eliminating Ans Choice A- It purports to establish its conclusion by making a claim that, if true, would actually contradict that conclusion.?
- My understanding of A is - 
A claim if true - Laura claimed that since theoram is provable   Would actually contradict  That  conclusion- joseph's conclusion will be contradicted?
isn't this the flaw in Laura's reasoning? Because, if true, this doesn't necessarily contradict Joseph's conclusion.

GMATNinja · Answer

Joseph claims that Fermat was lying or mistaken when he said he proved his theorem. Laura concludes that Joseph's claim is wrong. To reach this conclusion, Laura points out that Fermat's theorem is provable, since someone recently proved it. The correct answer should describe an error in Laura's argument.

Let's now consider (A):

Let's start by identifying Laura's conclusion and her claim.

Laura's conclusion : the idea that Fermat was either lying or mistaken is wrong (i.e. Fermat was NOT lying or mistaken).   Laura's claim : Fermat's theorem is provable.

So does her claim contradict the conclusion? In other words, does the fact that Fermat's theorem is provable contradict the idea that Fermat was NOT either lying or mistaken? Or put another way, does the fact that Fermat's theorem is provable mean that Fermat  was  lying or mistaken?

Well, Fermat claimed that he proved his theorem. Does the fact that his theorem was provable mean that he was lying or mistaken? Not at all. Just because his theorem is provable doesn't mean that he was lying or mistaken when he claimed to have proved it.

In fact, the idea that Fermat's theorem is provable actually  supports  the idea that Fermat might have proven his theorem. Because if the theorem is provable, then maybe he did prove it? (Whereas if it isn't provable, he definitely didn't prove it). So if anything, Laura's claim actually  supports  her conclusion.

Bottom line, the claim that Fermat's theorem is provable doesn't support the idea that he was lying or mistaken about having proved it. So it doesn't contradict the idea that Fermat was NOT lying or mistaken. And because Laura's claim doesn't contradict her conclusion, we can eliminate (A).

I hope that helps!

VerbalBot · Answer

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Joseph: My encyclopedia says that the mathematician Pierre

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