GMAT question - symantic problem?

[stinkypete]

i just don't see how anyone could think that using the words "not equal" to mean "unique" when 3 digits are in question is what was intended.

[borisp]

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I read the question as "How many different possible entries exist in which all three digits ARE equal?"
Then I took the the 'not' as meaning "all the other cases".
Obviously too simplistic, but I can't quite figure out why.

luckyme

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This is the "correct" way to think about it, coming from a person that has taught these standardized tests. It is probably what the writer was thinking.

A simple technique for SAT, LSAT, GMAT, etc., is that whenever a problem has a negation, remove the negation, and then evaluate the content. The negation means everything else.

[MC Chris]

didn't read any posts so far, but the answer is 990 and the question is perfectly clear.

[Philo]

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i just don't see how anyone could think that using the words "not equal" to mean "unique" when 3 digits are in question is what was intended.

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Consider the number 788. Now ask the question, "are all three digits not equal?" That is to say, are all three digits unequal? The first digit is not equal to either of the other two, so that digit has no equal, but this is not true of the second or the third digit. Therefore it is not the case that all three digits are unequal (since two of them are). I don't think there's anything unreasonable in parsing the sentence this way, and again, this type of scope ambiguity is quite common. The scope of the negation is ambiguous between "all three are not equal" and "not all three are equal."

[madnak]

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This is the "correct" way to think about it, coming from a person that has taught these standardized tests. It is probably what the writer was thinking.

A simple technique for SAT, LSAT, GMAT, etc., is that whenever a problem has a negation, remove the negation, and then evaluate the content. The negation means everything else.

[/ QUOTE ]

The majority of the posters here think the 990 interpretation is more intuitive, so I'm willing to concede that point.

But it doesn't matter; even a .1% rate of error due to sloppy writing should be considered unacceptable. Test questions should be written for clarity, and semantic ambiguity should never be tolerated. The test results affect people's lives, and it pisses me off that bad writing can skew them.

[Philo]

[ QUOTE ]
[ QUOTE ]
This is the "correct" way to think about it, coming from a person that has taught these standardized tests. It is probably what the writer was thinking.

A simple technique for SAT, LSAT, GMAT, etc., is that whenever a problem has a negation, remove the negation, and then evaluate the content. The negation means everything else.

[/ QUOTE ]

The majority of the posters here think the 990 interpretation is more intuitive, so I'm willing to concede that point.

But it doesn't matter; even a .1% rate of error due to sloppy writing should be considered unacceptable. Test questions should be written for clarity, and semantic ambiguity should never be tolerated. The test results affect people's lives, and it pisses me off that bad writing can skew them.

[/ QUOTE ]

I agree that the more common reading would be the one with the answer 990. But the question still contains a scope ambiguity. Even students of logic have a hard time discerning ambiguous questions involving scope ambiguities like this, because they are used to interpreting the scope of the negation just one way. Unfortunately these types of poorly written questions do appear too often on standardized tests like the GRE, LSAT, and GMAT.

Unless I've missed it in the thread somewhere I haven't seen anyone explain what they think is wrong with the second reading where the negation scopes over just the equality, as in "all three digits are not equal," which is the actual wording of the question, and which translates as "for all x, if x is a digit, then x is not equal to any other digit."

[borisp]

I guess a reasonable response to this is that one must recognize a bit of metagame with regard to these standardized tests. But I agree that the wording is ambiguous, and either interpretation is valid, outside of this scope.

[vulturesrow]

Wow you can tell this forum definitely leans in the direction of math guys, cant believe there is 46 posts on this. I thinks it patently obvious that it should be read in the manner that gives you 720.

Question metagame analysis : 990 is way too easy to come up with. [img]/images/graemlins/wink.gif[/img]

PS FWIW I scored a perfect on the reading comprehension portion of the ACT [img]/images/graemlins/wink.gif[/img]

[Philo]

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That's what I got too, but the answer explanation says 990. There are 1000 ways to pick numbers, but 10 of them have all three with the same number (1 1 1, 2 2 2, etc).

I would buy this if the question read, "in which not all three digits are equal" rather than "in which all three digits are not equal."

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Your analysis is correct. The first way of phrasing it is unambiguous since the negation scopes over the universal quantifier 'all'. The second way of phrasing it, which was the way it was phrased in the original question, is ambiguous since it does not make clear what the scope of the negation is supposed to be.

[willie24]

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PS FWIW I scored a perfect on the reading comprehension portion of the ACT

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