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No mathematician today would flatly refuse to accept the [#permalink]

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24 Jul 2010, 22:39

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35% (02:10) wrong based on 102 sessions

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No mathematician today would flatly refuse to accept the results of an enormous computation as an adequate demonstration of the truth of a theorem. In 1976, however, this was not the case. Some mathematicians at that time refused to accept the results of a complex computer demonstration of a very simple mapping theorem. Although some mathematicians still hold a strong belief that a simple theorem ought to have a short, simple proof, in fact, some simple theorems have required enormous proofs.

If all of the statements in the passage are true, which one of the following must also be true?

(A) Today, some mathematicians who believe that a simple theorem ought to have a simple proof would consider accepting the results of an enormous computation as a demonstration of the truth of a theorem.

(B) Some individuals who believe that a simple theorem ought to have a simple proof are not mathematicians.

(C) Today, some individuals who refuse to accept the results of an enormous computation as a demonstration of the truth of a theorem believe that a simple theorem ought to have a simple proof.

(D) Some individuals who do not believe that a simple theorem ought to have a simple proof would not be willing to accept the results of an enormous computation as proof of a complex theorem.

(E) Some nonmathematicians do not believe that a simple theorem ought to have a simple proof.

I picked A as it was the closest to the argument. I want to confirm another thing. The reason why I negated other answers was that in B,C and D individuals in mentioned though we are talking of "mathematicians" here. Is my reasoning correct?

I picked A as it was the closest to the argument. I want to confirm another thing. The reason why I negated other answers was that in B,C and D individuals in mentioned though we are talking of "mathematicians" here. Is my reasoning correct?

with these questions most of the time it is difficult to come up with answers in our own words. this is why POE is the key to working inference questions and avoid answer choices that contains words that the broader or more extreme. The word mathematician limits the scope of the premise as opposed to actual no of individuals _________________

a mathematician can also be labeled as an individual so I don't think we can eliminate b, c and d simply because they use the term individuals. The more imp point is that they can be eliminated because B and C for instance may or may not be true. D is completely false because those who DONT believe that simple theorems SHOULD NOT HAVE SIMPLE PROOFS have not been talked about at all in the passage

I believe this is the fastest way. The hard way is POE. I believe you got the result in less than 60 secs.

Using POE I can easily eliminate B, D and E. C is difficult to eliminate if you don't focus on key words "No mathematician".

Premise : No mathematician today would flatly refuse to accept the results of an enormous computation (C) Today, some individuals who refuse to accept the results of an enormous computation ----- the first part contradicts the premise. C does NOT sound plausible now. OUT

A it is.

rohitgoel15 wrote:

I picked A as it was the closest to the argument. I want to confirm another thing. The reason why I negated other answers was that in B,C and D individuals in mentioned though we are talking of "mathematicians" here. Is my reasoning correct?

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No mathematician today would flatly refuse to accept the results of an enormous computation as an adequate demonstration of the truth of a theorem. In 1976, however, this was not the case. Some mathematicians at that time refused to accept the results of a complex computer demonstration of a very simple mapping theorem. Although some mathematicians still hold a strong belief that a simple theorem ought to have a short, simple proof, in fact, some simple theorems have required enormous proofs.

If all of the statements in the passage are true, which one of the following must also be true?

(A) Today, some mathematicians who believe that a simple theorem ought to have a simple proof would consider accepting the results of an enormous computation as a demonstration of the truth of a theorem.

(B) Some individuals who believe that a simple theorem ought to have a simple proof are not mathematicians.

(C) Today, some individuals who refuse to accept the results of an enormous computation as a demonstration of the truth of a theorem believe that a simple theorem ought to have a simple proof.

(D) Some individuals who do not believe that a simple theorem ought to have a simple proof would not be willing to accept the results of an enormous computation as proof of a complex theorem.

(E) Some nonmathematicians do not believe that a simple theorem ought to have a simple proof.

I picked A as it was the closest to the argument. I want to confirm another thing. The reason why I negated other answers was that in B,C and D individuals in mentioned though we are talking of "mathematicians" here. Is my reasoning correct?

definitely correct explanation. All the choices other than A talk about individuals/non-mathematicians.

1) no mathm today would refuse to accept results of enormous computation as an adequate demonstration of truth of theorem. 2) (1) was not the case in 1976. 3) in 1976 some mathms refused to accept results of very simple mapping theorem. 4) Although some mathems still belif simple theorem should have simple proof, but this is not the case.

Based on (4) and (1) we can divide mathematicians into two groups: i) mathematicians who "would consider accepting results of computer" and believe "a simple theorem should have a simple proof" ii) mathematicians who "would consider accepting results of computer" and do not believe "a simple theorem should have a simple proof"

A) Says basically that "Today, some mathematicians fall into category i)" This is the correct answer because it MUST logically follow from the passage B) Does not HAVE to be true. It might be true, it might not. The passage doesn't indicate either way. C) Since all mathms today would consider accepting the results of a computer, this answer choice is referring to nonmathematicians. We don't know anything about what non mathematicians believe. D) Similar to (C), anyone not willing to accept the results of a computer must not be mathematicians, and we don't know anything about what they believe. E) Same as C and D. We don't know anything about what they believe.

I go with A, so this is a "Must be True" questions and only A qualifies that

Can someone clearly explain why E is incorrect?

Sure, the passage never gives any information about what non-mathematicians believe. Therefore E may be true, or it may not, but we have no information either way.

Also, I wanted to clarify something. A good number of posters above eliminated answer choices because they used the term 'individual' instead of mathematicians.

This alone isn't a legitimate reason to eliminate an answer choice.

The passage actually gives us a great deal of information that MUST be true regarding individuals. 1) In present day, some individuals would not refuse to accept the results of a computer process. 2) In 1976, some individuals would. 3) Some individuals believe a simple theorem should have a simple proof. 4) Some individuals do not believe a simple theorem should have a simple proof. These 4 statements (and possibly others) all MUST be true based on the statements of the passage.

The thing that disqualifies the other answer choices, is that they're using the term "individuals" but the answer choice actually limits it further to "non-mathematicians".

For example, the answer choice: "(C) Today, some individuals who refuse to accept the results of an enormous computation as a demonstration of the truth of a theorem believe that a simple theorem ought to have a simple proof." Is wrong not because it uses the term "individuals" but because it's making a claim about "non-mathematicians", which we know nothing about.

i think A is the answer by POE , but it took me 2 mins 30 sec + . so is there any shorter procedure to reduce the time consumed in such CR questions ? _________________

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Re: No mathematician today
[#permalink]
26 Apr 2011, 12:24

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