[quote]tedro wrote:
[quote]spar4tee wrote:
If the question wasn’t multiple choice, there would be a lot of people getting fucked over. Which is my point.[/quote]
And my point is that this is much more than a basic arithmetic question. The question is not meant to test your ability to multiply and add fractions, but to deduce your basic logic skills.[/quote]
I understand that. The problem is that there is more than one logical pathway to follow. This question fell short to me.
[quote]spar4tee wrote:
[quote]tedro wrote:
[quote]spar4tee wrote:
“There are” is present tense. So as the first sentence is read, there are 96 screws in each jar. Next sentence goes “In one” meaning inside of the jar. “1/4 is being used” meaning that, as this is being read, a portion of the screws are being used. The partitioning of the other jars reads the same way.
[/quote]
Agreed through here.
Assuming the 2/5 scenario is intended: the occurrences of “in” in the second sentence of the problem are poor usage, because the “one” and “another” following the “in” have no logical antecedent other than “jar”. Probably would be better wording to replace each such “in” with “for”. That would maintain the trickiness of the question without depending on phantom antecedents for “one” and “another”; or depending on excessive elasticity for the meaning of “in”: because “for” each jar certainly could include things outside the jar.
[quote]undoredo wrote:
[quote]spar4tee wrote:
[quote]tedro wrote:
[quote]spar4tee wrote:
“There are” is present tense. So as the first sentence is read, there are 96 screws in each jar. Next sentence goes “In one” meaning inside of the jar. “1/4 is being used” meaning that, as this is being read, a portion of the screws are being used. The partitioning of the other jars reads the same way.
[/quote]
Agreed through here.
Assuming the 2/5 scenario is intended: the occurrences of “in” in the second sentence of the problem are poor usage, because the “one” and “another” following the “in” have no logical antecedent other than “jar”. Probably would be better wording to replace each such “in” with “for”. That would maintain the trickiness of the question without depending on phantom antecedents for “one” and “another”; or depending on excessive elasticity for the meaning of “in”: because “for” each jar certainly could include things outside the jar.
[/quote]
Exactly.
[quote]spar4tee wrote:
I disagree. Too much ambiguity for my liking. In context of testing, I’d prefer not to gamble with intended meaning in an environment in which I am unable to argue for my interpretation of said intent.[/quote]
Yup.
Logic doesn’t mean you can interpret ambiguous statements (like this question here). It means, among many other things, that you can take established “truths” and extrapolate a whole lot of things from said “truths”.
Ambiguity is the last thing logic wants to work with.
[quote]tedro wrote:
Your problem here is that you want to disregard what you already know. Each jar has 96 screws in it.[/quote]
How did you come to this conclusion?
The word “each” complicates the first sentence, and makes it impossible to interpret without adding certain assumptions. You can’t take it at face-value.
The first sentence gets fixed immediately by the addition of a comma, thereby making it-
“There are 4 jars, each with 96 screws in them.”
Which could be simplified immensely by being reworded as-
“There are 4 jars, and each jar contains 96 screws.”
In this case the conclusion you made in the quote above works.
But until you add said comma, the sentence cannot be interpreted as such unless you make the assumption that there should have been a comma there.
Even as a logic problem this is a terrible problem. The only defense is that since it is multiple choice, you might expect the student to come up with all possible interpretations and chose the interpretation that leads to an answer that is one of the possible choices.
The use of the word ‘in’ makes the 2/5 interpretation rather tenuous. If I plan a project using screws and know that I will need 48 screws, then I can easily say that I am using half of the screws in a jar containing 96, even if they are still in the jar. That is not to say I find the 2/5 interpretation wrong but rather that the only thing that conclusively indicates the 15/32 interpretation is wrong is that it wasn’t a given choice.
Also, the ability to come to innumerate multiple possible interpretations of ambiguous language isn’t exactly a logic problem.
[quote]magick wrote:
[quote]tedro wrote:
Your problem here is that you want to disregard what you already know. Each jar has 96 screws in it.[/quote]
How did you come to this conclusion?
The word “each” complicates the first sentence, and makes it impossible to interpret without adding certain assumptions. You can’t take it at face-value.
The first sentence gets fixed immediately by the addition of a comma, thereby making it-
“There are 4 jars, each with 96 screws in them.”
Which could be simplified immensely by being reworded as-
“There are 4 jars, and each jar contains 96 screws.”
In this case the conclusion you made in the quote above works.
But until you add said comma, the sentence cannot be interpreted as such unless you make the assumption that there should have been a comma there.[/quote]
How can you take the first statement any other way? There are 4 jars each with 96 screws. A comma may add clarity here, but by no means is it necessary. The only people taking the first statement incorrectly are those that are making assumptions about later statements and attempting to reinterpret it to fit those assumptions. It doesn’t work and is unnecessary. 4 jars each with 96 screws. Quit overthinking it because you didn’t understand the rest of the question.
[quote]undoredo wrote:
Assuming the 2/5 scenario is intended: the occurrences of “in” in the second sentence of the problem are poor usage, because the “one” and “another” following the “in” have no logical antecedent other than “jar”. Probably would be better wording to replace each such “in” with “for”. That would maintain the trickiness of the question without depending on phantom antecedents for “one” and “another”; or depending on excessive elasticity for the meaning of “in”: because “for” each jar certainly could include things outside the jar.
[/quote]
The interesting thing is that you actually interpreted the question exactly right the first time you attempted the problem, but second guessed yourself when your math was incorrect.
[quote]Silyak wrote:
The use of the word ‘in’ makes the 2/5 interpretation rather tenuous. If I plan a project using screws and know that I will need 48 screws, then I can easily say that I am using half of the screws in a jar containing 96, even if they are still in the jar. That is not to say I find the 2/5 interpretation wrong but rather that the only thing that conclusively indicates the 15/32 interpretation is wrong is that it wasn’t a given choice.
[/quote]
The only way to get to 15/32 is to disregard the fact that the first statement already told you that each jar has 96 screws in it. Not 72. 96. It doesn’t say 1/4 are being taken out. It says 1/4 of Jar 1’s screws are being used. If 1/4 are being used, and 96 are in the jar, the problem can only be solved one way.
[quote]tedro wrote:
[quote]undoredo wrote:
Assuming the 2/5 scenario is intended: the occurrences of “in” in the second sentence of the problem are poor usage, because the “one” and “another” following the “in” have no logical antecedent other than “jar”. Probably would be better wording to replace each such “in” with “for”. That would maintain the trickiness of the question without depending on phantom antecedents for “one” and “another”; or depending on excessive elasticity for the meaning of “in”: because “for” each jar certainly could include things outside the jar.
[/quote]
The interesting thing is that you actually interpreted the question exactly right the first time you attempted the problem, but second guessed yourself when your math was incorrect.
[/quote]
That is true, except that I did not initially believe the wording unambiguously meant that; I said we would have to make some assumptions as to what was meant.
[quote]tedro wrote:
[quote]Silyak wrote:
The use of the word ‘in’ makes the 2/5 interpretation rather tenuous. If I plan a project using screws and know that I will need 48 screws, then I can easily say that I am using half of the screws in a jar containing 96, even if they are still in the jar. That is not to say I find the 2/5 interpretation wrong but rather that the only thing that conclusively indicates the 15/32 interpretation is wrong is that it wasn’t a given choice.
[/quote]
The only way to get to 15/32 is to disregard the fact that the first statement already told you that each jar has 96 screws in it. Not 72. 96. It doesn’t say 1/4 are being taken out. It says 1/4 of Jar 1’s screws are being used. If 1/4 are being used, and 96 are in the jar, the problem can only be solved one way.
[/quote]
But the only way to get to 2/5 is to disregard the fact that there is no logical antecedent for “one” and “another” other than “jar”; or to disregard the fact that in the English language “in” with an object of “jar” (indirectly via antecedent in this case) implies inside the jar. Remember: “In one 1/4 is being used in another 5/8, in another 3/4 …”
Either 15/32 or 2/5 requires disregarding something.
[quote]undoredo wrote:
But the only way to get to 2/5 is to disregard the fact that there is no logical antecedent for “one” and “another” other than “jar”; or to disregard the fact that in the English language “in” with an object of “jar” (indirectly via antecedent in this case) implies inside the jar. Remember: “In one 1/4 is being used in another 5/8, in another 3/4 …”
Either 15/32 or 2/5 requires disregarding something.
[/quote]
[i]in -
used to indicate location or position within something
used to indicate that someone or something belongs to or is included as part of something [/i]
The second use of in does not imply that the used screws are in the jar, it implies they belong to the jar. This is clarified in the question as the screws are described as being used. They cannot be used if they are within the jar (which is hardly an assumption) and of course we already know there are 96 within the jar.
[quote]tedro wrote:
[quote]Silyak wrote:
The use of the word ‘in’ makes the 2/5 interpretation rather tenuous. If I plan a project using screws and know that I will need 48 screws, then I can easily say that I am using half of the screws in a jar containing 96, even if they are still in the jar. That is not to say I find the 2/5 interpretation wrong but rather that the only thing that conclusively indicates the 15/32 interpretation is wrong is that it wasn’t a given choice.
[/quote]
The only way to get to 15/32 is to disregard the fact that the first statement already told you that each jar has 96 screws in it. Not 72. 96. It doesn’t say 1/4 are being taken out. It says 1/4 of Jar 1’s screws are being used. If 1/4 are being used, and 96 are in the jar, the problem can only be solved one way.[/quote]
As I already said, it’s not impossible to be ‘using’ something that is in a jar. Say you are screwing something together and you have a jar of screws. Someone comes and grabs the jar and starts to walk off with it. You might say, “I am using those.” Then the person says he only needs a couple of them. Then you say, “I’m really only using half of them.” All the while, all of the screws are in the jar.
That’s not the only way to interpret the question, but it does seem consistent and non-contradictory.
[quote]Silyak wrote:
[quote]tedro wrote:
[quote]Silyak wrote:
The use of the word ‘in’ makes the 2/5 interpretation rather tenuous. If I plan a project using screws and know that I will need 48 screws, then I can easily say that I am using half of the screws in a jar containing 96, even if they are still in the jar. That is not to say I find the 2/5 interpretation wrong but rather that the only thing that conclusively indicates the 15/32 interpretation is wrong is that it wasn’t a given choice.
[/quote]
The only way to get to 15/32 is to disregard the fact that the first statement already told you that each jar has 96 screws in it. Not 72. 96. It doesn’t say 1/4 are being taken out. It says 1/4 of Jar 1’s screws are being used. If 1/4 are being used, and 96 are in the jar, the problem can only be solved one way.[/quote]
As I already said, it’s not impossible to be ‘using’ something that is in a jar. Say you are screwing something together and you have a jar of screws. Someone comes and grabs the jar and starts to walk off with it. You might say, “I am using those.” Then the person says he only needs a couple of them. Then you say, “I’m really only using half of them.” All the while, all of the screws are in the jar.
That’s not the only way to interpret the question, but it does seem consistent and non-contradictory. [/quote]
But the question states “in use”, not “being used”.
[quote]tedro wrote:
[quote]Silyak wrote:
[quote]tedro wrote:
[quote]Silyak wrote:
The use of the word ‘in’ makes the 2/5 interpretation rather tenuous. If I plan a project using screws and know that I will need 48 screws, then I can easily say that I am using half of the screws in a jar containing 96, even if they are still in the jar. That is not to say I find the 2/5 interpretation wrong but rather that the only thing that conclusively indicates the 15/32 interpretation is wrong is that it wasn’t a given choice.
[/quote]
The only way to get to 15/32 is to disregard the fact that the first statement already told you that each jar has 96 screws in it. Not 72. 96. It doesn’t say 1/4 are being taken out. It says 1/4 of Jar 1’s screws are being used. If 1/4 are being used, and 96 are in the jar, the problem can only be solved one way.[/quote]
As I already said, it’s not impossible to be ‘using’ something that is in a jar. Say you are screwing something together and you have a jar of screws. Someone comes and grabs the jar and starts to walk off with it. You might say, “I am using those.” Then the person says he only needs a couple of them. Then you say, “I’m really only using half of them.” All the while, all of the screws are in the jar.
That’s not the only way to interpret the question, but it does seem consistent and non-contradictory. [/quote]
But the question states “in use”, not “being used”.[/quote]
No, the question uses the phrase, “being used.”
All the same, are you trying to imply that if someone says, “I’m using those,” they wouldn’t also agree that the objects in question are both “being used” and “in use”? Or if something is being used is it not in use and vice versa?
In various occupation or situation specific usages these two phrases can of course mean different things, but in general English I would contend that they are effectively synonymous.
[quote]Silyak wrote:
But the question states “in use”, not “being used”.[/quote]
No, the question uses the phrase, “being used.”
[/quote]
I misspoke. Apparently three pages of jars and screws is my limit.
That’s exactly what I’m stating. As your example solidified, “I’m using those” is likely not an accurate statement when referring to a jar of screws, as the user is probably only using a fraction of the screws. In the case of the question it is specific as to which fraction is being used, and that 96 are in the jar.
[quote]tedro wrote:
[quote]Silyak wrote:
But the question states “in use”, not “being used”.[/quote]
No, the question uses the phrase, “being used.”
[/quote]
I misspoke. Apparently three pages of jars and screws is my limit.
[quote]Silyak wrote:
All the same, are you trying to imply that if someone says, “I’m using those,” they wouldn’t also agree that the objects in question are both “being used” and “in use”? Or if something is being used is it not in use and vice versa?
[/quote]
That’s exactly what I’m stating. As your example solidified, “I’m using those” is likely not an accurate statement when referring to a jar of screws, as the user is probably only using a fraction of the screws. In the case of the question it is specific as to which fraction is being used, and that 96 are in the jar.
[/quote]
It’s certainly possible to be using an entire jar of 96 screws. But that’s beside the point. The point is that it’s grammatically correct to say that you are using something (and that accordingly it is being used and in use) even if you are still storing it.
On the other hand, it’s not correct to say that you are using 1/4 of the screws in one jar when those screws are not in the jar. While this contradiction is concealed by some weird antecedents, that is essentially what is required for the 2/5 interpretation to be correct.
[quote]Silyak wrote:
It’s certainly possible to be using an entire jar of 96 screws. But that’s beside the point. The point is that it’s grammatically correct to say that you are using something (and that accordingly it is being used and in use) even if you are still storing it. [/quote]
It’s grammatically correct, but pragmatically and semantically incorrect. And to repeat myself again, the question does not state that 1/4 are physically in the jar. It states 1/4 of the screws that belong to the jar are being used and previously and unequivocally states that there are 96 screws inside the jar.
[quote]
On the other hand, it’s not correct to say that you are using 1/4 of the screws in one jar when those screws are not in the jar. While this contradiction is concealed by some weird antecedents, that is essentially what is required for the 2/5 interpretation to be correct. [/quote]
A weird antecedent? 4 jars each with 96 screws. What part of that statement on its own is hard to understand?
And it would be just fine to say you are using 1/4 of the jar’s screws, if you are in fact using them. You are choosing to ignore the multiple meanings of ‘in’.
[quote]tedro wrote:
[quote]Silyak wrote:
It’s certainly possible to be using an entire jar of 96 screws. But that’s beside the point. The point is that it’s grammatically correct to say that you are using something (and that accordingly it is being used and in use) even if you are still storing it. [/quote]
It’s grammatically correct, but pragmatically and semantically incorrect. And to repeat myself again, the question does not state that 1/4 are physically in the jar. It states 1/4 of the screws that belong to the jar are being used and previously and unequivocally states that there are 96 screws inside the jar.
[quote]
On the other hand, it’s not correct to say that you are using 1/4 of the screws in one jar when those screws are not in the jar. While this contradiction is concealed by some weird antecedents, that is essentially what is required for the 2/5 interpretation to be correct. [/quote]
A weird antecedent? 4 jars each with 96 screws. What part of that statement on its own is hard to understand?
And it would be just fine to say you are using 1/4 of the jar’s screws, if you are in fact using them. You are choosing to ignore the multiple meanings of ‘in’.[/quote]
You are taking the element of chronologic progression out of the question which is implied. You start with 96 screws in each of the jars. Then you use 1/4th the screws in one jar, and so on.
I would be interested to know where the people are from that think that 2/5ths is a more appropriate answer than 15/32’s??
[quote]jbpick86 wrote:
I would be interested to know where the people are from that think that 2/5ths is a more appropriate answer than 15/32’s??
[/quote]
I was starting to wonder the same thing. To me, it’s not that 2/5ths is a completely inconceivable interpretation. It’s just that assuming that ‘in’ doesn’t mean physically inside of the jar is a much bigger inconsistency in meaning than assuming that a screw can be considered used even while it is still in the jar.
I currently reside in Massachusetts but grew up in Washington state (and spent some of childhood in the mountain west and outside of Chicago).