GMAT question - symantic problem?

[stinkypete]

[ QUOTE ]
[ QUOTE ]
imo 990 is the only correct way to interpret this,

[/ QUOTE ]

If the question is ambiguous there cannot be only one correct way to interpret it.

[/ QUOTE ]

and?

[willie24]

[ QUOTE ]
This was in a GMAT book, and I think the wording is a little ambiguous. I can see how to get two answers depending on how I read it. Thoughts?

Entries in a particular lottery game are made up of three digits, each 0 through 9. If the order of digits in the entries matters, how many different possible entries exist in which all three digits are not equal?


[/ QUOTE ]

if 720 is right, the question should read: "...in which none of the 3 digits are equal"

if 990 is right (which is the way i read it) it should be something like "...excluding those where all 3 digits are equal"

despite the ambiguity, it seems to me that the reader should be able to figure out that the writer meant 990. it would be an awfully stupid way to write the 720 question...in other words, if the writer meant 720, he would have to struggle to arrive at such an odd wording. for 990, i think the words could easily come out how they did- and the writer might not notice the ambiguity, since his grammer can be correct for what he means.

[Philo]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
imo 990 is the only correct way to interpret this,

[/ QUOTE ]

If the question is ambiguous there cannot be only one correct way to interpret it.

[/ QUOTE ]

and?

[/ QUOTE ]

And the question is ambiguous would probably be the next line.

[madnak]

[ QUOTE ]
despite the ambiguity, it seems to me that the reader should be able to figure out that the writer meant 990. it would be an awfully stupid way to write the 720 question...in other words, if the writer meant 720, he would have to struggle to arrive at such an odd wording. for 990, i think the words could easily come out how they did- and the writer might not notice the ambiguity, since his grammer can be correct for what he means.

[/ QUOTE ]

I disagree, and on the contrary I can't see how anyone could write the 990 question like that. But there's enough dissent here that the interpretations are probably equivalent.

I still think the 720 question makes more sense, because the 990 question is inane. I mean this is the GMAT, not Kindergarten.

[willie24]

when i try to read the question with the 720 meaning in mind...

"If the order of digits in the entries matters, how many different possible entries exist in which all three digits are not equal?"

i find myself asking the writer - equal to what?

[madnak]

That's implied - the other digits. It's identical in both interpretations.

[willie24]

im not so sure it's identical.

the subject is: each of the digits within the group of digits
they can either "be equal" or "not be equal." the idea of them "being not equal" (trying to mean that each is unique) is extremely awkward to me for some reason.

maybe it's because for each to be unique, inequality has to be established between digit A and B, between digit A and C and between digit B and C. inequality (meaning uniqueness) throughout the group must be established through inequality of each pair - and relationships between individual pairs is NOT implied in the sentence.

for instance, to solve this issue, you would say: "...in which each of the 3 digits is not equal to either of the other 2."

im not 100% positive that i'm right, but that's the hang up for me with the 720 meaning

[willie24]

in other words, i guess im saying that 3 digits cannot be unequal. only 2 of anything can be unequal.

on the other hand, an infinite number of digits can be equal or not be equal.

[madnak]

[ QUOTE ]
maybe it's because for each to be unique, inequality has to be established between digit A and B, between digit A and C and between digit B and C. inequality (meaning uniqueness) throughout the group must be established through inequality of each pair - and relationships between individual pairs is NOT implied in the sentence.

[/ QUOTE ]

If you're breaking it down this way, it's easy to put it the same way wrt "equal." Equality has to be established between digits A and B, between digits A and C, and between digits B and C.

If digit C is equal to the other digits, then it must be equal to A, it must be equal to B, etc. But the pairing seems pathological. It seems like you're using pairing because there are three digits and you're stuck on the "one digit in, two digits out" mode of thinking. So just imagine it with 5 digits instead to resolve that issue.

"All five of the digits are equal" and "all five of the digits are unique" describe similar properties. Both statements indicate a relationship each digit has with the other digits. Both statements must apply without exception (in the former case, if any two of the digits are different the statement is false, and in the latter case, if any two of the digits are the same the statement is false).

I can see one logical difference (maybe this is what you're getting at) - it's easier to evaluate the claim of the first statement because the relations are transitive, while the relations in the second statement are intransitive. That is, if a=b and b=c, then a=c. But if a!=b and b!=c, that doesn't mean that a!=c. But this is a logical difference - it doesn't affect the grammar. I can see it playing an intuitive role - fair enough. But my intuition doesn't match yours. It's hard for me to read this in the 990 way. The 720 interpretation seems simpler and more obvious.

[madnak]

[ QUOTE ]
in other words, i guess im saying that 3 digits cannot be unequal. only 2 of anything can be unequal.

[/ QUOTE ]

Logically I see equality as a binary relation. I admit that I could be wrong.

If you're right, then the 990 statement may work better. Maybe "equal" can apply to a collective noun, while "unequal" can't. That seems strange to me, but it's possible.

Can someone clarify these points?